This is the extended model described the article:
Bifurcation analysis of the regulatory modules of the mammalian G1/S transition.
Swat M, Kel A, Herzel H. Bioinformatics 2004 Jul 10;20(10):1506-11. PMID: 15231543 , doi: 10.1093/bioinformatics/bth110
Abstract:
MOTIVATION: Mathematical models of the cell cycle can contribute to an understanding of its basic mechanisms. Modern simulation tools make the analysis of key components and their interactions very effective. This paper focuses on the role of small modules and feedbacks in the gene-protein network governing the G1/S transition in mammalian cells. Mutations in this network may lead to uncontrolled cell proliferation. Bifurcation analysis helps to identify the key components of this extremely complex interaction network.
RESULTS: We identify various positive and negative feedback loops in the network controlling the G1/S transition. It is shown that the positive feedback regulation of E2F1 and a double activator-inhibitor module can lead to bistability. Extensions of the core module preserve the essential features such as bistability. The complete model exhibits a transcritical bifurcation in addition to bistability. We relate these bifurcations to the cell cycle checkpoint and the G1/S phase transition point. Thus, core modules can explain major features of the complex G1/S network and have a robust decision taking function.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2010 The BioModels Team.
To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

In summary, you are entitled to use this encoded model in absolutely any manner you deem suitable, verbatim, or with modification, alone or embedded it in a larger context, redistribute it, commercially or not, in a restricted way or not..

To cite BioModels Database, please use Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

This a model from the article:
Prediction and validation of the distinct dynamics of transient and sustained ERK activation.
Sasagawa S, Ozaki Y, Fujita K, Kuroda S Nat. Cell Biol. [2005 Apr; Volume: 7 (Issue: 4 )]: 365-73 15793571 ,
Abstract:
To elucidate the hidden dynamics of extracellular-signal-regulated kinase (ERK) signalling networks, we developed a simulation model of ERK signalling networks by constraining in silico dynamics based on in vivo dynamics in PC12 cells. We predicted and validated that transient ERK activation depends on rapid increases of epidermal growth factor and nerve growth factor (NGF) but not on their final concentrations, whereas sustained ERK activation depends on the final concentration of NGF but not on the temporal rate of increase. These ERK dynamics depend on Ras and Rap1 dynamics, the inactivation processes of which are growth-factor-dependent and -independent, respectively. Therefore, the Ras and Rap1 systems capture the temporal rate and concentration of growth factors, and encode these distinct physical properties into transient and sustained ERK activation, respectively.

Dynamics of active Ras, active Rap1 and phosphorylated ERK were correctly reproduced with CellDesigner 3.0

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2012 The BioModels.net Team.
For more information see the terms of use .
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

The model reproduces Fig 2 A of the paper. Simulation results successfully reproduced using MathSBML and Jarnac

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

This a model from the article:
Hypoxia-dependent sequestration of an oxygen sensor by a widespread structural motif can shape the hypoxic response - a predictive kinetic model
Bernhard Schmierer, Béla Novák1 and Christopher J Schofield BMC Systems Biology 2010, 4:139 20955552 ,
Abstract:
Background
The activity of the heterodimeric transcription factor hypoxia inducible factor (HIF) is regulated by the post-translational, oxygen-dependent hydroxylation of its α-subunit by members of the prolyl hydroxylase domain (PHD or EGLN)-family and by factor inhibiting HIF (FIH). PHD-dependent hydroxylation targets HIFα for rapid proteasomal degradation; FIH-catalysed asparaginyl-hydroxylation of the C-terminal transactivation domain (CAD) of HIFα suppresses the CAD-dependent subset of the extensive transcriptional responses induced by HIF. FIH can also hydroxylate ankyrin-repeat domain (ARD) proteins, a large group of proteins which are functionally unrelated but share common structural features. Competition by ARD proteins for FIH is hypothesised to affect FIH activity towards HIFα; however the extent of this competition and its effect on the HIF-dependent hypoxic response are unknown.
Results
To analyse if and in which way the FIH/ARD protein interaction affects HIF-activity, we created a rate equation model. Our model predicts that an oxygen-regulated sequestration of FIH by ARD proteins significantly shapes the input/output characteristics of the HIF system. The FIH/ARD protein interaction is predicted to create an oxygen threshold for HIFα CAD-hydroxylation and to significantly sharpen the signal/response curves, which not only focuses HIFα CAD-hydroxylation into a defined range of oxygen tensions, but also makes the response ultrasensitive to varying oxygen tensions. Our model further suggests that the hydroxylation status of the ARD protein pool can encode the strength and the duration of a hypoxic episode, which may allow cells to memorise these features for a certain time period after reoxygenation.
Conclusions
The FIH/ARD protein interaction has the potential to contribute to oxygen-range finding, can sensitise the response to changes in oxygen levels, and can provide a memory of the strength and the duration of a hypoxic episode. These emergent properties are predicted to significantly shape the characteristics of HIF activity in animal cells. We argue that the FIH/ARD interaction should be taken into account in studies of the effect of pharmacological inhibition of the HIF-hydroxylases and propose that the interaction of a signalling sensor with a large group of proteins might be a general mechanism for the regulation of signalling pathways.

There are there models described in the paper. 1) Skeleton Model 1 (SKM1) - HIFα CAD-hydroxylation in the absence of the FIH/AR-interaction. 2) Skeleton Model 2 (SKM2) - FIG sequestration by ARD proteins and oxygen-dependent FIH-release. 3) Full Model (Fusion of SKM1 and SKM2) - the effects of the FIH/ARD proteins interaction on HIFα CAD-hydroxylation.

This model corresponds to the "Full Model" described in the paper. The model reproduces figure 5 of the publication.

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2011 The BioModels.net Team.
For more information see the terms of use .
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

This model is from the article:
A quantitative comparison of Calvin–Benson cycle models
Anne Arnold, Zoran Nikoloski Trends in Plant Science 2011 Oct 14. 22001849 ,
Abstract:
The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering.

Note: Model of the Calvin cycle with focus on the RuBisCO reaction by Farquhar et al. (1980, DOI:10.1007/BF00386231 ).

The initial metabolite values are chosen from the data set of Zhu et al. (2007, DOI:10.1104/pp.107.103713 ). A detailed description of all modifications is given in the model described by Arnold and Nikoloski (2011, PMID:22001849 .

This model 2 described in the supplement of the article below. It is parameterized for the WT at 24°C. To reproduce figure 6 the results have to be rescaled to circadian time by multiplying time by 24/ tau , with tau being the period of the free-running oscillator. For the wild-type parameter set tau is equal to 22.7149.
Article:
Isoform switching facilitates period control in the Neurospora crassa circadian clock.
Akman OE, Locke JC, Tang S, Carré I, Millar AJ, Rand DA. Mol Syst Biol. 2008;4:164. Epub 2008 Feb 12. PMID: 18277380 , doi: 10.1038/msb.2008.5
Abstract:
A striking and defining feature of circadian clocks is the small variation in period over a physiological range of temperatures. This is referred to as temperature compensation, although recent work has suggested that the variation observed is a specific, adaptive control of period. Moreover, given that many biological rate constants have a Q(10) of around 2, it is remarkable that such clocks remain rhythmic under significant temperature changes. We introduce a new mathematical model for the Neurospora crassa circadian network incorporating experimental work showing that temperature alters the balance of translation between a short and long form of the FREQUENCY (FRQ) protein. This is used to discuss period control and functionality for the Neurospora system. The model reproduces a broad range of key experimental data on temperature dependence and rhythmicity, both in wild-type and mutant strains. We present a simple mechanism utilising the presence of the FRQ isoforms (isoform switching) by which period control could have evolved, and argue that this regulatory structure may also increase the temperature range where the clock is robustly rhythmic.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2009 The BioModels Team.
For more information see the terms of use .
To cite BioModels Database, please use Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

NCBS Curation Comments: This model shows the control mechanism of Jak-Stat pathway, here SOCS1 (Suppressor of cytokine signaling-I) was identified as the negative regulator of Jak and STAT signal transduction pathway. This is the knockout version of Jak-Stat pathway in this model the SOCS1 has been knocked out i.e it formation is not shown. The graphs are almost similar to the graphs as shown in the paper but STAT1n graph has some ambiguities. Thanks to Dr Satoshi Yamada for clarifying some of those ambiguities and providing the values used in simulations.

Biomodels Curation Comments: The model reproduces the figures 2 (B,D,F,H,J,L,N) corresponding to JAK/STAT activation in SOCS1 knock out cells. The model was successfully tested on MathSBML

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2006 The BioModels Team.
For more information see the terms of use .

described in: Systems-level interactions between insulin-EGF networks amplify mitogenic signaling.
Borisov N, Aksamitiene E, Kiyatkin A, Legewie S, Berkhout J, Maiwald T, Kaimachnikov NP, Timmer J, Hoek JB, Kholodenko BN.; Mol Syst Biol. 2009;5:256. Epub 2009 Apr 7. PMID: 19357636 ; doi: 10.1038/msb.2009.19
Abstract:
Crosstalk mechanisms have not been studied as thoroughly as individual signaling pathways. We exploit experimental and computational approaches to reveal how a concordant interplay between the insulin and epidermal growth factor (EGF) signaling networks can potentiate mitogenic signaling. In HEK293 cells, insulin is a poor activator of the Ras/ERK (extracellular signal-regulated kinase) cascade, yet it enhances ERK activation by low EGF doses. We find that major crosstalk mechanisms that amplify ERK signaling are localized upstream of Ras and at the Ras/Raf level. Computational modeling unveils how critical network nodes, the adaptor proteins GAB1 and insulin receptor substrate (IRS), Src kinase, and phosphatase SHP2, convert insulin-induced increase in the phosphatidylinositol-3,4,5-triphosphate (PIP(3)) concentration into enhanced Ras/ERK activity. The model predicts and experiments confirm that insulin-induced amplification of mitogenic signaling is abolished by disrupting PIP(3)-mediated positive feedback via GAB1 and IRS. We demonstrate that GAB1 behaves as a non-linear amplifier of mitogenic responses and insulin endows EGF signaling with robustness to GAB1 suppression. Our results show the feasibility of using computational models to identify key target combinations and predict complex cellular responses to a mixture of external cues.

An extracellular compartment with 34 times the volume of the cell was added and the association rate as well as the dissociation constants for Insulin and EGF binding were altered (k _on '=34*k _on , K _D '=K _D /34). This was done to allow using the concentrations for those species given in the article and retaining the same dynamics and Ligand depletion as in the matlab file the SBML file was exported from.

SBML model exported from PottersWheel on 2008-10-14 16:26:44.

This model is from the article:
Analyzing the functional properties of the creatine kinase system with multiscale 'sloppy' modeling.
Hettling H, van Beek JH PLoS Comput Biol. 2011 Aug;7(8):e1002130. PMEDID ,
Abstract:
In this study the function of the two isoforms of creatine kinase (CK; EC 2.7.3.2) in myocardium is investigated. The 'phosphocreatine shuttle' hypothesis states that mitochondrial and cytosolic CK plays a pivotal role in the transport of high-energy phosphate (HEP) groups from mitochondria to myofibrils in contracting muscle. Temporal buffering of changes in ATP and ADP is another potential role of CK. With a mathematical model, we analyzed energy transport and damping of high peaks of ATP hydrolysis during the cardiac cycle. The analysis was based on multiscale data measured at the level of isolated enzymes, isolated mitochondria and on dynamic response times of oxidative phosphorylation measured at the whole heart level. Using 'sloppy modeling' ensemble simulations, we derived confidence intervals for predictions of the contributions by phosphocreatine (PCr) and ATP to the transfer of HEP from mitochondria to sites of ATP hydrolysis. Our calculations indicate that only 15±8% (mean±SD) of transcytosolic energy transport is carried by PCr, contradicting the PCr shuttle hypothesis. We also predicted temporal buffering capabilities of the CK isoforms protecting against high peaks of ATP hydrolysis (3750 µM*s(-1)) in myofibrils. CK inhibition by 98% in silico leads to an increase in amplitude of mitochondrial ATP synthesis pulsation from 215±23 to 566±31 µM*s(-1), while amplitudes of oscillations in cytosolic ADP concentration double from 77±11 to 146±1 µM. Our findings indicate that CK acts as a large bandwidth high-capacity temporal energy buffer maintaining cellular ATP homeostasis and reducing oscillations in mitochondrial metabolism. However, the contribution of CK to the transport of high-energy phosphate groups appears limited. Mitochondrial CK activity lowers cytosolic inorganic phosphate levels while cytosolic CK has the opposite effect.

This a model from the article:
Bistability from double phosphorylation in signal transduction. Kinetic and structural requirements.
Ortega F, Garcés JL, Mas F, Kholodenko BN, Cascante M. FEBS J. 2006 Sep;273(17):3915-26. 16934033 ,
Abstract:
Previous studies have suggested that positive feedback loops and ultrasensitivity are prerequisites for bistability in covalent modification cascades. However, it was recently shown that bistability and hysteresis can also arise solely from multisite phosphorylation. Here we analytically demonstrate that double phosphorylation of a protein (or other covalent modification) generates bistability only if: (a) the two phosphorylation (or the two dephosphorylation) reactions are catalyzed by the same enzyme; (b) the kinetics operate at least partly in the zero-order region; and (c) the ratio of the catalytic constants of the phosphorylation and dephosphorylation steps in the first modification cycle is less than this ratio in the second cycle. We also show that multisite phosphorylation enlarges the region of kinetic parameter values in which bistability appears, but does not generate multistability. In addition, we conclude that a cascade of phosphorylation/dephosphorylation cycles generates multiple steady states in the absence of feedback or feedforward loops. Our results show that bistable behavior in covalent modification cascades relies not only on the structure and regulatory pattern of feedback/feedforward loops, but also on the kinetic characteristics of their component proteins.

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2010 The BioModels.net Team.
For more information see the terms of use .
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

This model is from the article:
Mass and information feedbacks through receptor endocytosis govern insulin signaling as revealed using a parameter-free modeling framework.
Brannmark C, Palmer R, Glad ST, Cedersund G, Stralfors P. J Biol Chem. 2010 Jun 25;285(26):20171-9. 20421297 ,
Abstract:
Insulin and other hormones control target cells through a network of signal-mediating molecules. Such networks are extremely complex due to multiple feedback loops in combination with redundancy, shared signal mediators, and cross-talk between signal pathways. We present a novel framework that integrates experimental work and mathematical modeling to quantitatively characterize the role and relation between co-existing submechanisms in complex signaling networks. The approach is independent of knowing or uniquely estimating model parameters because it only relies on (i) rejections and (ii) core predictions (uniquely identified properties in unidentifiable models). The power of our approach is demonstrated through numerous iterations between experiments, model-based data analyses, and theoretical predictions to characterize the relative role of co-existing feedbacks governing insulin signaling. We examined phosphorylation of the insulin receptor and insulin receptor substrate-1 and endocytosis of the receptor in response to various different experimental perturbations in primary human adipocytes. The analysis revealed that receptor endocytosis is necessary for two identified feedback mechanisms involving mass and information transfer, respectively. Experimental findings indicate that interfering with the feedback may substantially increase overall signaling strength, suggesting novel therapeutic targets for insulin resistance and type 2 diabetes. Because the central observations are present in other signaling networks, our results may indicate a general mechanism in hormonal control.

Bruce Shapiro: Generated by Cellerator Version 1.0 update 3.0303 using Mathematica 4.1 for Microsoft Windows (June 13, 2001), April 2, 2003 16:49:13, using (PC,x86, Microsoft Windows,WindowsNT,Windows)

Bruce Shapiro: Corrected 29 March 2005

Nicolas Le Novère: Added Dbt and Cyc species, and the corresponding reactions. 23 April 2005

SBML creators: Armando Reyes-Palomares * , Carlos Rodríguez-Caso +, Raul Montañez * , Marta Cascante $, Francisca Sánchez-Jiménez * , Miguel A. Medina *

* ProCel Group, Department of Molecular Biology and Biochemistry, Faculty of Sciences, Campus de Teatinos, University of Malaga and CIBER de Enfermedades Raras (CIBER-ER). + Complex Systems Lab (ICREA-UPF), Barcelona Biomedical Research Park (PRBB-GRIB). $ Department of Biochemistry and Molecular Biology, Faculty of Biology, Universitat de Barcelona.

http://asp.uma.es

Metabolic modeling of polyamine metabolism in mammals.
Rodríguez-Caso,C et al.: J Biol Chem 2006 : 281:21799-812.
The model reproduces the dynamical behavior of the polyamine metabolism in mammals. In this model there are some additions and corrections to the publication. All perturbations and analysis have produced results very close to the published experiments. The model was successfully tested on CoPaSi v.4.4 (build 26).

Parameters not included in the publication:

1. Parameters for SSAT kinetic constants:

KmAcCoA = 1.5 µM

KmCoA = 40 µM

2. Parameters for equation MAT (table 1):

Vmax_MAT = 0.45 µM/min

Km_MAT = 41 µM

Ki_MET_MAT = 50 µM

3. Erratum.: The corrected ODE for time-dependent variable Antz is:

KsANTZ*(1-1/(1+Keq*0.01*([D]+[S])))-KdANTZ*[Antz]

According to these modifications the new steady-state analysis results are:

Metabolites:

[P]= 104.681 µM

[D]= 76.7492 µM

[S]= 58.0135 µM

[SAM]= 52.327 µM

[A]= 0.0101962 µM

[aS]= 0.0245375 µM

[aD]= 0.832236 µM

Time-dependent global parameters:

[Antz] = 0.574038 µM

Vmaxodc = 1.28315 µM/min

Vmaxssat = 0.673814 µM/min

Vmaxsamdc = 0.36829 µM/min

This a model from the article:
Channel sharing in pancreatic beta -cells revisited: enhancement of emergent bursting by noise.
De Vries G, Sherman A. J Theor Biol 2000 Dec 21;207(4):513-30 11093836 ,
Abstract:
Secretion of insulin by electrically coupled populations of pancreatic beta -cells is governed by bursting electrical activity. Isolated beta -cells, however, exhibit atypical bursting or continuous spike activity. We study bursting as an emergent property of the population, focussing on interactions among the subclass of spiking cells. These are modelled by equipping the fast subsystem with a saddle-node-loop bifurcation, which makes it monostable. Such cells can only spike tonically or remain silent when isolated, but can be induced to burst with weak diffusive coupling. With stronger coupling, the cells revert to tonic spiking. We demonstrate that the addition of noise dramatically increases, via a phenomenon like stochastic resonance, the coupling range over which bursting is seen. Copyright 2000 Academic Press.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: De Vries G, Sherman A. (2000) - version01

The model reproduces the oscillations for mRNA and protein species as depicted in Fig 3 of the plot. The model differs slightly from that given in the paper and this was made after a communication from the authors. The values of parameters tcvriclkp, tcdvpmt and dccpt are slightly different. Also, although it is not given in the paper, rate laws for reactions re20, re28, re35, re42, re43 and re45 are multiplied by a specie. Model was successfully tested on MathSBML

This is a model of the coupled Natch, Wnt and FGF modules as described in:
A. Goldbeter and O. Pourquié , Modeling the segmentation clock as a network of coupled oscillations in the Notch, Wnt and FGF signaling pathways. J Theor Biol. 2008 Jun 7;252(3):574-85, pubmed ID: 18308339
To uncouple the modules remove the reaction MAx_trans_Xa and set vsFK=vsF .
The SBML version of the model was converted from the CellML version by Catherine Lloyd for the CellML repository .

Model is according to the paper Contribution of Persistent Na+ Current and M-Type K+ Current to Somatic Bursting in CA1 Pyramidal Cell: Combined Experimental. This is the second model from this paper for the non-zero [Ca2+] initial value, parameters and the kinetics quations from Table2 in the paper. Figure9Aa has been reproduced by MathSBML. The original model from ModelDB. http://senselab.med.yale.edu/modeldb/

This is the model described in the article:
Integrating life history and cross-immunity into the evolutionary dynamics of pathogens.
Restif O, Grenfell BT. Proc Biol Sci. 2006 Feb 22;273(1585):409-16. PMID: 16615206 , doi: 10.1098/rspb.2005.3335 ;
Abstract:
Models for the diversity and evolution of pathogens have branched into two main directions: the adaptive dynamics of quantitative life-history traits (notably virulence) and the maintenance and invasion of multiple, antigenically diverse strains that interact with the host's immune memory. In a first attempt to reconcile these two approaches, we developed a simple modelling framework where two strains of pathogens, defined by a pair of life-history traits (infectious period and infectivity), interfere through a given level of cross-immunity. We used whooping cough as a potential example, but the framework proposed here could be applied to other acute infectious diseases. Specifically, we analysed the effects of these parameters on the invasion dynamics of one strain into a population, where the second strain is endemic. Whereas the deterministic version of the model converges towards stable coexistence of the two strains in most cases, stochastic simulations showed that transient epidemic dynamics can cause the extinction of either strain. Thus ecological dynamics, modulated by the immune parameters, eventually determine the adaptive value of different pathogen genotypes. We advocate an integrative view of pathogen dynamics at the crossroads of immunology, epidemiology and evolution, as a way towards efficient control of infectious diseases.

This version of the model can be used for both the stochastic and the deterministic simulations described in the article. For deterministic interpretations with infinite population sizes, set the population size N = 1. The model reproduces the deterministic time courses. Stochastic interpretation with Copasi UI gave results similar to the article, but was not extensively tested. The initial conditions for competition simulations can be derived by equilibrating the system for one pathogen and then adding a starting concentration for the other.

Originally created by libAntimony v1.3 (using libSBML 4.1.0-b1)

This a model from the article:
Systems analysis of iron metabolism: the network of iron pools and fluxes
Tiago JS Lopes, Tatyana Luganskaja, Maja Vujic-Spasic, Matthias W Hentze, Martina U Muckenthaler, K laus Schumann and Jens G Reich BMC Systems Biology 2010, Aug 13;4(1):112. 20704761 ,
Abstract:
Background
Every cell of the mammalian organism needs iron in numerous oxido-reductive processes as well as fo r transport and storage of oxygen. The versatility of ionic iron makes it a toxic entity which can catalyze the production of radicals that damage vital membranous and macromolecular assemblies in t he cell. The mammalian organism maintains therefore a complex regulatory network of iron uptake, ex cretion and intra-div distribution. Intracellular regulation in different cell types is intertwine d with a global hormonal signaling structure. Iron deficiency as well as excess of iron are frequen t and serious human disorders. They can affect every cell, but also the organism as a whole.
Results
Here, we present a kinematic model of the dynamic system of iron pools and fluxes. It is based on f errokinetic data and chemical measurements in C57BL6 wild-type mice maintained on iron-deficient, i ron-adequate, or iron-loaded diet. The tracer iron levels in major tissues and organs (16 compartme nt) were followed for 28 days. The evaluation resulted in a whole-div model of fractional clearanc e rates. The analysis permits calculation of absolute flux rates in the steady-state, of iron distr ibution into different organs, of tracer-accessible pool sizes and of residence times of iron in th e different compartments in response to three states of iron-repletion induced by the dietary regim e.
Conclusions
This mathematical model presents a comprehensive physiological picture of mice under three differen t diets with varying iron contents. The quantitative results reflect systemic properties of iron me tabolism: dynamic closedness, hierarchy of time scales, switch-over response and dynamics of iron s torage in parenchymal organs. Therefore, we could assess which parameters will change under dietary perturbations and study in quantitative terms when those changes take place.

This model corresponds to the Iron Adequate condition - Mice

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2010 The BioModels Team.
For more information see the terms of use .
To cite BioModels Database, please use Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

This a model from the article:
Which model to use for cortical spiking neurons?
Izhikevich EM. IEEE Trans Neural Netw. 2004 Sep;15(5):1063-70. 15484883 ,
Abstract:
We discuss the biological plausibility and computational efficiency of some of the most useful models of spiking and bursting neurons. We compare their applicability to large-scale simulations of cortical neural networks.

The model is according to the paper Which Model to Use for Cortical Spiking Neurons? Figure1(S) inhibition-induced spiking has been reproduced by MathSBML. The ODE and the parameters values are taken from the a paper Simple Model of Spiking Neurons The original format of the models are encoded in the MATLAB format existed in the ModelDB with Accession number 39948

Figure1 are the simulation results of the same model with different choices of parameters and different stimulus function or events.a=-0.02; b=-1; c=-60; d=8; V=-63.8; u=b*V;

This model is from the article:
Modelling thrombin generation in human ovarian follicular fluid
Bungay Sharene D., Gentry Patricia A., Gentry Rodney D. Bulletin of Mathematical Biology Volume 68, Issue 8, 12 July 2006, Pages 2283-302 16838084 ,
Abstract:
A mathematical model is constructed to study thrombin production in human ovarian follicular fluid. The model results show that the amount of thrombin that can be produced in ovarian follicular fluid is much lower than that in blood plasma, failing to reach the level required for fibrin formation, and thereby supporting the hypothesis that in follicular fluid thrombin functions to initiate cellular activities via intracellular signalling receptors. It is also concluded that the absence of the amplification pathway to thrombin production in follicular fluid is a major factor in restricting the amount of thrombin that can be produced. Titration of the initial concentrations of the various reactants in the model lead to predictions for the amount of tissue factor and phospholipid that is required to maintain thrombin production in the follicle, as well as to the conclusion that tissue factor pathway inhibitor has little effect on the time that thrombin generation is sustained. Numerical experiments to determine the effect of factor V, which is at a much reduced level in follicular fluid compared to plasma, and thrombomodulin, illustrate the importance for further experimental work to determine values for several parameters that have yet to be reported in the literature.

Edelstein1996 - EPSP ACh species

Model of a nicotinic Excitatory Post-Synaptic Potential in a Torpedo electric organ. Acetylcholine is represented explicitely as a molecular species.

This model has initially been encoded using StochSim.

This model is described in the article:

A kinetic mechanism for nicotinic acetylcholine receptors based on multiple allosteric transitions.

Edelstein SJ, Schaad O, Henry E, Bertrand D, Changeux JP.

Biol. Cybern. 1996 Nov; 75(5):361-79

Abstract:

Nicotinic acetylcholine receptors are transmembrane oligomeric proteins that mediate interconversions between open and closed channel states under the control of neurotransmitters. Fast in vitro chemical kinetics and in vivo electrophysiological recordings are consistent with the following multi-step scheme. Upon binding of agonists, receptor molecules in the closed but activatable resting state (the Basal state, B) undergo rapid transitions to states of higher affinities with either open channels (the Active state, A) or closed channels (the initial Inactivatable and fully Desensitized states, I and D). In order to represent the functional properties of such receptors, we have developed a kinetic model that links conformational interconversion rates to agonist binding and extends the general principles of the Monod-Wyman-Changeux model of allosteric transitions. The crucial assumption is that the linkage is controlled by the position of the interconversion transition states on a hypothetical linear reaction coordinate. Application of the model to the peripheral nicotine acetylcholine receptor (nAChR) accounts for the main properties of ligand-gating, including single-channel events, and several new relationships are predicted. Kinetic simulations reveal errors inherent in using the dose-response analysis, but justify its application under defined conditions. The model predicts that (in order to overcome the intrinsic stability of the B state and to produce the appropriate cooperativity) channel activation is driven by an A state with a Kd in the 50 nM range, hence some 140-fold stronger than the apparent affinity of the open state deduced previously. According to the model, recovery from the desensitized states may occur via rapid transit through the A state with minimal channel opening, thus without necessarily undergoing a distinct recovery pathway, as assumed in the standard 'cycle' model. Transitions to the desensitized states by low concentration 'pre-pulses' are predicted to occur without significant channel opening, but equilibrium values of IC50 can be obtained only with long pre-pulse times. Predictions are also made concerning allosteric effectors and their possible role in coincidence detection. In terms of future developments, the analysis presented here provides a physical basis for constructing more biologically realistic models of synaptic modulation that may be applied to artificial neural networks.

This model is hosted on BioModels Database and identified by: BIOMD0000000002 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

Notes of the BioModels curators:

The current model reproduce the figure 7, panel B of the paper. Note that there is a typo in the figure. The ordinates represent the concentration of peroxyde, as stated in the legend, and not of oxygen. The model has been tested in COPASI (http://www.copasi.org/, build 13).

Notes of the original version of the SBML file:

SBML level 2 code generated for the JWS Online project by Jacky Snoep using PySCeS
Run this model online at http://jjj.biochem.sun.ac.za
To cite JWS Online please refer to: Olivier, B.G. and Snoep, J.L. (2004) Web-based modelling using JWS Online , Bioinformatics, 20:2143-2144

This model is from the article:
Overexpression limits of fission yeast cell-cycle regulators in vivo and in silico.
Moriya H, Chino A, Kapuy O, Csikász-Nagy A, Novák B. Mol Syst Biol. 2011 Dec 6;7:556. 22146300 ,
Abstract:
Cellular systems are generally robust against fluctuations of intracellular parameters such as gene expression level. However, little is known about expression limits of genes required to halt cellular systems. In this study, using the fission yeast Schizosaccharomyces pombe, we developed a genetic 'tug-of-war' (gTOW) method to assess the overexpression limit of certain genes. Using gTOW, we determined copy number limits for 31 cell-cycle regulators; the limits varied from 1 to >100. Comparison with orthologs of the budding yeast Saccharomyces cerevisiae suggested the presence of a conserved fragile core in the eukaryotic cell cycle. Robustness profiles of networks regulating cytokinesis in both yeasts (septation-initiation network (SIN) and mitotic exit network (MEN)) were quite different, probably reflecting differences in their physiologic functions. Fragility in the regulation of GTPase spg1 was due to dosage imbalance against GTPase-activating protein (GAP) byr4. Using the gTOW data, we modified a mathematical model and successfully reproduced the robustness of the S. pombe cell cycle with the model.

This a model from the article:
Synthetic in vitro transcriptional oscillators.
Kim J, Winfree E Mol. Syst. Biol. 2011 Feb 1;7:465. 21283141 ,
Abstract:
The construction of synthetic biochemical circuits from simple components illuminates how complex beha viors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteri ophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In t his study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA si gnals, showed up to five complete cycles. To demonstrate modularity and to explore the design space fu rther, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design p rocess, identified experimental conditions likely to yield oscillations, and explained the system's ro bust response to interference by short degradation products. Synthetic transcriptional oscillators cou ld prove valuable for systematic exploration of biochemical circuit design principles and for controll ing nanoscale devices and orchestrating processes within artificial cells.

Note:

The paper describes 7 models (MODEL1012090000-6) and all these are submitted by the authors. This model (MODEL1012090000) corresponds to the Simple model for both mode I and II (Design I and II). The model reproduces timecourse figure plotted in the supplementary material (page 10 of Supplementary material) of the reference publication.

This is model is according to the paper Toward a detailed computational model for the mammalian circadian clock

In this model interlocked negative and positive regulation of Per,Cry,Bmal,REV-ERBalpha genes are all involved.The model is actually robust so the initial conditions are unimportant.We gave every entity zero as initial value,and start the graph at time=132h.

The simulation results in figure 8B can be reproduced by roadRunner online and Copasi. We use a ceiling function to simulate the day-light cycle.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2011 The BioModels.net Team.
For more information see the terms of use .
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

This a model from the article:
Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic beta-cells.
Chay TR Biophys J. 1997 Sep;73(3):1673-88. 9284334 ,
Abstract:
The extracellular calcium concentration has interesting effects on bursting of pancreatic beta-cells. The mechanism underlying the extracellular Ca2+ effect is not well understood. By incorporating a low-threshold transient inward current to the store-operated bursting model of Chay, this paper elucidates the role of the extracellular Ca2+ concentration in influencing electrical activity, intracellular Ca2+ concentration, and the luminal Ca2+ concentration in the intracellular Ca2+ store. The possibility that this inward current is a carbachol-sensitive and TTX-insensitive Na+ current discovered by others is discussed. In addition, this paper explains how these three variables respond when various pharmacological agents are applied to the store-operated model.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Chay TR (1997) - version05
The original CellML model was created by:
Lloyd, Catherine, May
c.lloyd@aukland.ac.nz
The University of Auckland
The Bioengineering Institute

This model corresponds to the Iron Deficient condition - Mice

The model is according to the paper Which Model to Use for Cortical Spiking Neurons? Figure1(I) spike latency has been reproduced by MathSBML. The ODE and the parameters values are taken from the a paper Simple Model of Spiking Neurons The original format of the models are encoded in the MATLAB format existed in the ModelDB with Accession number 39948

Figure1 are the simulation results of the same model with different choices of parameters and different stimulus function or events. In this model a=0.02; b=0.2; c=-65; d=6; V=-70; u=b*V=0.2*(-70);

This a model from the article:
A modelling approach to quantify dynamic crosstalk between the pheromone and the starvation pathway in baker's yeast.
Schaber J, Kofahl B, Kowald A, Klipp E FEBS J. 2006 Aug; 273(15):3520-33 16884493 ,
Abstract:
Cells must be able to process multiple information in parallel and, moreover, they must also be able to combine this information in order to trigger the appropriate response. This is achieved by wiring signalling pathways such that they can interact with each other, a phenomenon often called crosstalk. In this study, we employ mathematical modelling techniques to analyse dynamic mechanisms and measures of crosstalk. We present a dynamic mathematical model that compiles current knowledge about the wiring of the pheromone pathway and the filamentous growth pathway in yeast. We consider the main dynamic features and the interconnections between the two pathways in order to study dynamic crosstalk between these two pathways in haploid cells. We introduce two new measures of dynamic crosstalk, the intrinsic specificity and the extrinsic specificity. These two measures incorporate the combined signal of several stimuli being present simultaneously and seem to be more stable than previous measures. When both pathways are responsive and stimulated, the model predicts that (a) the filamentous growth pathway amplifies the response of the pheromone pathway, and (b) the pheromone pathway inhibits the response of filamentous growth pathway in terms of mitogen activated protein kinase activity and transcriptional activity, respectively. Among several mechanisms we identified leakage of activated Ste11 as the most influential source of crosstalk. Moreover, we propose new experiments and predict their outcomes in order to test hypotheses about the mechanisms of crosstalk between the two pathways. Studying signals that are transmitted in parallel gives us new insights about how pathways and signals interact in a dynamical way, e.g., whether they amplify, inhibit, delay or accelerate each other.

Biomodels Curation: The paper refers to the model equations present in Bakker et al's " Glycolysis in bloodstream from Trypanosoma brucei can be understood in terms of the kinetics of glycolytic enzymes" (Pubmed ID: 9013556), also, the authors claim that some of the modifications in these equations were made based on the experimental results from the paper "Contribution of glucose transport in the control of glycolytic flux in Trypanosoma brucei" (Pubmed ID: 10468568). The model reproduces the various flux values in Fig 3 for 100% TPI activity. It also matches with the values provided in Table 2 of the paper. The model was successfully tested with Copasi and SBML ODE Solver.
The volumes are set to the values containing 1 mg of total protein per microlitre total cell volume. To change the protein concentration use Vt , the total cell volume in micro litre per mg protein.
To change the TPI activity use the global parameter TPIact .

This model is from the article:
The clock gene circuit in Arabidopsis includes a repressilator with additional feedback loops
Pokhilko A, Fernández AP, Edwards KD, Southern MM, Halliday KJ, Millar AJ. Mol Syst Biol. 2012 Mar 6;8:574. 22395476 ,
Abstract:
Circadian clocks synchronise biological processes with the day/night cycle, using molecular mechanisms that include interlocked, transcriptional feedback loops. Recent experiments identified the evening complex (EC) as a repressor that can be essential for gene expression rhythms in plants. Integrating the EC components in this role significantly alters our mechanistic, mathematical model of the clock gene circuit. Negative autoregulation of the EC genes constitutes the clock's evening loop, replacing the hypothetical component Y. The EC explains our earlier conjecture that the morning gene PSEUDO-RESPONSE REGULATOR 9 was repressed by an evening gene, previously identified with TIMING OF CAB EXPRESSION1 (TOC1). Our computational analysis suggests that TOC1 is a repressor of the morning genes LATE ELONGATED HYPOCOTYL and CIRCADIAN CLOCK ASSOCIATED1 rather than an activator as first conceived. This removes the necessity for the unknown component X (or TOC1mod) from previous clock models. As well as matching timeseries and phase-response data, the model provides a new conceptual framework for the plant clock that includes a three-component repressilator circuit in its complex structure.

McAuley2012 - Whole-div Cholesterol Metabolism

Lipid metabolism has a key role to play in human longevity and healthy aging. A whole-div mathematical model of cholesterol metabolism that explores the changes in both the rate of intestinal cholesterol absorption and the hepatic rate of clearance of LDL-C from the plasma, has been presented here. The model showed that of these two mechanisms, changes to the rate of LDL-C removal from the plasma with age had the most significant effect on cholesterol metabolism.

The original SBML model file was generated using MathSBML 2.5.1.

This model is described in the article:

A whole-div mathematical model of cholesterol metabolism and its age-associated dysregulation.

Mc Auley MM, Wilkinson DJ, Jones JJ, Kirkwood TT.

BMC Syst Biol. 2012 Oct 10;6(1):130.

Abstract:

BACKGROUND: Global demographic changes have stimulated marked interest in the process of ageing. There has been, and will continue to be, an unrelenting rise in the number of the oldest old ( >85 years of age). Together with an ageing population there comes an increase in the prevalence of age related disease. Of the diseases of ageing, cardiovascular disease (CVD) has by far the highest prevalence. It is regarded that a finely tuned lipid profile may help to prevent CVD as there is a long established relationship between alterations to lipid metabolism and CVD risk. In fact elevated plasma cholesterol, particularly Low Density Lipoprotein Cholesterol (LDL-C) has consistently stood out as a risk factor for having a cardiovascular event. Moreover it is widely acknowledged that LDL-C may rise with age in both sexes in a wide variety of groups. The aim of this work was to use a whole-div mathematical model to investigate why LDL-C rises with age, and to test the hypothesis that mechanistic changes to cholesterol absorption and LDL-C removal from the plasma are responsible for the rise. The whole-div mechanistic nature of the model differs from previous models of cholesterol metabolism which have either focused on intracellular cholesterol homeostasis or have concentrated on an isolated area of lipoprotein dynamics. The model integrates both current and previously published data relating to molecular biology, physiology, ageing and nutrition in an integrated fashion.

RESULTS: The model was used to test the hypothesis that alterations to the rate of cholesterol absorption and changes to the rate of removal of LDL-C from the plasma are integral to understanding why LDL-C rises with age. The model demonstrates that increasing the rate of intestinal cholesterol absorption from 50% to 80% by age 65 years can result in an increase of LDL-C by as much as 34mg/dL in a hypothetical male subject. The model also shows that decreasing the rate of hepatic clearance of LDL-C gradually to 50% by age 65 years can result in an increase of LDL-C by as much as 116mg/dL.

CONCLUSIONS: Our model clearly demonstrates that of the two putative mechanisms that have been implicated in the dysregulation of cholesterol metabolism with age, alterations to the removal rate of plasma LDL-C has the most significant impact on cholesterol metabolism and small changes to the number of hepatic LDL receptors can result in a significant rise in LDL-C. This first whole-div systems based model of cholesterol balance could potentially be used as a tool to further improve our understanding of whole-div cholesterol metabolism and its dysregulation with age. Furthermore, given further fine tuning the model may help to investigate potential dietary and lifestyle regimes that have the potential to mitigate the effects aging has on cholesterol metabolism.

This model is hosted on BioModels Database and identified by: MODEL1206010000 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

The model reproduces Figures 4,5 and 6 of the publication. The analytical functions for cometabolites Catp, Camp, Cnadph, and Cnadp slightly differ from the equations given in the paper. These changes were made in consultation with Dr. Christophe Chassagnole and are essential for reproducing the figures. The dependency of the rate of change of extracellular glucose concentration on the ratio of biomass concentration to specific weight of biomass (Cx*rPTS/Rhox) is taken into account by appropriately adjusting the stoichiometries of the species involved in the phosphotransferase system (rPTS). The rmax values for the various reactions are obtained from experiments and are not provided in the paper. However, these were personally communicated to the JWS repository. The model has been successfully tested on MathSBML.

This model is from the article:
Reduction of off-flavor generation in soybean homogenates: a mathematical model.
Mellor N , Bligh F , Chandler I , Hodgman C J. Food Sci. 2010 Sep; 75(7): R131-8; PMID: 2153556 ,
Abstract:
The generation of off-flavors in soybean homogenates such as n-hexanal via the lipoxygenase (LOX) pathway can be a problem in the processed food industry. Previous studies have examined the effect of using soybean varieties missing one or more of the 3 LOX isozymes on n-hexanal generation. A dynamic mathematical model of the soybean LOX pathway using ordinary differential equations was constructed using parameters estimated from existing data with the aim of predicting how n-hexanal generation could be reduced. Time-course simulations of LOX-null beans were run and compared with experimental results. Model L(2), L(3), and L(12) beans were within the range relative to the wild type found experimentally, with L(13) and L(23) beans close to the experimental range. Model L(1) beans produced much more n-hexanal relative to the wild type than those in experiments. Sensitivity analysis indicates that reducing the estimated K(m) parameter for LOX isozyme 3 (L-3) would improve the fit between model predictions and experimental results found in the literature. The model also predicts that increasing L-3 or reducing L-2 levels within beans may reduce n-hexanal generation. PRACTICAL APPLICATION: This work describes the use of mathematics to attempt to quantify the enzyme-catalyzed conversions of compounds in soybean homogenates into undesirable flavors, primarily from the compound n-hexanal. The effect of different soybean genotypes and enzyme kinetic constants was also studied, leading to recommendations on which combinations might minimize off-flavor levels and what further work might be carried out to substantiate these conclusions.

The model reproduces the circadian charecteristics as given in Table 1 for the PRR7-PRR9-Y model. The model makes use of the event section to introduce light at 30 hours. The Zeitgeber (ZT) times for species shown in Table 1 can be reproduced by looking at the time it takes for species to reach peak values after the introduction of light. The model was successfully tested on MathSBML.

This a model from the article:
Calcium and glycolysis mediate multiple bursting modes in pancreatic islets.
Bertram R, Satin L, Zhang M, Smolen P, Sherman A. Biophys J 2004 Nov;87(5):3074-87 15347584 ,
Abstract:
Pancreatic islets of Langerhans produce bursts of electrical activity when exposed to stimulatory glucose levels. These bursts often have a regular repeating pattern, with a period of 10-60 s. In some cases, however, the bursts are episodic, clustered into bursts of bursts, which we call compound bursting. Consistent with this are recordings of free Ca2+ concentration, oxygen consumption, mitochondrial membrane potential, and intraislet glucose levels that exhibit very slow oscillations, with faster oscillations superimposed. We describe a new mathematical model of the pancreatic beta-cell that can account for these multimodal patterns. The model includes the feedback of cytosolic Ca2+ onto ion channels that can account for bursting, and a metabolic subsystem that is capable of producing slow oscillations driven by oscillations in glycolysis. This slow rhythm is responsible for the slow mode of compound bursting in the model. We also show that it is possible for glycolytic oscillations alone to drive a very slow form of bursting, which we call "glycolytic bursting." Finally, the model predicts that there is bistability between stationary and oscillatory glycolysis for a range of parameter values. We provide experimental support for this model prediction. Overall, the model can account for a diversity of islet behaviors described in the literature over the past 20 years.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Bertram R, Satin L, Zhang M, Smolen P, Sherman A. (2004) - version=1.0
The original CellML model was created by:
Catherine Lloyd
c.lloyd@auckland.ac.nz
The University of Auckland

This model is from the article:
The auxin signalling network translates dynamic input into robust patterning at the shoot apex.
Vernoux T, Brunoud G, Farcot E, Morin V, Van den Daele H, Legrand J, Oliva M, Das P, Larrieu A, Wells D, Guédon Y, Armitage L, Picard F, Guyomarc'h S, Cellier C, Parry G, Koumproglou R, Doonan JH, Estelle M, Godin C, Kepinski S, Bennett M, De Veylder L, Traas J. Mol Syst Biol. 2011 Jul 5;7:508. 21734647 ,
Abstract:
The plant hormone auxin is thought to provide positional information for patterning during development. It is still unclear, however, precisely how auxin is distributed across tissues and how the hormone is sensed in space and time. The control of gene expression in response to auxin involves a complex network of over 50 potentially interacting transcriptional activators and repressors, the auxin response factors (ARFs) and Aux/IAAs. Here, we perform a large-scale analysis of the Aux/IAA-ARF pathway in the shoot apex of Arabidopsis, where dynamic auxin-based patterning controls organogenesis. A comprehensive expression map and full interactome uncovered an unexpectedly simple distribution and structure of this pathway in the shoot apex. A mathematical model of the Aux/IAA-ARF network predicted a strong buffering capacity along with spatial differences in auxin sensitivity. We then tested and confirmed these predictions using a novel auxin signalling sensor that reports input into the signalling pathway, in conjunction with the published DR5 transcriptional output reporter. Our results provide evidence that the auxin signalling network is essential to create robust patterns at the shoot apex.

Note:

Figure 4 of the supplementary material of the reference article has been reproduced here. In this model, the fluctuations of auxin level is represented using sinux function. Time evolution of the variables AUX/IAA (I) and mRNA (R) are plotted, under the influence of fluctuations of auxin level. pi_A is varied between 0 and 2 by steps of 0.1.

Gardner1998 - Cell Cycle Goldbeter

Mathematical modeling of cell division cycle (CDC) dynamics.

The SBML file has been generated by MathSBML 2.6.0.p960929 (Prerelease Version of 29-Sept-2006) 1-October-2006 15:36:36.076517.

This model is described in the article:

A theory for controlling cell cycle dynamics using a reversibly binding inhibitor.

Gardner TS, Dolnik M, Collins JJ

Proc. Natl. Acad. Sci. U.S.A. 1998:95(24):14190-14195

Abstract:

We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, we show that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo.

This model is hosted on BioModels Database and identified by: BIOMD0000000008 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

Note: Model of the Calvin cycle and the related end-product pathway to starch synthesis by Poolman et al. (2000, DOI:10.1093/jexbot/51.suppl_1.319 ).

The parameter values are widely taken from Pettersson and Ryde-Pettersson (1988, DOI:10.1111/j.1432-1033.1988.tb14242.x ) and Poolman (1999, [click here for PDF] ). The initial metabolite values are chosen from the data set of Zhu et al. (2007, DOI:10.1104/pp.107.103713 ). A detailed description of all modifications is given in the model described by Arnold and Nikoloski (2011, PMID:22001849 .

This a model from the article:
Sensitivity analysis of parameters controlling oscillatory signalling in the NF-kappaB pathway: the roles of IKK and IkappaBalpha.
Ihekwaba AE, Broomhead DS, Grimley RL, Benson N, Kell DB Syst Biol (Stevenage) [2004 Jun;1(1):93-103 17052119 ,
Abstract:
Analysis of cellular signalling interactions is expected to create an enormous informatics challenge, perhaps even greater than that of analysing the genome. A key step in the evolution towards a more quantitative understanding of signalling is to specify explicitly the kinetics of all chemical reaction steps in a pathway. We have reconstructed a model of the nuclear factor, kappaB (NF-kappaB) signalling pathway, containing 64 parameters and 26 variables, including steps in which the activation of the NF-kappaB transcription factor is intimately associated with the phosphorylation and ubiquitination of its inhibitor kappaB by a membrane-associated kinase, and its translocation from the cytoplasm to the nucleus. We apply sensitivity analysis to the model. This identifies those parameters in this (IkappaB)/NF-kappaB signalling system (containing only induced IkappaBalpha isoform) that most affect the oscillatory concentration of nuclear NF-kappaB (in terms of both period and amplitude). The intention is to provide guidance on which proteins are likely to be most significant as drug targets or should be exploited for further, more detailed experiments. The sensitivity coefficients were found to be strongly dependent upon the magnitude of the parameter change studied, indicating the highly non-linear nature of the system. Of the 64 parameters in the model, only eight to nine exerted a major control on nuclear NF-kappaB oscillations, and each of these involved as reaction participants either the IkappaB kinase (IKK) or IkappaBalpha, directly. This means that the dominant dynamics of the pathway can be reflected, in addition to that of nuclear NF-kappaB itself, by just two of the other pathway variables. This is conveniently observed in a phase-plane plot.

The model correctly reproduces all the figures from the paper. The curation has been done using SBMLodeSolver.

This a model from the article:
A mathematical model of parathyroid hormone response to acute changes in plasma ionized calcium concentration in humans.
Shrestha RP, Hollot CV, Chipkin SR, Schmitt CP, Chait Y. Math Biosci. 2010 Jul;226(1):46-57. 20406649 ,
Abstract:
A complex bio-mechanism, commonly referred to as calcium homeostasis, regulates plasma ionized calcium (Ca(2+)) concentration in the human div within a narrow range which is crucial for maintaining normal physiology and metabolism. Taking a step towards creating a complete mathematical model of calcium homeostasis, we focus on the short-term dynamics of calcium homeostasis and consider the response of the parathyroid glands to acute changes in plasma Ca(2+) concentration. We review available models, discuss their limitations, then present a two-pool, linear, time-varying model to describe the dynamics of this calcium homeostasis subsystem, the Ca-PTH axis. We propose that plasma PTH concentration and plasma Ca(2+) concentration bear an asymmetric reverse sigmoid relation. The parameters of our model are successfully estimated based on clinical data corresponding to three healthy subjects that have undergone induced hypocalcemic clamp tests. In the first validation of this kind, with parameters estimated separately for each subject we test the model's ability to predict the same subject's induced hypercalcemic clamp test responses. Our results demonstrate that a two-pool, linear, time-varying model with an asymmetric reverse sigmoid relation characterizes the short-term dynamics of the Ca-PTH axis.

The model corresponds to hypercalcemic clamp test explained in the paper and parameter values used in the model are that of "subject 1". In order to obtain the plots corresponding to "subject 2" and "subject 3" the following parameters to be changed: lambda_1, lambda_2, m1, m2, R, beta, x1_n, x2_n, x2_min, x2_max, t0, Ca0, Ca1 and alpha.

parameter	Subject 1	Subject 2	Subject 3
lambda_1	0.0125	0.0122	0.0269
lambda_2	0.5595	0.4642	0.4935
m1	112.5200	150.0000	90.8570
m2	15.0000	15.0000	15.0000
R	1.2162	1.1627	1.1889
beta	10e+06	10e+06	10e+06
x1_n	490.7800	452.8200	298.8200
x2_n	6.6290	9.5894	5.4600
x2_min	0.6697	1.4813	0.8287
x2_max	14.0430	17.8710	15.1990
Ca0	1.2200	1.2513	1.2480
Ca1	0.2624	0.2267	0.2132
t0	575	575	575
alpha	0.0569	0.0563	0.0421

This model is from the article:
Asymmetric positive feedback loops reliably control biological responses
Alexander V Ratushny, Ramsey A Saleem, Katherine Sitko, Stephen A Ramsey & John D Aitchison Mol Syst Biol. 2012 Apr 24;8:577. 22531117 ,
Abstract:
Positive feedback is a common mechanism enabling biological systems to respond to stimuli in a switch-like manner. Such systems are often characterized by the requisite formation of a heterodimer where only one of the pair is subject to feedback. This ASymmetric Self-UpREgulation (ASSURE) motif is central to many biological systems, including cholesterol homeostasis (LXRα/RXRα), adipocyte differentiation (PPARγ/RXRα), development and differentiation (RAR/RXR), myogenesis (MyoD/E12) and cellular antiviral defense (IRF3/IRF7). To understand why this motif is so prevalent, we examined its properties in an evolutionarily conserved transcriptional regulatory network in yeast (Oaf1p/Pip2p). We demonstrate that the asymmetry in positive feedback confers a competitive advantage and allows the system to robustly increase its responsiveness while precisely tuning the response to a consistent level in the presence of varying stimuli. This study reveals evolutionary advantages for the ASSURE motif, and mechanisms for control, that are relevant to pharmacologic intervention and synthetic biology applications.

This a model from the article:
PKPD model of interleukin-21 effects on thermoregulation in monkeys--application and evaluation of stochastic differential equations.
Overgaard RV, Holford N, Rytved KA, Madsen H. Pharm Res. 2007 Feb;24(2):298-309. PUBMED ,
Abstract:
PURPOSE: To describe the pharmacodynamic effects of recombinant human interleukin-21 (IL-21) on core div temperature in cynomolgus monkeys using basic mechanisms of heat regulation. A major effort was devoted to compare the use of ordinary differential equations (ODEs) with stochastic differential equations (SDEs) in pharmacokinetic pharmacodynamic (PKPD) modelling. METHODS: A temperature model was formulated including circadian rhythm, metabolism, heat loss, and a thermoregulatory set-point. This model was formulated as a mixed-effects model based on SDEs using NONMEM. RESULTS: The effects of IL-21 were on the set-point and the circadian rhythm of metabolism. The model was able to describe a complex set of IL-21 induced phenomena, including 1) disappearance of the circadian rhythm, 2) no effect after first dose, and 3) high variability after second dose. SDEs provided a more realistic description with improved simulation properties, and further changed the model into one that could not be falsified by the autocorrelation function. CONCLUSIONS: The IL-21 induced effects on thermoregulation in cynomolgus monkeys are explained by a biologically plausible model. The quality of the model was improved by the use of SDEs.

This model is according to the paper from Axel Kowald Alternative pathways as mechanism for the negative effects associated with overexpression of superoxide dismutase.

Reactions from 1 to 17 are listed in the paper, note that for clarity species whose concentrations are assumed to be constant (e.g.water, oxygen,protons, metal ions) are omitted from the diagram. In the paper, v16 is a fast reaction, but we do not use fast reaction in the model.

Figure2 has been reproduced by both SBMLodeSolver and Copasi4.0.20(development) . Figure 3 has been obtained with Copasi4.0.20(development) using parameter scan.

The steady-state of [LOO*] a little bit lower than showed on the paper, I guess it may be the simulation method used in the paper use fast reaction and also the reaction (5) listed on Page 831 on the paper is slightly different from equation (2) on Page 832. The rest of them are the quite the same.

This is a folate model that includes folate polyglutamation.

Morrison and Allegra, JBC:264,10552-10566 (1989)

Folate cycle kinetics in breast cancer cells

Note: two flow BCs were converted into two downstream concentration BCs, thus removing the GAR and dUMP state variables.

This dropped the number of ODEs from 21 to 19.

from:
Schemes of fluc control in a model of Saccharomyces cerevisiae glycolysis

Pritchard, L and Kell, DB Eur. J. Biochem. 269(2002), 3894-3904.
It represents a modified version of Teusink et al. Eur. J. Biochem. 267(2000), 5313-5329.
The model is a translation from the GEPASI file encoded by Leighton Pritchard.
This version uses the Vmaxes found by the best fit (R1) of Table 1 of the Pritchard and Kell paper and simulates a decrease of external glucose concentration from 100 to 2 mM.
To reproduce the values in table 2 of the publication, set GLCo to 50 mM and compute the steady state.

This a model from the article:
Systems analysis of iron metabolism: the network of iron pools and fluxes
Tiago JS Lopes, Tatyana Luganskaja, Maja Vujic-Spasic, Matthias W Hentze, Martina U Muckenthaler, Klaus Schumann and Jens G Reich BMC Systems Biology 2010, Aug 13;4(1):112. 20704761 ,
Abstract:
Background
Every cell of the mammalian organism needs iron in numerous oxido-reductive processes as well as for transport and storage of oxygen. The versatility of ionic iron makes it a toxic entity which can catalyze the production of radicals that damage vital membranous and macromolecular assemblies in the cell. The mammalian organism maintains therefore a complex regulatory network of iron uptake, excretion and intra-div distribution. Intracellular regulation in different cell types is intertwined with a global hormonal signaling structure. Iron deficiency as well as excess of iron are frequent and serious human disorders. They can affect every cell, but also the organism as a whole.
Results
Here, we present a kinematic model of the dynamic system of iron pools and fluxes. It is based on ferrokinetic data and chemical measurements in C57BL6 wild-type mice maintained on iron-deficient, iron-adequate, or iron-loaded diet. The tracer iron levels in major tissues and organs (16 compartment) were followed for 28 days. The evaluation resulted in a whole-div model of fractional clearance rates. The analysis permits calculation of absolute flux rates in the steady-state, of iron distribution into different organs, of tracer-accessible pool sizes and of residence times of iron in the different compartments in response to three states of iron-repletion induced by the dietary regime.
Conclusions
This mathematical model presents a comprehensive physiological picture of mice under three different diets with varying iron contents. The quantitative results reflect systemic properties of iron metabolism: dynamic closedness, hierarchy of time scales, switch-over response and dynamics of iron storage in parenchymal organs. Therefore, we could assess which parameters will change under dietary perturbations and study in quantitative terms when those changes take place.

This model corresponds to the Iron Loaded condition - Mice

In this model the values of "free CDK" (Id: x2), "cdc25_P" (x4) "Wee1_P" (Id: y5) and "APC" (Id: y6) are assigned using the parameters describing the total concentrations totcdk (Id: c)), totcdc5, totwee1 and totAPC. So if you want to change the levels of these proteins, you need to change the values ofthese parameters.

PLoS ONE (2008), p. e1555

In-Silicio Modeling of the Mitotic Spindle Assembly Checkpoint

Bashar Ibrahim, Stephan Diekmann, Eberhard Schmitt, Peter Dittrich

This model describes the controlled dissociation variant of the mitotic spindle assembly checkpoint. If the tool you use has problems with events, you can uncomment the assignment rules for u and u_prime and comment out the list of events.

In accordance with the authors due to typos in the original publication some initial conditions and parameters were slightly changed in the model:

article model

[O-Mad2] 1.5e-7 M 1.3e-7 M

[BubR1:Bub3] 1.30e-7 M 1.27e-7 M

k _-4 0.01 M ^-1 s ^-1 0.02 M ^-1 s ^-1
k _-5 0.1 M ^-1 s ^-1 0.2 M ^-1 s ^-1

	article	model
[O-Mad2]	1.5e-7 M	1.3e-7 M
[BubR1:Bub3]	1.30e-7 M	1.27e-7 M
k _-4	0.01 M ^-1 s ^-1	0.02 M ^-1 s ^-1
k _-5	0.1 M ^-1 s ^-1	0.2 M ^-1 s ^-1

The model describes the double phosphorylation of MAP kinase by an ordered mechanism using the Michaelis-Menten formalism. Two different enzymes, MAPKK1 and MAPKK2, successively phosphorylate the MAP kinase, but one and the same phosphatase dephosphorylates both sites.
The model reproduces figure S9 in the supplemental material of the article.

The model is further described in:
Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. Markevich NI, Hoek JB, Kholodenko BN. J Cell Biol. 2004 Feb 2;164(3):353-9.
PMID: 14744999 ; DOI: 10.1083/jcb.200308060
Abstract:
Mitogen-activated protein kinase (MAPK) cascades can operate as bistable switches residing in either of two different stable states. MAPK cascades are often embedded in positive feedback loops, which are considered to be a prerequisite for bistable behavior. Here we demonstrate that in the absence of any imposed feedback regulation, bistability and hysteresis can arise solely from a distributive kinetic mechanism of the two-site MAPK phosphorylation and dephosphorylation. Importantly, the reported kinetic properties of the kinase (MEK) and phosphatase (MKP3) of extracellular signal-regulated kinase (ERK) fulfill the essential requirements for generating a bistable switch at a single MAPK cascade level. Likewise, a cycle where multisite phosphorylations are performed by different kinases, but dephosphorylation reactions are catalyzed by the same phosphatase, can also exhibit bistability and hysteresis. Hence, bistability induced by multisite covalent modification may be a widespread mechanism of the control of protein activity.

This is the 2 state model of Myosin V movement described in the article:
A simple kinetic model describes the processivity of myosin-v.
Kolomeisky AB , Fisher ME Biophys. J. 84(3):1642-50 (2003); PubmedID: 12609867

Abstract:
Myosin-V is a motor protein responsible for organelle and vesicle transport in cells. Recent single-molecule experiments have shown that it is an efficient processive motor that walks along actin filaments taking steps of mean size close to 36 nm. A theoretical study of myosin-V motility is presented following an approach used successfully to analyze the dynamics of conventional kinesin but also taking some account of step-size variations. Much of the present experimental data for myosin-V can be well described by a two-state chemical kinetic model with three load-dependent rates. In addition, the analysis predicts the variation of the mean velocity and of the randomness-a quantitative measure of the stochastic deviations from uniform, constant-speed motion-with ATP concentration under both resisting and assisting loads, and indicates a substep of size d(0) approximately 13-14 nm (from the ATP-binding state) that appears to accord with independent observations.

The model differs slightly from the published version. The ATP and ADP bound forms of myosin are called S0 and S1. The state transition and binding constants are called k_1, k_2, k_3 and k_4 instead of k ⁰₀ , u ⁰₁ , k ^'₀ and w ⁰₁ . Similarly the state loading factors are named th_1, th_2, th_3 and th_4 instead of θ ⁺₀ , θ ⁺₁ , θ ^-₀ and θ ^-₁ . The species fwd_step1, fwd_step2, back_step1 and back_step2 count the number of state changes of each kind the myosine molecules have taken over time.
The model can be evaluated in a deterministic continuous or stochastic discreet fashion. The parameter V holds the (forward) speed at each time point, the V_avg the overall way divided by the simulation time and the amount of myosine molecules.

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

This a model from the article:
Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tuberculosis, and its application to assessment of drugtargets.
Singh VK , Ghosh I Theor Biol Med Model 2006 Aug 3;3:27 16887020 ,
Abstract:
BACKGROUND: Targeting persistent tubercule bacilli has become an important challenge in the development of anti-tuberculous drugs. As the glyoxylate bypass is essential for persistent bacilli, interference with it holds the potential for designing new antibacterial drugs. We have developed kinetic models of the tricarboxylic acid cycle and glyoxylate bypass in Escherichia coli and Mycobacterium tuberculosis, and studied the effects of inhibition of various enzymes in the M. tuberculosis model. RESULTS: We used E. coli to validate the pathway-modeling protocol and showed that changes in metabolic flux can be estimated from gene expression data. The M. tuberculosis model reproduced the observation that deletion of one of the two isocitrate lyase genes has little effect on bacterial growth in macrophages, but deletion of both genes leads to the elimination of the bacilli from the lungs. It also substantiated the inhibition of isocitrate lyases by 3-nitropropionate. On the basis of our simulation studies, we propose that: (i) fractional inactivation of both isocitrate dehydrogenase 1 and isocitrate dehydrogenase 2 is required for a flux through the glyoxylate bypass in persistent mycobacteria; and (ii) increasing the amountof active isocitrate dehydrogenases can stop the flux through the glyoxylate bypass, so the kinase that inactivates isocitrate dehydrogenase 1 and/or the proposed inactivator of isocitrate dehydrogenase 2 is a potential target for drugs against persistent mycobacteria. In addition, competitive inhibition of isocitrate lyases along with a reduction in the inactivation of isocitrate dehydrogenases appears to be a feasible strategy for targeting persistent mycobacteria. CONCLUSION: We used kinetic modeling of biochemical pathways to assess various potential anti-tuberculous drug targets that interfere with the glyoxylate bypass flux, and indicated the type of inhibition needed to eliminate the pathogen. The advantage of such an approach to the assessment of drug targets is that it facilitates the study of systemic effect(s) of the modulation of the target enzyme(s) in the cellular environment.

This is an SBML implementation the model of the activator inhibitor oscillator (figure 2b) described in the article:
Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell.
Tyson JJ, Chen KC, Novak B. Curr Opin Cell Biol. 2003 Apr;15(2):221-31. PubmedID: 12648679 ; DOI: 10.1016/S0955-0674(03)00017-6 ;

Abstract:
The physiological responses of cells to external and internal stimuli are governed by genes and proteins interacting in complex networks whose dynamical properties are impossible to understand by intuitive reasoning alone. Recent advances by theoretical biologists have demonstrated that molecular regulatory networks can be accurately modeled in mathematical terms. These models shed light on the design principles of biological control systems and make predictions that have been verified experimentally.

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

This a model from the article:
Theoretical and experimental evidence for hysteresis in cell proliferation.
Bai S, Goodrich D, Thron CD, Tecarro E, Obeyesekere M. Cell Cycle. 2003 Jan-Feb;2(1):46-52. 12695688 ,
Abstract:
We propose a mathematical model for the regulation of the G1-phase of the mammalian cell cycle taking into account interactions of cyclin D/cdk4, cyclin E/cdk2, Rb and E2F. Mathematical analysis of this model predicts that a change in the proliferative status in response to a change in concentrations of serum growth factors will exhibit the property of hysteresis: the concentration of growth factors required to induce proliferation is higher than the concentration required to maintain proliferation. We experimentally confirmed this prediction in mouse embryonic fibroblasts in vitro. In agreement with the mathematical model, this indicates that changes in proliferative mode caused by small changes in concentrations of growth factors are not easily reversible. Based on this study, we discuss the importance of proliferation hysteresis for cell cycle regulation.

The original model was taken from the Cell Cycle DataBase (CCDB).

Variable added: assignment rule for denoting phosphorylated Rb (Rb_phosphorylated i.e(RT-RS-R)) created.

The model reproduces Fig 3 of the paper corresponding to the transition to S phase. Units have not been defined for this model because the paper mentions the use of arbitrary units for the various species and parameters. Model reproduced using MathSBML.

This is the extended model described in eq. 2 of the article:
A model of phosphofructokinase and glycolytic oscillations in the pancreatic beta-cell.
Westermark PO and Lansner A. Biophys J. 2003 Jul;85(1):126-39. PMID: 12829470 , doi: 10.1016/S0006-3495(03)74460-9
Abstract:
We have constructed a model of the upper part of the glycolysis in the pancreatic beta-cell. The model comprises the enzymatic reactions from glucokinase to glyceraldehyde-3-phosphate dehydrogenase (GAPD). Our results show, for a substantial part of the parameter space, an oscillatory behavior of the glycolysis for a large range of glucose concentrations. We show how the occurrence of oscillations depends on glucokinase, aldolase and/or GAPD activities, and how the oscillation period depends on the phosphofructokinase activity. We propose that the ratio of glucokinase and aldolase and/or GAPD activities are adequate as characteristics of the glucose responsiveness, rather than only the glucokinase activity. We also propose that the rapid equilibrium between different oligomeric forms of phosphofructokinase may reduce the oscillation period sensitivity to phosphofructokinase activity. Methodologically, we show that a satisfying description of phosphofructokinase kinetics can be achieved using the irreversible Hill equation with allosteric modifiers. We emphasize the use of parameter ranges rather than fixed values, and the use of operationally well-defined parameters in order for this methodology to be feasible. The theoretical results presented in this study apply to the study of insulin secretion mechanisms, since glycolytic oscillations have been proposed as a cause of oscillations in the ATP/ADP ratio which is linked to insulin secretion.

This a model from the article:
The smallest chemical reaction system with bistability
Thomas Wilhelm BMC Systems Biology 2009;Sep 8;3:90. 19737387 ,
Abstract:
Background
Bistability underlies basic biological phenomena, such as cell division, differentiation, cancer onset, and apoptosis. So far biologists identified two necessary conditions for bistability: positive feedback and ultrasensitivity.
Results
Biological systems are based upon elementary mono- and bimolecular chemical reactions. In order to definitely clarify all necessary conditions for bistability we here present the corresponding minimal system. According to our definition, it contains the minimal number of (i) reactants, (ii) reactions, and (iii) terms in the corresponding ordinary differential equations (decreasing importance from i-iii). The minimal bistable system contains two reactants and four irreversible reactions (three bimolecular, one monomolecular). We discuss the roles of the reactions with respect to the necessary conditions for bistability: two reactions comprise the positive feedback loop, a third reaction filters out small stimuli thus enabling a stable 'off' state, and the fourth reaction prevents explosions. We argue that prevention of explosion is a third general necessary condition for bistability, which is so far lacking discussion in the literature. Moreover, in addition to proving that in two-component systems three steady states are necessary for bistability (five for tristability, etc.), we also present a simple general method to design such systems: one just needs one production and three different degradation mechanisms (one production, five degradations for tristability, etc.). This helps modelling multistable systems and it is important for corresponding synthetic biology projects.
Conclusion
The presented minimal bistable system finally clarifies the often discussed question for the necessary conditions for bistability. The three necessary conditions are: positive feedback, a mechanism to filter out small stimuli and a mechanism to prevent explosions. This is important for modelling bistability with simple systems and for synthetically designing new bistable systems. Our simple model system is also well suited for corresponding teaching purposes.

This is a Systems Biology Markup Language (SBML) file, generated by MathSBML 2.9.0 [8-Oct-2008] 30-Jun-2009 17:26:58(GMT+00:59). SBML is a form of XML, and most XML files will not display properly in an internet browser. To view the contents of an XML file use the "Page Source" or equivalent button on you browser.

This a model from the article:
The phantom burster model for pancreatic beta-cells.
Bertram R, Previte J, Sherman A, Kinard TA, Satin LS. Biophys J 2000 Dec;79(6):2880-92 11106596 ,
Abstract:
Pancreatic beta-cells exhibit bursting oscillations with a wide range of periods. Whereas periods in isolated cells are generally either a few seconds or a few minutes, in intact islets of Langerhans they are intermediate (10-60 s). We develop a mathematical model for beta-cell electrical activity capable of generating this wide range of bursting oscillations. Unlike previous models, bursting is driven by the interaction of two slow processes, one with a relatively small time constant (1-5 s) and the other with a much larger time constant (1-2 min). Bursting on the intermediate time scale is generated without need for a slow process having an intermediate time constant, hence phantom bursting. The model suggests that isolated cells exhibiting a fast pattern may nonetheless possess slower processes that can be brought out by injecting suitable exogenous currents. Guided by this, we devise an experimental protocol using the dynamic clamp technique that reliably elicits islet-like, medium period oscillations from isolated cells. Finally, we show that strong electrical coupling between a fast burster and a slow burster can produce synchronized medium bursting, suggesting that islets may be composed of cells that are intrinsically either fast or slow, with few or none that are intrinsically medium.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Bertram R, Previte J, Sherman A, Kinard TA, Satin LS. (2000) - version02

SBML model of Cell cycle control mechanism

This is a hypothetical model of the cell cycle control mechanism by Chen et al(2004). The model reproduces the time profiles of the different species in Fig 2 of the paper. The figure depicts the cycle of a daughter cell. Since,the Mass Doubling Time(MDT) is 90 minutes, time t=90 from the model simulation will correspond to time t=0 in the paper. The model was successfully tested using MathSBML and SBML odeSolver.
To create valid SBML a local parameter k = 1 was added in reaction: "Inactivation_274_CDC20".

The model reproduces time profile of p53 and Mdm2 as depicted in Fig 6B of the paper for Model 2. Results obtained using MathSBML.

The model reproduces Fig 1A of the paper. The model was successfully tested on MathSBML.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2006 The BioModels Team.
For more information see the terms of use .

Contact Ryan Gutenkunst (rng7@cornell.edu) for any questions on the SBMLization or annotation of this model.

KS Brown KS and JP Sethna
"Statistical mechanical approaches to models with many poorly known parameters."
Physical Review E 68:021904 (2003)
PMID: 14525003

KS Brown, CC Hill, GA Calero, CR Myers, KH Lee, JP Sethna, and RA Cerione
"The statistical mechanics of complex signaling networks: nerve growth factor signaling"
Physical Biology 1:184-195 (2004)
PMID: not yet indexed

Notes:

The figures in the paper show results from computations performed over an ensemble of all parameter sets that fit the avaiable data. This file contains only the best fit parameters. The full ensemble of parameters is available at http://www.lassp.cornell.edu/sethna/GeneDynamics/PC12DataFiles/ (Also, the best-fit parameter set produces a curve for DN Rap1 that is less "peakish" than the ensemble average.)

The conversion factors for EGF and NGF concentrations account for their molecular weights and the density of cells in the culture dish. These concentrations are saturating, so the exact values are not critical.

Because the Erk data fit to measure only fold changes in activity, there is no absolute scale for the y-axes. Thus the curves from this file have different magnitudes than those published.

To reproduce the figures from the paper:
2a) For EGF stimulation, set the initial concentration of EGF to 100 ng/ml * 100020 (molecule/cell)/(ng/ml) = 10002000.
For NGF stimulation, set the initial concentration of NGF to 50 ng/ml * 4560 (molecule/cell)/(ng/ml) = 456000
5a) To simulate LY294002 addition, set kPI3KRas and kPI3K to 0.
5b) To simulate a dominant negative Rap1, set kRap1ToBRaf to 0.
To simulate a dominant negative Ras, set kRasToRaf1 and kPI3KRas to 0.

Almost all the data fit with this model by the authors are from Western blots. Given the uncertainties in antidiv effectiveness and other factors, one can't a priori derive a conversion between the arbitrary units for a given set of data and molecules per cell. So the authors used an adjustable "scale factor" that converts between molecules per cell and Western blot units.

For the EGF stimulation data in figure 2a) the scale factor conversion is 1.414e-05 (U/mg)/(molecule/cell). For the NGF stimulation data in figure 2a) it is 7.135e-06 (U/mg)/(molecule/cell).

This a model from the article:
A role for calcium release-activated current (CRAC) in cholinergic modulation of electrical activity in pancreatic beta-cells.
Bertram R, Smolen P, Sherman A, Mears D, Atwater I, Martin F, Soria B. Biophys J 1995 Jun;68(6):2323-32 7647236 ,
Abstract:
S. Bordin and colleagues have proposed that the depolarizing effects of acetylcholine and other muscarinic agonists on pancreatic beta-cells are mediated by a calcium release-activated current (CRAC). We support this hypothesis with additional data, and present a theoretical model which accounts for most known data on muscarinic effects. Additional phenomena, such as the biphasic responses of beta-cells to changes in glucose concentration and the depolarizing effects of the sarco-endoplasmic reticulum calcium ATPase pump poison thapsigargin, are also accounted for by our model. The ability of this single hypothesis, that CRAC is present in beta-cells, to explain so many phenomena motivates a more complete characterization of this current.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Bertram R, Smolen P, Sherman A, Mears D, Atwater I, Martin F, Soria B. (1995) - version=1.0
The original CellML model was created by:
Catherine Lloyd
c.lloyd@auckland.ac.nz
The University of Auckland

The model corresponds to the schema 3 of Markevich et al 2004, as described in the figure 2 and the supplementary table S3, and modelled using Michaelis-Menten like kinetics. Phosphorylations follow distributive random kinetics, while dephosphorylations follow an ordered mechanism.

The model reproduces active Caspase-3 time profile corresponding to the total Apaf-1 value of 20 nM as depicted in Fig 2-A . The model was successfully tested on MathSBML.

The paper describes both wild-type and mutant cells of G protein cycle by using different values of G protein deactivation. We chosed the wild-type, k=0.11 s-1.

The unit of the concentration for the proteins are numbers of molecules per cell.

Figure5(A) was reproduced with COPASI 4.0 (Build 18) and SBML_odeSolver. Figure5(B) was reproduced with COPASI 4.0 (Build 18).

This is an SBML implementation the model of the substrate depletion oscillator (figure 2c) described in the article:
Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell.
Tyson JJ, Chen KC, Novak B. Curr Opin Cell Biol. 2003 Apr;15(2):221-31. PubmedID: 12648679 ; DOI: 10.1016/S0955-0674(03)00017-6 ;

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

The model reproduces the time profile of TOC1 and Y mRNA for a 8:16 cycle as depicted in Fig7A and 7B. A simple algorithm in the event section accomplishes the 8 hour light and 16 hour dark cycle. The model was successfully tested on MathSBML

Bianconi2012 - EGFR and IGF1R pathway in lung cancer

EGFR and IGF1R pathways play a key role in various human cancers and are crucial for tumour transformation and survival of malignant cells. High EGFR and IGF1R expression and activity has been associated with multiple aspects of cancer progression including tumourigenesis, metastasis, resistance to chemotherapeutics and other molecularly targeted drugs. Here, the biological relationship between the proteins involved in EGFR and IGF1R pathways and the downstream MAPK and PIK3 networks has been modelled to study the time behaviour of the overall system, and the functional interdependencies among the receptors, the proteins and kinases involved.

This model is described in the article:

Computational model of EGFR and IGF1R pathways in lung cancer: a Systems Biology approach for Translational Oncology.

Bianconi F, Baldelli E, Ludovini V, Crinò L, Flacco A, Valigi P.

Biotechnol Adv. 2012 Jan-Feb;30(1):142-53.

Abstract:

In this paper we propose a Systems Biology approach to understand the molecular biology of the Epidermal Growth Factor Receptor (EGFR, also known as ErbB1/HER1) and type 1 Insulin-like Growth Factor (IGF1R) pathways in non-small cell lung cancer (NSCLC). This approach, combined with Translational Oncology methodologies, is used to address the experimental evidence of a close relationship among EGFR and IGF1R protein expression, by immunohistochemistry (IHC) and gene amplification, by in situ hybridization (FISH) and the corresponding ability to develop a more aggressive behavior. We develop a detailed in silico model, based on ordinary differential equations, of the pathways and study the dynamic implications of receptor alterations on the time behavior of the MAPK cascade down to ERK, which in turn governs proliferation and cell migration. In addition, an extensive sensitivity analysis of the proposed model is carried out and a simplified model is proposed which allows us to infer a similar relationship among EGFR and IGF1R activities and disease outcome.

This model is hosted on BioModels Database and identified by: BIOMD0000000427 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

The model reproduces the time profiles of p27, E2F and aE/cdk2 as depicted in Figure 5 c of the paper. Model was simulated on MathSBML.

This is the distributive model described the article:
Theoretical and experimental analysis links isoform-specific ERK signalling to cell fate decisions.
Schilling M, Maiwald T, Hengl S, Winter D, Kreutz C, Kolch W, Lehmann WD, Timmer J and Klingmueller U; Mol Syst Biol. 2009;5:334. PubmedID: 20029368 ; DOI: 10.1038/msb.2009.91
Abstract:
Cell fate decisions are regulated by the coordinated activation of signalling pathways such as the extracellular signal-regulated kinase (ERK) cascade, but contributions of individual kinase isoforms are mostly unknown. By combining quantitative data from erythropoietin-induced pathway activation in primary erythroid progenitor (colony-forming unit erythroid stage, CFU-E) cells with mathematical modelling, we predicted and experimentally confirmed a distributive ERK phosphorylation mechanism in CFU-E cells. Model analysis showed bow-tie-shaped signal processing and inherently transient signalling for cytokine-induced ERK signalling. Sensitivity analysis predicted that, through a feedback-mediated process, increasing one ERK isoform reduces activation of the other isoform, which was verified by protein over-expression. We calculated ERK activation for biochemically not addressable but physiologically relevant ligand concentrations showing that double-phosphorylated ERK1 attenuates proliferation beyond a certain activation level, whereas activated ERK2 enhances proliferation with saturation kinetics. Thus, we provide a quantitative link between earlier unobservable signalling dynamics and cell fate decisions.

SBML model exported from PottersWheel on 2009-04-20 18:57:44.
Below follows the source code for the model definition file in PottersWheel/Matlab:

% PottersWheel model definition file

function m = getModel()

m             = pwGetEmptyModel();

%% Meta information

m.ID          = 'ERK_distributive_model';
m.name        = 'ERK_distributive_model';
m.description = 'ERK model calibrated to CFU-E as described in Schilling et al.';
m.authors     = {'Marcel Schilling','Thomas Maiwald'};
m.dates       = {'2009'};
m.type        = 'PW-2-0';

%% Dynamic variables
% m = pwAddX(m, ID, startValue, type, minValue, maxValue, unit, compartment, name, description, typeOfStartValue)

m = pwAddX(m, 'JAK2'         ,       2, 'fix'   ,   1, 3.7,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'EpoR'         ,       1, 'fix'   , 0.5, 1.5,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'SHP1'         , 10.7991, 'global', 0.1, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'SOS'          ,  2.5101, 'fix'   , 0.1, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'Raf'          ,  3.7719, 'global', 0.1, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'MEK2'         ,      11, 'fix'   ,   8,  14,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'MEK1'         ,      24, 'fix'   ,  18,  30,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'ERK1'         ,       7, 'global',   6,   9,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'ERK2'         ,      21, 'fix'   ,  16,  26,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'pJAK2'        ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'pEpoR'        ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'mSHP1'        ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'actSHP1'      ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'mSOS'         ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'pRaf'         ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'ppMEK2'       ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'ppMEK1'       ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'ppERK1'       ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'ppERK2'       ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'pSOS'         ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'pMEK2'        ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'pMEK1'        ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'pERK1'        ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'pERK2'        ,       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'Delay01_mSHP1',       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'Delay02_mSHP1',       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'Delay03_mSHP1',       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'Delay04_mSHP1',       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'Delay05_mSHP1',       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'Delay06_mSHP1',       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'Delay07_mSHP1',       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );
m = pwAddX(m, 'Delay08_mSHP1',       0, 'fix'   ,   0, 100,   [], 'cell', []  ,   [], 'concentration', []  );

%% Reactions
% m = pwAddR(m, reactants, products, modifiers, type, options, rateSignature, parameters, description, ID, name, fast, compartments, parameterTrunks, designerProps)

m = pwAddR(m, {'JAK2'         }, {'pJAK2'        }, {'Epo'    }, 'E' , [] , []  , {'JAK2_phosphorylation_by_Epo'         }, '...', 'reaction0001', [], [], {}, {}, {});
m = pwAddR(m, {'EpoR'         }, {'pEpoR'        }, {'pJAK2'  }, 'E' , [] , []  , {'EpoR_phosphorylation_by_pJAK2'       }, '...', 'reaction0002', [], [], {}, {}, {});
m = pwAddR(m, {'SHP1'         }, {'mSHP1'        }, {'pEpoR'  }, 'E' , [] , []  , {'SHP1_activation_by_pEpoR'            }, '...', 'reaction0003', [], [], {}, {}, {});
m = pwAddR(m, {'mSHP1'        }, {'Delay01_mSHP1'}, {         }, 'MA', [] , []  , {'SHP1_activation_by_pEpoR'            }, '...', 'reaction0004', [], [], {}, {}, {});
m = pwAddR(m, {'Delay01_mSHP1'}, {'Delay02_mSHP1'}, {         }, 'MA', [] , []  , {'SHP1_activation_by_pEpoR'            }, '...', 'reaction0005', [], [], {}, {}, {});
m = pwAddR(m, {'Delay02_mSHP1'}, {'Delay03_mSHP1'}, {         }, 'MA', [] , []  , {'SHP1_activation_by_pEpoR'            }, '...', 'reaction0006', [], [], {}, {}, {});
m = pwAddR(m, {'Delay03_mSHP1'}, {'Delay04_mSHP1'}, {         }, 'MA', [] , []  , {'SHP1_activation_by_pEpoR'            }, '...', 'reaction0007', [], [], {}, {}, {});
m = pwAddR(m, {'Delay04_mSHP1'}, {'Delay05_mSHP1'}, {         }, 'MA', [] , []  , {'SHP1_activation_by_pEpoR'            }, '...', 'reaction0008', [], [], {}, {}, {});
m = pwAddR(m, {'Delay05_mSHP1'}, {'Delay06_mSHP1'}, {         }, 'MA', [] , []  , {'SHP1_activation_by_pEpoR'            }, '...', 'reaction0009', [], [], {}, {}, {});
m = pwAddR(m, {'Delay06_mSHP1'}, {'Delay07_mSHP1'}, {         }, 'MA', [] , []  , {'SHP1_activation_by_pEpoR'            }, '...', 'reaction0010', [], [], {}, {}, {});
m = pwAddR(m, {'Delay07_mSHP1'}, {'Delay08_mSHP1'}, {         }, 'MA', [] , []  , {'SHP1_activation_by_pEpoR'            }, '...', 'reaction0011', [], [], {}, {}, {});
m = pwAddR(m, {'Delay08_mSHP1'}, {'actSHP1'      }, {         }, 'MA', [] , []  , {'SHP1_activation_by_pEpoR'            }, '...', 'reaction0012', [], [], {}, {}, {});
m = pwAddR(m, {'actSHP1'      }, {'SHP1'         }, {         }, 'MA', [] , []  , {'actSHP1_deactivation'                }, '...', 'reaction0005', [], [], {}, {}, {});
m = pwAddR(m, {'pEpoR'        }, {'EpoR'         }, {'actSHP1'}, 'E' , [] , []  , {'pEpoR_dephosphorylation_by_actSHP1'  }, '...', 'reaction0006', [], [], {}, {}, {});
m = pwAddR(m, {'pJAK2'        }, {'JAK2'         }, {'actSHP1'}, 'E' , [] , []  , {'pJAK2_dephosphorylation_by_actSHP1'  }, '...', 'reaction0007', [], [], {}, {}, {});
m = pwAddR(m, {'SOS'          }, {'mSOS'         }, {'pEpoR'  }, 'E' , [] , []  , {'SOS_recruitment_by_pEpoR'            }, '...', 'reaction0008', [], [], {}, {}, {});
m = pwAddR(m, {'mSOS'         }, {'SOS'          }, {         }, 'MA', [] , []  , {'mSOS_release_from_membrane'          }, '...', 'reaction0009', [], [], {}, {}, {});
m = pwAddR(m, {'Raf'          }, {'pRaf'         }, {'mSOS'   }, 'E' , [] , []  , {'mSOS_induced_Raf_phosphorylation'    }, '...', 'reaction0010', [], [], {}, {}, {});
m = pwAddR(m, {'pRaf'         }, {'Raf'          }, {         }, 'MA', [] , []  , {'pRaf_dephosphorylation'              }, '...', 'reaction0011', [], [], {}, {}, {});
m = pwAddR(m, {'MEK2'         }, {'pMEK2'        }, {'pRaf'   }, 'E' , [] , []  , {'First_MEK2_phosphorylation_by_pRaf'  }, '...', 'reaction0012', [], [], {}, {}, {});
m = pwAddR(m, {'MEK1'         }, {'pMEK1'        }, {'pRaf'   }, 'E' , [] , []  , {'First_MEK1_phosphorylation_by_pRaf'  }, '...', 'reaction0013', [], [], {}, {}, {});
m = pwAddR(m, {'pMEK2'        }, {'ppMEK2'       }, {'pRaf'   }, 'E' , [] , []  , {'Second_MEK2_phosphorylation_by_pRaf' }, '...', 'reaction0014', [], [], {}, {}, {});
m = pwAddR(m, {'pMEK1'        }, {'ppMEK1'       }, {'pRaf'   }, 'E' , [] , []  , {'Second_MEK1_phosphorylation_by_pRaf' }, '...', 'reaction0015', [], [], {}, {}, {});
m = pwAddR(m, {'ppMEK2'       }, {'pMEK2'        }, {         }, 'MA', [] , []  , {'First_MEK_dephosphorylation'         }, '...', 'reaction0016', [], [], {}, {}, {});
m = pwAddR(m, {'ppMEK1'       }, {'pMEK1'        }, {         }, 'MA', [] , []  , {'First_MEK_dephosphorylation'         }, '...', 'reaction0017', [], [], {}, {}, {});
m = pwAddR(m, {'pMEK2'        }, {'MEK2'         }, {         }, 'MA', [] , []  , {'Second_MEK_dephosphorylation'        }, '...', 'reaction0018', [], [], {}, {}, {});
m = pwAddR(m, {'pMEK1'        }, {'MEK1'         }, {         }, 'MA', [] , []  , {'Second_MEK_dephosphorylation'        }, '...', 'reaction0019', [], [], {}, {}, {});
m = pwAddR(m, {'ERK1'         }, {'pERK1'        }, {'ppMEK2' }, 'E' , [] , []  , {'First_ERK1_phosphorylation_by_ppMEK' }, '...', 'reaction0020', [], [], {}, {}, {});
m = pwAddR(m, {'ERK2'         }, {'pERK2'        }, {'ppMEK2' }, 'E' , [] , []  , {'First_ERK2_phosphorylation_by_ppMEK' }, '...', 'reaction0021', [], [], {}, {}, {});
m = pwAddR(m, {'ERK1'         }, {'pERK1'        }, {'ppMEK1' }, 'E' , [] , []  , {'First_ERK1_phosphorylation_by_ppMEK' }, '...', 'reaction0022', [], [], {}, {}, {});
m = pwAddR(m, {'ERK2'         }, {'pERK2'        }, {'ppMEK1' }, 'E' , [] , []  , {'First_ERK2_phosphorylation_by_ppMEK' }, '...', 'reaction0023', [], [], {}, {}, {});
m = pwAddR(m, {'pERK1'        }, {'ppERK1'       }, {'ppMEK2' }, 'E' , [] , []  , {'Second_ERK1_phosphorylation_by_ppMEK'}, '...', 'reaction0024', [], [], {}, {}, {});
m = pwAddR(m, {'pERK2'        }, {'ppERK2'       }, {'ppMEK2' }, 'E' , [] , []  , {'Second_ERK2_phosphorylation_by_ppMEK'}, '...', 'reaction0025', [], [], {}, {}, {});
m = pwAddR(m, {'pERK1'        }, {'ppERK1'       }, {'ppMEK1' }, 'E' , [] , []  , {'Second_ERK1_phosphorylation_by_ppMEK'}, '...', 'reaction0026', [], [], {}, {}, {});
m = pwAddR(m, {'pERK2'        }, {'ppERK2'       }, {'ppMEK1' }, 'E' , [] , []  , {'Second_ERK2_phosphorylation_by_ppMEK'}, '...', 'reaction0027', [], [], {}, {}, {});
m = pwAddR(m, {'ppERK1'       }, {'pERK1'        }, {         }, 'MA', [] , []  , {'First_ERK_dephosphorylation'         }, '...', 'reaction0028', [], [], {}, {}, {});
m = pwAddR(m, {'ppERK2'       }, {'pERK2'        }, {         }, 'MA', [] , []  , {'First_ERK_dephosphorylation'         }, '...', 'reaction0029', [], [], {}, {}, {});
m = pwAddR(m, {'pERK1'        }, {'ERK1'         }, {         }, 'MA', [] , []  , {'Second_ERK_dephosphorylation'        }, '...', 'reaction0030', [], [], {}, {}, {});
m = pwAddR(m, {'pERK2'        }, {'ERK2'         }, {         }, 'MA', [] , []  , {'Second_ERK_dephosphorylation'        }, '...', 'reaction0031', [], [], {}, {}, {});
m = pwAddR(m, {'mSOS'         }, {'pSOS'         }, {'ppERK1' }, 'E' , [] , []  , {'ppERK_neg_feedback_on_mSOS'          }, '...', 'reaction0032', [], [], {}, {}, {});
m = pwAddR(m, {'mSOS'         }, {'pSOS'         }, {'ppERK2' }, 'E' , [] , []  , {'ppERK_neg_feedback_on_mSOS'          }, '...', 'reaction0033', [], [], {}, {}, {});
m = pwAddR(m, {'pSOS'         }, {'SOS'          }, {         }, 'MA', [] , []  , {'pSOS_dephosphorylation'              }, '...', 'reaction0034', [], [], {}, {}, {});

%% Compartments
% m = pwAddC(m, ID, size,  outside, spatialDimensions, name, unit, constant)

m = pwAddC(m, 'cell', 1, [], 3, 'cell', [], 1);

%% Dynamical parameters
% m = pwAddK(m, ID, value, type, minValue, maxValue, unit, name, description)

m = pwAddK(m, 'JAK2_phosphorylation_by_Epo'         , 0.0122149, 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'EpoR_phosphorylation_by_pJAK2'       , 3.15714  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'SHP1_activation_by_pEpoR'            , 0.408408 , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'SHP1_delay'                          , 0.408408 , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'actSHP1_deactivation'                , 0.0248773, 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'pEpoR_dephosphorylation_by_actSHP1'  , 1.19995  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'pJAK2_dephosphorylation_by_actSHP1'  , 0.368384 , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'SOS_recruitment_by_pEpoR'            , 0.10271  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'mSOS_release_from_membrane'          , 15.5956  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'mSOS_induced_Raf_phosphorylation'    , 0.144515 , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'pRaf_dephosphorylation'              , 0.374228 , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'First_MEK2_phosphorylation_by_pRaf'  , 3.11919  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'Second_MEK2_phosphorylation_by_pRaf' , 215.158  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'First_MEK1_phosphorylation_by_pRaf'  , 0.687193 , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'Second_MEK1_phosphorylation_by_pRaf' , 667.957  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'First_MEK_dephosphorylation'         , 0.130937 , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'Second_MEK_dephosphorylation'        , 0.0732724, 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'First_ERK1_phosphorylation_by_ppMEK' , 2.4927   , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'Second_ERK1_phosphorylation_by_ppMEK', 59.5251  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'First_ERK2_phosphorylation_by_ppMEK' , 2.44361  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'Second_ERK2_phosphorylation_by_ppMEK', 53.0816  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'First_ERK_dephosphorylation'         , 39.0886  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'Second_ERK_dephosphorylation'        , 3.00453  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'ppERK_neg_feedback_on_mSOS'          , 5122.68  , 'fix', 1e-006, 10000, [], [], []);
m = pwAddK(m, 'pSOS_dephosphorylation'              , 0.124944 , 'fix', 1e-006, 10000, [], [], []);

%% Default driving input
% m = pwAddU(m, ID, uType, uTimes, uValues, compartment, name, description, u2Values)

m = pwAddU(m, 'Epo', 'steps', [-60 0]  , [0 50]  , 'cell', [], [], [0 0]);

%% Default sampling time points
m.t = 0:1:35;

%% Observables
% m = pwAddY(m, rhs, ID, scalingParameter, errorModel, noiseType, unit, name, description)

m = pwAddY(m, 'pEpoR'     , 'pEpoR_obs' , 'scale_pEpoR_obs', 'y * 0.05 + max(y) * 0.05', 'Gaussian', [], [], []);
m = pwAddY(m, 'pJAK2'     , 'pJAK2_obs' , 'scale_pJAK2_obs', 'y * 0.05 + max(y) * 0.05', 'Gaussian', [], [], []);
m = pwAddY(m, 'ppMEK2'    , 'ppMEK2_obs', 'scale_ppMEK_obs', 'y * 0.05 + max(y) * 0.05', 'Gaussian', [], [], []);
m = pwAddY(m, 'ppMEK1'    , 'ppMEK1_obs', 'scale_ppMEK_obs', 'y * 0.05 + max(y) * 0.05', 'Gaussian', [], [], []);
m = pwAddY(m, 'ppERK1'    , 'ppERK1_obs', 'scale_ppERK_obs', 'y * 0.05 + max(y) * 0.05', 'Gaussian', [], [], []);
m = pwAddY(m, 'ppERK2'    , 'ppERK2_obs', 'scale_ppERK_obs', 'y * 0.05 + max(y) * 0.05', 'Gaussian', [], [], []);
m = pwAddY(m, 'pSOS'      , 'pSOS_obs'  , 'scale_SOS_obs'  , 'y * 0.05 + max(y) * 0.05', 'Gaussian', [], [], []);
m = pwAddY(m, 'SOS + mSOS', 'SOS_obs'   , 'scale_SOS_obs'  , 'y * 0.05 + max(y) * 0.05', 'Gaussian', [], [], []);

%% Scaling parameters
% m = pwAddS(m, ID, value, type, minValue, maxValue, unit, name, description)

m = pwAddS(m, 'scale_pEpoR_obs', 0.493312, 'fix', 0.01, 50, [], [], []);
m = pwAddS(m, 'scale_pJAK2_obs',  0.21008, 'fix', 0.01, 50, [], [], []);
m = pwAddS(m, 'scale_ppMEK_obs',  40.5364, 'fix', 0.01, 50, [], [], []);
m = pwAddS(m, 'scale_ppERK_obs',  13.5981, 'fix', 0.01, 50, [], [], []);
m = pwAddS(m, 'scale_SOS_obs'  ,  1.10228, 'fix', 0.01, 50, [], [], []);

%% Derived variables
% m = pwAddZ(m, rhs, ID, unit, name, description)

m = pwAddZ(m, 'ppERK1', 'ppERK1', [], [], []);
m = pwAddZ(m, 'ppERK2', 'ppERK2', [], [], []);

%% Derived parameters
% m = pwAddP(m, rhs, ID, unit, name, description)

%m = pwAddP(m, 'JAK2_phosphorylation_by_Epo');
%m = pwAddP(m, 'EpoR_phosphorylation_by_pJAK2');
%m = pwAddP(m, 'SHP1_activation_by_pEpoR');
%m = pwAddP(m, 'SHP1_delay');
%m = pwAddP(m, 'actSHP1_deactivation');
%m = pwAddP(m, 'pEpoR_dephosphorylation_by_actSHP1');
%m = pwAddP(m, 'pJAK2_dephosphorylation_by_actSHP1');
%m = pwAddP(m, 'SOS_recruitment_by_pEpoR');
%m = pwAddP(m, 'mSOS_release_from_membrane');
%m = pwAddP(m, 'mSOS_induced_Raf_phosphorylation');
%m = pwAddP(m, 'pRaf_dephosphorylation');
%m = pwAddP(m, 'First_MEK2_phosphorylation_by_pRaf');
%m = pwAddP(m, 'Second_MEK2_phosphorylation_by_pRaf');
%m = pwAddP(m, 'First_MEK1_phosphorylation_by_pRaf');
%m = pwAddP(m, 'Second_MEK1_phosphorylation_by_pRaf');
%m = pwAddP(m, 'First_MEK_dephosphorylation');
%m = pwAddP(m, 'Second_MEK_dephosphorylation');
%m = pwAddP(m, 'First_ERK1_phosphorylation_by_ppMEK');
%m = pwAddP(m, 'Second_ERK1_phosphorylation_by_ppMEK');
%m = pwAddP(m, 'First_ERK2_phosphorylation_by_ppMEK');
%m = pwAddP(m, 'Second_ERK2_phosphorylation_by_ppMEK');
%m = pwAddP(m, 'First_ERK_dephosphorylation');
%m = pwAddP(m, 'Second_ERK_dephosphorylation');
%m = pwAddP(m, 'ppERK_neg_feedback_on_mSOS');
%m = pwAddP(m, 'pSOS_dephosphorylation');
%m = pwAddP(m, 'JAK2');
%m = pwAddP(m, 'EpoR');
%m = pwAddP(m, 'SHP1');
%m = pwAddP(m, 'SOS');
%m = pwAddP(m, 'Raf');
%m = pwAddP(m, 'MEK2');
%m = pwAddP(m, 'MEK1');
%m = pwAddP(m, 'ERK1');
%m = pwAddP(m, 'ERK2');
%m = pwAddP(m, 'pJAK2');
%m = pwAddP(m, 'pEpoR');
%m = pwAddP(m, 'mSHP1');
%m = pwAddP(m, 'actSHP1');
%m = pwAddP(m, 'mSOS');
%m = pwAddP(m, 'pRaf');
%m = pwAddP(m, 'ppMEK2');
%m = pwAddP(m, 'ppMEK1');
%m = pwAddP(m, 'ppERK1');
%m = pwAddP(m, 'ppERK2');
%m = pwAddP(m, 'pSOS');
%m = pwAddP(m, 'pMEK2');
%m = pwAddP(m, 'pMEK1');
%m = pwAddP(m, 'pERK1');
%m = pwAddP(m, 'pERK2');
%m = pwAddP(m, 'Delay01_mSHP1');
%m = pwAddP(m, 'Delay02_mSHP1');
%m = pwAddP(m, 'Delay03_mSHP1');
%m = pwAddP(m, 'Delay04_mSHP1');
%m = pwAddP(m, 'Delay05_mSHP1');
%m = pwAddP(m, 'Delay06_mSHP1');
%m = pwAddP(m, 'Delay07_mSHP1');
%m = pwAddP(m, 'Delay08_mSHP1');
%m = pwAddP(m, 'scale_pEpoR_obs');
%m = pwAddP(m, 'scale_pJAK2_obs');
%m = pwAddP(m, 'scale_ppMEK_obs');
%m = pwAddP(m, 'scale_ppERK_obs');
%m = pwAddP(m, 'scale_SOS_obs');

%% Rules
% m = pwAddRule(m, lhs, reactants, parameters, ruleSignature, type, description, ID)


%% Constraints
% m = pwAddConstraint(m, lhs, operator, rhs, reactants, parameters, lambda)

m = pwAddConstraint(m, 'max(r1)/max(r2)', '=', '0.2', {'pERK1','ERK1'}, {}, 200);
m = pwAddConstraint(m, 'max(r1)/max(r2)', '=', '0.2', {'pERK2','ERK2'}, {}, 200);
m = pwAddConstraint(m, 'max(r1)/max(r2)', '=', '0.1', {'ppERK1','ERK1'}, {}, 200);
m = pwAddConstraint(m, 'max(r1)/max(r2)', '=', '0.1', {'ppERK2','ERK2'}, {}, 200);

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2010 The BioModels.net Team.
For more information see the terms of use .
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

This is the reduced model of the voltage oscillations in barnacle muscle fibers, generally known as the Morris-Lecar model (eg. wikipedia ), described in the article:
Voltage oscillations in the barnacle giant muscle fiber.
Morris C, Lecar H. Biophys J. 1981 Jul;35(1):193-213. PubmedID: 7260316 ; DOI: 10.1016/S0006-3495(81)84782-0
Abstract:
Barnacle muscle fibers subjected to constant current stimulation produce a variety of types of oscillatory behavior when the internal medium contains the Ca++ chelator EGTA. Oscillations are abolished if Ca++ is removed from the external medium, or if the K+ conductance is blocked. Available voltage-clamp data indicate that the cell's active conductance systems are exceptionally simple. Given the complexity of barnacle fiber voltage behavior, this seems paradoxical. This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior.

The model consists of the differential equations (9) and (2) given on pages 205 and 196 of the article. There seems to be a typo in the figure caption of figure 9. Using V2 = 15 instead of -15 allows to reproduce the results.

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

Model of the Complement System

This is the continuous deterministic (ODE) model of the complement system described in the article:
Computational and Experimental Study of the Regulatory Mechanisms of the Complement System.
Liu B, Zhang J, Tan PY, Hsu D, Blom AM, Leong B, Sethi S, Ho B, Ding JL and Thiagarajan PS. PLoS Comp. Bio. 2011 Jan. 7:1; doi: 10.1371/journal.pcbi.1001059

Abstract:
The complement system is key to innate immunity and its activation is necessary for the clearance of bacteria and apoptotic cells. However, insufficient or excessive complement activation will lead to immune-related diseases. It is so far unknown how the complement activity is up- or down- regulated and what the associated pathophysiological mechanisms are. To quantitatively understand the modulatory mechanisms of the complement system, we built a computational model involving the enhancement and suppression mechanisms that regulate complement activity. Our model consists of a large system of Ordinary Differential Equations (ODEs) accompanied by a dynamic Bayesian network as a probabilistic approximation of the ODE dynamics. Applying Bayesian inference techniques, this approximation was used to perform parameter estimation and sensitivity analysis. Our combined computational and experimental study showed that the antimicrobial response is sensitive to changes in pH and calcium levels, which determines the strength of the crosstalk between CRP and L-ficolin. Our study also revealed differential regulatory effects of C4BP. While C4BP delays but does not decrease the classical complement activation, it attenuates but does not significantly delay the lectin pathway activation. We also found that the major inhibitory role of C4BP is to facilitate the decay of C3 convertase. In summary, the present work elucidates the regulatory mechanisms of the complement system and demonstrates how the bio-pathway machinery maintains the balance between activation and inhibition. The insights we have gained could contribute to the development of therapies targeting the complement system.

Comment:
Reproduction of figures in the article:
Figure 5: the effects of C4BP
Fig 5A: set initial concentrations PC=0.0327796, GlcNac=0, vary the initial concentration of C4BP from 2.6 to 2600 using parameter scan
Fig 5B: set initial concentrations PC=0, GlcNac=0.0327796, vary the initial concentration of C4BP from 2.6 to 2600 using parameter scan
Figure 6: knockout simulations
Set PC=0.0327796, GlcNac=0
Fig 6A: kf01=0, kf02=0
Fig 6B: kf04=0, kf06=0, kf07=0
Fig 6C: kf05=0
Fig 6D: kf03=0

This is a purine metabolism model that is geared toward studies of gout.

The model is fully described in Curto et al., MBSC 151 (1998) pp 1-49

The model uses Generalized Mass Action (GMA;i.e. power law) descriptions of reaction rate laws.

Such descriptions are local approximations that assume independent substrate binding.

This model is from the article:
Kinetic modeling and exploratory numerical simulation of chloroplastic starch degradation.
Nag A, Lunacek M, Graf PA, Chang CH. BMC Syst Biol. 2011 Jun 18;5:94. 21682905 ,
Abstract:
BACKGROUND: Higher plants and algae are able to fix atmospheric carbon dioxide through photosynthesis and store this fixed carbon in large quantities as starch, which can be hydrolyzed into sugars serving as feedstock for fermentation to biofuels and precursors. Rational engineering of carbon flow in plant cells requires a greater understanding of how starch breakdown fluxes respond to variations in enzyme concentrations, kinetic parameters, and metabolite concentrations. We have therefore developed and simulated a detailed kinetic ordinary differential equation model of the degradation pathways for starch synthesized in plants and green algae, which to our knowledge is the most complete such model reported to date. RESULTS: Simulation with 9 internal metabolites and 8 external metabolites, the concentrations of the latter fixed at reasonable biochemical values, leads to a single reference solution showing β-amylase activity to be the rate-limiting step in carbon flow from starch degradation. Additionally, the response coefficients for stromal glucose to the glucose transporter kcat and KM are substantial, whereas those for cytosolic glucose are not, consistent with a kinetic bottleneck due to transport. Response coefficient norms show stromal maltopentaose and cytosolic glucosylated arabinogalactan to be the most and least globally sensitive metabolites, respectively, and β-amylase kcat and KM for starch to be the kinetic parameters with the largest aggregate effect on metabolite concentrations as a whole. The latter kinetic parameters, together with those for glucose transport, have the greatest effect on stromal glucose, which is a precursor for biofuel synthetic pathways. Exploration of the steady-state solution space with respect to concentrations of 6 external metabolites and 8 dynamic metabolite concentrations show that stromal metabolism is strongly coupled to starch levels, and that transport between compartments serves to lower coupling between metabolic subsystems in different compartments. CONCLUSIONS: We find that in the reference steady state, starch cleavage is the most significant determinant of carbon flux, with turnover of oligosaccharides playing a secondary role. Independence of stationary point with respect to initial dynamic variable values confirms a unique stationary point in the phase space of dynamically varying concentrations of the model network. Stromal maltooligosaccharide metabolism was highly coupled to the available starch concentration. From the most highly converged trajectories, distances between unique fixed points of phase spaces show that cytosolic maltose levels depend on the total concentrations of arabinogalactan and glucose present in the cytosol. In addition, cellular compartmentalization serves to dampen much, but not all, of the effects of one subnetwork on another, such that kinetic modeling of single compartments would likely capture most dynamics that are fast on the timescale of the transport reactions.

Model of the Ubiquitin-Proteasome System

Description of the Model

This is a stochastic model of the ubiquitin-proteasome system for a generic pool of native proteins (NatP) which have a half-life of about 10 hours under normal conditions. It is assumed that these proteins are only degraded after they have lost their native structure due to a damage event. This is represented in the model by the misfolding reaction which depends on the level of reactive oxygen species (ROS) in the cell. Misfolded proteins (MisP) are first bound by an E3 ubiquitin ligase. Ubiquitin (Ub) is activated by E1 (ubiquitin-activating enzyme) and then passed to E2 (ubiquitin-conjugating enzyme). The E2 enzyme then passes the ubiquitin molecule to the E3/MisP complex with the net effect that the misfolded protein is monoubiquitinated and both E2 and E3 are released. Further ubiquitin molecules are added in a step-wise manner. When the chain of ubiquitin molecules is of length 4 or more, the polyubiquitinated misfolded protein may bind to the proteasome. The model also includes de-ubiquitinating enzymes (DUB) which cleave ubiquitin molecules from the chain in a step-wise manner. They work on chains attached to misfolded proteins both unbound and bound to the proteasomes. Misfolded proteins bound to the proteasome may be degraded releasing ubiquitin. Misfolded proteins including ubiquitinated proteins may also aggregate. Aggregates (AggP) may be sequestered (Seq_AggP) which takes them out of harm's way or they may bind to the proteasome (AggP_Proteasome). Proteasomes bound by aggregates are no longer available for protein degradation.

Figure 2 and Figure 3 has been simulated using Gillespie2.

This model is from the article:
A model for the stoichiometric regulation of blood coagulation.
Hockin MF, Jones KC, Everse SJ, Mann KG. Journal of Biological Chemistry Volume 277, Issue 21, 24 May 2002, Pages 18322 -18333 11893748 ,
Abstract:
We have developed a model of the extrinsic blood coagulation system that includes the stoichiometric anticoagulants. The model accounts for the formation, expression, and propagation of the vitamin K-dependent procoagulant complexes and extends our previous model by including: (a) the tissue factor pathway inhibitor (TFPI)-mediated inactivation of tissue factor (TF).VIIa and its product complexes; (b) the antithrombin-III (AT-III)-mediated inactivation of IIa, mIIa, factor VIIa, factor IXa, and factor Xa; (c) the initial activation of factor V and factor VIII by thrombin generated by factor Xa-membrane; (d) factor VIIIa dissociation/activity loss; (e) the binding competition and kinetic activation steps that exist between TF and factors VII and VIIa; and (f) the activation of factor VII by IIa, factor Xa, and factor IXa. These additions to our earlier model generate a model consisting of 34 differential equations with 42 rate constants that together describe the 27 independent equilibrium expressions, which describe the fates of 34 species. Simulations are initiated by "exposing" picomolar concentrations of TF to an electronic milieu consisting of factors II, IX, X, VII, VIIa, V, and VIIII, and the anticoagulants TFPI and AT-III at concentrations found in normal plasma or associated with coagulation pathology. The reaction followed in terms of thrombin generation, proceeds through phases that can be operationally defined as initiation, propagation, and termination. The generation of thrombin displays a nonlinear dependence upon TF, AT-III, and TFPI and the combination of these latter inhibitors displays kinetic thresholds. At subthreshold TF, thrombin production/expression is suppressed by the combination of TFPI and AT-III; for concentrations above the TF threshold, the bolus of thrombin produced is quantitatively equivalent. A comparison of the model with empirical laboratory data illustrates that most experimentally observable parameters are captured, and the pathology that results in enhanced or deficient thrombin generation is accurately described.

This model is described inthe article:
Metabolic control mechanisms. 5. A solution for the equations representing interaction between glycolysis and respiration in ascites tumor cells.
Britton Chance, David Garfinkel, Joseph Higgins and Benno Hess, J Biol Chem. 1960 35:2426-2439. PubmedID: 13692276
Abstract:
The other papers of this series present experimental evidence for possible relationships between the kinetics of oxygen, glucose, adenosine diphosphate, adenosine triphosphate, and phosphate and those of the cytochromes and pyridine nucleotides of the ascites tumor cell. From these general experiments we are able to formulate, under the law of mass action, a minimum hypothesis under which the four metabolic regulations previously described can be observed. In brief, the system can be represented by the known enzyme systems, a relatively higher ADP affinity in respiration than in glycolysis, the mitochondrial membrane, a segregation of ATP into two compartments, and an ATP-utilizing system that is responsive to small decreases of the intracellular ADP level. The chemical equations for the pathway from glucose to oxygen are solved by a digital computer method so that the responses of the chemical equations and of the living cell can be accurately compared.
For reasons already described, we greatly prefer a com- puter representation based upon a physical or chemical law representing the action of the system to a model simulating the operation of the chemical system but not based upon funda- mental laws for the reactions involved; such a representation would not adequately represent the kinetics of the system, as in an electric circuit network or in some types of hydraulic ana- logues.

The model gives solutions of the reaction kinetics for three types of metabolism:

0 - 64s, metabolism of endogenous substrate
64s - 119s, metabolism of added glucose, illustrating the activated and inhibited aspects of glucose metabolism
119s - 153s, relief of glucose and oxygen inhibition by the addition of an uncoupling agent

This a model from the article:
Which model to use for cortical spiking neurons?
Izhikevich, EM Neural Networks, IEEE Transactions on 2004:15(5):1063-1070 15484883 ,
Abstract:
We discuss the biological plausibility and computational efficiency of some of the most useful models of spiking and bursting neurons. We compare their applicability to large-scale simulations of cortical neural networks.

The model is according to the paper Which Model to Use for Cortical Spiking Neurons? Figure1(L) integrator has been reproduced by MathSBML. The ODE and the parameters values are taken from the a paper Simple Model of Spiking Neurons The original format of the models are encoded in the MATLAB format existed in the ModelDB with Accession number 39948

Figure1 are the simulation results of the same model with different choices of parameters and different stimulus function or events. a=0.02; b=-0.1; c=-55; d=6; V=-60; u=b*V;

This a model from the article:
Metabolic engineering of lactic acid bacteria, the combined approach: kinetic modelling, metabolic control and experimental analysis.
Hoefnagel MH, Starrenburg MJ, Martens DE, Hugenholtz J, Kleerebezem M, Van Swam II, Bongers R, Westerhoff HV, Snoep JL Microbiology 2002 Apr; 148(4):1003-13 11932446 ,
Abstract:
Everyone who has ever tried to radically change metabolic fluxes knows that it is often harder to determine which enzymes have to be modified than it is to actually implement these changes. In the more traditional genetic engineering approaches ’bottle-necks’ are pinpointed using qualitative, intuitive approaches, but the alleviation of suspected ’rate-limiting’ steps has not often been successful. Here the authors demonstrate that a model of pyruvate distribution in Lactococcus lactis based on enzyme kinetics in combination with metabolic control analysis clearly indicates the key control points in the flux to acetoin and diacetyl, important flavour compounds. The model presented here (available at http://jjj.biochem.sun.ac.za/wcfs.html) showed that the enzymes with the greatest effect on this flux resided outside the acetolactate synthase branch itself. Experiments confirmed the predictions of the model, i.e. knocking out lactate dehydrogenase and overexpressing NADH oxidase increased the flux through the acetolactate synthase branch from 0 to 75% of measured product formation rates.

The paper does not have any figure to be put as a curation figure in the BioModels database. The model does reproduce the fluxes and control-coefficients given in Figure 2 and Table 4. To reproduce the results, the model was changed from the description in the article according to the model on JWS: the parameter Kmpyr was changed to 2.5 from 25. The equillibrium constant for PTA reaction (R4) was changed from 0.0281 to 0.0065. The Km for oxygen in the NOX reaction (R13) was changed from 0.01 to 0.2. Slight deviations between the values in the article and the model results may stem from different algorithms used for finding the steady state.

The model reproduces the temporal evolution of four variables depicted in Fig 2a. The solution is generated for median parameter values as given in Table 3. Result shown was generated by MathSBML.

This is the model described the article:
GSK3 and p53 - is there a link in Alzheimer's disease?
Carole J Proctor and Douglas A Gray Molecular Neurodegeneration 2010, 5:7; doi: 10.1186/1750-1326-5-7
Abstract:
Background: Recent evidence suggests that glycogen synthase kinase-3beta (GSK3beta) is implicated in both sporadic and familial forms of Alzheimer's disease. The transcription factor, p53 also plays a role and has been linked to an increase in tau hyperphosphorylation although the effect is indirect. There is also evidence that GSK3beta and p53 interact and that the activity of both proteins is increased as a result of this interaction. Under normal cellular conditions, p53 is kept at low levels by Mdm2 but when cells are stressed, p53 is stabilised and may then interact with GSK3beta. We propose that this interaction has an important contribution to cellular outcomes and to test this hypothesis we developed a stochastic simulation model.
Results: The model predicts that high levels of DNA damage leads to increased activity of p53 and GSK3beta and low levels of aggregation but if DNA damage is repaired, the aggregates are eventually cleared. The model also shows that over long periods of time, aggregates may start to form due to stochastic events leading to increased levels of ROS and damaged DNA. This is followed by increased activity of p53 and GSK3beta and a vicious cycle ensues.
Conclusions: Since p53 and GSK3beta are both involved in the apoptotic pathway, and GSK3beta overactivity leads to increased levels of plaques and tangles, our model might explain the link between protein aggregation and neuronal loss in neurodegeneration.

Notes: The original model submitted by the author had events in it. Since, this model is intended for Stochastic Simulation run and Copasi cannot handle events in Stochastic run, I have replaced the events with piecewise assignment rule. -Viji

This model is an extension of Proctor_p53_Mdm2_ATM ( BIOMD0000000188> ).

The model is according to the paper Which Model to Use for Cortical Spiking Neurons? Figure1(G) Class 1 excitable has been reproduced by MathSBML. The ODE and the parameters values are originally taken from the a paper Simple Model of Spiking Neurons The original format of the models are encoded in the MATLAB format existed in the ModelDB with Accession number 39948

Figure1 are the simulation results of the same model with different choices of parameters and different stimulus function or events.a=0.02; b=-0.1; c=-55; d=6; V=-60; u=b*V;

The model reproduces time profile of p53 and Mdm2 as depicted in Fig 6B of the paper for Model 4. Results obtained using MathSBML.

This model is from the article:
Root gravitropism is regulated by a transient lateral auxin gradient controlled by a tipping-point mechanism.
Band LR, Wells DM, Larrieu A, Sun J, Middleton AM, French AP, Brunoud G, Sato EM, Wilson MH, Péret B, Oliva M, Swarup R, Sairanen I, Parry G, Ljung K, Beeckman T, Garibaldi JM, Estelle M, Owen MR, Vissenberg K, Hodgman TC, Pridmore TP, King JR, Vernoux T, Bennett MJ. Proc Natl Acad Sci U S A. 2012 Mar 20;109(12):4668-73 22393022 ,
Abstract:
Gravity profoundly influences plant growth and development. Plants respond to changes in orientation by using gravitropic responses to modify their growth. Cholodny and Went hypothesized over 80 years ago that plants bend in response to a gravity stimulus by generating a lateral gradient of a growth regulator at an organ's apex, later found to be auxin. Auxin regulates root growth by targeting Aux/IAA repressor proteins for degradation. We used an Aux/IAA-based reporter, domain II (DII)-VENUS, in conjunction with a mathematical model to quantify auxin redistribution following a gravity stimulus. Our multidisciplinary approach revealed that auxin is rapidly redistributed to the lower side of the root within minutes of a 90° gravity stimulus. Unexpectedly, auxin asymmetry was rapidly lost as bending root tips reached an angle of 40° to the horizontal. We hypothesize roots use a "tipping point" mechanism that operates to reverse the asymmetric auxin flow at the midpoint of root bending. These mechanistic insights illustrate the scientific value of developing quantitative reporters such as DII-VENUS in conjunction with parameterized mathematical models to provide high-resolution kinetics of hormone redistribution.

This model corresponds to the simplified model described in the article. It is assumed that, on the timescale of DII-VENUS degradation, the concentrations of auxin, TIR1/AFB, and their complexes can be approximated by quasi-steady-state expressions. This reduced the full model to a single ODE that describes how the DII-VENUS dynamics depend on the auxin influx and four parameter groupings.

A mathematical model of the pancreatic duct cell generating high bicarbonate concentrations in pancreatic juice
David C Whitcomb, G Bard Ermentrout, Pancreas 2004 29:e30-40; PubMedID: 15257112

Abstract:
OBJECTIVE: To develop a simple, physiologically based mathematical model of pancreatic duct cell secretion using experimentally derived parameters that generates pancreatic fluid bicarbonate concentrations of >140 mM after CFTR activation.
METHODS: A new mathematical model was developed simulating a duct cell within a proximal pancreatic duct and included a sodium-2-bicarbonate cotransporter (NBC) and sodium-potassium pump (NaK pump) on a chloride-impermeable basolateral membrane, CFTR on the luminal membrane with 0.2 to 1 bicarbonate to chloride permeability ratio. Chloride-bicarbonate antiporters (Cl/HCO3 AP) were added or subtracted from the basolateral (APb) and luminal (APl) membranes. The model was integrated over time using XPPAUT.
RESULTS: This model predicts robust, NaK pump-dependent bicarbonate secretion with opening of the CFTR, generates and maintains pancreatic fluid secretion with bicarbonate concentrations >140 mM, and returns to basal levels with CFTR closure. Limiting CFTR permeability to bicarbonate, as seen in some CFTR mutations, markedly inhibited pancreatic bicarbonate and fluid secretion.
CONCLUSIONS: A simple CFTR-dependent duct cell model can explain active, high-volume, high-concentration bicarbonate secretion in pancreatic juice that reproduces the experimental findings. This model may also provide insight into why CFTR mutations that predominantly affect bicarbonate permeability predispose to pancreatic dysfunction in humans.

This SBML version of the model was created directly from the XPPAUT code found in the appendix with the exception of the parameter vr , the ratio between the duct cell volume and the duct lumen, which is defined inversely to the main text in the XPPAUT code. vr was defined as the ratio of the duct cell volume to the duct lumen volume as in the main text. The model reproduces the figures found in the article. The model uses initial assignments for the lumen volume and events to trigger CFTR opening, so only tools supporting these features can be used to simulate it (eg. Copasi and SBW/Roadrunner).

The model reproduces the time series of cytosolic and phagosomal species as depicted in Figure 2 of the paper. Model successfully reproduced using MathSBML and Jarnac

This model is from the article:
A model of beta-cell mass, insulin, and glucose kinetics: pathways to diabetes.
Topp B, Promislow K, deVries G, Miura RM, Finegood DT. J Theor Biol. 2000 Oct 21;206(4):605-19. 11013117 ,
Abstract:
Diabetes is a disease of the glucose regulatory system that is associated with increased morbidity and early mortality. The primary variables of this system are beta-cell mass, plasma insulin concentrations, and plasma glucose concentrations. Existing mathematical models of glucose regulation incorporate only glucose and/or insulin dynamics. Here we develop a novel model of beta -cell mass, insulin, and glucose dynamics, which consists of a system of three nonlinear ordinary differential equations, where glucose and insulin dynamics are fast relative to beta-cell mass dynamics. For normal parameter values, the model has two stable fixed points (representing physiological and pathological steady states), separated on a slow manifold by a saddle point. Mild hyperglycemia leads to the growth of the beta -cell mass (negative feedback) while extreme hyperglycemia leads to the reduction of the beta-cell mass (positive feedback). The model predicts that there are three pathways in prolonged hyperglycemia: (1) the physiological fixed point can be shifted to a hyperglycemic level (regulated hyperglycemia), (2) the physiological and saddle points can be eliminated (bifurcation), and (3) progressive defects in glucose and/or insulin dynamics can drive glucose levels up at a rate faster than the adaptation of the beta -cell mass which can drive glucose levels down (dynamical hyperglycemia).

This the model used in the article:
Quantitative analysis of pathways controlling extrinsic apoptosis in single cells.
Albeck JG, Burke JM, Aldridge BB, Zhang M, Lauffenburger DA, Sorger PK. Mol Cell. 2008 Apr 11;30(1):11-25. PMID: 18406323 , doi: 10.1016/j.molcel.2008.02.012
Abstract:
Apoptosis in response to TRAIL or TNF requires the activation of initiator caspases, which then activate the effector caspases that dismantle cells and cause death. However, little is known about the dynamics and regulatory logic linking initiators and effectors. Using a combination of live-cell reporters, flow cytometry, and immunoblotting, we find that initiator caspases are active during the long and variable delay that precedes mitochondrial outer membrane permeabilization (MOMP) and effector caspase activation. When combined with a mathematical model of core apoptosis pathways, experimental perturbation of regulatory links between initiator and effector caspases reveals that XIAP and proteasome-dependent degradation of effector caspases are important in restraining activity during the pre-MOMP delay. We identify conditions in which restraint is impaired, creating a physiologically indeterminate state of partial cell death with the potential to generate genomic instability. Together, these findings provide a quantitative picture of caspase regulatory networks and their failure modes.
The mitochondrial compartment is just added as a logical partition and its volume is not used in the mathematical formulas, to stick closer to the expressions used in the matlab files distributed with the original publication. There only the rate constants for bimolecular reactions are adapted by division by v , the ration of the volumes of the mitochondrial compartment and the total cell.
For BCL2 overexpression in figure 5, the initial BCL2 amount was increased by a factor 12 to 2.4*10 ⁵ . For siRNA downregulation of XIAP its amount was multiplied by 0.13 to 1.3*10 ⁴ .

This is an SBML implementation the model of mutual inhibition (figure 1f) described in the article:
Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell.
Tyson JJ, Chen KC, Novak B. Curr Opin Cell Biol. 2003 Apr;15(2):221-31. PubmedID: 12648679 ; DOI: 10.1016/S0955-0674(03)00017-6 ;

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

The model corresponds to hypocalcemic clamp test explained in the paper and parameter values used in the model are that of "subject 1". In order to obtain the plots corresponding to "subject 2" and "subject 3" the following parameters to be changed: lambda_1, lambda_2, m1, m2, R, beta, x1_n, x2_n, x2_min, x2_max, Ca0, Ca1, t0 and alpha.

parameter	Subject 1	Subject 2	Subject 3
lambda_1	0.0125	0.0122	0.0269
lambda_2	0.5595	0.4642	0.4935
m1	112.5200	150.0000	90.8570
m2	15.0000	15.0000	15.0000
R	1.2162	1.1627	1.1889
beta	10e+06	10e+06	10e+06
x1_n	490.7800	452.8200	298.8200
x2_n	6.6290	9.5894	5.4600
x2_min	0.6697	1.4813	0.8287
x2_max	14.0430	17.8710	15.1990
Ca0	1.2550	1.2369	1.2475
Ca1	0.1817	0.2211	0.1985
t0	575	577	575
alpha	0.0442	0.0488	0.0472

No inititial conditions are specified in the paper. Because there is a basal rate of transcription for each gene, it doesn't matter much. With the agreement of Paul Smolen, I put all the initial concentration at 0.001 nanomoles. N Le Novère.

Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry.
Teusink,B et al.: Eur J Biochem 2000 Sep;267(17):5313-29.
The model reproduces the steady-state fluxes and metabolite concentrations of the branched model as given in Table 4 of the paper. It is derived from the model on JWS online, but has the ATP consumption in the succinate branch with the same stoichiometrie as in the publication. The model was successfully tested on copasi v.4.4(build 26).
For Vmax values, please note that there is a conversion factor of approx. 270 to convert from U/mg-protein as shown in Table 1 of the paper to mmol/(min*L_cytosol). The equilibrium constant for the ADH reaction in the paper is given for the reverse reaction (Keq = 1.45*10 ⁴ ). The value used in this model is for the forward reaction: 1/Keq = 6.9*10 ^-5 .
Vmax parameters values used (in [mM/min] except VmGLT):

VmGLT 97.264 mmol/min

VmGLK 226.45

VmPGI 339.667

VmPFK 182.903

VmALD 322.258

VmGAPDH_f 1184.52

VmGAPDH_r 6549.68

VmPGK 1306.45

VmPGM 2525.81

VmENO 365.806

VmPYK 1088.71

VmPDC 174.194

VmG3PDH 70.15

The result of the G6P steady state concentration (marked in red) differs slightly from the one given in table 4. of the publication
Results for steady state:

orig. article this model

Fluxes[mM/min]

Glucose 88 88

Ethanol 129 129

Glycogen 6 6

Trehalose 4.8 4.8 (G6P flux through trehalose branch)

Glycerol 18.2 18.2

Succinate 3.6 3.6

Conc.[mM]

G6P 1.07 1.03

F6P 0.11 0.11

F1,6P 0.6 0.6

DHAP 0.74 0.74

3PGA 0.36 0.36

2PGA 0.04 0.04

PEP 0.07 0.07

PYR 8.52 8.52

AcAld 0.17 0.17

ATP 2.51 2.51

ADP 1.29 1.29

AMP 0.3 0.3

NAD 1.55 1.55

NADH 0.04 0.04

Authors of the publication also mentioned a few misprints in the original article:
in the kinetic law for ADH :

	orig. article	this model
Fluxes[mM/min]
Glucose	88	88
Ethanol	129	129
Glycogen	6	6
Trehalose	4.8	4.8	(G6P flux through trehalose branch)
Glycerol	18.2	18.2
Succinate	3.6	3.6
Conc.[mM]
G6P	1.07	1.03
F6P	0.11	0.11
F1,6P	0.6	0.6
DHAP	0.74	0.74
3PGA	0.36	0.36
2PGA	0.04	0.04
PEP	0.07	0.07
PYR	8.52	8.52
AcAld	0.17	0.17
ATP	2.51	2.51
ADP	1.29	1.29
AMP	0.3	0.3
NAD	1.55	1.55
NADH	0.04	0.04

the species a should denote NAD and b Ethanol
the last term in the equation should read bpq /( K _ib K _iq K _p )

in the kinetic law for PFK :

R = 1 + λ ₁ + λ ₂ + g _r λ ₁ λ ₂
equation L should read: L = L0*(..) ² *(..) ² *(..) ² not L = L0*(..) ² *(..) ² *(..)

To make the model easier to curate, the species ATP , ADP and AMP were added. These are calculated via assignment rules from the active phosphate species, P , and the sum of all AXP , SUM_P .

This is an implementation of the Hodgkin-Huxley model of the electrical behavior of the squid axon membrane from:
A quantitative description of membrane current and its application to conduction and excitation in nerve.
A. L. Hodgkin and A. F. Huxley. (1952 ) Journal of Physiology 119(4): pp 500-544; pmID: 12991237 .

Abstract:
This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre (Hodgkin,Huxley & Katz, 1952; Hodgkin & Huxley, 1952 a-c). Its general object is to discuss the results of the preceding papers (Part I), to put them into mathematical form (Part II) and to show that they will account for conduction and excitation in quantitative terms (Part III).

This SBML model uses the same formalism as the one described in the paper, contrary to modern versions:
* V describes the the membrane depolarisation relative to the resting potential of the membrane
* opposing to modern practice, depolarization is negative , not positive , so the sign of V is different
* inward transmembrane currents are considered positive (inward current positive), contrary to modern use
The changeable parameters are the equilibrium potentials( E_R, E_K, E_L, E_Na ), the membrane depolarization ( V ) and the initial sodium and potassium channel activation and inactivation coefficients ( m,h,n ). The initial values of m,h,n for the model were calculated for V = 0 using the equations from the article: n _t=0 = α_n _V=0 /(α_n _V=0 + β_n _V=0 ) and equivalent expressions for h and m .
For single excitations apply a negative membrane depolarization (V < 0). To achieve oscillatory behavior either change the resting potential to a more positive value or apply a constant negative ionic current (I < 0).
Two assignments for parameters in the model, alpha_n and alpha_m, are not defined at V=-10 resp. -25 mV. We did not change this to keep the formulas similar to the original publication and as most integrators seem not to have any problem with it. The limits at V=-10 and -25 mV are 0.1 for alpha_n resp. 1 for alpha_m.
We thank Mark W. Johnson for finding a bug in the model and his helpful comments.

This a model from the article:
Quantifying robustness of biochemical network models.
Ma L, Iglesias PA. BMC Bioinformatics. 2002 Dec 13;3:38. 12482327 ,
Abstract:
BACKGROUND: Robustness of mathematical models of biochemical networks is important for validation purposes and can be used as a means of selecting between different competing models. Tools for quantifying parametric robustness are needed. RESULTS: Two techniques for describing quantitatively the robustness of an oscillatory model were presented and contrasted. Single-parameter bifurcation analysis was used to evaluate the stability robustness of the limit cycle oscillation as well as the frequency and amplitude of oscillations. A tool from control engineering--the structural singular value (SSV)--was used to quantify robust stability of the limit cycle. Using SSV analysis, we find very poor robustness when the model's parameters are allowed to vary. CONCLUSION: The results show the usefulness of incorporating SSV analysis to single parameter sensitivity analysis to quantify robustness.

This model is originally proposed by Laub and Loomis (1998).[Laub MT, Loomis WF (1998). A molecular network that produces spontaneous oscillations in excitable cells of Dictyostelium. Mol Biol Cell. 9(12):3521-32. PubMED: 12482327 .
The parameters used in this model (Ma and Iglesias, 2002), are different from that used in the original model (Laub and Loomis, 1998), because of the typographical errors in the original paper. The parameters used in the model presented by Ma and Iglesias, are obtained directly from the authors of original publication (Laub and Loomis, 1998). These parameters are also used in the website for the Laub-Loomis model, http://www-biology.ucsd.edu/labs/loomis/network/laubloomis.html .
By using this model, Kim et al., 2006 [Kim J, Bates DG, Postlethwaite I, Ma L, Iglesias PA. (2006) Robustness analysis of biochemical network models. Syst Biol (Stevenage). 153(3):96-104. PubMED: 16984084 ], validate and extend the analysis approach proposed by Ma and Iglesias (2002), by showing how hybrid optimisation can be used to compute worst-case parameter combinations in the model.

This features the two step binding of NO to soluble Guanylyl Cyclase as proposed by Stone JR, Marletta MA. Biochemistry (1996) 35(4):1093-9 . There is a fast step binding scheme and a slow step binding scheme. The difference lies in the binding of a NO to a non-heme site on sGC, which may not necessarily be the same site of binding during the initial binding. The rates have been directly used models.

This the single cell model from the article:
A multiscale model to investigate circadian rhythmicity of pacemaker neurons in the suprachiasmatic nucleus.
Vasalou C, Henson MA. PLoS Comput Biol 2010 Mar 12;6(3):e1000706. PMID: 20300645 , DOI: 10.1371/journal.pcbi.1000706 ;

Abstract:
The suprachiasmatic nucleus (SCN) of the hypothalamus is a multicellular system that drives daily rhythms in mammalian behavior and physiology. Although the gene regulatory network that produces daily oscillations within individual neurons is well characterized, less is known about the electrophysiology of the SCN cells and how firing rate correlates with circadian gene expression. We developed a firing rate code model to incorporate known electrophysiological properties of SCN pacemaker cells, including circadian dependent changes in membrane voltage and ion conductances. Calcium dynamics were included in the model as the putative link between electrical firing and gene expression. Individual ion currents exhibited oscillatory patterns matching experimental data both in current levels and phase relationships. VIP and GABA neurotransmitters, which encode synaptic signals across the SCN, were found to play critical roles in daily oscillations of membrane excitability and gene expression. Blocking various mechanisms of intracellular calcium accumulation by simulated pharmacological agents (nimodipine, IP3- and ryanodine-blockers) reproduced experimentally observed trends in firing rate dynamics and core-clock gene transcription. The intracellular calcium concentration was shown to regulate diverse circadian processes such as firing frequency, gene expression and system periodicity. The model predicted a direct relationship between firing frequency and gene expression amplitudes, demonstrated the importance of intracellular pathways for single cell behavior and provided a novel multiscale framework which captured characteristics of the SCN at both the electrophysiological and gene regulatory levels.

Originally created by libAntimony v1.3 (using libSBML 4.1.0-b1)

The model reproduces the time profile of cytosolic and intracellular calcium as depicted in the upper panel of Fig 2 in the paper. The model was successfully tested on MathSBML and Jarnac.

This a model from the article:
Experimental validation of a predicted feedback loop in the multi-oscillator clock of Arabidopsis thaliana.
Locke JC, Kozma-Bognár L, Gould PD, Fehér B, Kevei E, Nagy F, Turner MS, Hall A, Millar AJ Mol. Syst. Biol. 2006;Volume:2;Page:59 17102804 ,
Abstract:
Our computational model of the circadian clock comprised the feedback loop between LATE ELONGATED HYPOCOTYL (LHY), CIRCADIAN CLOCK ASSOCIATED 1 (CCA1) and TIMING OF CAB EXPRESSION 1 (TOC1), and a predicted, interlocking feedback loop involving TOC1 and a hypothetical component Y. Experiments based on model predictions suggested GIGANTEA (GI) as a candidate for Y. We now extend the model to include a recently demonstrated feedback loop between the TOC1 homologues PSEUDO-RESPONSE REGULATOR 7 (PRR7), PRR9 and LHY and CCA1. This three-loop network explains the rhythmic phenotype of toc1 mutant alleles. Model predictions fit closely to new data on the gi;lhy;cca1 mutant, which confirm that GI is a major contributor to Y function. Analysis of the three-loop network suggests that the plant clock consists of morning and evening oscillators, coupled intracellularly, which may be analogous to coupled, morning and evening clock cells in Drosophila and the mouse.

The model describes a three loops model of the Arabidopsis circadian clock. It provides initial conditions, parameter values and reactions for the production rates of the following species: LHY mRNA (cLm), cytoplasmic LHY (cLc), nuclear LHY (cLn), TOC1 mRNA (cTm), cytoplasmic TOC1 (cTc), nuclear TOC1 (cTn), X mRNA (cXm), cytoplasmic X (cXc), nuclear X (cXn), Y mRNA (cYm), cytoplasmic Y (cYc), nuclear Y (cYn), nuclear P (cPn), APRR7/9 mRNA, cytoplasmic APRR7/9, and nuclear APRR7/9.

The paper describes the behaviour of the model in constant light (LL) and day-night cycle (LD). However, the current model only contains the LL cycle. Some parameter values should be changed from the wild-type (WT) ones in order to simulate the effect of mutations. These changes are listed in the notes of relevant parameters.

deBack2012 - Lineage Specification in Pancreas Development

This model of two neighbouring pancreas precursor cells, describes the exocrine versus endocrine lineage specification process. To account for the tissue scale patterns, this couplet model has been extended to hundreds of coupled cells.

This model is described in the article:

On the role of lateral stabilization during early patterning in the pancreas

de Back W., Zhou JX, Brusch L

J. R. Soc. Interface 6 February 2013 vol. 10 no. 79 20120766

Abstract:

The cell fate decision of multi-potent pancreatic progenitor cells between the exocrine and endocrine lineages is regulated by Notch signalling, mediated by cell–cell interactions. However, canonical models of Notch-mediated lateral inhibition cannot explain the scattered spatial distribution of endocrine cells and the cell-type ratio in the developing pancreas. Based on evidence from acinar-to-islet cell transdifferentiation in vitro, we propose that lateral stabilization, i.e. positive feedback between adjacent progenitor cells, acts in parallel with lateral inhibition to regulate pattern formation in the pancreas. A simple mathematical model of transcriptional regulation and cell–cell interaction reveals the existence of multi-stability of spatial patterns whose simultaneous occurrence causes scattering of endocrine cells in the presence of noise. The scattering pattern allows for control of the endocrine-to-exocrine cell-type ratio by modulation of lateral stabilization strength. These theoretical results suggest a previously unrecognized role for lateral stabilization in lineage specification, spatial patterning and cell-type ratio control in organ development.

This model is hosted on BioModels Database and identified by: MODEL1211010000 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

In order to reproduce the model, the volume of all compartment is set to 1, and the stoichiometry of CaER and CaM has been set to 0.25, corresponding to betaER/rhoER and betaM/rhoM described in the paper.

NGF dependent Akt pathway model

made by Kazuhiro A. Fujita.

This is the NGF dependent Akt pathway model described in:
Decoupling of receptor and downstream signals in the Akt pathway by its low-pass filter characteristics.
Fujita KA, Toyoshima Y, Uda S, Ozaki Y, Kubota H, and Kuroda S. Sci Signal. 2010 Jul 27;3(132):ra56. PMID: 20664065 ; DOI: 10.1126/scisignal.2000810
Abstract:
In cellular signal transduction, the information in an external stimulus is encoded in temporal patterns in the activities of signaling molecules; for example, pulses of a stimulus may produce an increasing response or may produce pulsatile responses in the signaling molecules. Here, we show how the Akt pathway, which is involved in cell growth, specifically transmits temporal information contained in upstream signals to downstream effectors. We modeled the epidermal growth factor (EGF)–dependent Akt pathway in PC12 cells on the basis of experimental results. We obtained counterintuitive results indicating that the sizes of the peak amplitudes of receptor and downstream effector phosphorylation were decoupled; weak, sustained EGF receptor (EGFR) phosphorylation, rather than strong, transient phosphorylation, strongly induced phosphorylation of the ribosomal protein S6, a molecule downstream of Akt. Using frequency response analysis, we found that a three-component Akt pathway exhibited the property of a low-pass filter and that this property could explain decoupling of the peak amplitudes of receptor phosphorylation and that of downstream effectors. Furthermore, we found that lapatinib, an EGFR inhibitor used as an anticancer drug, converted strong, transient Akt phosphorylation into weak, sustained Akt phosphorylation, and, because of the low-pass filter characteristics of the Akt pathway, this led to stronger S6 phosphorylation than occurred in the absence of the inhibitor. Thus, an EGFR inhibitor can potentially act as a downstream activator of some effectors.

The different versions of input, step, pulse and ramp, can be simulated using the parameters NGF_conc_pulse , NGF_conc_step and NGF_conc_ramp . Depending on which one is set unequal to 0, either a continous pulse with value NGF_conc_pulse , a 60 second step with NGF_conc_step or a signal increasing from 0 to NGF_conc_pulse over a time periode of 3600 seconds are used as input. In case more than one parameter is set to values greater than 0 these input profiles are added to each other. The pulse time and the time over which the ramp input increases can be set by pulse_time and ramp_time .

NCBS Curation Comments This model shows the control mechanism of Jak-Stat pathway, here SOCS1 (Suppressor of cytokine signaling-I) was identified as the negative regulator of Jak and STAT signal transduction pathway. Note: There are a few ambiguities in the paper like initial concentration of IFN and some reactions were missing in the paper that were employed for obtaining the results. The graphs are almost similar to the graphs as shown in the paper but still some ambiguities regarding the concentration are there. Thanks to Dr Satoshi Yamada for clarifying some of those ambiguities and providing the values used in simulations.

Biomodels Curation Comments The model reproduces Fig 2 (A,C,E,G,I,K,M) of the paper. The set of equations present in the paper are inadequate to reproduce the figures mentioned . The model appears to have been fine tuned after correspondence between the curators at NCBS and the authors. There is however a slight discrepancy between the simulation results and the plots in the paper. The model was tested on MathSBML.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2006 The BioModels Team.
For more information see the terms of use .

This model is from the article:
Systems biology reveals new strategies for personalizing cancer medicine and confirms the role of PTEN in resistance to trastuzumab.
Faratian D, Goltsov A, Lebedeva G, Sorokin A, Moodie S, Mullen P, Kay C, Um IH, Langdon S, Goryanin I, Harrison DJ Cancer Res. 2009; 69(16): 6713-20 19638581 ,
Abstract:
Resistance to targeted cancer therapies such as trastuzumab is a frequent clinical problem not solely because of insufficient expression of HER2 receptor but also because of the overriding activation states of cell signaling pathways. Systems biology approaches lend themselves to rapid in silico testing of factors, which may confer resistance to targeted therapies. Inthis study, we aimed to develop a new kinetic model that could be interrogated to predict resistance to receptor tyrosine kinase (RTK) inhibitor therapies and directly test predictions in vitro and in clinical samples. The new mathematical model included RTK inhibitor antidiv binding, HER2/HER3 dimerization and inhibition, AKT/mitogen-activated protein kinase cross-talk, and the regulatory properties of PTEN. The model was parameterized using quantitative phosphoprotein expression data from cancer cell lines using reverse-phase protein microarrays. Quantitative PTEN protein expression was found to be the key determinant of resistance to anti-HER2 therapy in silico, which was predictive of unseen experiments in vitro using the PTEN inhibitor bp(V). When measured in cancer cell lines, PTEN expression predicts sensitivity to anti-HER2 therapy; furthermore, this quantitative measurement is more predictive of response (relative risk, 3.0; 95% confidence interval, 1.6-5.5; P < 0.0001) than other pathway components taken in isolation and when tested by multivariate analysis in a cohort of 122 breast cancers treated with trastuzumab. For the first time, a systems biology approach has successfully been used to stratify patients for personalized therapy in cancer and is further compelling evidence that PTEN, appropriately measured in the clinical setting, refines clinical decision making in patients treated with anti-HER2 therapies.

This a model from the article:
Kinetic modelling of Amadori N-(1-deoxy-D-fructos-1-yl)-glycine degradation pathways. Part II--kinetic analysis.
Martins SI, Van Boekel MA. Carbohydr Res 2003 Jul;338(16):1665-78. 12873422 ,
Abstract:
A kinetic model for N-(1-deoxy-Image -fructos-1-yl)-glycine (DFG) thermal decomposition was proposed. Two temperatures (100 and 120 °C) and two pHs (5.5 and 6.8) were studied. The measured responses were DFG, 3-deoxyosone, 1-deoxyosone, methylglyoxal, acetic acid, formic acid, glucose, fructose, mannose and melanoidins. For each system the model parameters, the rate constants, were estimated by non-linear regression, via multiresponse modelling. The determinant criterion was used as the statistical fit criterion. Model discrimination was performed by both chemical insight and statistical tests (Posterior Probability and Akaike criterion). Kinetic analysis showed that at lower pH DFG 1,2-enolization is favoured whereas with increasing pH 2,3-enolization becomes a more relevant degradation pathway. The lower amount observed of 1-DG is related with its high reactivity. It was shown that acetic acid, a main degradation product from DFG, was mainly formed through 1-DG degradation. Also from the estimated parameters 3-DG was found to be the main precursor in carbohydrate fragments formation, responsible for colour formation. Some indication was given that as the reaction proceeded other compounds besides DFG become reactants themselves with the formation among others of methylglyoxal. The multiresponse kinetic analysis was shown to be both helpful in deriving relevant kinetic parameters as well as in obtaining insight into the reaction mechanism.

Model was intially tested in Jarnac.

The model was recently updated on 9th July 2010. The reference publication has reported two models M1 and M2, where the parameter values are given for conditions A) 100 ^o C, pH5.5, B) 120 ^o C, pH5.5, C) 100 ^o C, pH6.8 and D) 120 ^o C, pH6.8.

This model corresponds to the model M2 with condition 100 ^o C, pH6.8

The model reproduces Figure 6 of the reference publication. The curation figure was recently added

This a model from the article:
Monte Carlo analysis of an ODE Model of the Sea Urchin Endomesoderm Network.
Kühn C, Wierling C, Kühn A, Klipp E, Panopoulou G, Lehrach H, Poustka AJ. BMC Syst Biol. 2009 Aug 23;3:83. 19698179 ,
Abstract:
BACKGROUND: Gene Regulatory Networks (GRNs) control the differentiation, specification and function of cells at the genomic level. The levels of interactions within large GRNs are of enormous depth and complexity. Details about many GRNs are emerging, but in most cases it is unknown to what extent they control a given process, i.e. the grade of completeness is uncertain. This uncertainty stems from limited experimental data, which is the main bottleneck for creating detailed dynamical models of cellular processes. Parameter estimation for each node is often infeasible for very large GRNs. We propose a method, based on random parameter estimations through Monte-Carlo simulations to measure completeness grades of GRNs. RESULTS: We developed a heuristic to assess the completeness of large GRNs, using ODE simulations under different conditions and randomly sampled parameter sets to detect parameter-invariant effects of perturbations. To test this heuristic, we constructed the first ODE model of the whole sea urchin endomesoderm GRN, one of the best studied large GRNs. We find that nearly 48% of the parameter-invariant effects correspond with experimental data, which is 65% of the expected optimal agreement obtained from a submodel for which kinetic parameters were estimated and used for simulations. Randomized versions of the model reproduce only 23.5% of the experimental data. CONCLUSION: The method described in this paper enables an evaluation of network topologies of GRNs without requiring any parameter values. The benefit of this method is exemplified in the first mathematical analysis of the complete Endomesoderm Network Model. The predictions we provide deliver candidate nodes in the network that are likely to be erroneous or miss unknown connections, which may need additional experiments to improve the network topology. This mathematical model can serve as a scaffold for detailed and more realistic models. We propose that our method can be used to assess a completeness grade of any GRN. This could be especially useful for GRNs involved in human diseases, where often the amount of connectivity is unknown and/or many genes/interactions are missing.

The paper describes several models, Mi, i=1...n, where M0 correspond to the unperturbed model and all the others correspond to the perturbed model. This model is the unperturbed model. The model reproduces figure 5 of the reference publication. The figures were generated by running 1 simulation, whereas in the paper the plotted values are the means of 800 simulations using randomly samples parameter sets. Additional information from the Author: The parameter that were randomly samples are the transcription parameters c_Proteins... and k_Proteins. The parameter were sampled from a lognormal distribution with sigma = 1.5 and mu = 0.5

Repressilator: Elowitz MB, Leibler S. (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403: 335-338.

Repressilator: A synthetic oscillatory network of transcriptional regulators

Citation
Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature.403 : 335 - 338. http:// www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v403/n6767/full/ 403335a0_fs.html

Description
This file describes the deterministic version of the repressilator system. The authors of this model (see reference) use three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network that they called the repressilator. The model system was induced in Escherichia coli. In this system, LacI (variable X is the mRNA, variable PX is the protein) inhibits the tetracycline-resistance transposon tetR (Y, PY describe mRNA and protein). Protein tetR inhibits the gene Cl from phage Lambda (Z, PZ: mRNA, protein),and protein Cl inhibits lacI expression. With appropriate parameter values this system oscillates. The model is based upon the equations in Box 1 of the paper; however, these equations as printed are dimensionless, and the correct dimensions have been returned to the equations, and the parameters set to reproduce Figure 1C (left).

Description

This file describes the deterministic version of the repressilator system.

The authors of this model (see reference) use three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network that they called the repressilator. The model system was induced in Escherichia coli.

In this system, LacI (variable X is the mRNA, variable PX is the protein) inhibits the tetracycline-resistance transposon tetR (Y, PY describe mRNA and protein). Protein tetR inhibits the gene Cl from phage Lambda (Z, PZ: mRNA, protein),and protein Cl inhibits lacI expression. With appropriate parameter values this system oscillates.

The model is based upon the equations in Box 1 of the paper; however, these equations as printed are dimensionless, and the correct dimensions have been returned to the equations, and the parameters set to reproduce Figure 1C (left).

The original Model was Generated by B.E. Shapiro using Cellerator Version 1.0 update 2.1127 using Mathematica 4.2 for Mac OS X (June 4, 2002), November 27, 2002 12:15:32, using (PowerMac,PowerPC, Mac OS X,MacOSX,Darwin)

Nicolas Le Novere: Corrected version generated by SBMLeditor on Sun Aug 20 00:44:05 BST 2006. Removal of EmptySet species. Ran fine on COPASI 4.0 build 18

Bruce Shapiro: Revised with SBML editor 23 October 2006 20:39 PST. Define default units and correct reactions. The original cellerator reactions while being mathematically correct did not accurately reflect the intent of the authors.' The original notes were mostly removed because they were mostly incorrect in the revised version. Tested with MathSBML 2.6.0

Nicolas Le Novere: changed the volume to 1 cubic micrometre, to allow for stochastic simulation.

Changed by Lukas Endler to use the average livetime of mRNA instead of its halflife and a corrected value of alpha and alpha0.
To clarify the equations used in this model:
The equations given in box 1 the original publication are rescaled in three respects (lowercase letters denote the rescaled, uppercase letters the unscaled number of molecules per cell):

the time is rescaled to the average mRNA lifetime, t_ave: τ = t/t_ave
the mRNA concentration is rescaled to the translation efficiency eff: m = M/eff
the protein concentration is rescaled to Km: p = P/Km

α in the equations should be in units of rescaled proteins per promotor and cell, and β is the ratio of the protein to the mRNA decay rates or the ratio of the mRNA to the protein halflife.
In this version of the model α and β are calculated correspondingly to the article, while p and m where just replaced by P/Km resp. M/eff and all equations multiplied by 1/t_ave . Also, to make the equations easier to read, commonly used variables derived from the parameters given in the article by simple rules were introduced.
The parameters given in the article were:

promotor strength (repressed) ( tps_repr ):	5*10 ^-4	transcripts/(promotor*s)
promotor strength (full) ( tps_active ):	0.5	transcripts/(promotor*s)
mRNA half life, τ _1/2,mRNA :	2	min
protein half life, τ _1/2,prot :	10	min
K _M :	40	monomers/cell
Hill coefficient n:	2

from these the following constants can be derived:

average mRNA lifetime ( t_ave ):	τ _1/2,mRNA /ln(2)	= 2.89 min
mRNA decay rate ( kd_mRNA ):	ln(2)/ τ _1/2,mRNA	= 0.347 min ^-1
protein decay rate ( kd_prot ):	ln(2)/ τ _1/2,prot
transcription rate ( a_tr ):	tps_active60*	= 29.97 transcripts/min
transcription rate (repressed) ( a0_tr ):	tps_repr60*	= 0.03 transcripts/min
translation rate ( k_tl ):	effkd_mRNA*	= 6.93 proteins/(mRNA*min)
α :	a_treffτ _1/2,prot /(ln(2)K _M )*	= 216.4 proteins/(promotorcellKm)
α ₀ :	a0_treffτ _1/2,prot /(ln(2)K _M )*	= 0.2164 proteins/(promotorcellKm)
β :	k_dp/k_dm	= 0.2

Annotation by the Kinetic Simulation Algorithm Ontology (KiSAO)

To reproduce the simulations run published by the authors, the model has to be simulated with any of two different approaches. First, one could use a deterministic method (KISAO:0000035) with continuous variables (KISAO:0000018). One sample algorithm to use is the CVODE solver (KISAO:0000019). Second, one could simulate the system using Gillespie's direct method (KiSAO:0000029) - which is a stochastic method (KISAO:0000036) supporting adaptive timesteps (KISAO:0000041) and using discrete variables (KISAO:0000016).

This model was automatically converted from model BIOMD0000000042 by using libSBML .

According to the BioModels Database terms of use , this generated model is not related with model BIOMD0000000042 any more.

This is a model of neuronal Nitric Oxide Synthase expressed in Escherichia coli based on Santolini J. et al. J Biol Chem. (2001) 276(2):1233-43 .
Differing from the article, oxygen explicitly included in the reaction 2, 5 and 10 (numbers as in scheme 1 in the article). In the article the assumed oxygen concentration of 140 uM was included in the pseudo first order rate constant.
Fig 2E in the article shows different time courses for citrulline and NO than the ones produced by this model. Dr. Santolini, one of the authors of the article, wrote that the legends in fig. 2E might be mixed up and should rather denote NO and NO3 instead of citrulline and NO.

The model reproduces ion and adenylate pool concentration corresponding to line 2 of Fig 3 of the publication. This model was tested successfully on Jarnac

This is the compartmental model for L-Dopa pharmocokinetics without simultaneous donation of benserazide as described in the article:
A pharmacokinetic model to predict the PK interaction of L-dopa and benserazide in rats.
Grange S, Holford NH and Guentert TW.
Pharm Res. 2001 AUg; 18(8):1174-84 11587490

Abstract:

PURPOSE: To study the PK interaction of L-dopa/benserazide in rats. METHODS: Male rats received a single oral dose of 80 mg/kg L-dopa or 20 mg/kg benserazide or 80/20 mg/kg L-dopa/benserazide. Based on plasma concentrations the kinetics of L-dopa, 3-O-methyldopa (3-OMD), benserazide, and its metabolite Ro 04-5127 were characterized by noncompartmental analysis and a compartmental model where total L-dopa clearance was the sum of the clearances mediated by amino-acid-decarboxylase (AADC), catechol-O-methyltransferase and other enzymes. In the model Ro 04-5127 inhibited competitively the L-dopa clearance by AADC.

RESULTS: The coadministration of L-dopa/benserazide resulted in a major increase in systemic exposure to L-dopa and 3-OMD and a decrease in L-dopa clearance. The compartmental model allowed an adequate description of the observed L-dopa and 3-OMD concentrations in the absence and presence of benserazide. It had an advantage over noncompartmental analysis because it could describe the temporal change of inhibition and recovery of AADC.

CONCLUSIONS: Our study is the first investigation where the kinetics of benserazide and Ro 04-5127 have been described by a compartmental model. The L-dopa/benserazide model allowed a mechanism-based view of the L-dopa/benserazide interaction and supports the hypothesis that Ro 04-5127 is the primary active metabolite of benserazide.

The volumes and variables in this model are taken for a rat with 0.25 kg. The inital dose for L_Dopa (L_Dopa_per_kg_rat) is to be given in umole per kg. 80 mg/kg L-Dopa correspond to 404 umol/kg. To change the model to a different mass of rat the compartment volumes, and the parameters rat_div_mass and Q have to changed accordingly.

Note:

The model has a species (A-dopa) whose initial concentration is calculated from a listOfInitialAssignments . While running for the first time the time-course (24hrs) for this model in COPASI (up to version 4.6, Build 33), the resulting graph displays only straight lines for all the species. Any subsequent runs should provide proper plots (i.e. without making any change to the model, just by clicking the "run" button again).

The above issue is caused by some initial assignments which are not calculated when COPASI imports the file. This issue should not be present in newer releases of COPASI.

Copyright:

This model corresponds to the full model described in the article.

This is the coherent feed forward loop with an AND-gate like control of the response operon described in the article:
Network motifs in the transcriptional regulation network of Escherichia coli
Shai S. Shen-Orr, Ron Milo, Shmoolik Mangan, Uri Alon, Nat Genet 2002 31:64-68; PMID: 11967538 ; DOI: 10.1038/ng881 ;

Abstract:
Little is known about the design principles of transcriptional regulation networks that control gene expression in cells. Recent advances in data collection and analysis, however, are generating unprecedented amounts of information about gene regulation networks. To understand these complex wiring diagrams, we sought to break down such networks into basic building blocks. We generalize the notion of motifs, widely used for sequence analysis, to the level of networks. We define 'network motifs' as patterns of interconnections that recur in many different parts of a network at frequencies much higher than those found in randomized networks. We applied new algorithms for systematically detecting network motifs to one of the best-characterized regulation networks, that of direct transcriptional interactions in Escherichia coli. We find that much of the network is composed of repeated appearances of three highly significant motifs. Each network motif has a specific function in determining gene expression, such as generating temporal expression programs and governing the responses to fluctuating external signals. The motif structure also allows an easily interpretable view of the entire known transcriptional network of the organism. This approach may help define the basic computational elements of other biological networks.

This model reproduces the timecourse presented in Figure 2a. All species and parameters in the model are dimensionless.

This model is from the article:
Downregulation of PP2A(Cdc55) phosphatase by separase initiates mitotic exit in budding yeast.
Queralt E, Lehane C, Novak B, Uhlmann F. Cell. 2006 May 19;125(4):719-32. 16713564 ,
Abstract:
After anaphase, the high mitotic cyclin-dependent kinase (Cdk) activity is downregulated to promote exit from mitosis. To this end, in the budding yeast S. cerevisiae, the Cdk counteracting phosphatase Cdc14 is activated. In metaphase, Cdc14 is kept inactive in the nucleolus by its inhibitor Net1. During anaphase, Cdk- and Polo-dependent phosphorylation of Net1 is thought to release active Cdc14. How Net1 is phosphorylated specifically in anaphase, when mitotic kinase activity starts to decline, has remained unexplained. Here, we show that PP2A(Cdc55) phosphatase keeps Net1 underphosphorylated in metaphase. The sister chromatid-separating protease separase, activated at anaphase onset, interacts with and downregulates PP2A(Cdc55), thereby facilitating Cdk-dependent Net1 phosphorylation. PP2A(Cdc55) downregulation also promotes phosphorylation of Bfa1, contributing to activation of the "mitotic exit network" that sustains Cdc14 as Cdk activity declines. These findings allow us to present a new quantitative model for mitotic exit in budding yeast.

Model reproduces the various plots in Figure 6 and 7 of the paper. It was successfully tested on MathSBML.

The model reproduces the time profile of active MPF at cyclin concentration of 100nM as depicted in Fig 4A of the paper. Please note that active MPF and cyclin concentrations in the paper are given relative to total cdc2 concentration (100nM). Active MPF (dimer_p) is the cyclin-cdc2 complex that is phosphorylated at Thr161. The model was successfully tested on MathSBML and Jarnac.

This model is from the article:
Mathematical modeling elucidates the role of transcriptional feedback in gibberellin signaling.
Middleton AM , Úbeda-Tomás S , Griffiths J , Holman T , Hedden P , Thomas SG , Phillips AL , Holdsworth MJ , Bennett MJ , King JR, Owen MR Proc. Natl. Acad. Sci. U.S.A. 2012 May; 109(19): 7571-6 22523240 ,
Abstract:
The hormone gibberellin (GA) is a key regulator of plant growth. Many of the components of the gibberellin signal transduction [e.g., GIBBERELLIN INSENSITIVE DWARF 1 (GID1) and DELLA], biosynthesis [e.g., GA 20-oxidase (GA20ox) and GA3ox], and deactivation pathways have been identified. Gibberellin binds its receptor, GID1, to form a complex that mediates the degradation of DELLA proteins. In this way, gibberellin relieves DELLA-dependent growth repression. However, gibberellin regulates expression of GID1, GA20ox, and GA3ox, and there is also evidence that it regulates DELLA expression. In this paper, we use integrated mathematical modeling and experiments to understand how these feedback loops interact to control gibberellin signaling. Model simulations are in good agreement with in vitro data on the signal transduction and biosynthesis pathways and in vivo data on the expression levels of gibberellin-responsive genes. We find that GA-GID1 interactions are characterized by two timescales (because of a lid on GID1 that can open and close slowly relative to GA-GID1 binding and dissociation). Furthermore, the model accurately predicts the response to exogenous gibberellin after a number of chemical and genetic perturbations. Finally, we investigate the role of the various feedback loops in gibberellin signaling. We find that regulation of GA20ox transcription plays a significant role in both modulating the level of endogenous gibberellin and generating overshoots after the removal of exogenous gibberellin. Moreover, although the contribution of other individual feedback loops seems relatively small, GID1 and DELLA transcriptional regulation acts synergistically with GA20ox feedback.

The model reproduces the percentage change of PIP_PM, PIP2_PM and IP3_Cyt as depicted in Figure 1 of the paper. The model also contains the equations for the analysis of PH-GFP experiments, however the initial value of PH_GFP has been set to zero to more accurately reproduce Figure 1. The units of cytosolic species are given in molecules/um^3. In order to convert them to uM, divide the concentration by 602. For the analysis of PH_GFP experiments, one should plug in the values of PH_GFP, IP3_PHGFP and PIP2_PHGFP from Table AI in the appendix. The model was successfully tested on MathSBML.

This is a model described in the article:
Thermodynamically Consistent Model Calibration in Chemical Kinetics.
Garrett Jenkinson and John Goutsias, BMC Systems Biology 2011 May 6;5(1):64.; PMID: 21548948 .

ABSTRACT:
BACKGROUND:
The dynamics of biochemical reaction systems are constrained by the fundamental laws of thermodynamics, which impose well-defined relationships among the reaction rate constants characterizing these systems. Constructing biochemical reaction systems from experimental observations often leads to parameter values that do not satisfy the necessary thermodynamic constraints. This can result in models that are not physically realizable and may lead to inaccurate, or even erroneous, descriptions of cellular function.
RESULTS:
We introduce a thermodynamically consistent model calibration (TCMC) method that can be effectively used to provide thermodynamically feasible values for the parameters of an open biochemical reaction system. The proposed method formulates the model calibration problem as a constrained optimization problem that takes thermodynamic constraints (and, if desired, additional non-thermodynamic constraints) into account. By calculating thermodynamically feasible values for the kinetic parameters of a well-known model of the EGF/ERK signaling cascade, we demonstrate the qualitative and quantitative significance of imposing thermodynamic constraints on these parameters and the effectiveness of our method for accomplishing this important task. MATLAB software, using the Systems Biology Toolbox 2.1, can be accessed from www.cis.jhu.edu/~goutsias/CSS lab/software.html. An SBML file containing the thermodynamically feasible EGF/ERK signaling cascade model can be found in the BioModels database.
CONCLUSIONS:
TCMC is a simple and flexible method for obtaining physically plausible values for the kinetic parameters of open biochemical reaction systems. It can be effectively used to recalculate a thermodynamically consistent set of parameter values for existing thermodynamically infeasible biochemical reaction models of cellular function as well as to estimate thermodynamically feasible values for the parameters of new models. Furthermore, TCMC can provide dimensionality reduction, better estimation performance, and lower computational complexity, and can help to alleviate the problem of data overfitting.

This model is a thermodynamically feasible version of a previous model in the BioModels database, BIOMD0000000019 , described in Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Schoeberl et al (2002), PMID: 11923843 .
The only difference between the present model and the model listed under BIOMD0000000019 are the values of the parameters.

This model is from the article:
Queueing up for enzymatic processing: correlated signaling through coupled degradation.
Natalie A Cookson, William H Mather, Tal Danino, Octavio Mondragón-Palomino, Ruth J Williams, Lev S Tsimring, & Jeff Hasty Molecular Systems Biology 2011; 7:561; DOI: 10.1038/msb.2011.94
Abstract:
High-throughput technologies have led to the generation of complex wiring diagrams as a post-sequencing paradigm for depicting the interactions between vast and diverse cellular species. While these diagrams are useful for analyzing biological systems on a large scale, a detailed understanding of the molecular mechanisms that underlie the observed network connections is critical for the further development of systems and synthetic biology. Here, we use queueing theory to investigate how ‘waiting lines’ can lead to correlations between protein ‘customers’ that are coupled solely through a downstream set of enzymatic ‘servers’. Using the E. coli ClpXP degradation machine as a model processing system, we observe significant cross-talk between two networks that are indirectly coupled through a common set of processors. We further illustrate the implications of enzymatic queueing using a synthetic biology application, in which two independent synthetic networks demonstrate synchronized behavior when common ClpXP machinery is overburdened. Our results demonstrate that such post-translational processes can lead to dynamic connections in cellular networks and may provide a mechanistic understanding of existing but currently inexplicable links.

Note:
Individual stochastic trajectories for a queueing system in three different conditions, 1) Underloaded, 2) Balanced and 3) Overloaded, demonstrate correlation resonance. The parameter values in this model correspond to the Balanced Condition.

This a model from the article:
Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora.
Leloup JC, Gonze D, Goldbeter A. J Biol Rhythms. 1999 Dec;14(6):433-48. 10643740 ,
Abstract:
We examine theoretical models for circadian oscillations based on transcriptional regulation in Drosophila and Neurospora. For Drosophila, the molecular model is based on the negative feedback exerted on the expression of the per and tim genes by the complex formed between the PER and TIM proteins. For Neurospora, similarly, the model relies on the feedback exerted on the expression of the frq gene by its protein product FRQ. In both models, sustained rhythmic variations in protein and mRNA levels occur in continuous darkness, in the form of limit cycle oscillations. The effect of light on circadian rhythms is taken into account in the models by considering that it triggers degradation of the TIM protein in Drosophila, and frq transcription in Neurospora. When incorporating the control exerted by light at the molecular level, we show that the models can account for the entrainment of circadian rhythms by light-dark cycles and for the damping of the oscillations in constant light, though such damping occurs more readily in the Drosophila model. The models account for the phase shifts induced by light pulses and allow the construction of phase response curves. These compare well with experimental results obtained in Drosophila. The model for Drosophila shows that when applied at the appropriate phase, light pulses of appropriate duration and magnitude can permanently or transiently suppress circadian rhythmicity. We investigate the effects of the magnitude of light-induced changes on oscillatory behavior. Finally, we discuss the common and distinctive features of circadian oscillations in the two organisms.

This particular version of the model has been translated from equations 4a-4c (Neurospora).

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Leloup JC, Gonze D, Goldbeter A. (1999) - version02
The original CellML model was created by:
Lloyd, Catherine, May
c.lloyd@aukland.ac.nz
The University of Auckland
The Bioengineering Institute

A Synthetic Gene-Metabolic Oscillator

Reference: Fung et al; Nature (2005) 435:118-122

Name of kinetic law	Reaction
Glycolytic flux, V_gly:	nil -> AcCoA;
Flux to TCA cycle/ETOH, V_TCA:	AcCoA -> TCA/EtOH;
HOAc ex/import,reversible, V_out:	HOAc -> HOAc_E
V_Pta:	AcCoA + Pi -> AcP + CoA
reversible, V_Ack:	AcP + ADP -> OAc + ATP
V_Acs:	OAC + ATP -> AcCoA +PPi
Acetic acid-base equillibrium, reversible, V_Ace:	OAC + H -> HOAc
Expression of LacI, R_LacI:	nil -> LacI
Expression of Acs, R_Acs:	nil -> Acs
Expression of Pta, R_Pta:	nil -> Pta
LacI degradation, R_dLacI:	LacI -> nil
Acs degradation, R_dAcs:	Acs -> nil
Pta degradation, R_dPta:	Pta -> nil

For this model the differential equation for V_Ace was changed from:
C*(AcP*H-K_eq*OAC) with C = 100 in the supplemental material
to C*(OAc*H-K_eq*HOAc) with C = 100, as in Bulter et. al; PNAS(2004),101,2299-2304 , and a value for K_eq of 5*10^-4 after communication with the authors.

translated to SBML by:
Lukas Endler(luen at tbi.univie.ac.at), Christoph Flamm (xtof at tbi.univie.ac.at)

Biomodels Curation The model reproduces 3a of the paper for glycolytic flux Vgly = 0.5. The authors have agreed that the values on Y-axis are marked wrong and hence there is a discrepancy between model simulation results and the figure. Also, note that the values of concentration and time are in dimensionless units. The model was successfully tested on MathSBML and Jarnac.

This model is from the article:
Multiple light inputs to a simple clock circuit allow complex biological rhythms
Troein C, Corellou F, Dixon LE, van Ooijen G, O'Neill JS, Bouget FY, Millar AJ. Plant J. 2011 Apr;66(2):375-85. 21219507 ,
Abstract:
Circadian clocks are biological timekeepers that allow living cells to time their activity in anticipation of predictable environmental changes. Detailed understanding of the circadian network of higher plants, such as Arabidopsis thaliana, is hampered by the high number of partially redundant genes. However, the picoeukaryotic alga Ostreococcus tauri, which was recently shown to possess a small number of non-redundant clock genes, presents an attractive alternative target for detailed modelling of circadian clocks in the green lineage. Based on extensive time-series data from in vivo reporter gene assays, we developed a model of the Ostreococcus clock as a feedback loop between the genes TOC1 and CCA1. The model reproduces the dynamics of the transcriptional and translational reporters over a range of photoperiods. Surprisingly, the model is also able to predict the transient behaviour of the clock when the light conditions are altered. Despite the apparent simplicity of the clock circuit, it displays considerable complexity in its response to changing light conditions. Systematic screening of the effects of altered day length revealed a complex relationship between phase and photoperiod, which is also captured by the model. The complex light response is shown to stem from circadian gating of light-dependent mechanisms. This study provides insights into the contributions of light inputs to the Ostreococcus clock. The model suggests that a high number of light-dependent reactions are important for flexible timing in a circadian clock with only one feedback loop.

Note: Two-gene model of the Ostreococcus circadian clock

This is a model of the circadian clock of Ostreococcus tauri, with a negative feedback loop between TOC1 and CCA1 (a.k.a. LHY) and multiple light inputs. It was used and described in Troein et al., Plant Journal (2011).

The model incorporates luciferase reporters, and in this SBML model the four different versions of the model for transcriptional and translational reporter lines (pTOC1::LUC, pCCA1::LUC, TOC1-LUC and CCA1-LUC) are all accessible by setting one of the rep_X parameters to 1 and the others to 0. You can also set all four to 0 to only simulate the non-reporter core of the system.

Input to the system should be provided by modifying the "light" function. An implementation of LD 12:12 is provided as an example, but the model was also used with more complicated light regimes that vary between data sets and are not convenient to express directly in SBML.

The functions "ox_cca1" and "ox_toc1" can be altered to add overexpression of CCA1 and TOC1. Setting either to x gives additional, constitutive transcription at x times the maximal (and typically not realizable) transcription rate of the native gene. The overexpression mutant fits in Figure 7 of Troein et al. (2011) used ox_cca1 = 0.115 and oc_toc1 = 0.0584, respectively.

The functions "copies_toc1" and "copies_cca1" are normally 1 but can be lowered to simulate knockdown experiments. The functions "transcription", "translation" and "proteasome" can be modified to simulate the effects of altering the overall rate of transcription, translation and protein degradation.

The parameters were fitted specifically to data from transgenic reporter lines TOC8, pTOC3, LHY7 and pLHY7 (Corellou et al., Plant Cell 2009). Parameters that begin with "effcopies" describe the effective number of copies of CCA1 or TOC1 in the respective translational fusion lines, with anything above 1 due to the fusion proteins.

For the model fitting, the initial values were fitted to the data in the various time courses. The initial values given here correspond to the limit cycle of the system in LD 12:12. The system converges to the limit cycle in just a few days under most light conditions, so these initial values are biologically meaningful.

The species cca1luc_c and cca1luc_n have been merged into cca1luc (which corresponds to the observable luminescence signal), because Copasi refused to run the system otherwise. For TOC1-LUC, the predicted output signal is the sum of toc1luc_1 and toc1luc_2.

Model reproduces the various plots in the publication for "Control" concentrations. Model successfully tested on MathSBML.

The model reproduces time profile of p53 and Mdm2 as depicted in Fig 6B of the paper for Model 5. Results obtained using MathSBML.

This a model from the article:
Increased glycolytic flux as an outcome of whole-genome duplication in yeast.
Conant GC, Wolfe KH Mol. Syst. Biol. [2007 ; Volume: 3 (Issue: )]: 129 17667951 ,
Abstract:
After whole-genome duplication (WGD), deletions return most loci to single copy. However, duplicate loci may survive through selection for increased dosage. Here, we show how the WGD increased copy number of some glycolytic genes could have conferred an almost immediate selective advantage to an ancestor of Saccharomyces cerevisiae, providing a rationale for the success of the WGD. We propose that the loss of other redundant genes throughout the genome resulted in incremental dosage increases for the surviving duplicated glycolytic genes. This increase gave post-WGD yeasts a growth advantage through rapid glucose fermentation; one of this lineage's many adaptations to glucose-rich environments. Our hypothesis is supported by data from enzyme kinetics and comparative genomics. Because changes in gene dosage follow directly from post-WGD deletions, dosage selection can confer an almost instantaneous benefit after WGD, unlike neofunctionalization or subfunctionalization, which require specific mutations. We also show theoretically that increased fermentative capacity is of greatest advantage when glucose resources are both large and dense, an observation potentially related to the appearance of angiosperms around the time of WGD.

This model reproduces fig. 2C from the corrigendum to the publication
The parameter Vmax_PDH was corrected by a factor 60 from 6.32 mM/min in the publication to 379.2 mM/min in accordance with the authors.
see the corrigendum at msb or its pubmed entry (pmid:18594520)

This model comprises the glycolysis model from Pritchard and Kell (2002) with an extension for the metabolisation of pyruvate in the mitochondria by pyruvate dehydrogenase and an additional parameter, WGD_E , to adjust for the differing enzyme concentrations before the whole genome duplication (WGD).
To switch off transport of pyruvate to the mitochondria, set the parameter t_m = 0.
Figure 2C from the article can be reproduced by manually changing the value of parameter WGD_E in the range between 0.65 and 1.0 and calculating the ratios of ratio of PDC/PDH fluxes in the altered model to the one of the model with WGD_E = 1.

O'Dea, E.L., Barken, D., Peralta, R.Q., Tran K.T., Werner, S.L., Kearns, J.D., Levchenko, A., Hoffmann, A. A homeostatic model of IkB metabolism to control constitutive activity. Molecular Systems Biology, 3:111, pp. 1-7. 2007

Questions concerning the paper should be addressed to the corresponding author. Alexander Hoffmann (ahoffmann@ucsd.edu)

The original model was written and simulated within MathWorks MatLab 2006a using the ode15s (stiff/NDF) solver. It is highly recommended that those wanting to model this system use the MatLab version which we will freely provide upon request. As always, simulation results vary according to the numerical solver used.

Translation to SBML Level 2.1 was performed via reconstruction of the model within MathWorks SimBiology Desktop (version 2.1) followed by an Export to SBML. Please address questions about this SBML model to Jeff Kearns (jkearns@ucsd.edu).

BioModels DB curation: The model reproduces the values of diffferent species depicted in Fig 3A and 3B (wt) of the paper corresponding to Model1.1. To depict the the total IkB alpha, beta epsilon species, three additional parameters and their corresponding assignment rules have been introduced in this model by the creator. Model succesfully tested on MathSBML.

This model is from the article:
Modeling temperature entrainment of circadian clocks using the Arrhenius equation and a reconstructed model from Chlamydomonas reinhardtii
Ines Heiland, Christian Bodenstein, Thomas Hinze, Olga Weisheit, Oliver Ebenhoeh, Maria Mittag and Stefan Schuster Journal of Biological Physics 4 March 2012; pp 1-16; doi: 10.1007/s10867-012-9264-x ,
Abstract:
Endogenous circadian rhythms allow living organisms to anticipate daily variations in their natural environment. Temperature regulation and entrainment mechanisms of circadian clocks are still poorly understood. To better understand the molecular basis of these processes, we built a mathematical model based on experimental data examining temperature regulation of the circadian RNA-binding protein CHLAMY1 from the unicellular green alga Chlamydomonas reinhardtii , simulating the effect of temperature on the rates by applying the Arrhenius equation. Using numerical simulations, we demonstrate that our model is temperature-compensated and can be entrained to temperature cycles of various length and amplitude. The range of periods that allow entrainment of the model depends on the shape of the temperature cycles and is larger for sinusoidal compared to rectangular temperature curves. We show that the response to temperature of protein (de)phosphorylation rates play a key role in facilitating temperature entrainment of the oscillator in Chlamydomonas reinhardtii . We systematically investigated the response of our model to single temperature pulses to explain experimentally observed phase response curves.

Huang1996 - MAPK ultrasens

Ultrasensitivity in the mitogen-activated protein kinase cascade.

This model is described in the article:

Ultrasensitivity in the mitogen-activated protein kinase cascade.

Huang CY, Ferrell JE Jr

Proc. Natl. Acad. Sci. U.S.A. 1996:93(19):10078-83

Abstract:

The mitogen-activated protein kinase (MAPK) cascade is a highly conserved series of three protein kinases implicated in diverse biological processes. Here we demonstrate that the cascade arrangement has unexpected consequences for the dynamics of MAPK signaling. We solved the rate equations for the cascade numerically and found that MAPK is predicted to behave like a highly cooperative enzyme, even though it was not assumed that any of the enzymes in the cascade were regulated cooperatively. Measurements of MAPK activation in Xenopus oocyte extracts confirmed this prediction. The stimulus/response curve of the MAPK was found to be as steep as that of a cooperative enzyme with a Hill coefficient of 4-5, well in excess of that of the classical allosteric protein hemoglobin. The shape of the MAPK stimulus/ response curve may make the cascade particularly appropriate for mediating processes like mitogenesis, cell fate induction, and oocyte maturation, where a cell switches from one discrete state to another.

The species K_PP_norm, KKK_P_norm and KK_PP_norm are the relative concentrations of the active MAPK, MAPKK and MAPKKK, that is the double, or single resp. phophorylated forms divided by the total concentrations of each kinase. For MAPK additionally the also active MAPK divided by the maximal concentration of active MAPK is given by rel_K_PP_max. The parameter K_PP_norm_max, the maximal ratio of active MapK, has to be calculated for each change of parameters.

This model is hosted on BioModels Database and identified by: BIOMD0000000009 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This is the core model described in the article:
Covering a Broad Dynamic Range: Information Processing at the Erythropoietin Receptor
Verena Becker, Marcel Schilling, Julie Bachmann, Ute Baumann, Andreas Raue, Thomas Maiwald, Jens Timmer and Ursula Klingmüller; Science Published Online May 20, 2010; DOI: 10.1126/science.1184913 PMID: 20488988
Abstract:
Cell surface receptors convert extracellular cues into receptor activation, thereby triggering intracellular signaling networks and controlling cellular decisions. A major unresolved issue is the identification of receptor properties that critically determine processing of ligand-encoded information. We show by mathematical modeling of quantitative data and experimental validation that rapid ligand depletion and replenishment of cell surface receptor are characteristic features of the erythropoietin (Epo) receptor (EpoR). The amount of Epo-EpoR complexes and EpoR activation integrated over time corresponds linearly to ligand input, covering a broad range of ligand concentrations. This relation solely depends on EpoR turnover independent of ligand binding, suggesting an essential role of large intracellular receptor pools. These receptor properties enable the system to cope with basal and acute demand in the hematopoietic system.

SBML model exported from PottersWheel.

% PottersWheel model definition file

function m = BeckerSchilling2010_EpoR_CoreModel()

m             = pwGetEmptyModel();

%% Meta information

m.ID          = 'BeckerSchilling2010_EpoR_CoreModel';
m.name        = 'BeckerSchilling2010_EpoR_CoreModel';
m.description = 'BeckerSchilling2010_EpoR_CoreModel';
m.authors     = {'Verena Becker',' Marcel Schilling'};
m.dates       = {'2010'};
m.type        = 'PW-2-0-42';

%% X: Dynamic variables
% m = pwAddX(m, ID, startValue, type, minValue, maxValue, unit, compartment, name, description, typeOfStartValue)

m = pwAddX(m, 'EpoR'     ,     516, 'fix'   ,    0, 10000,   [], 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'Epo'      , 2030.19, 'global', 1890,  2310,   [], 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'Epo_EpoR' ,       0, 'fix'   ,    0, 10000,   [], 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'Epo_EpoRi',       0, 'fix'   ,    0, 10000,   [], 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'dEpoi'    ,       0, 'fix'   ,    0, 10000,   [], 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'dEpoe'    ,       0, 'fix'   ,    0, 10000,   [], 'cell', []  , []  , []             , []  , 'protein.generic');


%% R: Reactions
% m = pwAddR(m, reactants, products, modifiers, type, options, rateSignature, parameters, description, ID, name, fast, compartments, parameterTrunks, designerPropsR, stoichiometry, reversible)

m = pwAddR(m, {            }, {'EpoR'      }, {  }, 'C' , [] , 'k1*k2', {'kt','Bmax'}, [], 'reaction0001');
m = pwAddR(m, {'EpoR'      }, {            }, {  }, 'MA', [] , []     , {'kt'       }, [], 'reaction0002');
m = pwAddR(m, {'Epo','EpoR'}, {'Epo_EpoR'  }, {  }, 'MA', [] , []     , {'kon'      }, [], 'reaction0003');
m = pwAddR(m, {'Epo_EpoR'  }, {'Epo','EpoR'}, {  }, 'MA', [] , []     , {'koff'     }, [], 'reaction0004');
m = pwAddR(m, {'Epo_EpoR'  }, {'Epo_EpoRi' }, {  }, 'MA', [] , []     , {'ke'       }, [], 'reaction0005');
m = pwAddR(m, {'Epo_EpoRi' }, {'Epo','EpoR'}, {  }, 'MA', [] , []     , {'kex'      }, [], 'reaction0006');
m = pwAddR(m, {'Epo_EpoRi' }, {'dEpoi'     }, {  }, 'MA', [] , []     , {'kdi'      }, [], 'reaction0007');
m = pwAddR(m, {'Epo_EpoRi' }, {'dEpoe'     }, {  }, 'MA', [] , []     , {'kde'      }, [], 'reaction0008');



%% C: Compartments
% m = pwAddC(m, ID, size,  outside, spatialDimensions, name, unit, constant)

m = pwAddC(m, 'cell', 1);


%% K: Dynamical parameters
% m = pwAddK(m, ID, value, type, minValue, maxValue, unit, name, description)

m = pwAddK(m, 'kt'  , 0.0329366 , 'global', 1e-007, 1000);
m = pwAddK(m, 'Bmax', 516       , 'fix'   , 492   , 540 );
m = pwAddK(m, 'kon' , 0.00010496, 'global', 1e-007, 1000);
m = pwAddK(m, 'koff', 0.0172135 , 'global', 1e-007, 1000);
m = pwAddK(m, 'ke'  , 0.0748267 , 'global', 1e-007, 1000);
m = pwAddK(m, 'kex' , 0.00993805, 'global', 1e-007, 1000);
m = pwAddK(m, 'kdi' , 0.00317871, 'global', 1e-007, 1000);
m = pwAddK(m, 'kde' , 0.0164042 , 'global', 1e-007, 1000);


%% Default sampling time points
m.t = 0:3:99;


%% Y: Observables
% m = pwAddY(m, rhs, ID, scalingParameter, errorModel, noiseType, unit, name, description, alternativeIDs, designerProps)

m = pwAddY(m, 'Epo + dEpoe'      , 'Epo_extracellular_obs');
m = pwAddY(m, 'Epo_EpoR'         , 'Epo_cellsurface_obs'  );
m = pwAddY(m, 'Epo_EpoRi + dEpoi', 'Epo_intracellular_obs');


%% S: Scaling parameters
% m = pwAddS(m, ID, value, type, minValue, maxValue, unit, name, description)

m = pwAddS(m, 'scale_Epo_extracellular_obs', 1, 'fix', 0, 100);
m = pwAddS(m, 'scale_Epo_cellsurface_obs'  , 1, 'fix', 0, 100);
m = pwAddS(m, 'scale_Epo_intracellular_obs', 1, 'fix', 0, 100);


%% Designer properties (do not modify)
m.designerPropsM = [1 1 1 0 0 0 400 250 600 400 1 1 1 0 0 0 0];

Note: Model of the Calvin cycle by Giersch et al. (1990, DOI:10.1007/BF00032595 ).

The parameter values are taken from Figure 4 and 5. The initial metabolite values are chosen from the data set of Zhu et al. (2007, DOI:10.1104/pp.107.103713 ). A detailed description of all modifications is given in the model described by Arnold and Nikoloski (2011, PMID:22001849 .

This model is from the article:
A systems biology approach to model neural stem cell regulation by notch, shh, wnt, and EGF signaling pathways.
Sivakumar KC, Dhanesh SB, Shobana S, James J, Mundayoor S. OMICS 2011 Oct;15(10):729-37. 21978399 ,
Abstract:
The Notch, Sonic Hedgehog (Shh), Wnt, and EGF pathways have long been known to in fluence cell fate specification in the developing nervous system. Here we attempt ed to evaluate the contemporary knowledge about neural stem cell differentiation promoted by various drug-based regulations through a systems biology approach. Ou r model showed the phenomenon of DAPT-mediated antagonism of Enhancer of split [E (spl)] genes and enhancement of Shh target genes by a SAG agonist that were effec tively demonstrated computationally and were consistent with experimental studies . However, in the case of model simulation of Wnt and EGF pathways, the model net work did not supply any concurrent results with experimental data despite the fac t that drugs were added at the appropriate positions. This paves insight into the potential of crosstalks between pathways considered in our study. Therefore, we manually developed a map of signaling crosstalk, which included the species conne cted by representatives from Notch, Shh, Wnt, and EGF pathways and highlighted th e regulation of a single target gene, Hes-1, based on drug-induced simulations. T hese simulations provided results that matched with experimental studies. Therefo re, these signaling crosstalk models complement as a tool toward the discovery of novel regulatory processes involved in neural stem cell maintenance, proliferati on, and differentiation during mammalian central nervous system development. To o ur knowledge, this is the first report of a simple crosstalk map that highlights the differential regulation of neural stem cell differentiation and underscores t he flow of positive and negative regulatory signals modulated by drugs.

This is the reduced model described in the article:
A synthetic Escherichia coli predator–prey ecosystem
Balagaddé FK, Song H, Ozaki J, Collins CH, Barnet M, Arnold FH, Quake SR, You L. Mol Syst Biol. 2008;4:187. Epub 2008 Apr 15. PMID: 18414488 ; DOI: 10.1038/msb.2008.24

Abstract:
We have constructed a synthetic ecosystem consisting of two Escherichia coli populations, which communicate bi-directionally through quorum sensing and regulate each other's gene expression and survival via engineered gene circuits. Our synthetic ecosystem resembles canonical predator–prey systems in terms of logic and dynamics. The predator cells kill the prey by inducing expression of a killer protein in the prey, while the prey rescue the predators by eliciting expression of an antidote protein in the predator. Extinction, coexistence and oscillatory dynamics of the predator and prey populations are possible depending on the operating conditions as experimentally validated by long-term culturing of the system in microchemostats. A simple mathematical model is developed to capture these system dynamics. Coherent interplay between experiments and mathematical analysis enables exploration of the dynamics of interacting populations in a predictable manner.

In the article the cell density is given in per 10 ³ cells per microlitre. To evade a conversion factor in the SBML implementation, the unit for the cell densities was just left the same as for the AHLs A and A2 (nM).

This model encoded according to the paper Hormone induced Calcium Oscillations in Liver Cells Can Be Explained by a Simple One Pool Model. The values of parameters a and alpha are varioused inorder to simulate results in different situations. For Figure 3A, a=3.5,alpha=1.2 ; Figure 3B, a=3,alpha=5 ; Figure 3C a= 0.95, alpha=1.5; Figure3D, a=1, alpha=5. Keep in mind that the value for the xy axies are arbitrary value. Figures3 in the paper are reproduced by COPASI 4.0.20(development) , and SBMLodeSolver online.

Biomodels Curation: The model reproduces Fig 2f of the paper. The Vmax values for different reactions are obtained by multiplying the specific activites given in Table 3 of the paper with the protein concentration and an assay correction factor that was provided by the authors. The protein concentration is 202 mg/litre. The specific activities that need to be taken into consideration are those given for "variable threonine" in Table 3. The following are the assay correction factors provided by the authors: vak1=1.49; vak3=1.12; vasd=1.14; vhsd=1.42; vts=1.15; vhk=1.13. The model was successfully tested on MathSBML and Jarnac

Sarma2012 - Interaction topologies of MAPK cascade (M4_K2_QSS_USEQ)

The paper presents the various interaction topologies between the kinases and phosphatases of MAPK cascade. They are represented as M1, M2, M3 and M4. The kinases of the cascades are MKKK, MKK and MK, and Phos1, Phos2 and Phos3 are phosphatases of the system. All three kinases in a M1 type network have specific phosphatases Phos1, Phos2 and Phos3 for the dephosphorylation process. In a M2 type system, kinases MKKK and MKK are dephosphorylated by Phos1 and MK is dephosphorylated by Phos2. The architecture of system like M3 is such that MKKK gets dephosphorylated by Phos1, whereas Phos2 dephosphorylates both MKK and MK. Finally, the MAPK cascade exhibiting more complex design of interaction such as M4 is such that MKKK and MKK are dephosphorylated by Phos1 whereas MKK and MK are dephosphorylated by Phos2. In addition, as it is plausible that the kinases can sequester their respective phosphatases by binding to them, this is considered in the design of the systems (PSEQ-sequestrated system; USEQ-Unsequestrated system). The robustness of different interaction designs of the systems is checked, considering both MichaelisMenten type kinetics (K1) and elementary mass action kinetics (K2). In the living systems, the MAPK cascade transmit both short and long duration signals where short duration signals trigger proliferation and long duration signals trigger cell differentiation. These signal variants are considered to interpret the systems behaviour. It is also tested how the robustness and signal response behaviour of K2 models are affected when K2 assumes quasi steady state (QSS). The combinations of the above variants resulted in 40 models (MODEL1204280001-MODEL1204280040). All these 40 models are available from BioModels Database .

Models that correspond to type M4 with mass-action kinetics K2, in four condition 1) USEQ [ MODEL1204280020 - M4_K2_USEQ], 2) PSEQ [ MODEL1204280024 - M4_K2_PSEQ], 3) QSS_USEQ [ MODEL1204280036 - M4_K2_QSS_USEQ] and 4) QSS_PSEQ [ MODEL1204280040 - M4_K2_QSS_PSEQ] are available from the curated branch. The remaining 36 models can be accessed from the non-curated branch.

This model [ MODEL1204280036 - M4_K2_QSS_USEQ] correspond to type M4 with mass-action kinetics K2, in QSS (quasi steady state) and USEQ (Unsequestrated ) condition. .

This model is described in the article:

Different designs of kinase-phosphatase interactions and phosphatase sequestration shapes the robustness and signal flow in the MAPK cascade.

Sarma U, Ghosh I.

BMC Syst Biol. 2012 Jul 2;6(1):82.

Abstract:

BACKGROUND: The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.

RESULTS: We have built four models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.

CONCLUSIONS: Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design.

This model is hosted on BioModels Database and identified by: BIOMD0000000432 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

Default parameter values are those in the right hand panel of Fig 12. The other panels may be obtained by setting X to 1, 2 or 4, and K3 to 0, 1/2 or 1.

This model is described in:
The kinetics of the enzyme-substrate compound of peroxidase.
Britton Chance, Journal of Biological Chemistry , 151, 553-577, 1943. PDF at JBC
reprinted in: Adv Enzymol Relat Areas Mol Biol. 1999;73:3-23. PubmedID: 10218104 >
Abstract:
Under the narrow range of experimental conditions, and at a temperature of approximately 25 degrees, the following data were obtained. 1. The equilibrium constant of peroxidase and hydrogen peroxide has a minimum value of 2 x 10(-8). 2. The velocity constant for the formation of peroxidase-H2O2 Complex I is 1.2 x 10(7) liter mole-1 sec.-1, +/- 0.4 x 10(7). 3. The velocity constant for the reversible breakdown of peroxidase-H2O2 Complex I is a negligible factor in the enzyme-substrate kinetics and is calculated to be less than 0.2 sec.-1. 4. The velocity constant, k3, for the enzymatic breakdown of peroxidase-H2O2 Complex I varies from nearly zero to higher than 5 sec.-1, depending upon the acceptor and its concentration. The quotient of k3 and the leucomalachite green concentration is 3.0 x 10(4) liter mole-1 sec.-1. For ascorbic acid this has a value of 1.8 x 10(5) liter mole-1 sec.-1. 5. For a particular acceptor concentration, k3 is determined solely from the enzyme-substrate kinetics and is found to be 4.2 sec.-1. 6. For the same conditions, k3 is determined from a simple relationship derived from mathematical solutions of the Michaelis theory and is found to be 5.2 sec.-1. 7. For the same conditions, k3 is determined from the over-all enzyme action and is found to be 5.1 sec.-1. 8. The Michaelis constant determined from kinetic data alone is found to be 0.44 x 10(-6). 9. The Michaelis constant determined from steady state measurements is found to be 0.41 x 10(-6). 10. The Michaelis constant determined from measurement of the overall enzyme reaction is found to be 0.50 x 10(-6). 11. The kinetics of the enzyme-substrate compound closely agree with mathematical solutions of an extension of the Michaelis theory obtained for experimental values of concentrations and reaction velocity constants. 12. The adequacy of the criteria by which experiment and theory were correlated has been examined critically and the mathematical solutions have been found to be sensitive to variations in the experimental conditions. 13. The critical features of the enzyme-substrate kinetics are Pmax, and curve shape, rather than t1/2. t1/2 serves as a simple measure of dx/dt. 14. A second order combination of enzyme and substrate to form the enzyme-substrate compound, followed by a first order breakdown of the compound, describes the activity of peroxidase for a particular acceptor concentration. 15. The kinetic data indicate a bimolecular combination of acceptor and enzyme-substrate compound.

This model is the one described in the appendix of the article. It reproduces, amongst others, figure 12. The parameters and concentrations used are rescaled as stated in the article. K2 and K3 stand for k2 and k3, respectively, divided by k1.

This a model from the article:
Minimum criteria for DNA damage-induced phase advances in circadian rhythms.
Hong CI, Zámborszky J, Csikász-Nagy A. PLoS Comput Biol. 2009 May;5(5):e1000384. 19424508 ,
Abstract:
Robust oscillatory behaviors are common features of circadian and cell cycle rhythms. These cyclic processes, however, behave distinctively in terms of their periods and phases in response to external influences such as light, temperature, nutrients, etc. Nevertheless, several links have been found between these two oscillators. Cell division cycles gated by the circadian clock have been observed since the late 1950s. On the other hand, ionizing radiation (IR) treatments cause cells to undergo a DNA damage response, which leads to phase shifts (mostly advances) in circadian rhythms. Circadian gating of the cell cycle can be attributed to the cell cycle inhibitor kinase Wee1 (which is regulated by the heterodimeric circadian clock transcription factor, BMAL1/CLK), and possibly in conjunction with other cell cycle components that are known to be regulated by the circadian clock (i.e., c-Myc and cyclin D1). It has also been shown that DNA damage-induced activation of the cell cycle regulator, Chk2, leads to phosphorylation and destruction of a circadian clock component (i.e., PER1 in Mus or FRQ in Neurospora crassa). However, the molecular mechanism underlying how DNA damage causes predominantly phase advances in the circadian clock remains unknown. In order to address this question, we employ mathematical modeling to simulate different phase response curves (PRCs) from either dexamethasone (Dex) or IR treatment experiments. Dex is known to synchronize circadian rhythms in cell culture and may generate both phase advances and delays. We observe unique phase responses with minimum delays of the circadian clock upon DNA damage when two criteria are met: (1) existence of an autocatalytic positive feedback mechanism in addition to the time-delayed negative feedback loop in the clock system and (2) Chk2-dependent phosphorylation and degradation of PERs that are not bound to BMAL1/CLK.

The original xpp file of the model is available as a supplement of the article ( Text S1 ).

The model should reproduce the figure 1C of the article (successfully reproduced in MathSBML). If your software does not support the variable "time", you can replace the assignmentRule:
n = n0 * [ exp(-kbN*time) + kappa * (1 - exp(-kbN*time))]
by
n = n0 * kappa

Note: Model of the Calvin cycle with focus on the RuBisCO reaction by Sharkey et al. (2007, DOI:10.1111/j.1365-3040.2007.01710.x ).

The parameter values are partly taken from Farquhar et al. (1980, DOI:10.1007/BF00386231 ) and Medlyn et al. (2002, DOI:10.1046/j.1365-3040.2002.00891.x ). The initial metabolite values are chosen from the data set of Zhu et al. (2007, DOI:10.1104/pp.107.103713 ). A detailed description of all modifications is given in the model described by Arnold and Nikoloski (2011, PMID:22001849 .

This model is according to the paper Prediction of temporal gene expression metabolic optimization by re-distribution of enzyme activities. The model describe optimal enzyme profiles and meatbolite time courses for the linear metabolic pathway (n=2). Figure1 has been reproduced by roadRunner. The value for k1 and k2 have not explicitly given in the paper, but calculations were performed for equal catalytic efficiencies of the enzymes (ki=k). So curator gave k1=k2=1. Also enzyme concentrations are given in units of Etot; times are given in units of 1/(k*Etot) in the papaer, for simplicity , we use defalut units of the SBML to present the concentration and time.

The original model submitted by the authors was slightly altered and now comprises the models originally submitted as MODEL2426780967, MODEL2427021978, MODEL2427095802. It reproduces figures 2A,3A and 3B from the publication.

This model uses the glycolysis model from Pritchard and Kell (2002) with an additional parameter, WGD_E , to adjust for the differing enzyme conzentrations before the whole genome duplication (WGD) and parameters fV_xxx that adjust the Vmax of the different reactions (xxx eg. HXT or PYK).
Figure 3A from the article can be reproduced by changing the value of the parameters fV_xxx to 0.9 indiviually, with xxx signifying the different enzymes (HXT, HXK ...)
Figure 3B from the publication can be reproduced by setting the parameter WGD_E to 0.75 and individually setting the parameters fV_xxx to 1.333.
To reproduce figure 2A from the article change the parameter WGD_E in the range between 0.65 and 1.0.

This a model from the article:
A computational model for understanding stem cell, trophectoderm and endoderm lineage determination.
Chickarmane V, Peterson C PLoS ONE 2008;3(10):Page info: e3478 18941526 ,
Abstract:
BACKGROUND: Recent studies have associated the transcription factors, Oct4, Sox2 and Nanog as parts of a self-regulating network which is responsible for maintaining embryonic stem cell properties: self renewal and pluripotency. In addition, mutual antagonism between two of these and other master regulators have been shown to regulate lineage determination. In particular, an excess of Cdx2 over Oct4 determines the trophectoderm lineage whereas an excess of Gata-6 over Nanog determines differentiation into the endoderm lineage. Also, under/over-expression studies of the master regulator Oct4 have revealed that some self-renewal/pluripotency as well as differentiation genes are expressed in a biphasic manner with respect to the concentration of Oct4. METHODOLOGY/PRINCIPAL FINDINGS: We construct a dynamical model of a minimalistic network, extracted from ChIP-on-chip and microarray data as well as literature studies. The model is based upon differential equations and makes two plausible assumptions; activation of Gata-6 by Oct4 and repression of Nanog by an Oct4-Gata-6 heterodimer. With these assumptions, the results of simulations successfully describe the biphasic behavior as well as lineage commitment. The model also predicts that reprogramming the network from a differentiated state, in particular the endoderm state, into a stem cell state, is best achieved by over-expressing Nanog, rather than by suppression of differentiation genes such as Gata-6. CONCLUSIONS: The computational model provides a mechanistic understanding of how different lineages arise from the dynamics of the underlying regulatory network. It provides a framework to explore strategies of reprogramming a cell from a differentiated state to a stem cell state through directed perturbations. Such an approach is highly relevant to regenerative medicine since it allows for a rapid search over the host of possibilities for reprogramming to a stem cell state.

This version of the model is very close to the version described in the paper with one exception: the binding of aspartate to the various receptor complexes, as well as the formation of the different complexes are modeled using chemical kinetics (mass action law), rather than instant equilibrium. The qualitative behaviour of the model is unchanged. Note that in order to quantitatively replicate the figure 8b, and in particular to have a basal bias of 0.7, we have to change the rate constant of the aspartate-triggered dephosphorylation of CheY from 59000 to 70000. The peaks have then slightly different values.

This model is from the article:
A mathematical model of lipid-mediated thrombin generation
Bungay Sharene D., Gentry Patricia A., Gentry Rodney D. Mathematical Medicine and Biology Volume 20, Issue 1, 1 March 2003, Pages 105-29 12974500 ,
Abstract:
Thrombin is an enzyme that is generated in both vascular and non-vascular systems. In blood coagulation, a fundamental process in all species, thrombin induces the formation of a fibrin clot. A dynamical model of thrombin generation in the presence of lipid surfaces is presented. This model also includes the self-regulating thrombin feedback reactions, the thrombomodulin-protein C-protein S inhibitory system, tissue factor pathway inhibitor (TFPI), and the inhibitor, antithrombin (AT). The dynamics of this complex system were found to be highly lipid dependent, as would be expected from experimental studies. Simulations of this model indicate that a threshold lipid level is required to generate physiologically relevant amounts of thrombin. The dependence of the onset, the peak levels, and the duration of thrombin generation on lipid was saturable. The lipid concentration affects the way in which the inhibitors modulate thrombin production. A novel feature of this model is the inclusion of the dynamical protein C pathway, initiated by thrombin feedback. This inhibitory system exerts its effects on the lipid surface, where its substrates are formed. The maximum impact of TFPI occurs at intermediate vesicle concentrations. Inhibition by AT is only indirectly affected by the lipid since AT irreversibly binds only to solution phase proteins. In a system with normal plasma concentrations of the proteins involved in thrombin formation, the combination of these three inhibitors is sufficient both to effectively stop thrombin generation prior to the exhaustion of its precursor, prothrombin, and to inhibit all thrombin formed. This model can be used to predict thrombin generation under extreme lipid conditions that are difficult to implement experimentally and to examine thrombin generation in non-vascular systems.

This is the model described in the article:
A mathematical model of glutathione metabolism.
Michael C Reed, Rachel L Thomas, Jovana Pavisic, S. Jill James, Cornelia M Ulrich and H. Frederik Nijhout, Theor Biol Med Model 2008,5:8; PubmedID: 18442411 ; DOI: 10.1186/1742-4682-5-8 ;
Abstract:
BACKGROUND: Glutathione (GSH) plays an important role in anti-oxidant defense and detoxification reactions. It is primarily synthesized in the liver by the transsulfuration pathway and exported to provide precursors for in situ GSH synthesis by other tissues. Deficits in glutathione have been implicated in aging and a host of diseases including Alzheimer's disease, Parkinson's disease, cardiovascular disease, cancer, Down syndrome and autism.
APPROACH: We explore the properties of glutathione metabolism in the liver by experimenting with a mathematical model of one-carbon metabolism, the transsulfuration pathway, and glutathione synthesis, transport, and breakdown. The model is based on known properties of the enzymes and the regulation of those enzymes by oxidative stress. We explore the half-life of glutathione, the regulation of glutathione synthesis, and its sensitivity to fluctuations in amino acid input. We use the model to simulate the metabolic profiles previously observed in Down syndrome and autism and compare the model results to clinical data.
CONCLUSION: We show that the glutathione pools in hepatic cells and in the blood are quite insensitive to fluctuations in amino acid input and offer an explanation based on model predictions. In contrast, we show that hepatic glutathione pools are highly sensitive to the level of oxidative stress. The model shows that overexpression of genes on chromosome 21 and an increase in oxidative stress can explain the metabolic profile of Down syndrome. The model also correctly simulates the metabolic profile of autism when oxidative stress is substantially increased and the adenosine concentration is raised. Finally, we discuss how individual variation arises and its consequences for one-carbon and glutathione metabolism.

parameter	orig. article	this model
Vm_CBS	700000	420000
Vm_GNMT	245	260
K_sam_GNMT	32	63
Vr_MTD(mito)	600000	595000
V_CBS	kinetic law	rearranged
V_bmetc	913	913.4
Vm_GR	8925	892.5

This version of the model contains a feeding rhythm as used in figure 5 of the original article. Four parameters, breakfast , lunch dinner and fasting , describe the relative level of amino acids, described by the parameter aa_input or Aminoacid_input , in the blood. To remove the daily feeding rhythm, either set the parameters for meals and fasting to 1 (or for figure 3 to 0.333), or remove the assignment rule for the Aminoacid_input . For the steady state evaluations for figure 6, the mealtime parameters were set to one, which, while making Copasi complain about explicit time dependency, still gives valid results.

This version of the model differs slightly from the version described in the supplement, in which contains some typos. It was corrected using the version of JWS-online , created using the original matlab files, thankfully provided by the articles authors. Many thanks to Jacky Snoep for his help and support.

In the SBML version of the model the volumes of the mitochondrion, the cytoplasm and the cell were all set to one to obtain the same equations as described in the supplemental materials of the article. The total folate is equally split between the cytosol and the mitochondrion and divided by 3/4 for the cytosol and 1/4 for the mitochondrion, respectively. To obtain an SBML model in which the volumes of the compartments, cytosol and mito , are used, the model needs to be altered as follows:

for the initial distribution of folate the terms 3/4 and 1/4 have to be replaced by volumes of cytosol and mitochondria respectively
in the transport reactions between mitochondrion and cytosol the stoichiometry of the mitochondrial reactants has to be set from 3 to 1 and in the first part of the according rate laws the factor mito/3 should simply be replaced with mito .
the stoichiometries of src and dmg have to be changed to cell/mito for mitchondrial and cell/cytosol for cytosolic reactions involving these two species (for the relative volumes used in the article this would be 4 for mitochondrial reactions and 1.33333 for cytosolic ones).

While the concentrations stay the same after these alteration, the reaction fluxes change by a factor of cytosol and mito for cytosolic and mitchondrial reactions, respectively.

Originally created by libAntimony v1.3 (using libSBML 3.4.1)

Note: Notch is a transmembrane receptor that mediates local cell-cell co mmunication and coordinates a signaling cascade. It plays a key role in modulati ng cell fate decisions throughout the development of invertebrate and vertebrate species and the misregulation leads to a number of human diseases. Eg: 11112321 , 12366684 , 12651094 , 12676578 & 14973298 .

This model is from the article:
A comprehensive model for the humoral coagulation network in humans.
Wajima T, Isbister GK, Duffull SB. Clinical Pharmacology and therapeutics Volume 86, Issue 3, 10 June 2009, EPub 19516255 ,
Abstract:
Coagulation is an important process in hemostasis and comprises a complicated interaction of multiple enzymes and proteins. We have developed a mechanistic quantitative model of the coagulation network. The model accurately describes the time courses of coagulation factors following in vivo activation as well as in vitro blood coagulation tests of prothrombin time (PT, often reported as international normalized ratio (INR)) and activated partial thromboplastin time (aPTT). The model predicts the concentration-time and time-effect profiles of warfarin, heparins, and vitamin K in humans. The model can be applied to predict the time courses of coagulation kinetics in clinical situations (e.g., hemophilia) and for biomarker identification during drug development. The model developed in this study is the first quantitative description of the comprehensive coagulation network.

This a model from the article:
Meal simulation model of the glucose-insulin system.
Dalla Man C, Rizza RA, Cobelli C. IEEE Trans Biomed Eng. 2007 Oct;54(10):1740-9. 17926672 ,
Abstract:
A simulation model of the glucose-insulin system in the postprandial state can be useful in several circumstances, including testing of glucose sensors, insulin infusion algorithms and decision support systems for diabetes. Here, we present a new simulation model in normal humans that describes the physiological events that occur after a meal, by employing the quantitative knowledge that has become available in recent years. Model parameters were set to fit the mean data of a large normal subject database that underwent a triple tracer meal protocol which provided quasi-model-independent estimates of major glucose and insulin fluxes, e.g., meal rate of appearance, endogenous glucose production, utilization of glucose, insulin secretion. By decomposing the system into subsystems, we have developed parametric models of each subsystem by using a forcing function strategy. Model results are shown in describing both a single meal and normal daily life (breakfast, lunch, dinner) in normal. The same strategy is also applied on a smaller database for extending the model to type 2 diabetes

Biophysical Chemistry 134 (2008) 93-100

Mad2 binding is not sufficient for complete Cdc20 sequestering in mitotic transition control (an in silico study)

Bashar Ibrahim, Peter Dittrich, Stephan Diekmann, Eberhard Schmitt

This model is from the article:
Building a Kinetic Model of Trehalose Biosynthesis in Saccharomyces cerevisiae.
Smallbone K, Malys N, Messiha HL, Wishart JA, Simeonidis E. Methods Enzymol. 2011;500:355-70. 21943906 ,
Abstract:
In this chapter, we describe the steps needed to create a kinetic model of a metabolic pathway based on kinetic data from experimental measurements and literature review. Our methodology is presented by utilizing the example of trehalose metabolism in yeast. The biology of the trehalose cycle is briefly reviewed and discussed.

This SBML model is made available under the Creative Commons Attribution-Share Alike 3.0 Unported Licence (see www.creativecommons.org ).

This is the scaled model described in the article:
Birhythmicity, chaos, and other patterns of temporal self-organization in a multiply regulated biochemical system
Olivier Decroly, Albert Goldbeter, Proc Natl Acad Sci USA 1982 79:6917-6921; PMID: 6960354 ;

Abstract:
We analyze on a model biochemical system the effect of a coupling between two instability-generating mechanisms. The system considered is that of two allosteric enzymes coupled in series and activated by their respective products. In addition to simple periodic oscillations, the system can exhibit a variety of new modes of dynamic behavior; coexistence between two stable periodic regimes (birhythmicity), random oscillations (chaos), and coexistence of a stable periodic regime with a stable steady state (hard excitation) or with chaos. The relationship between these patterns of temporal self-organization is analyzed as a function of the control parameters of the model. Chaos and birhythmicity appear to be rare events in comparison with simple periodic behavior. We discuss the relevance of these results with respect to the regularity of most biological rhythms.

The parameters q1 = 50 and q2 = 0.02 are explicitely included as the stoichiometric coefficients of beta and gamma in the reactions r2 and r3, respectively. Parameter values and initial conditions [ks=1.99/sec, alpha(0)=29.19988, beta(0)=188.8, gamma(0)=0.3367] are for the chaotic regime presented in the upper-curve of Figure 3b.

This a model from the article:
Mitochondrial energetic metabolism: a simplified model of TCA cycle with ATP production.
Nazaret C, Heiske M, Thurley K, Mazat JP J. Theor. Biol. 2009 Jun;258(3):455-64 19007794 ,
Abstract:
Mitochondria play a central role in cellular energetic metabolism. The essential parts of this metabolism are the tricarboxylic acid (TCA) cycle, the respiratory chain and the adenosine triphosphate (ATP) synthesis machinery. Here a simplified model of these three metabolic components with a limited set of differential equations is presented. The existence of a steady state is demonstrated and results of numerical simulations are presented. The relevance of a simple model to represent actual in vivo behavior is discussed.

This is a model of one presynaptic and one postsynaptic cell, as described in the article:
Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model.
Wang XJ, Buzsáki G. J Neurosci. 1996 Oct 15;16(20):6402-13. PMID: 8815919 ;

Abstract:
Fast neuronal oscillations (gamma, 20-80 Hz) have been observed in the neocortex and hippocampus during behavioral arousal. Using computer simulations, we investigated the hypothesis that such rhythmic activity can emerge in a random network of interconnected GABAergic fast-spiking interneurons. Specific conditions for the population synchronization, on properties of single cells and the circuit, were identified. These include the following: (1) that the amplitude of spike afterhyperpolarization be above the GABAA synaptic reversal potential; (2) that the ratio between the synaptic decay time constant and the oscillation period be sufficiently large; (3) that the effects of heterogeneities be modest because of a steep frequency-current relationship of fast-spiking neurons. Furthermore, using a population coherence measure, based on coincident firings of neural pairs, it is demonstrated that large-scale network synchronization requires a critical (minimal) average number of synaptic contacts per cell, which is not sensitive to the network size. By changing the GABAA synaptic maximal conductance, synaptic decay time constant, or the mean external excitatory drive to the network, the neuronal firing frequencies were gradually and monotonically varied. By contrast, the network synchronization was found to be high only within a frequency band coinciding with the gamma (20-80 Hz) range. We conclude that the GABAA synaptic transmission provides a suitable mechanism for synchronized gamma oscillations in a sparsely connected network of fast-spiking interneurons. In turn, the interneuronal network can presumably maintain subthreshold oscillations in principal cell populations and serve to synchronize discharges of spatially distributed neurons.

The presynaptic and postsynaptic cell have identical parameters and the variables in each cell are identified by using _pre or _post as a postfix to their names. The presynaptic cell influences the postsynaptic one via the synapse (variables and parameters: I_syn, E_syn, g_syn, F, theta_syn, alpha, beta). The applied current to the presynaptic cell, I_app_pre, is set to 2 microA/cm ² for 10 ms as in figure 1C of the article. The dependence of the postsynaptic cell on directly applied current can be investigated in isolation by setting I_app_pre to 0 and altering I_app_post.

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

The model corresponds to the knock out model of beta-/-, epsilon -/- and reproduces the upper panel in Fig 2C. In order to reproduce the other knock out models the transcription rate of the species that are not present must be set to zero and the rate of the one that is present must be set as seven times its corresponding value for the wild type model. This is done so as to compensate for the loss of other isoforms. Model was successfully tested on MathSBML.

The model corresponds to the schemas 1 and 2 of Markevich et al 2004, as described in the figure 1 and the supplementary table S1. Phosphorylations and dephosphorylations follow distributive ordered kinetics. The phosphorylations are modeled with three elementary reactions:
E+S<=>ES->E+P
The dephosphorylations are modeled with five elementary reactions:
E+S<=>ES->EP<=>E+P

This model describes the activation of immediate early genes such as cFos after EGF or heregulin (HRG) stimulation of the MAPK pathway. Phosphorylated cFos is a key transcription factor triggering downstream cascades of cell fate determination. The model can explain how the switch-like response of p-cFos emerges from the spatiotemporal dynamics. The model comprises lumped reaction kinetics of the signal transduction pathway, the transcriptional and the posttranslational feedback and feedforward loops. The parameter set implemented here corresponds to that used for generating Figs. 4 B,C,D (red curves for 10nM HRG) of the below article in Cell (2010). Moreover, we found that the same model described well the dynamics in different cell types (MCF-7 and PC-12), of different ligands (EGF and HRG) and at different doses (0.1nM, 1nM, 10nM) for a unique set of parameter values (as implemented here and reported in Table SD4_1 of the article) except for four parameters characterising the input, cytoplasmic ppERK. These four parameters K1, K2, tau1 and tau2 are used in the two equations involving species x1 and x2. These two equations define a phenomenological input module to describe the ligand-, dose- and cell type-dependent dynamics of ppERKc which are not modelled in mechanistic detail here. The four parameter values can be adjusted to model a specific ligand, dose and cell type. 8 parameter sets for different experiments are given in Table SD4_2 of the article. This SBML file, however, carries just one such parameter set. We have chosen that of MCF-7 cells stimulated by 10nM of HRG. To reproduce all simulations from the article, please replace the parameter values for K1, K2, tau1, tau2 as needed.

Ligand-specific c-Fos expression emerges from the spatiotemporal control of ErbB network dynamics.
Takashi Nakakuki(1), Marc R. Birtwistle(2,3,4), Yuko Saeki(1,5), Noriko Yumoto(1,5), Kaori Ide(1), Takeshi Nagashima(1,5), Lutz Brusch(6), Babatunde A. Ogunnaike(3), Mariko Hatakeyama(1,5), and Boris N. Kholodenko(2,4); Cell In Press, online 20 May 2010, doi: 10.1016/j.cell.2010.03.054
(1) RIKEN Advanced Science Institute, Computational Systems Biology Research Group, Advanced Computational Sciences Department, 1-7-22 Tsurumi-ku, Yokohama, Kanagawa, 230-0045, Japan
(2) Systems Biology Ireland, University College Dublin, Belfield, Dublin 4, Ireland
(3) University of Delaware, Department of Chemical Engineering, 150 Academy St., Newark, DE 19716, USA
(4) Thomas Jefferson University, Department of Pathology, Anatomy, and Cell Biology, 1020 Locust Street, Philadelphia, PA 19107, USA
(5) RIKEN Research Center for Allergy and Immunology, Laboratory for Cellular Systems Modeling, 1-7-22 Tsurumi-ku, Yokohama, 230-0045, Japan
(6) Dresden University of Technology, Center for Information Services and High Performance Computing, 01062 Dresden, Germany

This is the basic model described in eq. 1 of the article:
A model of phosphofructokinase and glycolytic oscillations in the pancreatic beta-cell.
Westermark PO and Lansner A. Biophys J. 2003 Jul;85(1):126-39. PMID: 12829470 , doi: 10.1016/S0006-3495(03)74460-9
Abstract:
We have constructed a model of the upper part of the glycolysis in the pancreatic beta-cell. The model comprises the enzymatic reactions from glucokinase to glyceraldehyde-3-phosphate dehydrogenase (GAPD). Our results show, for a substantial part of the parameter space, an oscillatory behavior of the glycolysis for a large range of glucose concentrations. We show how the occurrence of oscillations depends on glucokinase, aldolase and/or GAPD activities, and how the oscillation period depends on the phosphofructokinase activity. We propose that the ratio of glucokinase and aldolase and/or GAPD activities are adequate as characteristics of the glucose responsiveness, rather than only the glucokinase activity. We also propose that the rapid equilibrium between different oligomeric forms of phosphofructokinase may reduce the oscillation period sensitivity to phosphofructokinase activity. Methodologically, we show that a satisfying description of phosphofructokinase kinetics can be achieved using the irreversible Hill equation with allosteric modifiers. We emphasize the use of parameter ranges rather than fixed values, and the use of operationally well-defined parameters in order for this methodology to be feasible. The theoretical results presented in this study apply to the study of insulin secretion mechanisms, since glycolytic oscillations have been proposed as a cause of oscillations in the ATP/ADP ratio which is linked to insulin secretion.

This a model from the article:
Modeling hypertrophic IP3 transients in the cardiac myocyte.
Cooling M, Hunter P, Crampin EJ. Biophys J 2007 Nov 15;93(10):3421-33 17693463 ,
Abstract:
Cardiac hypertrophy is a known risk factor for heart disease, and at the cellular level is caused by a complex interaction of signal transduction pathways. The IP3-calcineurin pathway plays an important role in stimulating the transcription factor NFAT which binds to DNA cooperatively with other hypertrophic transcription factors. Using available kinetic data, we construct a mathematical model of the IP3 signal production system after stimulation by a hypertrophic alpha-adrenergic agonist (endothelin-1) in the mouse atrial cardiac myocyte. We use a global sensitivity analysis to identify key controlling parameters with respect to the resultant IP3 transient, including the phosphorylation of cell-membrane receptors, the ligand strength and binding kinetics to precoupled (with G(alpha)GDP) receptor, and the kinetics associated with precoupling the receptors. We show that the kinetics associated with the receptor system contribute to the behavior of the system to a great extent, with precoupled receptors driving the response to extracellular ligand. Finally, by reparameterizing for a second hypertrophic alpha-adrenergic agonist, angiotensin-II, we show that differences in key receptor kinetic and membrane density parameters are sufficient to explain different observed IP3 transients in essentially the same pathway.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Cooling M, Hunter P, Crampin EJ. (2007) - version02
The original CellML model was created by:
Cooling, Mike,
m.cooling@aukland.ac.nz
The University of Auckland
The Bioengineering Institute

This a model from the article:
Calcium spiking.
Meyer T, Stryer L Annu Rev Biophys Biophys Chem 1991:20:153-74 1867714 ,
Abstract:
No Abstract Available

The IP3-Ca2+ Crosscoupling Model (ICC) is reviewed by Meyer and Stryer in 1991, originally from Meyer and Stryer, 1988. PMID - 2455890 Parameters refer to figures 5 and 6 of the article which were reproduced by using Copasi 4.5 (Build 30). Species CaI and IP3 are buffered to 1% and 50% percent, respectively.

The model reproduces the same amplitude antiphase calcium oscillations of coupled cells depicted in Figure 5B of the publication. This model was successfully tested on Jarnac and MathSBML. The values of "h1" and "h2" are not given in the publication, but the antiphase oscillations are reproduced over a narrow range of values of h1, h2,c1,c2,D and p. The values of D and p are given, while the other values were plugged in, in order to simulate the time profiles shown in the Figure. The time t=0 in the figure may have been fixed after the system was allowed to settle, and hence does not correspond to the t=0 of the simulation.

Schaber2012 - Hog pathway in yeast

The high osmolarity glycerol (HOG) pathway in the yeast Saccharomyces cerevisiae is one of the best-studied mitogen-activated protein kinase (MAPK) pathways and serves as a prototype signalling system for eukaryotes. This pathway is necessary and sufficient to adapt to high external osmolarity. A key component of this pathway is the stress-activated protein kinase (SAPK) Hog1, which is rapidly phosphorylated by the SAPK kinase Pbs2 upon hyper-osmotic shock, and which is the terminal kinase of two parallel signalling pathways, subsequently called the Sho1 branch and the Sln1 branch, respectively. Ensemble modelling (192 models) is used to study the yeast HOG pathway, a prototype for eukaryotic mitogen-activated kinase signalling systems. The best fit model (Model Nr.22: described here) provides new insights into the function of this system, some of which are then experimentally validated.

This model is described in the article:

Modelling reveals novel roles of two parallel signalling pathways and homeostatic feedbacks in yeast.

Schaber J, Baltanas R, Bush A, Klipp E, Colman-Lerner A.

Mol Syst Biol. 2012 Nov 13;8:622.

Abstract:

The high osmolarity glycerol (HOG) pathway in yeast serves as a prototype signalling system for eukaryotes. We used an unprecedented amount of data to parameterise 192 models capturing different hypotheses about molecular mechanisms underlying osmo-adaptation and selected a best approximating model. This model implied novel mechanisms regulating osmo-adaptation in yeast. The model suggested that (i) the main mechanism for osmo-adaptation is a fast and transient non-transcriptional Hog1-mediated activation of glycerol production, (ii) the transcriptional response serves to maintain an increased steady-state glycerol production with low steady-state Hog1 activity, and (iii) fast negative feedbacks of activated Hog1 on upstream signalling branches serves to stabilise adaptation response. The best approximating model also indicated that homoeostatic adaptive systems with two parallel redundant signalling branches show a more robust and faster response than single-branch systems. We corroborated this notion to a large extent by dedicated measurements of volume recovery in single cells. Our study also demonstrates that systematically testing a model ensemble against data has the potential to achieve a better and unbiased understanding of molecular mechanisms.

This model is hosted on BioModels Database and identified by: BIOMD0000000429 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This is the model described in the article:
Vaccination and the dynamics of immune evasion.
Restif O, Grenfell BT. J R Soc Interface. 2007 Feb 22;4(12):143-53. PMID: 17210532 , doi: 10.1098/rsif.2006.0167 ;
Abstract:
Vaccines exert strong selective pressures on pathogens, favouring the spread of antigenic variants. We propose a simple mathematical model to investigate the dynamics of a novel pathogenic strain that emerges in a population where a previous strain is maintained at low endemic level by a vaccine. We compare three methods to assess the ability of the novel strain to invade and persist: algebraic rate of invasion; deterministic dynamics; and stochastic dynamics. These three techniques provide complementary predictions on the fate of the system. In particular, we emphasize the importance of stochastic simulations, which account for the possibility of extinctions of either strain. More specifically, our model suggests that the probability of persistence of an invasive strain (i) can be minimized for intermediate levels of vaccine cross-protection (i.e. immune protection against the novel strain) and (ii) is lower if cross-immunity acts through a reduced infectious period rather than through reduced susceptibility.

This version of the model can be used for both the stochastic and the deterministic simulations described in the article. For deterministic interpretations with infinite population sizes, set the population size N = 1. The model does reproduces the deterministic time course. The initial values are set to the steady state values for a latent infection with strain 1 with an invading infection of strain 2 (I2=1e-06), 100 percent vaccination with a susceptibility reduction τ=0.7 at birth (p=1), and all other parameters as in figure 3 of the publication.

To be compatible with older software tools, the english letter names instead of the greek symbols were used for parameter names:

parameter symbol name

transmission rate β beta

recovery rate γ gamma

birth/death rate μ mu

rate of loss of natural immunity σ sigma

rate of loss of vaccine immunity σ _v sigmaV

reduction of susceptibility by primary infection θ theta

reduction of infection period by primary infection ν nu

reduction of susceptibility by vaccination τ tau

reduction of infection period by vaccination η eta

parameter	symbol	name
transmission rate	β	beta
recovery rate	γ	gamma
birth/death rate	μ	mu
rate of loss of natural immunity	σ	sigma
rate of loss of vaccine immunity	σ _v	sigmaV
reduction of susceptibility by primary infection	θ	theta
reduction of infection period by primary infection	ν	nu
reduction of susceptibility by vaccination	τ	tau
reduction of infection period by vaccination	η	eta

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

This is the model described in the article:
Interaction of glycolysis and mitochondrial respiration in metabolic oscillations of pancreatic islets.
Bertram R, Satin LS, Pedersen MG, Luciani DS, Sherman A. Biophys J. 2007 Mar 1;92(5):1544-55. Pubmed ID: 17172305 , doi: 10.1529/biophysj.106.097154 .
Abstract:
Insulin secretion from pancreatic beta-cells is oscillatory, with a typical period of 2-7 min, reflecting oscillations in membrane potential and the cytosolic Ca(2+) concentration. Our central hypothesis is that the slow 2-7 min oscillations are due to glycolytic oscillations, whereas faster oscillations that are superimposed are due to Ca(2+) feedback onto metabolism or ion channels. We extend a previous mathematical model based on this hypothesis to include a more detailed description of mitochondrial metabolism. We demonstrate that this model can account for typical oscillatory patterns of membrane potential and Ca(2+) concentration in islets. It also accounts for temporal data on oxygen consumption in islets. A recent challenge to the notion that glycolytic oscillations drive slow Ca(2+) oscillations in islets are data showing that oscillations in Ca(2+), mitochondrial oxygen consumption, and NAD(P)H levels are all terminated by membrane hyperpolarization. We demonstrate that these data are in fact compatible with a model in which glycolytic oscillations are the key player in rhythmic islet activity. Finally, we use the model to address the recent finding that the activity of islets from some mice is uniformly fast, whereas that from islets of other mice is slow. We propose a mechanism for this dichotomy.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Bertram, Satin, Pedersen, Luciani, Sherman, 2007 version 02
The original CellML model was created and curated by:
Catherine May Lloyd
c.lloyd(at)auckland.ac.nz
The University of Auckland, Bioengineering Institute

This is an SBML implementation the model of mutual activation (figure 1e) described in the article:
Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell.
Tyson JJ, Chen KC, Novak B. Curr Opin Cell Biol. 2003 Apr;15(2):221-31. PubmedID: 12648679 ; DOI: 10.1016/S0955-0674(03)00017-6 ;

The article has a typo: the expression k2*X*R most likely should be k2*R

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

This is the model described in: Feedback between p21 and reactive oxygen production is necessary for cell senescence.
Passos JF, Nelson G, Wang C, Richter T, Simillion C, Proctor CJ, Miwa S, Olijslagers S, Hallinan J, Wipat A, Saretzki G, Rudolph KL, Kirkwood TB, von Zglinicki T. ; Mol Sys Biol 2010;6:347. Epub 2010 Feb 16. PMID: 20160708 doi: 10.1038/msb.2010.5 ;
Abstract:
Cellular senescence--the permanent arrest of cycling in normally proliferating cells such as fibroblasts--contributes both to age-related loss of mammalian tissue homeostasis and acts as a tumour suppressor mechanism. The pathways leading to establishment of senescence are proving to be more complex than was previously envisaged. Combining in-silico interactome analysis and functional target gene inhibition, stochastic modelling and live cell microscopy, we show here that there exists a dynamic feedback loop that is triggered by a DNA damage response (DDR) and, which after a delay of several days, locks the cell into an actively maintained state of 'deep' cellular senescence. The essential feature of the loop is that long-term activation of the checkpoint gene CDKN1A (p21) induces mitochondrial dysfunction and production of reactive oxygen species (ROS) through serial signalling through GADD45-MAPK14(p38MAPK)-GRB2-TGFBR2-TGFbeta. These ROS in turn replenish short-lived DNA damage foci and maintain an ongoing DDR. We show that this loop is both necessary and sufficient for the stability of growth arrest during the establishment of the senescent phenotype.

This a model from the article:
Sequential polarization and imprinting of type 1 T helper lymphocytes by interferon-gamma and interleukin-12.
Schulz EG, Mariani L, Radbruch A, Höfer T. Immunity. 2009;30(5):666-8. 19409816 ,
Abstract:
Differentiation of naive T lymphocytes into type I T helper (Th1) cells requires interferon-gamma and interleukin-12. It is puzzling that interferon-gamma induces the Th1 transcription factor T-bet, whereas interleukin-12 mediates Th1 cell lineage differentiation. We use mathematical modeling to analyze the expression kinetics of T-bet, interferon-gamma, and the IL-12 receptor beta2 chain (IL-12Rbeta2) during Th1 cell differentiation, in the presence or absence of interleukin-12 or interferon-gamma signaling. We show that interferon-gamma induced initial T-bet expression, whereas IL-12Rbeta2 was repressed by T cell receptor (TCR) signaling. The termination of TCR signaling permitted upregulation of IL-12Rbeta2 by T-bet and interleukin-12 signaling that maintained T-bet expression. This late expression of T-bet, accompanied by the upregulation of the transcription factors Runx3 and Hlx, was required to imprint the Th cell for interferon-gamma re-expression. Thus initial polarization and subsequent imprinting of Th1 cells are mediated by interlinked, sequentially acting positive feedback loops of TCR-interferon-gamma-Stat1-T-bet and interleukin-12-Stat4-T-bet signaling.

The original model was created by:
Edda G. Schulz
schulz@drfz.de
Theoretical Biophysics, Institute of Biology, Humboldt Universität, Invalidenstrasse 42, 10115 Berlin, Germany.

This a model from the article:
Data assimilation constrains new connections and components in a complex, eukaryotic circadian clock model.
Pokhilko A, Hodge SK, Stratford K, Knox K, Edwards KD, Thomson AW, Mizuno T, Millar AJ. Mol Syst Biol. 2010 Sep 21;6:416. 20865009 ,
Abstract:
Circadian clocks generate 24-h rhythms that are entrained by the day/night cycle. Clock circuits include several light inputs and interlocked feedback loops, with complex dynamics. Multiple biological components can contribute to each part of the circuit in higher organisms. Mechanistic models with morning, evening and central feedback loops have provided a heuristic framework for the clock in plants, but were based on transcriptional control. Here, we model observed, post-transcriptional and post-translational regulation and constrain many parameter values based on experimental data. The model's feedback circuit is revised and now includes PSEUDO-RESPONSE REGULATOR 7 (PRR7) and ZEITLUPE. The revised model matches data in varying environments and mutants, and gains robustness to parameter variation. Our results suggest that the activation of important morning-expressed genes follows their release from a night inhibitor (NI). Experiments inspired by the new model support the predicted NI function and show that the PRR5 gene contributes to the NI. The multiple PRR genes of Arabidopsis uncouple events in the late night from light-driven responses in the day, increasing the flexibility of rhythmic regulation.

This a model from the article:
The multifarious short-term regulation of ammonium assimilation of Escherichia coli: dissection using an in silico replica.
Bruggeman FJ, Boogerd FC, Westerhoff HV. FEBS J. 2005 Apr;272(8):1965-85. 15819889 ,
Abstract:
Ammonium assimilation in Escherichia coli is regulated through multiple mechanisms (metabolic, signal transduction leading to covalent modification, transcription, and translation), which (in-)directly affect the activities of its two ammonium-assimilating enzymes, i.e. glutamine synthetase (GS) and glutamate dehydrogenase (GDH). Much is known about the kinetic properties of the components of the regulatory network that these enzymes are part of, but the ways in which, and the extents to which the network leads to subtle and quasi-intelligent regulation are unappreciated. To determine whether our present knowledge of the interactions between and the kinetic properties of the components of this network is complete - to the extent that when integrated in a kinetic model it suffices to calculate observed physiological behaviour - we now construct a kinetic model of this network, based on all of the kinetic data on the components that is available in the literature. We use this model to analyse regulation of ammonium assimilation at various carbon statuses for cells that have adapted to low and high ammonium concentrations. We show how a sudden increase in ammonium availability brings about a rapid redirection of the ammonium assimilation flux from GS/glutamate synthase (GOGAT) to GDH. The extent of redistribution depends on the nitrogen and carbon status of the cell. We develop a method to quantify the relative importance of the various regulators in the network. We find the importance is shared among regulators. We confirm that the adenylylation state of GS is the major regulator but that a total of 40% of the regulation is mediated by ADP (22%), glutamate (10%), glutamine (7%) and ATP (1%). The total steady-state ammonium assimilation flux is remarkably robust against changes in the ammonium concentration, but the fluxes through GS and GDH are completely nonrobust. Gene expression of GOGAT above a threshold value makes expression of GS under ammonium-limited conditions, and of GDH under glucose-limited conditions, sufficient for ammonium assimilation.

This version of the model originates from JWS online . The original model can be retrieved here .

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2009 The BioModels Team.
To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Akt pathway model with EGFR inhibitor

made by Kazuhiro A. Fujita.

This is the Akt pathway model with an EGFR inhibitor described in:
Decoupling of receptor and downstream signals in the Akt pathway by its low-pass filter characteristics.
Fujita KA, Toyoshima Y, Uda S, Ozaki Y, Kubota H, and Kuroda S. Sci Signal. 2010 Jul 27;3(132):ra56. PMID: 20664065 ; DOI: 10.1126/scisignal.2000810
Abstract:
In cellular signal transduction, the information in an external stimulus is encoded in temporal patterns in the activities of signaling molecules; for example, pulses of a stimulus may produce an increasing response or may produce pulsatile responses in the signaling molecules. Here, we show how the Akt pathway, which is involved in cell growth, specifically transmits temporal information contained in upstream signals to downstream effectors. We modeled the epidermal growth factor (EGF)–dependent Akt pathway in PC12 cells on the basis of experimental results. We obtained counterintuitive results indicating that the sizes of the peak amplitudes of receptor and downstream effector phosphorylation were decoupled; weak, sustained EGF receptor (EGFR) phosphorylation, rather than strong, transient phosphorylation, strongly induced phosphorylation of the ribosomal protein S6, a molecule downstream of Akt. Using frequency response analysis, we found that a three-component Akt pathway exhibited the property of a low-pass filter and that this property could explain decoupling of the peak amplitudes of receptor phosphorylation and that of downstream effectors. Furthermore, we found that lapatinib, an EGFR inhibitor used as an anticancer drug, converted strong, transient Akt phosphorylation into weak, sustained Akt phosphorylation, and, because of the low-pass filter characteristics of the Akt pathway, this led to stronger S6 phosphorylation than occurred in the absence of the inhibitor. Thus, an EGFR inhibitor can potentially act as a downstream activator of some effectors.

The different versions of input, step, pulse and ramp, can be simulated using the parameters EGF_conc_pulse , EGF_conc_step and EGF_conc_ramp . Depending on which one is set unequal to 0, either a continous pulse with value EGF_conc_pulse , a 60 second step with EGF_conc_step or a signal increasing from 0 to EGF_conc_pulse over a time periode of 3600 seconds are used as input. In case more than one parameter are set to values greater than 0 these input profiles are added to each other. The pulse time and the time over which the ramp input increases can be set by pulse_time and ramp_time .

This is the S systems model described in the article:
Biochemical and genomic regulation of the trehalose cycle in yeast: review of observations and canonical model analysis
Eberhard O Voit, J Theor Biol 2003 223:55-78 PubmedID: 12782117 ; DOI: 10.1016/S0022-5193(03)00072-9
Abstract:
The physiological hallmark of heat-shock response in yeast is a rapid, enormous increase in the concentration of trehalose. Normally found in growing yeast cells and other organisms only as traces, trehalose becomes a crucial protector of proteins and membranes against a variety of stresses, including heat, cold, starvation, desiccation, osmotic or oxidative stress, and exposure to toxicants. Trehalose is produced from glucose 6-phosphate and uridine diphosphate glucose in a two-step process, and recycled to glucose by trehalases. Even though the trehalose cycle consists of only a few metabolites and enzymatic steps, its regulatory structure and operation are surprisingly complex. The article begins with a review of experimental observations on the regulation of the trehalose cycle in yeast and proposes a canonical model for its analysis. The first part of this analysis demonstrates the benefits of the various regulatory features by means of controlled comparisons with models of otherwise equivalent pathways lacking these features. The second part elucidates the significance of the expression pattern of the trehalose cycle genes in response to heat shock. Interestingly, the genes contributing to trehalose formation are up-regulated to very different degrees, and even the trehalose degrading trehalases show drastically increased activity during heat-shock response. Again using the method of controlled comparisons, the model provides rationale for the observed pattern of gene expression and reveals benefits of the counterintuitive trehalase up-regulation.

To induce a heat shock, set the parameter heat_shock from 0 to 1. This changess the parameter values of X8 to X19 from 1 to the values given in table 3 of th eoriginal publication.
As this is an S-systems model, it does not contain any reactions encoded in SBML.

This is the model of the RTC3 counter described in the article:
Synthetic gene networks that count.
Friedland AE, Lu TK, Wang X, Shi D, Church G, Collins JJ. Science. 2009 May 29;324(5931):1199-202. PMID: 19478183 , DOI: 10.1126/science.1172005

Abstract:
Synthetic gene networks can be constructed to emulate digital circuits and devices, giving one the ability to program and design cells with some of the principles of modern computing, such as counting. A cellular counter would enable complex synthetic programming and a variety of biotechnology applications. Here, we report two complementary synthetic genetic counters in Escherichia coli that can count up to three induction events: the first, a riboregulated transcriptional cascade, and the second, a recombinase-based cascade of memory units. These modular devices permit counting of varied user-defined inputs over a range of frequencies and can be expanded to count higher numbers.

The 3 arabinose pulses are implemented using events, one for the start of pulses and one for the end. The variable pulse_flag changes arabinose consumption to fit behaviour during pulses and in between. To simulate two pulses only, set the pulse length of the third pulse to a negative value (though with an absolute value smaller than the pulse intervall length).

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

This a model from the article:
Pharmacodynamic Model for the Time Course of Tumor Shrinkage by Gemcitabine + Carboplatin in Non–Small Cell Lung Cancer Patients
Lai-San Tham1, Lingzhi Wang1, Ross A. Soo1, Soo-Chin Lee1, How-Sung Lee2, Wei-Peng Yong1, Boon-Cher Goh1 and Nicholas H.G. Holford3 Clinical Cancer Research July 1, 2008 14, 4213 18594002 ,
Abstract:
PURPOSE: This tumor response pharmacodynamic model aims to describe primary lesion shrinkage in non-small cell lung cancer over time and determine if concentration-based exposure metrics for gemcitabine or that of its metabolites, 2',2'-difluorodeoxyuridine or gemcitabine triphosphate, are better than gemcitabine dose for prediction of individual response. EXPERIMENTAL DESIGN: Gemcitabine was given thrice weekly on days 1 and 8 in combination with carboplatin, which was given only on day 1 of every cycle. Gemcitabine amount in the div and area under the concentration-time curves of plasma gemcitabine, 2',2'-difluorodeoxyuridine, and intracellular gemcitabine triphosphate in white cells were compared to determine which best describes tumor shrinkage over time. Tumor growth kinetics were described using a Gompertz-like model. RESULTS: The apparent half-life for the effect of gemcitabine was 7.67 weeks. The tumor turnover time constant was 21.8 week.cm. Baseline tumor size and gemcitabine amount in the div to attain 50% of tumor shrinkage were estimated to be 6.66 cm and 10,600 mg. There was no evidence of relapse during treatment. CONCLUSIONS: Concentration-based exposure metrics for gemcitabine and its metabolites were no better than gemcitabine amount in predicting tumor shrinkage in primary lung cancer lesions. Gemcitabine dose-based models did marginally better than treatment-based models that ignored doses of drug administered to patients. Modeling tumor shrinkage in primary lesions can be used to quantify individual sensitivity and response to antitumor effects of anticancer drugs.

This is system 2, the model with Michelis Menten type antigen uptake by pAPCs, described in the article:
Self-tolerance and Autoimmunity in a Regulatory T Cell Model.
Alexander HK, Wahl LM. Bull Math Biol. 2010 Mar 2. PMID: 20195912 , doi: 10.1007/s11538-010-9519-2 ;
Abstract:
The class of immunosuppressive lymphocytes known as regulatory T cells (Tregs) has been identified as a key component in preventing autoimmune diseases. Although Tregs have been incorporated previously in mathematical models of autoimmunity, we take a novel approach which emphasizes the importance of professional antigen presenting cells (pAPCs). We examine three possible mechanisms of Treg action (each in isolation) through ordinary differential equation (ODE) models. The immune response against a particular autoantigen is suppressed both by Tregs specific for that antigen and by Tregs of arbitrary specificities, through their action on either maturing or already mature pAPCs or on autoreactive effector T cells. In this deterministic approach, we find that qualitative long-term behaviour is predicted by the basic reproductive ratio R (0) for each system. When R (0) < 1, only the trivial equilibrium exists and is stable; when R (0)>1, this equilibrium loses its stability and a stable non-trivial equilibrium appears. We interpret the absence of self-damaging populations at the trivial equilibrium to imply a state of self-tolerance, and their presence at the non-trivial equilibrium to imply a state of chronic autoimmunity. Irrespective of mechanism, our model predicts that Tregs specific for the autoantigen in question play no role in the system's qualitative long-term behaviour, but have quantitative effects that could potentially reduce an autoimmune response to sub-clinical levels. Our results also suggest an important role for Tregs of arbitrary specificities in modulating the qualitative outcome. A stochastic treatment of the same model demonstrates that the probability of developing a chronic autoimmune response increases with the initial exposure to self antigen or autoreactive effector T cells. The three different mechanisms we consider, while leading to a number of similar predictions, also exhibit key differences in both transient dynamics (ODE approach) and the probability of chronic autoimmunity (stochastic approach).

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

This sbml file describes the RECI model from:
"Mathematical modeling identifies Smad nucleocytoplasmic shuttling as a dynamic signal-interpreting system" by Bernhard Schmierer, Alexander L. Tournier, Paul A. Bates and Caroline S. Hill, Proc Natl Acad Sci U S A. 2008 May 6;105(18):6608-13.
All parameter and species names are as in Figure S3 of the original publication. The original model was done in copasi.
SB-431542 addition to a concentration of 10000 nM is set at 2700 sec. The initial concentration of SB, the time point of addition and the final concentration can be set by altering the parameters SB_0 , t_SB and SB_end .
This model file has been used to reproduce Figures 2D and 5A from the research paper using SBMLodesolver. To get the results for the figures, sum the corresponding concentrations:
fig 2D: nuclear EGFP-Smad2 = G_n + pG_n + G2_n + G4_n + 2* GG_n
fig 5A (either n or c for nucleus or cytosol):
monomeric Smad2 = S2_n/c + G_n/c
monomeric P-Smad2 = pS2_n/c + pG_n/c
Smad2/Smad4 complexes = S24_n/c + G4_n/c
Smad2/Smad2 complexes = S22_n/c + G2_n/c + GG_n/c

This model is the 3-step model from the article:
Onset dynamics of type A botulinum neurotoxin-induced paralysis.
Lebeda FJ, Adler M, Erickson K, Chushak Y J Pharmacokinet Pharmacodyn 2008 Jun; 35(3): 251-67 18551355 ,
Abstract:
Experimental studies have demonstrated that botulinum neurotoxin serotype A (BoNT/A) causes flaccid paralysis by a multi-step mechanism. Following its binding to specific receptors at peripheral cholinergic nerve endings, BoNT/A is internalized by receptor-mediated endocytosis. Subsequently its zinc-dependent catalytic domain translocates into the neuroplasm where it cleaves a vesicle-docking protein, SNAP-25, to block neurally evoked cholinergic neurotransmission. We tested the hypothesis that mathematical models having a minimal number of reactions and reactants can simulate published data concerning the onset of paralysis of skeletal muscles induced by BoNT/A at the isolated rat neuromuscular junction (NMJ) and in other systems. Experimental data from several laboratories were simulated with two different models that were represented by sets of coupled, first-order differential equations. In this study, the 3-step sequential model developed by Simpson (J Pharmacol Exp Ther 212:16-21,1980) was used to estimate upper limits of the times during which anti-toxins and other impermeable inhibitors of BoNT/A can exert an effect. The experimentally determined binding reaction rate was verified to be consistent with published estimates for the rate constants for BoNT/A binding to and dissociating from its receptors. Because this 3-step model was not designed to reproduce temporal changes in paralysis with different toxin concentrations, a new BoNT/A species and rate (k(S)) were added at the beginning of the reaction sequence to create a 4-step scheme. This unbound initial species is transformed at a rate determined by k(S) to a free species that is capable of binding. By systematically adjusting the values of k(S), the 4-step model simulated the rapid decline in NMJ function (k(S) >or= 0.01), the less rapid onset of paralysis in mice following i.m. injections (k (S) = 0.001), and the slow onset of the therapeutic effects of BoNT/A (k(S) < 0.001) in man. This minimal modeling approach was not only verified by simulating experimental results, it helped to quantitatively define the time available for an inhibitor to have some effect (t(inhib)) and the relation between this time and the rate of paralysis onset. The 4-step model predicted that as the rate of paralysis becomes slower, the estimated upper limits of (t(inhib)) for impermeable inhibitors become longer. More generally, this modeling approach may be useful in studying the kinetics of other toxins or viruses that invade host cells by similar mechanisms, e.g., receptor-mediated endocytosis.

This model is the reduced form of the model developed my Simpson 1980; PMID: 6243359 , i.e., it omits three unknown parameters that represents the binding sites for each species of the toxin.

This model is from the article:
Parallel adaptive feedback enhances reliability of the Ca2+ signaling system.
Abell E, Ahrends R, Bandara S, Park BO, Teruel MN. Proc Natl Acad Sci U S A. 2011 Aug 15. 21844332 ,
Abstract:
Despite large cell-to-cell variations in the concentrations of individual signaling proteins, cells transmit signals correctly. This phenomenon raises the question of what signaling systems do to prevent a predicted high failure rate. Here we combine quantitative modeling, RNA interference, and targeted selective reaction monitoring (SRM) mass spectrometry, and we show for the ubiquitous and fundamental calcium signaling system that cells monitor cytosolic and endoplasmic reticulum (ER) Ca(2+) levels and adjust in parallel the concentrations of the store-operated Ca(2+) influx mediator stromal interaction molecule (STIM), the plasma membrane Ca(2+) pump plasma membrane Ca-ATPase (PMCA), and the ER Ca(2+) pump sarco/ER Ca(2+)-ATPase (SERCA). Model calculations show that this combined parallel regulation in protein expression levels effectively stabilizes basal cytosolic and ER Ca(2+) levels and preserves receptor signaling. Our results demonstrate that, rather than directly controlling the relative level of signaling proteins in a forward regulation strategy, cells prevent transmission failure by sensing the state of the signaling pathway and using multiple parallel adaptive feedbacks.

Note:

There are two models described in the paper to simulate basal and receptor stimulated Ca ²⁺ signaling. 1) No adaptive feedback (this model: MODEL1108050000) and 2) with three slow adaptive feedback loops (MODEL1108050001).

Minimal Model for Circadian Oscillations

Citation
Vilar JMG, Kueh HY, Barkai N, Leibler S, (2002) . Mechanisms of noise resistance in genetic oscillators, PNAS, 99(9):5988-5992. http://www.pnas.org/cgi/content/abstract/ 99/9/5988

Description
A minimal model of genomically based oscillation, based on two mutually interacting genes, an activator and a repressor. Postive feedback is provided by the activator protein, which binds to the promotors of both the activator and the repressor genes. Negative feedback is provided by the repressor protein which binds to the activator protein.

Rate constant	Reaction
alphaA = 50	DA -> DA + MA
alphaAp = 500	DAp -> DAp + MA
alphaR = 0.01	DR -> DR + MR
alphaRp = 50	DRp -> DRp + MR
betaA = 50	MA -> A + MA
betaR = 5	MR -> MR + R
gammaA = 1	A + DA -> DAp
gammaC = 2	A + R -> C
gammaR = 1	A + DR -> DRp
deltaA = 1	A -> EmptySet
deltaA = 1	C -> R
deltaMA = 10	MA -> EmptySet
deltaMR = 0.5	MR -> EmptySet
deltaR = 0.2	R -> EmptySet
thetaA = 50	DAp -> A + DA
thetaR = 100	DRp -> A + DR

Variable	IC	ODE
A	0	A'[t] == -(deltaAA[t]) - gammaAA[t]DA[t] + thetaADAp[ t] - gammaRA[t]DR[t] + thetaRDRp[t] + betaAMA[t] - gammaCA[t]R[t]
C	0	C'[t] == -(deltaAC[t]) + gammaCA[t]*R[t]
DA	1	DA'[t] == -(gammaAA[t]DA[t]) + thetaA*DAp[t]
DAp	0	DAp'[t] == gammaAA[t]DA[t] - thetaA*DAp[t]
DR	1	DR'[t] == -(gammaRA[t]DR[t]) + thetaR*DRp[t]
DRp	0	DRp'[t] == gammaRA[t]DR[t] - thetaR*DRp[t]
MA	0	MA'[t] == alphaADA[t] + alphaApDAp[t] - deltaMA*MA[t]
MR	0	MR'[t] == alphaRDR[t] + alphaRpDRp[t] - deltaMR*MR[t]
R	0	R'[t] == deltaAC[t] + betaRMR[t] - deltaRR[t] - gammaCA[t]*R[t]

Generated by Cellerator Version 1.0 update 2.1127 using Mathematica 4.2 for Mac OS X (June 4, 2002), November 27, 2002 12:17:46, using (PowerMac,PowerPC, Mac OS X,MacOSX,Darwin)

author=B.E.Shapiro

This a model from the article:
Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tuberculosis, and its application to assessment of drug targets.
Singh VK , Ghosh I Theor Biol Med Model 2006 Aug 3;3:27 16887020 ,
Abstract:
BACKGROUND: Targeting persistent tubercule bacilli has become an important challenge in the development of anti-tuberculous drugs. As the glyoxylate bypass is essential for persistent bacilli, interference with it holds the potential for designing new antibacterial drugs. We have developed kinetic models of the tricarboxylic acid cycle and glyoxylate bypass in Escherichia coli and Mycobacterium tuberculosis, and studied the effects of inhibition of various enzymes in the M. tuberculosis model. RESULTS: We used E. coli to validate the pathway-modeling protocol and showed that changes in metabolic flux can be estimated from gene expression data. The M. tuberculosis model reproduced the observation that deletion of one of the two isocitrate lyase genes has little effect on bacterial growth in macrophages, but deletion of both genes leads to the elimination of the bacilli from the lungs. It also substantiated the inhibition of isocitrate lyases by 3-nitropropionate. On the basis of our simulation studies, we propose that: (i) fractional inactivation of both isocitrate dehydrogenase 1 and isocitrate dehydrogenase 2 is required for a flux through the glyoxylate bypass in persistent mycobacteria; and (ii) increasing the amount of active isocitrate dehydrogenases can stop the flux through the glyoxylate bypass, so the kinase that inactivates isocitrate dehydrogenase 1 and/or the proposed inactivator of isocitrate dehydrogenase 2 is a potential target for drugs against persistent mycobacteria. In addition, competitive inhibition of isocitrate lyases along with a reduction in the inactivation of isocitrate dehydrogenases appears to be a feasible strategy for targeting persistent mycobacteria. CONCLUSION: We used kinetic modeling of biochemical pathways to assess various potential anti-tuberculous drug targets that interfere with the glyoxylate bypass flux, and indicated the type of inhibition needed to eliminate the pathogen. The advantage of such an approach to the assessment of drug targets is that it facilitates the study of systemic effect(s) of the modulation of the target enzyme(s) in the cellular environment.

Locke2005 - Circadian Clock

SBML model of the interlocked feedback loop network

The model describes the circuit depicted in Fig. 4 and reproduces the simulations in Figure 5A and 5B. It provides initial conditions, parameter values and rules for the production rates of the following species: LHY mRNA (cLm), cytoplasmic LHY (cLc), nuclear LHY (cLn), TOC1 mRNA (cTm), cytoplasmic TOC1 (cTc), nuclear TOC1 (cTn),X mRNA (cXm), cytoplasmic X (cXc), nuclear X (cXn), Y mRNA (cYm), cytoplasmic Y (cYc), nuclear Y (cYn), nuclear P (cPn). This model was successfully tested on MathSBML and SBML ODE Solver.

Fig 5B is not in the right phase. However, the data is correct relative to the light/dark bars at the top of the figure.

This model is described in the article:

Extension of a genetic network model by iterative experimentation and mathematical analysis.

Locke JC, Southern MM, Kozma-Bognár L, Hibberd V, Brown PE, Turner MS, Millar AJ

Molecular Systems Biology [2005; 1: 2005.0013]

Abstract:

Circadian clocks involve feedback loops that generate rhythmic expression of key genes. Molecular genetic studies in the higher plant Arabidopsis thaliana have revealed a complex clock network. The first part of the network to be identified, a transcriptional feedback loop comprising TIMING OF CAB EXPRESSION 1 (TOC1), LATE ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK ASSOCIATED 1 (CCA1), fails to account for significant experimental data. We develop an extended model that is based upon a wider range of data and accurately predicts additional experimental results. The model comprises interlocking feedback loops comparable to those identified experimentally in other circadian systems. We propose that each loop receives input signals from light, and that each loop includes a hypothetical component that had not been explicitly identified. Analysis of the model predicted the properties of these components, including an acute light induction at dawn that is rapidly repressed by LHY and CCA1. We found this unexpected regulation in RNA levels of the evening-expressed gene GIGANTEA (GI), supporting our proposed network and making GI a strong candidate for this component.

This model is hosted on BioModels Database and identified by: BIOMD0000000055 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This a model from the article:
Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tuberculosis, and its application to assessment of drug targets.
Singh VK , Ghosh I Theor Biol Med Model 2006 Aug 3;3:27 16887020 ,
Abstract:
BACKGROUND: Targeting persistent tubercule bacilli has become an important challenge in the development of anti-tuberculous drugs. As the glyoxylate bypass is essential for persistent bacilli, interference with it holds the potential for designing new antibacterial drugs. We have developed kinetic models of the tricarboxylic acid cycle and glyoxylate bypass in Escherichia coli and Mycobacterium tuberculosis, and studied the effects of inhibition of various enzymes in the M. tuberculosis model. RESULTS: We used E. coli to validate the pathway-modeling protocol and showed that changes in metabolic flux can be estimated from gene expression data. The M. tuberculosis model reproduced the observation that deletion of one ofthe two isocitrate lyase genes has little effect on bacterial growth in macrophages, but deletion of both genes leads to the elimination of the bacilli from the lungs. It also substantiated the inhibition of isocitrate lyases by 3-nitropropionate. On the basis of our simulation studies, we propose that: (i) fractional inactivation of both isocitrate dehydrogenase 1 and isocitrate dehydrogenase 2 is required for a flux through the glyoxylate bypass in persistent mycobacteria; and (ii) increasing the amount of active isocitrate dehydrogenases can stop the flux through the glyoxylate bypass, so the kinase that inactivates isocitrate dehydrogenase 1 and/or the proposed inactivator of isocitrate dehydrogenase 2 is a potential target for drugs against persistent mycobacteria. In addition, competitive inhibition of isocitrate lyases along with a reduction in the inactivation of isocitrate dehydrogenases appears to be a feasible strategy for targeting persistent mycobacteria. CONCLUSION: We used kinetic modeling of biochemical pathways to assess various potential anti-tuberculous drug targets that interfere with the glyoxylate bypass flux, and indicated the type of inhibition needed to eliminate the pathogen. The advantage of such an approach to the assessment of drug targets is that it facilitates the study of systemic effect(s) of the modulation of the target enzyme(s) in the cellular environment.

The model reproduces Fig 3a of the paper. Please note that the authors mention that they used a value of 2 for n, n being the power in the positive feedback function for kinase autocatalysis, however the model here has n=1.95 because this results in a simulation that is identical to Fig 3a. The model was successfully tested on MathSBML.

Stortelder1997 - Thrombin Generation Amidolytic Activity

Mathematical modelling of a part of the blood coagulation mechanism.

This model is described in the article:

Mathematical modelling in blood coagulation : simulation and parameter estimation.

Stortelder W.J.H., Hemker P.W., Hemker, H.C.

CWI. Modelling, Analysis and Simulation, No. R 9720, p.1-11.

Abstract:

This paper describes the mathematical modelling of a part of the blood coagulation mechanism. The model includes the activation of factor X by a purified enzyme from Russel's Viper Venom (RVV), factor V and prothrombin, and also comprises the inactivation of the products formed. In this study we assume that in principle the mechanism of the process is known. However, the exact structure of the mechanism is unknown, and the process still can be described by different mathematical models. These models are put to test by measuring their capacity to explain the course of thrombin generation as observed in plasma after recalcification in presence of RVV. The mechanism studied is mathematically modelled as a system of differential-algebraic equations (DAEs). Each candidate model contains some freedom, which is expressed in the model equations by the presence of unknown parameters. For example, reaction constants or initial concentrations are unknown. The goal of parameter estimation is to determine these unknown parameters in such a way that the theoretical (i.e., computed) results fit the experimental data within measurement accuracy and to judge which modifications of the chemical reaction scheme allow the best fit. We present results on model discrimination and estimation of reaction constants, which are hard to obtain in another way.

This model is hosted on BioModels Database and identified by: BIOMD0000000358 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This a model from the article:
Transient heterogeneity in extracellular protease production by Bacillus subtilis.
Veening JW, Igoshin OA, Eijlander RT, Nijland R, Hamoen LW, Kuipers OP Mol. Syst. Biol. 2008 ; Volume: 4 : 184 18414485 ,
Abstract:
The most sophisticated survival strategy Bacillus subtilis employs is the differentiation of a subpopulation of cells into highly resistant endospores. To examine the expression patterns of non-sporulating cells within heterogeneous populations, we used buoyant density centrifugation to separate vegetative cells from endospore-containing cells and compared the transcriptome profiles of both subpopulations. This demonstrated the differential expression of various regulons. Subsequent single-cell analyses using promoter-gfp fusions confirmed our microarray results. Surprisingly, only part of the vegetative subpopulation highly and transiently expresses genes encoding the extracellular proteases Bpr (bacillopeptidase) and AprE (subtilisin), both of which are under the control of the DegU transcriptional regulator. As these proteases and their degradation products freely diffuse within the liquid growth medium, all cells within the clonal population are expected to benefit from their activities, suggesting that B. subtilis employs cooperative or even altruistic behavior. To unravel the mechanisms by which protease production heterogeneity within the non-sporulating subpopulation is established, we performed a series of genetic experiments combined with mathematical modeling. Simulations with our model yield valuable insights into how population heterogeneity may arise by the relatively long and variable response times within the DegU autoactivating pathway.

This model is from the article:
Switching from simple to complex oscillations in calcium signaling.
Kummer U, Olsen LF, Dixon CJ, Green AK, Bornberg-Bauer E, Baier G. Biophys J. 2000 Sep;79(3):1188-95. 10968983 ,
Abstract:
We present a new model for calcium oscillations based on experiments in hepatocytes. The model considers feedback inhibition on the initial agonist receptor complex by calcium and activated phospholipase C, as well as receptor type-dependent self-enhanced behavior of the activated G(alpha) subunit. It is able to show simple periodic oscillations and periodic bursting, and it is the first model to display chaotic bursting in response to agonist stimulations. Moreover, our model offers a possible explanation for the differences in dynamic behavior observed in response to different agonists in hepatocytes.

This a model from the article:
Fermentation pathway kinetics and metabolic flux control in suspended and immobilized Saccharomyces cerevisiae
Jorge L. Galazzo and James E. Bailey Enzyme and Microbial Technology Volume 12, Issue 3, 1990, Pages 162-172.
DOI: 10.1016/0141-0229(90)90033-M
Abstract:
Measurements of rates of glucose uptake and of glycerol and ethanol formation combined with knowledge of the metabolic pathways involved in S. cerevisiae were employed to obtain in vivo rates of reaction catalysed by pathway enzymes for suspended and alginate-entrapped cells at pH 4.5 and 5.5. Intracellular concentrations of substrates and effectors for most key pathway enzymes were estimated from in vivo phosphorus-31 nuclear magnetic resonance measurements. These data show the validity in vivo of kinetic models previously proposed for phosphofructokinase and pyruvate kinase based on in vitro studies. Kinetic representations of hexokinase, glycogen synthetase, and glyceraldehyde 3-phosphate dehydrogenase, which incorporate major regulatory properties of these enzymes, are all consistent with the in vivo data. This detailed model of pathway kinetics and these data on intracellular metabolite concentrations allow evaluation of flux-control coefficients for all key enzymes involved in glucose catabolism under the four different cell environments examined. This analysis indicates that alginate entrapment increases the glucose uptake rate and shifts the step most influencing ethanol production from glucose uptake to phosphofructokinase. The rate of ATP utilization in these nongrowing cells strongly limits ethanol production at pH 5.5 but is relatively insignificant at pH 4.5.

Biomodels Curation: The model reproduces Fig 2 of the paper. However, it appears that the figures are swapped, hence the plot for V/Vmax vs Glucose actually represnts V/Vmax vs ATP and the vice versa is true for the other figure. The rate of hexokinase reaction that is obtained upon simulation of the model is 17.24 mM/min, therefore V/Vmax has a value of 17.24/68.5=0.25. For steady state values of Glucose and ATP (0.038 and 1.213 mM respectively), the V/Vmax values correctly correspond to 0.25, if we were to assume that the figures are swapped.

BioModels Curation updated on 25 ^th November 2010: Figure 3 of the reference publication has been reproduced and added as a curation figure for the model.

The model reproduces Fig 5A of the paper. The ligand concentration is increased from 3E-5 to 0.01 at time t=2500 to ensure that the system reaches steady state. Hence, the time t=0 of the paper corresponds to t=2500 in the model. The peak value of the active ligand receptor complex is off by a value of 1.25, the authors have stated that this discrepancy is due to the fact that the figure in the paper corresponds to a slightly different parameter set. The model was successfully tested on MathSBML.

This model represents the non-competitive binding of XIAP to Casapase-3 and Caspase-9. In other words, XIAP mediated feedback is abolished in this model. The authors state that this leads to bistable-reversible behaviour as depicted in Fig 4C. The wild-type model displays a bistable-irreversible profile. This shows that irreversibility requires XIAP mediated feedback. The model was tested on MathSBML. However, please note that the paper does not contain any figure that corresponds to simulation of the Non-Competitive model.

This model is from the article:
Dynamics and feedback loops in the transforming growth factor β signaling pathway.
Wegner K, Bachmann A, Schad JU, Lucarelli P, Sahle S, Nickel P, Meyer C, Klingmüller U, Dooley S, Kummer U. Biophys Chem. 2012 Jan 5. 22284904 ,
Abstract:
Transforming growth factor β (TGF-β) ligands activate a signaling cascade with multiple cell context dependent outcomes. Disruption or disturbance leads to variant clinical disorders. To develop strategies for disease intervention, delineation of the pathway in further detail is required. Current theoretical models of this pathway describe production and degradation of signal mediating proteins and signal transduction from the cell surface into the nucleus, whereas feedback loops have not exhaustively been included. In this study we present a mathematical model to determine the relevance of feedback regulators (Arkadia, Smad7, Smurf1, Smurf2, SnoN and Ski) on TGF-β target gene expression and the potential to initiate stable oscillations within a realistic parameter space. We employed massive sampling of the parameters space to pinpoint crucial players for potential oscillations as well as transcriptional product levels. We identified Smad7 and Smurf2 with the highest impact on the dynamics. Based on these findings, we conducted preliminary time course experiments.

Note: Model of the Calvin cycle by Zhu et al. (2009, DOI:10.1016/j.nonrwa.2008.01.021 ).

The initial metabolite values are chosen from the data set of Zhu et al. (2007, DOI:10.1104/pp.107.103713 ).A detailed description of all modifications is given in the model described by Arnold and Nikoloski (2011, PMID:22001849 .

This model is from the article:
Interlinked mutual inhibitory positive feedbacks induce robust cellular memory effects.
Kim TH, Jung SH, Cho KH FEBS Lett. 2007 Oct; 581(25) 17892872 ,
Abstract:
Mutual inhibitory positive feedback (MIPF), or double-negative feedback, is a key regulatory motif of cellular memory with the capability of maintaining switched states for transient stimuli. Such MIPFs are found in various biological systems where they are interlinked in many cases despite a single MIPF can still realize such a memory effect. An intriguing question then arises about the advantage of interlinking MIPFs instead of exploiting an isolated single MIPF to realize the memory effect. We have investigated the advantages of interlinked MIPF systems through mathematical modeling and computer simulations. Our results revealed that interlinking MIPFs expands the parameter range of achieving the memory effect, or the memory region, thereby making the system more robust to parameter perturbations. Moreover, the minimal duration and amplitude of an external stimulus required for off-to-on state transition are increased and, as a result, external noises can more effectively be filtered out. Hence, interlinked MIPF systems can realize more robust cellular memories with respect to both parameter perturbations and external noises. Our study suggests that interlinked MIPF systems might be an evolutionary consequence acquired for a more reliable memory effect by enhancing robustness against noisy cellular environments.

Note: The model reproduces the simulation result for the symmetric model as depicted in Fig 3H of the paper. Model successfully tested on MathSBML

Figure4 and Figure5 can be simulated by Copasi. Figure4 can be simulated in MathSBML as well. There are some typos in the paper:K29=234, is it should k_29; Table2, reaction17, is there are "slash" missing in between the rate equation; reaction 33,"Akt-PI-PP" in the last term of denominator instead of "AktPI-P" . For plotting figure4, we create another extra parameter *_percent, and use assignment rule calculate percentage of each species.

Biomodels Curation The model reproduces the flux value of "Gpp p" (rate of Glycerol synthesis) as depicted in Fig 3 of the paper. The model reproduces the flux for early exponential phase , however it can be used to reproduce the values for other phases by plugging in appropriate values for maximal rates as given in Table 1 and metabolite concentrations as given in Table 2 of the paper. The model was succesfully reproduced using Jarnac.

This model is from the article:
Restriction point control of the mammalian cell cycle via the cyclin E/Cdk2:p27 complex.
Conradie R, Bruggeman FJ, Ciliberto A, Csikász-Nagy A, Novák B, Westerhoff HV, Snoep JL FEBS J. 2010 Jan; 277(2): 357-67 20015233 ,
Abstract:
Numerous top-down kinetic models have been constructed to describe the cell cycle. These models have typically been constructed, validated and analyzed using model species (molecular intermediates and proteins) and phenotypic observations, and therefore do not focus on the individual model processes (reaction steps). We have developed a method to: (a) quantify the importance of each of the reaction steps in a kinetic model for the positioning of a switch point [i.e. the restriction point (RP)]; (b) relate this control of reaction steps to their effects on molecular species, using sensitivity and co-control analysis; and thereby (c) go beyond a correlation towards a causal relationship between molecular species and effects. The method is generic and can be applied to responses of any type, but is most useful for the analysis of dynamic and emergent responses such as switch points in the cell cycle. The strength of the analysis is illustrated for an existing mammalian cell cycle model focusing on the RP [Novak B, Tyson J (2004) J Theor Biol230, 563-579]. The reactions in the model with the highest RP control were those involved in: (a) the interplay between retinoblastoma protein and E2F transcription factor; (b) those synthesizing the delayed response genes and cyclin D/Cdk4 in response to growth signals; (c) the E2F-dependent cyclin E/Cdk2 synthesis reaction; as well as (d) p27 formation reactions. Nine of the 23 intermediates were shown to have a good correlation between their concentration control and RP control. Sensitivity and co-control analysis indicated that the strongest control of the RP is mediated via the cyclin E/Cdk2:p27 complex concentration. Any perturbation of the RP could be related to a change in the concentration of this complex; apparent effects of other molecular species were indirect and always worked through cyclin E/Cdk2:p27, indicating a causal relationship between this complex and the positioning of the RP.

The rate constants presented in the paper have units [per tenth of an hour] and have been changed here to [per hour] (e.g. k16 = 0.25 not 0.025); for further confirmation of the correctness of this change, see the original model (Novak, J Theor Biol 2004 230:563).

Tyson1991 - Cell Cycle 6 var

Mathematical model of the interactions of cdc2 and cyclin.

This model is described in the article:

Modeling the cell division cycle: cdc2 and cyclin interactions.

Tyson JJ.

Proc. Natl. Acad. Sci. U.S.A. 1991; 88(16); 7328-32

Abstract:

The proteins cdc2 and cyclin form a heterodimer (maturation promoting factor) that controls the major events of the cell cycle. A mathematical model for the interactions of cdc2 and cyclin is constructed. Simulation and analysis of the model show that the control system can operate in three modes: as a steady state with high maturation promoting factor activity, as a spontaneous oscillator, or as an excitable switch. We associate the steady state with metaphase arrest in unfertilized eggs, the spontaneous oscillations with rapid division cycles in early embryos, and the excitable switch with growth-controlled division cycles typical of nonembryonic cells.

This model is hosted on BioModels Database and identified by: BIOMD0000000005 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This model is from the article:
The influence of cytokinin-auxin cross-regulation on cell-fate determination in Arabidopsis thaliana root development
Muraro D, Byrne H, King J, Voss U, Kieber J, Bennett M. J Theor Biol. 2011 Aug 21;283(1):152-67. PMID: 21640126 ,
Abstract:
Root growth and development in Arabidopsis thaliana are sustained by a specialised zone termed the meristem, which contains a population of dividing and differentiating cells that are functionally analogous to a stem cell niche in animals. The hormones auxin and cytokinin control meristem size antagonistically. Local accumulation of auxin promotes cell division and the initiation of a lateral root primordium. By contrast, high cytokinin concentrations disrupt the regular pattern of divisions that characterises lateral root development, and promote differentiation. The way in which the hormones interact is controlled by a genetic regulatory network. In this paper, we propose a deterministic mathematical model to describe this network and present model simulations that reproduce the experimentally observed effects of cytokinin on the expression of auxin regulated genes. We show how auxin response genes and auxin efflux transporters may be affected by the presence of cytokinin. We also analyse and compare the responses of the hormones auxin and cytokinin to changes in their supply with the responses obtained by genetic mutations of SHY2, which encodes a protein that plays a key role in balancing cytokinin and auxin regulation of meristem size. We show that although shy2 mutations can qualitatively reproduce the effect of varying auxin and cytokinin supply on their response genes, some elements of the network respond differently to changes in hormonal supply and to genetic mutations, implying a different, general response of the network. We conclude that an analysis based on the ratio between these two hormones may be misleading and that a mathematical model can serve as a useful tool for stimulate further experimental work by predicting the response of the network to changes in hormone levels and to other genetic mutations.

The model reproduces the time profile of cYm and cTm under light-dark cycles as depicted in Fig 4 and Fig 5 respectively. 12 hour light-dark cycles are accomplished using a simple algorithm in the event section. The model was successfully tested using MathSBML.

This is the auxiliary model described in the article:
Covering a Broad Dynamic Range: Information Processing at the Erythropoietin Receptor
Verena Becker, Marcel Schilling, Julie Bachmann, Ute Baumann, Andreas Raue, Thomas Maiwald, Jens Timmer and Ursula Klingmüller; Science Published Online May 20, 2010; DOI: 10.1126/science.1184913 PMID: 20488988
Abstract:
Cell surface receptors convert extracellular cues into receptor activation, thereby triggering intracellular signaling networks and controlling cellular decisions. A major unresolved issue is the identification of receptor properties that critically determine processing of ligand-encoded information. We show by mathematical modeling of quantitative data and experimental validation that rapid ligand depletion and replenishment of cell surface receptor are characteristic features of the erythropoietin (Epo) receptor (EpoR). The amount of Epo-EpoR complexes and EpoR activation integrated over time corresponds linearly to ligand input, covering a broad range of ligand concentrations. This relation solely depends on EpoR turnover independent of ligand binding, suggesting an essential role of large intracellular receptor pools. These receptor properties enable the system to cope with basal and acute demand in the hematopoietic system.

SBML model exported from PottersWheel.

% PottersWheel model definition file

function m = BeckerSchilling2010_EpoR_AuxiliaryMode()

m             = pwGetEmptyModel();

%% Meta information

m.ID          = 'BeckerSchilling2010_EpoR_AuxiliaryMode';
m.name        = 'BeckerSchilling2010_EpoR_AuxiliaryModel';
m.description = 'BeckerSchilling2010_EpoR_AuxiliaryModel';
m.authors     = {'Verena Becker',' Marcel Schilling'};
m.dates       = {'2010'};
m.type        = 'PW-2-0-42';

%% X: Dynamic variables
% m = pwAddX(m, ID, startValue, type, minValue, maxValue, unit, compartment, name, description, typeOfStartValue)

m = pwAddX(m, 'EpoR'     ,      76, 'fix'   ,   0, 10000,   [], 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'SAv'      , 999.293, 'global', 900,  1100,   [], 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'SAv_EpoR' ,       0, 'fix'   ,   0, 10000,   [], 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'SAv_EpoRi',       0, 'fix'   ,   0, 10000,   [], 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'dSAvi'    ,       0, 'fix'   ,   0, 10000,   [], 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'dSAve'    ,       0, 'fix'   ,   0, 10000,   [], 'cell', []  , []  , []             , []  , 'protein.generic');


%% R: Reactions
% m = pwAddR(m, reactants, products, modifiers, type, options, rateSignature, parameters, description, ID, name, fast, compartments, parameterTrunks, designerPropsR, stoichiometry, reversible)

m = pwAddR(m, {            }, {'EpoR'      }, {  }, 'C' , [] , 'k1*k2', {'kt','Bmax_SAv'}, [], 'reaction0001');
m = pwAddR(m, {'EpoR'      }, {            }, {  }, 'MA', [] , []     , {'kt'           }, [], 'reaction0002');
m = pwAddR(m, {'SAv','EpoR'}, {'SAv_EpoR'  }, {  }, 'MA', [] , []     , {'kon_SAv'      }, [], 'reaction0003');
m = pwAddR(m, {'SAv_EpoR'  }, {'SAv','EpoR'}, {  }, 'MA', [] , []     , {'koff_SAv'     }, [], 'reaction0004');
m = pwAddR(m, {'SAv_EpoR'  }, {'SAv_EpoRi' }, {  }, 'MA', [] , []     , {'kt'           }, [], 'reaction0005');
m = pwAddR(m, {'SAv_EpoRi' }, {'SAv'       }, {  }, 'MA', [] , []     , {'kex_SAv'      }, [], 'reaction0006');
m = pwAddR(m, {'SAv_EpoRi' }, {'dSAvi'     }, {  }, 'MA', [] , []     , {'kdi'          }, [], 'reaction0007');
m = pwAddR(m, {'SAv_EpoRi' }, {'dSAve'     }, {  }, 'MA', [] , []     , {'kde'          }, [], 'reaction0008');



%% C: Compartments
% m = pwAddC(m, ID, size,  outside, spatialDimensions, name, unit, constant)

m = pwAddC(m, 'cell', 1);


%% K: Dynamical parameters
% m = pwAddK(m, ID, value, type, minValue, maxValue, unit, name, description)

m = pwAddK(m, 'kt'      , 0.0329366   , 'global', 1e-007, 1000);
m = pwAddK(m, 'Bmax_SAv', 76          , 'fix'   , 61    , 91  );
m = pwAddK(m, 'kon_SAv' , 2.29402e-006, 'global', 1e-007, 1000);
m = pwAddK(m, 'koff_SAv', 0.00679946  , 'global', 1e-007, 1000);
m = pwAddK(m, 'kex_SAv' , 0.01101     , 'global', 1e-007, 1000);
m = pwAddK(m, 'kdi'     , 0.00317871  , 'global', 1e-007, 1000);
m = pwAddK(m, 'kde'     , 0.0164042   , 'global', 1e-007, 1000);


%% Default sampling time points
m.t = 0:3:99;


%% Y: Observables
% m = pwAddY(m, rhs, ID, scalingParameter, errorModel, noiseType, unit, name, description, alternativeIDs, designerProps)

m = pwAddY(m, 'SAv + dSAve'      , 'SAv_extracellular_obs');
m = pwAddY(m, 'SAv_EpoR'         , 'SAv_cellsurface_obs'  );
m = pwAddY(m, 'SAv_EpoRi + dSAvi', 'SAv_intracellular_obs');


%% S: Scaling parameters
% m = pwAddS(m, ID, value, type, minValue, maxValue, unit, name, description)

m = pwAddS(m, 'scale_SAv_extracellular_obs', 1, 'fix', 0, 100);
m = pwAddS(m, 'scale_SAv_cellsurface_obs'  , 1, 'fix', 0, 100);
m = pwAddS(m, 'scale_SAv_intracellular_obs', 1, 'fix', 0, 100);


%% Designer properties (do not modify)
m.designerPropsM = [1 1 1 0 0 0 400 250 600 400 1 1 1 0 0 0 0];

This a model from the article:
Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tuberculosis, and its application to assessment of drug targets.
Singh VK , Ghosh I Theor Biol Med Model 2006 Aug 3;3:27 16887020 ,
Abstract:
BACKGROUND: Targeting persistent tubercule bacilli has become an important challenge in the development of anti-tuberculous drugs. As the glyoxylate bypass is essential for persistent bacilli, interference with it holds the potential for designing new antibacterial drugs. We have developed kinetic models of the tricarboxylic acid cycle and glyoxylate bypass in Escherichia coli and Mycobacterium tuberculosis, and studied the effects of inhibition of various enzymes in the M. tuberculosis model. RESULTS: We used E. coli to validate the pathway-modeling protocol and showed that changes in metabolic flux can be estimated from gene expression data. The M. tuberculosis model reproduced the observation that deletion of one ofthe two isocitrate lyase genes has little effect on bacterial growth in macrophages, but deletion of both genes leads to the elimination of the bacilli from the lungs. It also substantiated the inhibition of isocitrate lyases by 3-nitropropionate. On the basis of our simulation studies, we propose that: (i) fractional inactivation of both isocitrate dehydrogenase 1 and isocitrate dehydrogenase 2 is required for a flux through the glyoxylate bypass in persistent mycobacteria; and (ii) increasing the amount of active isocitrate dehydrogenases can stop the flux through the glyoxylate bypass, so the kinase that inactivates isocitrate dehydrogenase 1 and/or the proposed inactivator of isocitrate dehydrogenase 2 is a potential target for drugs against persistent mycobacteria. In addition, competitive inhibition of isocitrate lyases along with a reduction in the inactivation of isocitrate dehydrogenases appears to be a feasible strategy for targeting persistent mycobacteria. CONCLUSION: We used kinetic modeling of biochemical pathways to assess various potential anti-tuberculous drug targets that interfere with the glyoxylate bypass flux, and indicated the type of inhibition needed to eliminate the pathogen. The advantage of such an approach to the assessment of drug targets is that it facilitates the study of systemic effect(s) of the modulation of the target enzyme(s) in the cellular environment.

The model reproduces the time profile of p53 and Mdm2 as depicted in Fig 6B of the plot for model 1. Results obtained on MathSBML.

MAPK cascade in solution (no scaffold)

Description
This model describes a basic 3- stage Mitogen Activated Protein Kinase (MAPK) cascade in solution. This cascade is typically expressed as RAF= =>MEK==>MAPK (alternative forms are K3==>K2==> K1 and KKK==>KK==>K) . The input signal is RAFK (RAF Kinase) and the output signal is MAPKpp ( doubly phosphorylated form of MAPK) . RAFK phosphorylates RAF once to RAFp. RAFp, the phosphorylated form of RAF induces two phoshporylations of MEK, to MEKp and MEKpp. MEKpp, the doubly phosphorylated form of MEK, induces two phosphorylations of MAPK to MAPKp and MAPKpp.

Description

This model describes a basic 3- stage Mitogen Activated Protein Kinase (MAPK) cascade in solution. This cascade is typically expressed as RAF= =>MEK==>MAPK (alternative forms are K3==>K2==> K1 and KKK==>KK==>K) . The input signal is RAFK (RAF Kinase) and the output signal is MAPKpp ( doubly phosphorylated form of MAPK) . RAFK phosphorylates RAF once to RAFp. RAFp, the phosphorylated form of RAF induces two phoshporylations of MEK, to MEKp and MEKpp. MEKpp, the doubly phosphorylated form of MEK, induces two phosphorylations of MAPK to MAPKp and MAPKpp.

Rate constant	Reaction
a10 = 5.	MAPKPH + MAPKpp -> MAPKppMAPKPH
a1 = 1.	RAF + RAFK -> RAFRAFK
a2 = 0.5	RAFp + RAFPH -> RAFpRAFPH
a3 = 3.3	MEK + RAFp -> MEKRAFp
a4 = 10.	MEKp + MEKPH -> MEKpMEKPH
a5 = 3.3	MEKp + RAFp -> MEKpRAFp
a6 = 10.	MEKPH + MEKpp -> MEKppMEKPH
a7 = 20.	MAPK + MEKpp -> MAPKMEKpp
a8 = 5.	MAPKp + MAPKPH -> MAPKpMAPKPH
a9 = 20.	MAPKp + MEKpp -> MAPKpMEKpp
d10 = 0.4	MAPKppMAPKPH -> MAPKPH + MAPKpp
d1 = 0.4	RAFRAFK -> RAF + RAFK
d2 = 0.5	RAFpRAFPH -> RAFp + RAFPH
d3 = 0.42	MEKRAFp -> MEK + RAFp
d4 = 0.8	MEKpMEKPH -> MEKp + MEKPH
d5 = 0.4	MEKpRAFp -> MEKp + RAFp
d6 = 0.8	MEKppMEKPH -> MEKPH + MEKpp
d7 = 0.6	MAPKMEKpp -> MAPK + MEKpp
d8 = 0.4	MAPKpMAPKPH -> MAPKp + MAPKPH
d9 = 0.6	MAPKpMEKpp -> MAPKp + MEKpp
k10 = 0.1	MAPKppMAPKPH -> MAPKp + MAPKPH
k1 = 0.1	RAFRAFK -> RAFK + RAFp
k2 = 0.1	RAFpRAFPH -> RAF + RAFPH
k3 = 0.1	MEKRAFp -> MEKp + RAFp
k4 = 0.1	MEKpMEKPH -> MEK + MEKPH
k5 = 0.1	MEKpRAFp -> MEKpp + RAFp
k6 = 0.1	MEKppMEKPH -> MEKp + MEKPH
k7 = 0.1	MAPKMEKpp -> MAPKp + MEKpp
k8 = 0.1	MAPKpMAPKPH -> MAPK + MAPKPH
k9 = 0.1	MAPKpMEKpp -> MAPKpp + MEKpp

Variable	IC	ODE
MAPK	0.3	MAPK'[t] == d7MAPKMEKpp[t] + k8MAPKpMAPKPH[t] - a7MAPK[t]MEKpp[t]
MAPKMEKpp	0	MAPKMEKpp'[t] == -(d7MAPKMEKpp[t]) - k7MAPKMEKpp[t] + a7MAPK[t]MEKpp[t]
MAPKp	0	MAPKp'[t] == k7MAPKMEKpp[t] - a8MAPKp[t]MAPKPH[t] + d8MAPKpMAPKPH[t] + d9MAPKpMEKpp[t] + k10 MAPKppMAPKPH[t] - a9MAPKp[t]MEKpp[t]
MAPKPH	0.3	MAPKPH'[t] == -(a8MAPKp[t]MAPKPH[t]) + d8MAPKpMAPKPH[ t] + k8MAPKpMAPKPH[t] - a10MAPKPH[t]MAPKpp[t] + d10MAPKppMAPKPH[t] + k10MAPKppMAPKPH[t]
MAPKpMAPKPH	0	MAPKpMAPKPH'[t] == a8MAPKp[t]MAPKPH[t] - d8* MAPKpMAPKPH[t] - k8*MAPKpMAPKPH[t]
MAPKpMEKpp	0	MAPKpMEKpp'[t] == -(d9MAPKpMEKpp[t]) - k9MAPKpMEKpp[t] + a9MAPKp[t]MEKpp[t]
MAPKpp	0	MAPKpp'[t] == k9MAPKpMEKpp[t] - a10MAPKPH[t]MAPKpp[t] + d10MAPKppMAPKPH[t]
MAPKppMAPKPH	0	MAPKppMAPKPH'[t] == a10MAPKPH[t]MAPKpp[t] - d10* MAPKppMAPKPH[t] - k10*MAPKppMAPKPH[t]
MEK	0.2	MEK'[t] == k4MEKpMEKPH[t] + d3MEKRAFp[t] - a3MEK[t]RAFp[t]
MEKp	0	MEKp'[t] == -(a4MEKp[t]MEKPH[t]) + d4MEKpMEKPH[t] + k6MEKppMEKPH[t] + d5MEKpRAFp[t] + k3MEKRAFp[ t] - a5MEKp[t]RAFp[t]
MEKPH	0.2	MEKPH'[t] == -(a4MEKp[t]MEKPH[t]) + d4MEKpMEKPH[t] + k4MEKpMEKPH[t] - a6MEKPH[t]MEKpp[t] + d6* MEKppMEKPH[t] + k6*MEKppMEKPH[t]
MEKpMEKPH	0	MEKpMEKPH'[t] == a4MEKp[t]MEKPH[t] - d4MEKpMEKPH[t] - k4MEKpMEKPH[t]
MEKpp	0	MEKpp'[t] == d7MAPKMEKpp[t] + k7MAPKMEKpp[t] + d9MAPKpMEKpp[t] + k9MAPKpMEKpp[t] - a7MAPK[t] MEKpp[t] - a9MAPKp[t]MEKpp[t] - a6MEKPH[t]MEKpp[t] + d6MEKppMEKPH[t] + k5MEKpRAFp[t]
MEKppMEKPH	0	MEKppMEKPH'[t] == a6MEKPH[t]MEKpp[t] - d6MEKppMEKPH[ t] - k6MEKppMEKPH[t]
MEKpRAFp	0	MEKpRAFp'[t] == -(d5MEKpRAFp[t]) - k5MEKpRAFp[t] + a5MEKp[t]RAFp[t]
MEKRAFp	0	MEKRAFp'[t] == -(d3MEKRAFp[t]) - k3MEKRAFp[t] + a3MEK[t]RAFp[t]
RAF	0.4	RAF'[t] == -(a1RAF[t]RAFK[t]) + k2RAFpRAFPH[t] + d1RAFRAFK[t]
RAFK	0.1	RAFK'[t] == -(a1RAF[t]RAFK[t]) + d1RAFRAFK[t] + k1RAFRAFK[t]
RAFp	0	RAFp'[t] == d5MEKpRAFp[t] + k5MEKpRAFp[t] + d3MEKRAFp[t] + k3MEKRAFp[t] - a3MEK[t]RAFp[t] - a5MEKp[t]RAFp[t] - a2RAFp[t]RAFPH[t] + d2* RAFpRAFPH[t] + k1*RAFRAFK[t]
RAFPH	0.3	RAFPH'[t] == -(a2RAFp[t]RAFPH[t]) + d2RAFpRAFPH[t] + k2RAFpRAFPH[t]
RAFpRAFPH	0	RAFpRAFPH'[t] == a2RAFp[t]RAFPH[t] - d2RAFpRAFPH[t] - k2RAFpRAFPH[t]
RAFRAFK	0	RAFRAFK'[t] == a1RAF[t]RAFK[t] - d1RAFRAFK[t] - k1RAFRAFK[t]

Generated by Cellerator Version 1.4.3 (6-March-2004) using Mathematica 5.0 for Mac OS X (November 19, 2003), March 6, 2004 12:18:07, using (PowerMac, PowerPC,Mac OS X,MacOSX,Darwin)

author=B.E.Shapiro

The model corresponds to the schemas 1 and 2 of Markevich et al 2004, as described in the figure 1 and modelled using Michaelis-Menten like kinetics. Phosphorylations and dephosphorylations follow distributive ordered kinetics.
It reproduces figure 3 in the main article.

This model is the reaction sequence SEQFB, a model pathway of a branched system with sequential feedback interactions found in bacterial amino acid synthesis. Its steady state is presented in Fig 4.

The model is described in:
METAMOD: software for steady-state modelling and control analysis of metabolic pathways on the BBC microcomputer.
JHS Hofmeyr and KJ van der Merwe, Comput Appl Biosci 1986 2:243-9; PubmedID: 3450367
Abstract:
METAMOD, a BBC microcomputer-based software package for steady-state modelling and control analysis of model metabolic pathways, is described, The package consists of two programs. METADEF allows the user to define the pathway in terms of reactions, rate equations and initial concentrations of metabolites. METACAL uses one of two algorithms to calculate the steady-state concentrations and fluxes. One algorithm uses the current ratio of production and consumption rates of variable metabolites to adjust iteratively their concentrations in such a way that they converge towards the steady state. The other algorithm solves the roots of the system equations by means of a quasi-Newtonian procedure. Control analysis allows the calculation of elasticity, control and response coefficients, by means of finite difference approximation. METAMOD is interactive and easy to use, and suitable for teaching and research purposes.

To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novere N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

This a model from the article:
Computer model for mechanisms underlying ultradian oscillations of insulin and glucose.
Sturis J, Polonsky KS, Mosekilde E, Van Cauter E. Am J Physiol. 1991 May;260(5 Pt 1):E801-9. 2035636 ,
Abstract:
Oscillations in human insulin secretion have been observed in two distinct period ranges, 10-15 min (i.e. rapid) and 100-150 min (i.e., ultradian). The cause of the ultradian oscillations remains to be elucidated. To determine whether the oscillations could result from the feedback loops between insulin and glucose, a parsimonious mathematical model including the major mechanisms involved in glucose regulation was developed. This model comprises two major negative feedback loops describing the effects of insulin on glucose utilization and glucose production, respectively, and both loops include the stimulatory effect of glucose on insulin secretion. Model formulations and parameters are representative of results from published clinical investigations. The occurrence of sustained insulin and glucose oscillations was found to be dependent on two essential features: 1) a time delay of 30-45 min for the effect of insulin on glucose production and 2) a sluggish effect of insulin on glucose utilization, because insulin acts from a compartment remote from plasma. When these characteristics were incorporated in the model, numerical simulations mimicked all experimental findings so far observed for these ultradian oscillations, including 1) self-sustained oscillations during constant glucose infusion at various rates; 2) damped oscillations after meal or oral glucose ingestion; 3) increased amplitude of oscillation after increased stimulation of insulin secretion, without change in frequency; and 4) slight advance of the glucose oscillation compared with the insulin oscillation.(ABSTRACT TRUNCATED AT 250 WORDS)

This a model from the article:
Experimental and computational analysis of polyglutamine-mediated cytotoxicity.
Tang MY, Proctor CJ, Woulfe J, Gray DA. PLoS Comput Biol. 2010 Sep 23;6(9). 20885783 ,
Abstract:
Expanded polyglutamine (polyQ) proteins are known to be the causative agents of a number of human neurodegenerative diseases but the molecular basis of their cytoxicity is still poorly understood. PolyQ tracts may impede the activity of the proteasome, and evidence from single cell imaging suggests that the sequestration of polyQ into inclusion bodies can reduce the proteasomal burden and promote cell survival, at least in the short term. The presence of misfolded protein also leads to activation of stress kinases such as p38MAPK, which can be cytotoxic. The relationships of these systems are not well understood. We have used fluorescent reporter systems imaged in living cells, and stochastic computer modeling to explore the relationships of polyQ, p38MAPK activation, generation of reactive oxygen species (ROS), proteasome inhibition, and inclusion div formation. In cells expressing a polyQ protein inclusion, div formation was preceded by proteasome inhibition but cytotoxicity was greatly reduced by administration of a p38MAPK inhibitor. Computer simulations suggested that without the generation of ROS, the proteasome inhibition and activation of p38MAPK would have significantly reduced toxicity. Our data suggest a vicious cycle of stress kinase activation and proteasome inhibition that is ultimately lethal to cells. There was close agreement between experimental data and the predictions of a stochastic computer model, supporting a central role for proteasome inhibition and p38MAPK activation in inclusion div formation and ROS-mediated cell death.

This the model from the article:
A biochemically structured model for Saccharomyces cerevisiae.
Lei F, Rotbøll M, Jørgensen SB. J Biotechnol. 2001 Jul 12;88(3):205-21. PMID: 11434967 ,DOI: 10.1016/S0168-1656(01)00269-3

Abstract:
A biochemically structured model for the aerobic growth of Saccharomyces cerevisiae on glucose and ethanol is presented. The model focuses on the pyruvate and acetaldehyde branch points where overflow metabolism occurs when the growth changes from oxidative to oxido-reductive. The model is designed to describe the onset of aerobic alcoholic fermentation during steady-state as well as under dynamical conditions, by triggering an increase in the glycolytic flux using a key signalling component which is assumed to be closely related to acetaldehyde. An investigation of the modelled process dynamics in a continuous cultivation revealed multiple steady states in a region of dilution rates around the transition between oxidative and oxido-reductive growth. A bifurcation analysis using the two external variables, the dilution rate, D, and the inlet concentration of glucose, S(f), as parameters, showed that a fold bifurcation occurs close to the critical dilution rate resulting in multiple steady-states. The region of dilution rates within which multiple steady states may occur depends strongly on the substrate feed concentration. Consequently a single steady state may prevail at low feed concentrations, whereas multiple steady states may occur over a relatively wide range of dilution rates at higher feed concentrations.

This model is from the article:
Heterogeneity Reduces Sensitivity of Cell Death for TNF-Stimuli
Schliemann M, Bullinger E, Borchers S, Allgower F, Findeisen R, Scheurich P. BMC Syst Biol. 2011 Dec 28;5(1):204. 22204418 ,
Abstract:
BACKGROUND: Apoptosis is a form of programmed cell death essential for the maintenance of homeostasis and the removal of potentially damaged cells in multicellular organisms. By binding its cognate membrane receptor, TNF receptor type 1 (TNF-R1), the proinflammatory cytokine Tumor Necrosis Factor (TNF) activates pro-apoptotic signaling via caspase activation, but at the same time also stimulates nuclear factor kappaB (NF-kappaB)-mediated survival pathways. Differential dose-response relationships of these two major TNF signaling pathways have been described experimentally and using mathematical modeling. However, the quantitative analysis of the complex interplay between pro- and anti-apoptotic signaling pathways is an open question as it is challenging for several reasons: the overall signaling network is complex, various time scales are present, and cells respond quantitatively and qualitatively in a heterogeneous manner. RESULTS: This study analyzes the complex interplay of the crosstalk of TNF-R1 induced pro- and anti-apoptotic signaling pathways based on an experimentally validated mathematical model. The mathematical model describes the temporal responses on both the single cell level as well as the level of a heterogeneous cell population, as observed in the respective quantitative experiments using TNF-R1 stimuli of different strengths and durations. Global sensitivity of the heterogeneous population was quantified by measuring the average gradient of time of death versus each population parameter. This global sensitivity analysis uncovers the concentrations of Caspase-8 and Caspase-3, and their respective inhibitors BAR and XIAP, as key elements for deciding the cell's fate. A simulated knockout of the NF-kappaB-mediated anti-apoptotic signaling reveals the importance of this pathway for delaying the time of death, reducing the death rate in the case of pulse stimulation and significantly increasing cell-to-cell variability. CONCLUSIONS: Cell ensemble modeling of a heterogeneous cell population including a global sensitivity analysis presented here allowed us to illuminate the role of the different elements and parameters on apoptotic signaling. The receptors serve to transmit the external stimulus; procaspases and their inhibitors control the switching from life to death, while NF-kappaB enhances the heterogeneity of the cell population. The global sensitivity analysis of the cell population model further revealed an unexpected impact of heterogeneity, i.e. the reduction of parametric sensitivity.

Note: SBML model generated from Matlab system description on 12-July-2011 21:08:15 by exportSBML Copyright Eric Bullinger 2007-2011

The model is encoded according to the paper Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents Figure5 has been reproduced by MathSBML. One need to change the value of ga in order to get the three correct results.

the xppaut file of the model is avaiable on the following address offered by the author , http://www.math.fsu.edu/%7Ebertram/software/pituitary/JCNS_07.ode

The model is according to the paper Which Model to Use for Cortical Spiking Neurons? Figure1(H) Class 2 excitable has been reproduced by MathSBML. The ODE and the parameters values are taken from the a paper Simple Model of Spiking Neurons The original format of the models are encoded in the MATLAB format existed in the ModelDB with Accession number 39948

Figure1 are the simulation results of the same model with different choices of parameters and different stimulus function or events.a=0.2; b=0.26; c=-65; d=0; V=-64; u=b*V;

This a model from the article:
Bifurcation and resonance in a model for bursting nerve cells.
Plant RE J Math Biol 1981 Jan; 11(1): 15-32 7252375 ,
Abstract:
In this paper we consider a model for the phenomenon of bursting in nerve cells. Experimental evidence indicates that this phenomenon is due to the interaction of multiple conductances with very different kinetics, and the model incorporates this evidence. As a parameter is varied the model undergoes a transition between two oscillatory waveforms; a corresponding transition is observed experimentally. After establishing the periodicity of the subcritical oscillatory solution, the nature of the transition is studied. It is found to be a resonance bifurcation, with the solution branching at the critical point to another periodic solution of the same period. Using this result a comparison is made between the model and experimental observations. The model is found to predict and allow an interpretation of these observations.

Also, look at http://www.scholarpedia.org/article/Plant_model

Note: Model of the Calvin cycle with focus on the RuBisCO reaction by Medlyn et al. (2002, DOI:10.1046/j.1365-3040.2002.00891.x ).

The parameter values are widely taken from Farquhar et al. (1980, DOI:10.1007/BF00386231 ). The initial metabolite values are chosen from the data set of Zhu et al. (2007, DOI:10.1104/pp.107.103713) . A detailed description of all modifications is given in the model described by Arnold and Nikoloski (2011, PMID:22001849 .

This is system 1, the model with linear antigen uptake by pAPCs, described in the article:
Self-tolerance and Autoimmunity in a Regulatory T Cell Model.
Alexander HK, Wahl LM. Bull Math Biol. 2010 Mar 2. PMID: 20195912 , doi: 10.1007/s11538-010-9519-2 ;
Abstract:
The class of immunosuppressive lymphocytes known as regulatory T cells (Tregs) has been identified as a key component in preventing autoimmune diseases. Although Tregs have been incorporated previously in mathematical models of autoimmunity, we take a novel approach which emphasizes the importance of professional antigen presenting cells (pAPCs). We examine three possible mechanisms of Treg action (each in isolation) through ordinary differential equation (ODE) models. The immune response against a particular autoantigen is suppressed both by Tregs specific for that antigen and by Tregs of arbitrary specificities, through their action on either maturing or already mature pAPCs or on autoreactive effector T cells. In this deterministic approach, we find that qualitative long-term behaviour is predicted by the basic reproductive ratio R (0) for each system. When R (0) < 1, only the trivial equilibrium exists and is stable; when R (0)>1, this equilibrium loses its stability and a stable non-trivial equilibrium appears. We interpret the absence of self-damaging populations at the trivial equilibrium to imply a state of self-tolerance, and their presence at the non-trivial equilibrium to imply a state of chronic autoimmunity. Irrespective of mechanism, our model predicts that Tregs specific for the autoantigen in question play no role in the system's qualitative long-term behaviour, but have quantitative effects that could potentially reduce an autoimmune response to sub-clinical levels. Our results also suggest an important role for Tregs of arbitrary specificities in modulating the qualitative outcome. A stochastic treatment of the same model demonstrates that the probability of developing a chronic autoimmune response increases with the initial exposure to self antigen or autoreactive effector T cells. The three different mechanisms we consider, while leading to a number of similar predictions, also exhibit key differences in both transient dynamics (ODE approach) and the probability of chronic autoimmunity (stochastic approach).

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

SBML model exported from PottersWheel on 2007-09-19 15:35:47.

The values for parameters and the inital concentrations of this model where directly provided by the main author:

Parameter values
parameter value unit

p1 0.0025 1/min

p2 0.0784 1/min

p3 0.0013 1/min

p4 0.0827 1/min

p5 0.0091 1/min

p6 0.000064 1/(nmole*min)

p7 0.0397 1/min

p8 1000 nmole

p9 0.0098 1/(nmole*min)

p10 1.6 1/min

p11 1000 nmole

p12 0.0003 ml/min

The basal chamber volume was taken as 1 ml, the apical as 1.5. As starting values x1 was set to 88 nmole, all other species to 0.

Parameter values
parameter	value	unit
p1	0.0025	1/min
p2	0.0784	1/min
p3	0.0013	1/min
p4	0.0827	1/min
p5	0.0091	1/min
p6	0.000064	1/(nmole*min)
p7	0.0397	1/min
p8	1000	nmole
p9	0.0098	1/(nmole*min)
p10	1.6	1/min
p11	1000	nmole
p12	0.0003	ml/min

Tan2012 - Antibiotic Treatment, Inoculum Effect

The efficacy of many antibiotics decreases with increasing bacterial density, a phenomenon called the ‘inoculum effect’ (IE). This study reveals that, for ribosome-targeting antibiotics, IE is due to bistable inhibition of bacterial growth, which reduces the efficacy of certain treatment frequencies.

This model is described in the article:

The inoculum effect and band-pass bacterial response to periodic antibiotic treatment.

Tan C, Phillip Smith R, Srimani JK, Riccione KA, Prasada S, Kuehn M, You L.

Mol Syst Biol. 2012 Oct 9; 8:617

Abstract:

The inoculum effect (IE) refers to the decreasing efficacy of an antibiotic with increasing bacterial density. It represents a unique strategy of antibiotic tolerance and it can complicate design of effective antibiotic treatment of bacterial infections. To gain insight into this phenomenon, we have analyzed responses of a lab strain of Escherichia coli to antibiotics that target the ribosome. We show that the IE can be explained by bistable inhibition of bacterial growth. A critical requirement for this bistability is sufficiently fast degradation of ribosomes, which can result from antibiotic-induced heat-shock response. Furthermore, antibiotics that elicit the IE can lead to 'band-pass' response of bacterial growth to periodic antibiotic treatment: the treatment efficacy drastically diminishes at intermediate frequencies of treatment. Our proposed mechanism for the IE may be generally applicable to other bacterial species treated with antibiotics targeting the ribosomes.

This model is hosted on BioModels Database and identified by: BIOMD0000000425 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

Sarma2012 - Interaction topologies of MAPK cascade (M4_K2_QSS_PSEQ)

This model [ MODEL1204280040 - M4_K2_QSS_PSEQ] correspond to type M4 with mass-action kinetics K2, in QSS (quasi steady state) and USEQ (Unsequestrated ) condition. .

This model is described in the article:

Different designs of kinase-phosphatase interactions and phosphatase sequestration shapes the robustness and signal flow in the MAPK cascade.

Sarma U, Ghosh I.

BMC Syst Biol. 2012 Jul 2;6(1):82.

Abstract:

This model is hosted on BioModels Database and identified by: BIOMD0000000433 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This is the model described in the article:
The danger of metabolic pathways with turbo design
Teusink B, Walsh MC, van Dam K, Westerhoff HV Trends Biochem. Sci. 1998 May; Volume: 23 (Issue: 5 ): 162-9 9612078 ,
Abstract:
Many catabolic pathways begin with an ATP-requiring activation step, after which further metabolism yields a surplus of ATP. Such a 'turbo' principle is useful but also contains an inherent risk. This is illustrated by a detailed kinetic analysis of a paradoxical Saccharomyces cerevisiae mutant; the mutant fails to grow on glucose because of overactive initial enzymes of glycolysis, but is defective only in an enzyme (trehalose 6-phosphate synthase) that appears to have little relevance to glycolysis. The ubiquity of pathways that possess an initial activation step, suggests that there might be many more genes that, when deleted, cause rather paradoxical regulation phenotypes (i.e. growth defects caused by enhanced utilization of growth substrate).

The model represents the wild-type cell: 'guarded' glycolysis, which is the inhibition of the HK module by hexose monophosphate. The model reproduces figures 3c and 3d of the reference publication.

To reproduce unguarded glycolysis, set parameter wild_type to '0'.

This is the model described in the article:
A bistable Rb-E2F switch underlies the restriction point
Guang Yao, Tae Jun Lee, Seiichi Mori, Joseph R. Nevins, Lingchong You, Nat Cell Biol 2008 10:476-482; PMID: 18364697 ; DOI: 10.1038/ncb1711 .

Abstract:
The restriction point (R-point) marks the critical event when a mammalian cell commits to proliferation and becomes independent of growth stimulation. It is fundamental for normal differentiation and tissue homeostasis, and seems to be dysregulated in virtually all cancers. Although the R-point has been linked to various activities involved in the regulation of G1-S transition of the mammalian cell cycle, the underlying mechanism remains unclear. Using single-cell measurements, we show here that the Rb-E2F pathway functions as a bistable switch to convert graded serum inputs into all-or-none E2F responses. Once turned ON by sufficient serum stimulation, E2F can memorize and maintain this ON state independently of continuous serum stimulation. We further show that, at critical concentrations and duration of serum stimulation, bistable E2F activation correlates directly with the ability of a cell to traverse the R-point.

This model reproduces the serum-pulse stimulation-protocol in Figure 3(b).

This model was created according to the paper Inhibition of Adenylate Cyclase Is Mediated by the High Affinity Conformation of the alpha2-Adrenergic Receptor published in 1988.

The figure4 (steady state curve) in the paper has been simulated having the same plot with Copasi 4.0.19 (development) and roadRunner(online).Because the initial concentration of R and D were not given in the paper ,so we gave it 1e-9 Mol/L and 1e-8 Mol/L respectively.

Pay attention that the simulations of steady state concentration of species in arbitrary units are shown for figure4 and figure6 in the paper.

Note: The model reproduces the simulation result for an asymmetric model as depicted in Fig 3G of the paper. Model successfully tested on MathSBML

Jiang2007 - GSIS system, Pancreatic Beta Cells

Description of a core kinetic model of the glucose-stimulated insulin secretion system (GSIS) in pancreatic beta cells.

This model is described in the article:

A kinetic core model of the glucose-stimulated insulin secretion network of pancreatic beta cells.

Jiang N, Cox RD, Hancock JM.

Mamm Genome 2007 Jul; 18(6-7):508-20.

Abstract:

The construction and characterization of a core kinetic model of the glucose-stimulated insulin secretion system (GSIS) in pancreatic beta cells is described. The model consists of 44 enzymatic reactions, 59 metabolic state variables, and 272 parameters. It integrates five subsystems: glycolysis, the TCA cycle, the respiratory chain, NADH shuttles, and the pyruvate cycle. It also takes into account compartmentalization of the reactions in the cytoplasm and mitochondrial matrix. The model shows expected behavior in its outputs, including the response of ATP production to starting glucose concentration and the induction of oscillations of metabolite concentrations in the glycolytic pathway and in ATP and ADP concentrations. Identification of choke points and parameter sensitivity analysis indicate that the glycolytic pathway, and to a lesser extent the TCA cycle, are critical to the proper behavior of the system, while parameters in other components such as the respiratory chain are less critical. Notably, however, sensitivity analysis identifies the first reactions of nonglycolytic pathways as being important for the behavior of the system. The model is robust to deletion of malic enzyme activity, which is absent in mouse pancreatic beta cells. The model represents a step toward the construction of a model with species-specific parameters that can be used to understand mouse models of diabetes and the relationship of these mouse models to the human disease state.

The model reproduces Figure 2 of the paper, and is built using files 'ModelNNT11.xml' and 'changed.m' available from http://www.har.mrc.ac.uk/research/bioinformatics/research_areas/systems_biology.html .

A couple of small errors in the model (in the original SBML file 'ModelNNT11.xml') have been corrected. The errors are:

v44 now produces Pyr rather than PYR
the kinetic law of v27 is now dependent on cytoplasmic (rather than mitochondrial) acetyl CoA and OXA

This model is hosted on BioModels Database and identified by: BIOMD0000000239 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

EGF dependent Akt pathway model

made by Kazuhiro A. Fujita.

This is the EGF dependent Akt pathway model described in:
Decoupling of receptor and downstream signals in the Akt pathway by its low-pass filter characteristics.
Fujita KA, Toyoshima Y, Uda S, Ozaki Y, Kubota H, and Kuroda S. Sci Signal. 2010 Jul 27;3(132):ra56. PMID: 20664065 ; DOI: 10.1126/scisignal.2000810
Abstract:
In cellular signal transduction, the information in an external stimulus is encoded in temporal patterns in the activities of signaling molecules; for example, pulses of a stimulus may produce an increasing response or may produce pulsatile responses in the signaling molecules. Here, we show how the Akt pathway, which is involved in cell growth, specifically transmits temporal information contained in upstream signals to downstream effectors. We modeled the epidermal growth factor (EGF)–dependent Akt pathway in PC12 cells on the basis of experimental results. We obtained counterintuitive results indicating that the sizes of the peak amplitudes of receptor and downstream effector phosphorylation were decoupled; weak, sustained EGF receptor (EGFR) phosphorylation, rather than strong, transient phosphorylation, strongly induced phosphorylation of the ribosomal protein S6, a molecule downstream of Akt. Using frequency response analysis, we found that a three-component Akt pathway exhibited the property of a low-pass filter and that this property could explain decoupling of the peak amplitudes of receptor phosphorylation and that of downstream effectors. Furthermore, we found that lapatinib, an EGFR inhibitor used as an anticancer drug, converted strong, transient Akt phosphorylation into weak, sustained Akt phosphorylation, and, because of the low-pass filter characteristics of the Akt pathway, this led to stronger S6 phosphorylation than occurred in the absence of the inhibitor. Thus, an EGFR inhibitor can potentially act as a downstream activator of some effectors.

This model is from the article:
Division of labor by dual feedback regulators controls JAK2/STAT5 signaling over broad ligand range.
Bachmann J, Raue A, Schilling M, Böhm ME, Kreutz C, Kaschek D, Busch H, Gretz N, Lehmann WD, Timmer J, Klingmüller U. Mol Syst Biol. 2011 Jul 19;7:516. 21772264 ,
Abstract:
Cellular signal transduction is governed by multiple feedback mechanisms to elicit robust cellular decisions. The specific contributions of individual feedback regulators, however, remain unclear. Based on extensive time-resolved data sets in primary erythroid progenitor cells, we established a dynamic pathway model to dissect the roles of the two transcriptional negative feedback regulators of the suppressor of cytokine signaling (SOCS) family, CIS and SOCS3, in JAK2/STAT5 signaling. Facilitated by the model, we calculated the STAT5 response for experimentally unobservable Epo concentrations and provide a quantitative link between cell survival and the integrated response of STAT5 in the nucleus. Model predictions show that the two feedbacks CIS and SOCS3 are most effective at different ligand concentration ranges due to their distinct inhibitory mechanisms. This divided function of dual feedback regulation enables control of STAT5 responses for Epo concentrations that can vary 1000-fold in vivo. Our modeling approach reveals dose-dependent feedback control as key property to regulate STAT5-mediated survival decisions over a broad range of ligand concentrations.

This model is according to the paper Dynamic Simulation on the Arachidonic Acid Metabolic Network . Figure 2A has been reproduced by SBML ode solver on line. In the original model, all the reactions are presented as ODE directly. So curator rewrite each reaction according to the semantics of the paper. In this paper, the authors used quict complex kinetics law to describe the catalysis in the network, curators did not necessarily know all the complete meanings of the paper.

The model is according to the paper Which Model to Use for Cortical Spiking Neurons? Figure1(J) subthreshold oscillations has been reproduced by MathSBML. The ODE and the parameters values are taken from the a paper Simple Model of Spiking Neurons The original format of the models are encoded in the MATLAB format existed in the ModelDB with Accession number 39948

Figure1 are the simulation results of the same model with different choices of parameters and different stimulus function or events.a=0.05; b=0.26; c=-60; d=0; V=-62; u=b*V;

This model is from the article:
A model for the tissue factor pathway to thrombin. II. A mathematical simulation.
Jones KC, Mann KG. J Biol Chem. 1994 Sep 16;269(37):23367-73. 8083242 ,
Abstract:
A mathematical simulation of the tissue factor pathway to the generation of thrombin has been developed using a combination of empirical, estimated, and deduced rate constants for reactions involving the activation of factor IX, X, V, and VIII, in the formation of thrombin, as well as rate constants for the assembly of the coagulation enzyme complexes which involve factor VIIIa-factor IXa (intrinsic tenase) and factor Va-Xa (prothrombinase) assembled on phospholipid membrane. Differential equations describing the fate of each species in the reaction were developed and solved using an interactive procedure based upon the Runge-Kutta technique. In addition to the theoretical considerations involving the reactions of the tissue factor pathway, a physical constraint associated with the stability of the factor VIIIa-factor IXa complex has been incorporated into the model based upon the empirical observations associated with the stability of this complex. The model system provides a realistic accounting of the fates of each of the proteins in the coagulation reaction through a range of initiator (factor VIIa-tissue factor) concentrations ranging from 5 pM to 5 nM. The model is responsive to alterations in the concentrations of factor VIII, factor V, and their respective activated species, factor VIIIa and factor Va, and overall provides a reasonable approximation of empirical data. The computer model permits the assessment of the reaction over a broad range of conditions and provides a useful tool for the development and management of reaction studies.

The model reproduces the time profile of the species as depicted in Fig 3A of the paper. Model successfully tested on MathSBML and Jarnac.

Edelstein1996 - EPSP ACh event

Model of a nicotinic Excitatory Post-Synaptic Potential in a Torpedo electric organ. Acetylcholine is not represented explicitely, but by an event that changes the constants of transition from unliganded to liganded.

This model has initially been encoded using StochSim.

This model is described in the article:

A kinetic mechanism for nicotinic acetylcholine receptors based on multiple allosteric transitions.

Edelstein SJ, Schaad O, Henry E, Bertrand D, Changeux JP.

Biol. Cybern. 1996 Nov; 75(5):361-79

Abstract:

This model is hosted on BioModels Database and identified by: BIOMD0000000001 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This model by Jana Wolf et al. 2001 is the first mechanistic model of respiratory oscillations in Saccharomyces cerevisae. It is based on the assumption that feedback inhibition of cysteine on the sulfate transporters leads to oscillations in this pathway and causes oscillations in respiratory activity via inhibition of cytochrome c oxidase by hydrogen disulfide. The model is qualitative/semi-quantitative and reproduces the respiratory oscillation pattern quite well. It is based on very coarse-grained representations of the mitochondrial tricarboxylic acid cycle and the mitochondrial electron transport chain (oxidative phosphorylation). The sulfate assimilatory pathways also contains some significant simplifcations.

The model corresponds to Fig. 2B of the paper, with a slight phase shift of the oscillations. No initial conditions were given in the paper, and thus they were chosen arbitrarily in a range that lies within the basin of attraction of the limit cycle oscillations. Species IDs correspond to IDs used by the authors, while SBML names are more common abbreviations.

Caveats:
1) Equilibrated transport:
The model assumes fast equilibration between mitochondria and cytoplasm for the metabolites NADH, NAD+, H2S and Acetyl-CoA.
2) Cytosolic mass conservation ATP/ADP:
The model uses mass conservation for cytosolic adenosine nucleotides with is however not encoded in the stoichiometry, but is implied by the lumped reaction v4. This reaction combines the enzymatic reactions of phosphoadenylyl-sulfate reductase (thioredoxin) (yeast protein Met16p, EC 1.8.4.8) and sulfite reductase (NADPH) (subunits Met5p and Met10p, EC 1.8.1.2). EC 1.8.4.8 also has adenosine-3',5'-bismonophosphate (PAP, not to confuse with ID pap in this model, standing for PAPS) as a product. PAP is the substrate for enzyme 3'(2'),5'-bisphosphate nucleotidase (Met22p, EC:3.1.3.7) which would revover AMP (and Pi). Then AMP can be assumed to be equilibrated with ATP and ADP via adenylate kinase, as often used in metabolic models. This AMP production is implied in the mass conservation for cytosolic adenosine phosphates. Accounting for these reactions explicitly does not change the dynamics of the model significantly. An according version can be obtained from the SBML creator (Rainer Machne, mailto:raim@tbi.univie.ac.at).
3) Redox balance:
The enzyme sulfite reductase (NADPH) (subunits Met5p and Met10p, EC 1.8.1.2, part of reaction v4) actually uses NADPH, and the authors assume equilibration of NADH and NADPH. But actually S. cerevisiae specifically is missing the according enzyme transhydrogenase (EC 1.6.1.1 or EC 1.6.1.2). EC 1.8.4.8 also oxidizes thioredoxin and would actually require an additional NADPH for thioredoxin recovery (reduction). This would slightly affect the redox balance of the model.
4) Energy balance:
Reaction v7 lumps NAD-dependent alcohol dehydrogenase (EC 1.1.1.1), aldehyde dehydrogenase (NAD+) (EC 1.2.1.3) and acetyl-CoA synthase (EC 6.2.1.1). The latter reaction would actually consume ATP as a co-factor, producing AMP+PPi, and this is not included in the model. This would slightly bias the model's energy balance.

This a model from the article:
Synthetic in vitro transcriptional oscillators.
Kim J, Winfree E Mol. Syst. Biol. 2011 Feb 1;7:465. 21283141 ,
Abstract:
The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells.

Notes:

The paper describes 7 models (MODEL1012090000-6) and all these are submitted by the authors. This model (MODEL1012090001) corresponds to the Simple model of the three-switch ring oscillator (Design III). The model reproduces figure 6 (central figures) of the reference publication. The time is rescaled by s=v_d/K_I*t where K_I=0.333 and v_d=1 (for alpha = 1) and v_d=0.5 (for alpha = 0.5). i.e. For alpha = 1, s = 0.003 * t (roughly 10 unitless time = 1hr; the time-course should be run for 60 timeunits (6hrs) to get figure 6a). For alpha = 2, s= 0.0015 * t (roughly 5 unitless time = 1hr; the time-course shoue be run for 100 timesunits (20hrs) to get figure 6b).

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2009 The BioModels Team.
For more information see the terms of use .
To cite BioModels Database, please use Le Nov��re N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

Field-Noyes Model of BZ Reaction

Citation
R.J.Field and R.M.Noyes,J.Chem.Phys.60,1877 (1974)

Description
Field Noyes Version of Belousov-Zhabotinsky Reaction. BrO3 is held constant; HOBr is typically ignored, and can be replaced by an empty-set. The stoichiometry f is typically taken as 1/2 or 1. .

Initially Generated by Cellerator Version 1.0 update 2.1220 using Mathematica 4.2 for Mac OS X (June 4, 2002), December 26, 2002 10:43:53, using (PowerMac,PowerPC, Mac OS X,MacOSX,Darwin). author=B.E.Shapiro

Modified with SBMLeditor by Nicolas Le Novère, to fit the original article.

This a model from the article:
Modeling the interactions between osteoblast and osteoclast activities in bone remodeling.
Lemaire V, Tobin FL, Greller LD, Cho CR, Suva LJ. J Theor Biol. 2004 Aug 7;229(3):293-309. 15234198 ,
Abstract:
We propose a mathematical model explaining the interactions between osteoblasts and osteoclasts, two cell types specialized in the maintenance of the bone integrity. Bone is a dynamic, living tissue whose structure and shape continuously evolves during life. It has the ability to change architecture by removal of old bone and replacement with newly formed bone in a localized process called remodeling. The model described here is based on the idea that the relative proportions of immature and mature osteoblasts control the degree of osteoclastic activity. In addition, osteoclasts control osteoblasts differentially depending on their stage of differentiation. Despite the tremendous complexity of the bone regulatory system and its fragmentary understanding, we obtain surprisingly good correlations between the model simulations and the experimental observations extracted from the literature. The model results corroborate all behaviors of the bone remodeling system that we have simulated, including the tight coupling between osteoblasts and osteoclasts, the catabolic effect induced by continuous administration of PTH, the catabolic action of RANKL, as well as its reversal by soluble antagonist OPG. The model is also able to simulate metabolic bone diseases such as estrogen deficiency, vitamin D deficiency, senescence and glucocorticoid excess. Conversely, possible routes for therapeutic interventions are tested and evaluated. Our model confirms that anti-resorptive therapies are unable to partially restore bone loss, whereas bone formation therapies yield better results. The model enables us to determine and evaluate potential therapies based on their efficacy. In particular, the model predicts that combinations of anti-resorptive and anabolic therapies provide significant benefits compared with monotherapy, especially for certain type of skeletal disease. Finally, the model clearly indicates that increasing the size of the pool of preosteoblasts is an essential ingredient for the therapeutic manipulation of bone formation. This model was conceived as the first step in a bone turnover modeling platform. These initial modeling results are extremely encouraging and lead us to proceed with additional explorations into bone turnover and skeletal remodeling.

This model corresponds to the core model published in the paper. There is no corresponding plot to reproduce for this model. To obtain each of the 9 plots in the Figure 2 of the reference publication, there are some changes to be made to the core model. The curation figure reproduces figure 2 of the reference publication. There is a corresponding SBML and Copasi files for each of the plot. See curation tab for more details.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2008 The BioModels Team.
For more information see the terms of use .
To cite BioModels Database, please use Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

This a model from the article:
Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling.
Komarova SV, Smith RJ, Dixon SJ, Sims SM, Wahl LM Bone 2003 Aug;33(2):206-15 14499354 ,
Abstract:
Bone remodeling occurs asynchronously at multiple sites in the adult skeleton and involves resorption by osteoclasts, followed by formation of new bone by osteoblasts. Disruptions in bone remodeling contribute to the pathogenesis of disorderssuch as osteoporosis, osteoarthritis, and Paget's disease. Interactions among cells of osteoblast and osteoclast lineages are critical in the regulation of bone remodeling. We constructed a mathematical model of autocrine and paracrine interactions among osteoblasts and osteoclasts that allowed us to calculate cell population dynamics and changes in bone mass at a discrete site of bone remodeling. Themodel predicted different modes of dynamic behavior: a single remodeling cycle in response to an external stimulus, a series of internally regulated cycles of bone remodeling, or unstable behavior similar to pathological bone remodeling in Paget's disease. Parametric analysis demonstrated that the mode of dynamic behaviorin the system depends strongly on the regulation of osteoclasts by autocrine factors, such as transforming growth factor beta. Moreover, simulations demonstratedthat nonlinear dynamics of the system may explain the differing effects of immunosuppressants on bone remodeling in vitro and in vivo. In conclusion, the mathematical model revealed that interactions among osteoblasts and osteoclasts result in complex, nonlinear system behavior, which cannot be deduced from studies of each cell type alone. The model will be useful in future studies assessing the impact of cytokines, growth factors, and potential therapies on the overall process ofremodeling in normal bone and in pathological conditions such as osteoporosis and Paget's disease.

The model reproduces Fig 2A and Fig 2B of the paper. Note that the Y-axis scale is not right, the osteoblast steadystate is approximatley 212 and not 0 as depicted in the figure. Also, there is atypo in the equation for x2_bar which has been corrected here. Model successfully tested on MathSBML.

Goldbeter1991 - Min Mit Oscil, Expl Inact

This model represents the inactive forms of CDC-2 Kinase and Cyclin Protease as separate species, unlike the ODEs in the published paper, in which the equations for the inactive forms are substituted into the equations for the active forms using a mass conservation rule M+MI=1,X+XI=1. Mass is still conserved in this model through the explicit reactions M<->MI and X<->XI. The terms in the kinetic laws are identical to the corresponding terms in the kinetic laws in the published paper.

This model has been generated by MathSBML 2.4.6 (14-January-2005) 14-January-2005 18:37:35.503857.

This model is described in the article:

A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase.

Goldbeter A.

Proc. Natl. Acad. Sci. USA 1991 Oct; 88(20):9107-11

Abstract:

A minimal model for the mitotic oscillator is presented. The model, built on recent experimental advances, is based on the cascade of post-translational modification that modulates the activity of cdc2 kinase during the cell cycle. The model pertains to the situation encountered in early amphibian embryos, where the accumulation of cyclin suffices to trigger the onset of mitosis. In the first cycle ofthe bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation, and in the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. That cyclin activates cdc2 kinase while the kinase triggers the degradation of cyclin has suggested that oscillations may originate from such a negative feedback loop [Félix, M. A., Labbé, J. C., Dorée, M., Hunt, T. & Karsenti, E. (1990) Nature (London) 346, 379-382]. Thisconjecture is corroborated by the model, which indicates that sustained oscillations of the limit cycle type can arise in the cascade, provided that a threshold exists in the activation of cdc2 kinase by cyclin and in the activation of cyclinproteolysis by cdc2 kinase. The analysis shows how miototic oscillations may readily arise from time lags associated with these thresholds and from the delayed negative feedback provided by cdc2-induced cyclin degradation. A mechanism for theorigin of the thresholds is proposed in terms of the phenomenon of zero-order ultrasensitivity previously described for biochemical systems regulated by covalent modification.

This model is hosted on BioModels Database and identified by: BIOMD0000000004 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This model is from the article:
Computational modelling of mitotic exit in budding yeast: the role of separase and Cdc14 endocycles
Vinod PK, Freire P, Rattani A, Ciliberto A, Uhlmann F, Novak B. J R Soc Interface. 2011 Aug 7;8(61):1128-41. Epub 2011 Feb 2. 21288956 ,
Abstract:
The operating principles of complex regulatory networks are best understood with the help of mathematical modelling rather than by intuitive reasoning. Hereby, we study the dynamics of the mitotic exit (ME) control system in budding yeast by further developing the Queralt's model. A comprehensive systems view of the network regulating ME is provided based on classical experiments in the literature. In this picture, Cdc20-APC is a critical node controlling both cyclin (Clb2 and Clb5) and phosphatase (Cdc14) branches of the regulatory network. On the basis of experimental situations ranging from single to quintuple mutants, the kinetic parameters of the network are estimated. Numerical analysis of the model quantifies the dependence of ME control on the proteolytic and non-proteolytic functions of separase. We show that the requirement of the non-proteolytic function of separase for ME depends on cyclin-dependent kinase activity. The model is also used for the systematic analysis of the recently discovered Cdc14 endocycles. The significance of Cdc14 endocycles in eukaryotic cell cycle control is discussed as well.

Model reproduces the dynamics of ATP and NADH as depicted in Fig 4 of the paper. Model successfully tested on Jarnac and MathSBML.

This model is according to the paper A systems biology dynamical model of mammalian G1 cell cycle progression. Supplementary Figure 2A has been reproduced by the MathSBML and CellDesigner. All the data of this model are from the set 2 of Supplementary talbe2.

The model is according to the paper Simple Model of Spiking Neurons In this paper, a simple spiking model is presented that is as biologically plausible as the Hodgkin-Huxley model, yet as computationally efficient as the integrate-and-fire model. Known types of neurons correspond to different values of the parameters a,b,c,d in the model. Figure2RS,IB,CH,FS,LTS have been simulated by MathSBML.

RS: a=0.02, b=0.2, c=-65, d=8.

IB: a=0.02,b=0.2,c=-55,d=4

CH: a=0.02,b=0.2,c=-50,d=2

FS:a=0.1b=0.2c=-65,d=2

LTS:a=0.02,b=0.25,c=-65,d=2

To cite BioModels Database, please use Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

This model is from the article:
Dynamics of the cell cycle: checkpoints, sizers, and timers.
Qu Z, MacLellan WR, Weiss JN Biophys. J. 2003 Dec; 85(6): 3600-11 14645053 ,
Abstract:
We have developed a generic mathematical model of a cell cycle signaling network in higher eukaryotes that can be used to simulate both the G1/S and G2/M transitions. In our model, the positive feedback facilitated by CDC25 and wee1 causes bistability in cyclin-dependent kinase activity, whereas the negative feedback facilitated by SKP2 or anaphase-promoting-complex turns this bistable behavior into limit cycle behavior. The cell cycle checkpoint is a Hopf bifurcation point. These behaviors are coordinated by growth and division to maintain normal cell cycle and size homeostasis. This model successfully reproduces sizer, timer, and the restriction point features of the eukaryotic cell cycle, in addition to other experimental findings.

Figure6B has been reproduced by both SBMLodeSolver online and MathSBML. We do not include the synthesis of cyclins is proportional to cell size (Equation 2 in Page3604 of the paper) in this model. The author of the paper keep all the variables and parameters dimensionless. But in the model, we choose to use default units of SBML.

This is an SBML implementation the model of homeostastis by negative feedback (figure 1g) described in the article:
Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell.
Tyson JJ, Chen KC, Novak B. Curr Opin Cell Biol. 2003 Apr;15(2):221-31. PubmedID: 12648679 ; DOI: 10.1016/S0955-0674(03)00017-6 ;

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

This is the simple model without diffusion described in th epublication
Sharp developmental thresholds defined through bistability by antagonistic gradients of retinoic acid and FGF signaling.
Goldbeter A, Gonze D, Pourquié O. Dev Dyn. 2007 Jun;236(6):1495-508. PMID: 17497689 , doi: 10.1016/j.jtbi.2008.01.006
Abstract:
The establishment of thresholds along morphogen gradients in the embryo is poorly understood. Using mathematical modeling, we show that mutually inhibitory gradients can generate and position sharp morphogen thresholds in the embryonic space. Taking vertebrate segmentation as a paradigm, we demonstrate that the antagonistic gradients of retinoic acid (RA) and Fibroblast Growth Factor (FGF) along the presomitic mesoderm (PSM) may lead to the coexistence of two stable steady states. Here, we propose that this bistability is associated with abrupt switches in the levels of FGF and RA signaling, which permit the synchronized activation of segmentation genes, such as mesp2, in successive cohorts of PSM cells in response to the segmentation clock, thereby defining the future segments. Bistability resulting from mutual inhibition of RA and FGF provides a molecular mechanism for the all-or-none transitions assumed in the "clock and wavefront" somitogenesis model. Given that mutually antagonistic signaling gradients are common in development, such bistable switches could represent an important principle underlying embryonic patterning.

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

The model is according to the paper Na+ Channel Mutation That Causes Both Brugada and Long-QT Syndrome Phenotypes: A Simulation Study of Mechanism Original model comes from ModelDB with accession number: 62661. This is the wide type model. All the values and reactions obtained from Data Supplement6: Appendix of the paper. Figure3 has been reproduced by MathSBML. The stimulus v=-30mV during the time from 5ms to 20 ms displayed in the event. The meaning for the keyword, C: Close states; O: Open states; IF: Fast inactivation states; IC: Closed-Inactivation states; IM: Intermediat Inactivation states.

This a model from the article:
A mathematical model of bone remodeling dynamics for normal bone cell populations and myeloma bone disease
Bruce P Ayati, Claire M Edwards, Glenn F Webb and John P Wikswo. Biology Direct 2010 Apr 20;5(28). 20406449 ,
Abstract:
BACKGROUND: Multiple myeloma is a hematologic malignancy associated with the development of a destructive osteolytic bone disease. RESULTS: Mathematical models are developed for normal bone remodeling and for the dysregulated bone remodeling that occurs in myeloma bone disease. The models examine the critical signaling between osteoclasts (bone resorption) and osteoblasts (bone formation). The interactions of osteoclasts and osteoblasts are modeled as a system of differential equations for these cell populations, which exhibit stable oscillations in the normal case and unstable oscillations in the myeloma case. In the case of untreated myeloma, osteoclasts increase and osteoblasts decrease, with net bone loss as the tumor grows. The therapeutic effects of targeting both myeloma cells and cells of the bone marrow microenvironment on these dynamics are examined. CONCLUSIONS: The current model accurately reflects myeloma bone disease and illustrates how treatment approaches may be investigated using such computational approaches.

Note:

The paper describes three models 1) Zero-dimensional Bone Model without Tumour, 2) Zero-dimensional Bone Model with Tumour and 3) Zero-dimensional Bone Model with Tumour and Drug Treatment. This model corresponds to the Zero-dimensional Bone Model without Tumour.

Typos in the publication:

Equation (4): The first term should be (β1/α1)^(g12/Γ) and not (β2/α2)^(g12/Γ)

Equation (14): The first term should be (β1/α1)^(((g12/(1+r12))/Γ) and not (β2/α2)^(((g12/(1+r12))/Γ)

Equation (13): The first term should be (β1/α1)^((1-g22+r22)/Γ) and not (β1/α1)^((1-g22-r22)/Γ)

All these corrections has been implemented in the model, with the authors agreement.

Beyond these, there are several mismatches between the equation numbers that are mentioned in for each equation and the reference that has been made to these equations in the figure legend.

This is the single cell model for analysis of hormonal crosstalk in Arabidopsis described in the article:
Modelling and experimental analysis of hormonal crosstalk in Arabidopsis.
Liu J, Mehdi S, Topping J, Tarkowski P and Lindsey K. Mol Syst Biol. 2010 Jun 8;6:373; PmID: 20531403 , DOI: 10.1038/msb.2010.26
Abstract:
An important question in plant biology is how genes influence the crosstalk between hormones to regulate growth. In this study, we model POLARIS (PLS) gene function and crosstalk between auxin, ethylene and cytokinin in Arabidopsis. Experimental evidence suggests that PLS acts on or close to the ethylene receptor ETR1, and a mathematical model describing possible PLS-ethylene pathway interactions is developed, and used to make quantitative predictions about PLS-hormone interactions. Modelling correctly predicts experimental results for the effect of the pls gene mutation on endogenous cytokinin concentration. Modelling also reveals a role for PLS in auxin biosynthesis in addition to a role in auxin transport. The model reproduces available mutants, and with new experimental data provides new insights into how PLS regulates auxin concentration, by controlling the relative contribution of auxin transport and biosynthesis and by integrating auxin, ethylene and cytokinin signalling. Modelling further reveals that a bell-shaped dose-response relationship between endogenous auxin and root length is established via PLS. This combined modelling and experimental analysis provides new insights into the integration of hormonal signals in plants.

This model was originally created using Copasi and taken from the supplementary materials of the MSB article. It uses equation 5 for the auxin biosynthesis and was altered to also contain the reactions for ACC, IAA and cytokinine import. Different from the supplementary material, the parameters for the auxin synthesis, v2, are set to k2c = 0.01 uM and k2=0.2 uM_per_sec and for the WT PLS transcription k6=0.3 . To obtain the model described in the first table of the supplementary materials, set k2c=k2=0 and k6=0.9 . For the pls and PLSox mutants, k6 should be set to 0 and 0.45, respectively.

SBML Level 2 code generated for the JWS Online project by Jacky Snoep using PySCeS .

Run this model online at http://jjj.biochem.sun.ac.za .

To cite JWS Online please refer to: Olivier, B.G. and Snoep, J.L. (2004) Web-based modelling using JWS Online , Bioinformatics, 20:2143-2144.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2010 The BioModels Team.
For more information see the terms of use .

To cite BioModels Database, please use Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

The model is according to the paper Which Model to Use for Cortical Spiking Neurons? Figure1(M) rebound spike has been reproduced by MathSBML. The ODE and the parameters values are taken from the a paper Simple Model of Spiking Neurons The original format of the models are encoded in the MATLAB format existed in the ModelDB with Accession number 39948

Figure1 are the simulation results of the same model with different choices of parameters and different stimulus function or events.a=0.03; b=0.25; c=-60; d=4; V=-64; u=b*V;

This is A431 IERMv1.0 model described in the article
Input-output behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data.
William W Chen, Birgit Schoeberl, Paul J Jasper, Mario Niepel, Ulrik B Nielsen, Douglas A Lauffenburger and Peter K Sorger. Molecular Systems Biology 2009; 5:239. PMID: 19156131 , DOI: 10.1038/msb.2008.74

Abstract:
The ErbB signaling pathways, which regulate diverse physiological responses such as cell survival, proliferation and motility, have been subjected to extensive molecular analysis. Nonetheless, it remains poorly understood how different ligands induce different responses and how this is affected by oncogenic mutations. To quantify signal flow through ErbB-activated pathways we have constructed, trained and analyzed a mass action model of immediate-early signaling involving ErbB1-4 receptors (EGFR, HER2/Neu2, ErbB3 and ErbB4), and the MAPK and PI3K/Akt cascades. We find that parameter sensitivity is strongly dependent on the feature (e.g. ERK or Akt activation) or condition (e.g. EGF or heregulin stimulation) under examination and that this context dependence is informative with respect to mechanisms of signal propagation. Modeling predicts log-linear amplification so that significant ERK and Akt activation is observed at ligand concentrations far below the K(d) for receptor binding. However, MAPK and Akt modules isolated from the ErbB model continue to exhibit switch-like responses. Thus, key system-wide features of ErbB signaling arise from nonlinear interaction among signaling elements, the properties of which appear quite different in context and in isolation.

The sbml model is available as supplemental material to the article and at http://www.cdpcenter.org/resources/models/chen-et-al-2008/ . It was slightly changed to make it valid SBML and to incorporate the step functions, described in the readme file and needed for inhibitor preincubation. the equilibration processes end at 1800 sec, so to reproduce the dynamics shown in the publication and supplemental material, only the time points after 1800 need to be considered. The parameter set is the hand fitted one used for Sfigure 3 in the supplemental materials. All species are in molecules, apart from HRG, EGF and Inh, which are in M.

The results shown in SFigure 3 can be calculated dividing the parameters ERK_PP , AKT_PP and ERB_B1_P_tot by ERK_t , AKT_t and EGFR_t , respectively. Somehow we did not find the right scaleing factor for the phosphorylated ErbB1 receptor. Therefore the model does only qualitatively reproduces the timecourses shown in the first row of Sfigure 3.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2010 The BioModels Team.
For more information see the terms of use .
To cite BioModels Database, please use Le Nov��re N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

Note:

There are two models described in the paper to simulate basal and receptor stimulated Ca ²⁺ signaling. 1) No adaptive feedback (MODEL1108050000) and 2) with three slow adaptive feedback loops (this model: MODEL1108050001).

Gupta2009 - Eicosanoid Metabolism

Integrated model of eicosanoid metabolism and signaling based on lipidomics flux analysis.

This model is described in the article:

An integrated model of eicosanoid metabolism and signaling based on lipidomics flux analysis.

Gupta S, Maurya MR, Stephens DL, Dennis EA, Subramaniam S.

Biophys. J. 2009 Jun; 96(11):4542-51.

Abstract:

There is increasing evidence for a major and critical involvement of lipids in signal transduction and cellular trafficking, and this has motivated large-scale studies on lipid pathways. The Lipid Metabolites and Pathways Strategy consortium is actively investigating lipid metabolism in mammalian cells and has made available time-course data on various lipids in response to treatment with KDO(2)-lipid A (a lipopolysaccharide analog) of macrophage RAW 264.7 cells. The lipids known as eicosanoids play an important role in inflammation. We have reconstructed an integrated network of eicosanoid metabolism and signaling based on the KEGG pathway database and the literature and have developed a kinetic model. A matrix-based approach was used to estimate the rate constants from experimental data and these were further refined using generalized constrained nonlinear optimization. The resulting model fits the experimental data well for all species, and simulated enzyme activities were similar to their literature values. The quantitative model for eicosanoid metabolism that we have developed can be used to design experimental studies utilizing genetic and pharmacological perturbations to probe fluxes in lipid pathways.

This model is hosted on BioModels Database and identified by: BIOMD0000000436 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This model is described in the article:
The mechanism of catalase action. II. Electric analog computer studies.
Britton Chance, David S Greenstein, Joseph Higgins, CC Yang, Arch Biochem. 1952 37:322-39. PubmedID: 14953444
Summary:
An electric analog computer has been constructed for a study of the kinetics of catalase action. This computer gives results for the formation and disappearance of the catalase-hydrogen peroxide complex that are in good agreement with the experimental data. The computer study verifies an approximate method for the computation of the velocity constant for the combination of hydrogen peroxide and catalase and justifies the simple formula used previously to compute the velocity constant for the reaction of the catalase-hydrogen peroxide complex with donor molecules. Finally, the computer data show that the binding of peroxide to catalase is a practically irreversible reaction.

The reaction of the enzyme-substrate complex, p, with the electron donor, a, is bimolecular, although in the article, as a is assumed to be constant, it is modelled using an apparent rate constant consisting of the product of the rate constant, k4, and the concentration of a. In this implementation, the concentration of a is set to 1 and the value of k4 just adapted so that the product equals the values given for k4*a in the article. The specific parameter values are taken from Fig 3. The graphs do not exactly match those in the paper, this may be due to the different simulators used.

This is the model described in the article:
Photosynthetic oscillations and the interdependence of photophosphorylation and electron transport as studied by a mathematical model.
Rovers W, Giersch C. Biosystems. 1995;35(1):63-73. PMID: 7772723
Abstract:
A simple mathematical model of photosynthetic carbon metabolism as driven by ATP and NADPH has been formulated to analyse photosynthetic oscillations. Two essential assumptions of this model are: (i) reduction of 3-phosphoglycerate to triosephosphate in the Clavin cycle is limited by ATP, not by NADPH, and (ii) photophosphorylation is affected by the availability of both ADP and NADP, while electron transport is limited by NADP only. The model produces oscillations of observed damping and period in ATP and NADP concentrations which are about 180 degrees out of phase, while three alternative proposals regarding coupling of electron transport and photophosphorylation do not produce oscillatory model solutions. The phases of ATP and NADPH are in reasonable agreement with the available experimental data. The model (which assumes that redox control of photophosphorylation is part of the oscillatory mechanism) is compared with an alternative proposal (that oscillations are due to interdependence of turnover of adenylates and Calvin cycle intermediates). From the similarity of the mathematical structures of both models it is inviting to speculate that both models are partial aspects of the oscillatory mechanism.

Note: EGFR belongs to the human epidermal receptor (HER) family of receptor tyrosine kinases, which consists of four closely related receptors (EGFR (HER1, erbB1), HER2 (neu, erbB2), HER3 (erbB3), and HER4 (erbB4)) that mediate cellular signaling pathways involved in growth and proliferation in response to the binding of a variety of growth factor ligands. There are currently six known endogenous ligands for EGFR: EGF, transforming growth factor- (TGF-), amphiregulin, betacellulin, heparin-binding EGF (HB-EGF), and epiregulin.Upon ligand binding, the EGFR forms homo- or heterodimeric complexes (usually with HER2), which leads to activation of the receptor tyrosine kinase, via autophosphorylation. References: 12813928 14527402 14561424 14766123

This is the model with unfitted parameters described in the article
Dynamic rerouting of the carbohydrate flux is key to counteracting oxidative stress
Markus Ralser, Mirjam M Wamelink, Axel Kowald, Birgit Gerisch, Gino Heeren, Eduard A Struys, Edda Klipp, Cornelis Jakobs, Michael Breitenbach, Hans Lehrach and Sylvia Krobitsch, J Biol 2007 6(4):10; PMID: 18154684 , doi: 10.1186/jbiol61
Abstract:
BACKGROUND: Eukaryotic cells have evolved various response mechanisms to counteract the deleterious consequences of oxidative stress. Among these processes, metabolic alterations seem to play an important role.
RESULTS: We recently discovered that yeast cells with reduced activity of the key glycolytic enzyme triosephosphate isomerase exhibit an increased resistance to the thiol-oxidizing reagent diamide. Here we show that this phenotype is conserved in Caenorhabditis elegans and that the underlying mechanism is based on a redirection of the metabolic flux from glycolysis to the pentose phosphate pathway, altering the redox equilibrium of the cytoplasmic NADP(H) pool. Remarkably, another key glycolytic enzyme, glyceraldehyde-3-phosphate dehydrogenase (GAPDH), is known to be inactivated in response to various oxidant treatments, and we show that this provokes a similar redirection of the metabolic flux.
CONCLUSION: The naturally occurring inactivation of GAPDH functions as a metabolic switch for rerouting the carbohydrate flux to counteract oxidative stress. As a consequence, altering the homoeostasis of cytoplasmic metabolites is a fundamental mechanism for balancing the redox state of eukaryotic cells under stress conditions.

Different realtive enzyme velocities can be simulated by varying the parameters k_rel_TPI and k_rel_GAPDH .

NFkB model M(14,25,28) - Lipniacky's NFkB model

This is a model of NFkB pathway functioning from hierarchy of models of decreasing complexity, created to demonstrate application of model reduction methods proposed in

This a model from the article:
Robust simplifications of multiscale biochemical networks.
Radulescu O, Gorban A., Zinovyev A., Lilienbaum. A. BMC Syst Biol 2008:2:86 18854041 ,
Abstract:
BACKGROUND: Cellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions. In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In systems biology we also need to compare models or to couple them as parts of larger models. In these situations reduction to a common level of complexity is needed. RESULTS: We propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as "pseudo-monomolecular" subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in 1. Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model. The methods are demonstrated for simple examples and for a more complex model of NF-kappaB pathway. CONCLUSION: Our approach allows critical parameter identification and produces hierarchies of models. Hierarchical modeling is important in "middle-out" approaches when there is need to zoom in and out several levels of complexity. Critical parameter identification is an important issue in systems biology with potential applications to biological control and therapeutics. Our approach also deals naturally with the presence of multiple time scales, which is a general property of systems biology models.

This model is originally proposed by Lipniacki 2004 (Lipniacki T, Paszek P, Brasier AR, Luxon B, Kimmel M.(2004). Mathematical model of NF-kappaB regulatory module. J. Theor. Biol. 228 (2): 195-215. 15094015

The models are provided in CellDesigner v3.5 format. The name of the model M(x,y,z) should be deciphered as following:

x - number of species y - number of reactions z - number of parameters

Simulation protocol: The model can be simulated in CellDesigner directly, or in any simulator supporting events. The simulation period should be set up in 20 hours (t=72000 sec). This model reproduces Figure 3b (M(14,25,28)) of the publication.

For additional information please contact Andrei.Zinovyev at curie.fr

This model is according to the paper Computational modeling reveals how interplay between components of a GTPase-cycle module regulates signal transduction by Bornheimer et al 2004.The figure 3 is reproduced by Copasi 4.0.19 (development) .It is three-dimensional logarithmic plots show the output of simulations of Z and v at various concentrations of R and GAP.

Sarma2012 - Interaction topologies of MAPK cascade (M4_K2_PSEQ)

This model [ MODEL1204280024 - M4_K2_PSEQ] correspond to type M4 with mass-action kinetics K2, in PSEQ (sequestrated ) condition. .

This model is described in the article:

Different designs of kinase-phosphatase interactions and phosphatase sequestration shapes the robustness and signal flow in the MAPK cascade.

Sarma U, Ghosh I.

BMC Syst Biol. 2012 Jul 2;6(1):82.

Abstract:

This model is hosted on BioModels Database and identified by: BIOMD0000000431 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This model is according to the paper of A model for the dynamics of human weight cycling by A. Goldbeter 2006.The figure3 (A) and (B) have been reproduced by Copasi 4.0.19(development) and SBMLodeSolver.The writer of the paper did not specify any units for the metabolites, so the creator of the model did not define the units as well.Both Q and R are normalized to vary between 0 and 1.

This model corresponds to the IkB-NFkB signaling in wild type cells and reproduces the dynamics of the species as depicted in Figure 2 F of the paper. The authors mention that the simulation is carried out in three phases, where the steady state values of the species in one phase are fed to the succeding phase. This model captures the simulation dynamics of two phases and makes use of the event section to introduce the stimulus and thereby transition to the next phase. Accordingly, a few terms have been introduced that make this transition possible, this in no way compromises the original model. Also, the simulation plots are not an exact reproduction of the figures in the paper, they do however match the simulation results that the authors shared with us. Model was successfully tested on MathSBML.

The model reproduces Fig 2B of the paper. Model successfully tested on MathSBML

This is the self maintaining metabolism model described in the article:
A Simple Self-Maintaining Metabolic System: Robustness, Autocatalysis, Bistability.
Piedrafita G, Montero F, Morán F, Cárdenas ML, Cornish-Bowden A, PLoS Computational Biology 2010, 6(8):e1000872. doi: 10.1371/journal.pcbi.1000872
Abstract:
A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the non-trivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them is an enzyme-maintaining mode, the entire network being necessary to maintain the two catalysts

As this is a theoretical model and no units are given in the article, the standard units (mol, seconds and litre) are used for the parameters. k8 and k11 are set equal to k4.

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

Note: The secreted protein Wnt activates the heptahelical receptor Frizzled on nieghboring cells. Activation of Frizzled causes the recruitment of additional membrane proteins which in turn result in 1) the activation of the protein Dishevelled via phosphorylation and 2) the activation of a heterotrimeric G protein of unknown type. Activation of Dishevelled results in the down-regulation of the Beta-Catenin destruction complex which causes ubiquitination of Beta-Catenin and its ultimate degradation via the proteasome. Inhibition of the Beta-Catenin destruction complex yields a higher cytosolic concentration of Beta-Catenin, which enters the nucleus, binds various transcriptional regulatory molecules including the TCF/LEF class of proteins, and results in the transcription of TCF/LEF target genes. Activation of the heterotrimeric G-protein pathway in turn activates Phospholipase C which in turn catalyzes the catalysis of PI(4,5)P2 into DAG and IP3. References: 12356903 , 12573432 & Wnt signaling pathway

This a model described in the article:
Understanding the regulation of aspartate metabolism using a model based on measured kinetic parameters.
Curien G, Bastien O, Robert-Genthon M, Cornish-Bowden A, Cárdenas ML, Dumas R. Mol Syst Biol. 2009;5:271. Epub 2009 May 19. PMID: 19455135 , doi: 10.1038/msb.2009.29
Abstract:
The aspartate-derived amino-acid pathway from plants is well suited for analysing the function of the allosteric network of interactions in branched pathways. For this purpose, a detailed kinetic model of the system in the plant model Arabidopsis was constructed on the basis of in vitro kinetic measurements. The data, assembled into a mathematical model, reproduce in vivo measurements and also provide non-intuitive predictions. A crucial result is the identification of allosteric interactions whose function is not to couple demand and supply but to maintain a high independence between fluxes in competing pathways. In addition, the model shows that enzyme isoforms are not functionally redundant, because they contribute unequally to the flux and its regulation. Another result is the identification of the threonine concentration as the most sensitive variable in the system, suggesting a regulatory role for threonine at a higher level of integration.

The limiting rates for the tRNA synthetase reactions, V_Lys_RS, V_Thr_RS and V_Ile_RS, are all assigned a joined value, Vmax_AA_RS, to facilitate reproduction of the results in the publication. To alter these rates seperately these assignments have to be changed or removed.

A mathematical model quantifying GnRH-induced LH secretion from gonadotropes by Blum et al (2000)

This paper includes three stages, and the model does not include the third stage. Also an event is included which remove the hormone GnRH at time=5min. Figure 1 and Figure 2 of the paper are reproduced, using SBML odeSolver. We choose to encode the model with the concentration of GnRH equal to 1.0nM.

The model was curated with XPP. The figure 3 was successfully reproduced.

Cut-out switch model

Membrane identity and GTPase cascades regulated by toggle and cut-out switches
Perla Del Conte-Zerial, Lutz Brusch, Jochen C Rink, Claudio Collinet, Yannis Kalaidzidis, Marino Zerial, and Andreas Deutsch: Molecular Systems Biology 4:206 15 July 2008 , doi:10.1038/msb.2008.45

This is the cut-out switch model for the Rab5 - Rab7 transition, also referred to as model 2 in the original publication.
This model is not completely described in all details in the publication. Thanks go to Barbara Szomolay and Lutz Brusch for finding and clarifying this. According to Dr. Brusch this model represents the mechanism identified by the qualitative analysis in the article in the scenario deemed most useful by the authors. For the time-course simulations it was necessary to add a time dependency to one of the parameters, which is only verbally described in the article.
As argued in the publication the switch between early and late endosomes can be triggered by a parameter change. While with fixed parameter values each switch just converges to one steady state from its initial conditions and stays there, endosomes should switch between two different states. These changes would in reality of course depend on many different factors, such as cargo composition and amount in the specific endosome, its location and some additional cellular control mechanisms and encompass many different parameters. To keep the model simple the authors chose to add a time dependency to only one reaction - ke in the activation of RAB5 is multiplied with a term monotonously increasing over time from 0 to 1. They also hard coded a time dependence in this term, 100 minutes, to make the switch occur after several hundred minutes. As long as this modulating term remains monotonic all resulting time courses should look similar, with the switching behavior depending on the initial conditions and whether the term is increasing or decreasing. Monotonic increase is a reasonable assumption for the described mechanism of cargo accumulation.
Not explicitly described in the article: activation of Rab5 (time) : r*ke* time/(100+time) /(1+e ^(kg-R)*kf ) instead of r*ke/(1+e ^(kg-R)*kf )

This is the original model from Richard FitzHugh, which led the famous FitzHugh–Nagumo model, still used for instance in computational neurosciences.
Impulses and Physiological States in Theoretical Models of Nerve Membrane
FitzHugh R Biophysical Journal, 1961 July:1(6):445-466 doi:10.1016/S0006-3495(61)86902-6 ,
Abstract:
Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting BVP model has two variables of state, representing excitability and refractoriness, and qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve. This BVP model serves as a simple representative of a class of excitable-oscillatory systems including the Hodgkin-Huxley (HH) model of the squid giant axon. The BVP phase plane can be divided into regions corresponding to the physiological states of nerve fiber (resting, active, refractory, enhanced, depressed, etc.) to form a physiological state diagram, with the help of which many physiological phenomena can be summarized. A properly chosen projection from the 4-dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable.

This model describes the budding yeast cell cycle model used in fig 8 a in
Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions.
Tyson JJ and Novak B., J Theor Biol 2001 May;210(2):249-63.
It consitsts of the equations (2)-(8), with mu=0.005 min ^-1 . It was taken from Cell Cycle DB ( file ) and only slightly altered.

This is an SBML implementation the model of the perfect adaptor (figure 1d) described in the article:
Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell.
Tyson JJ, Chen KC, Novak B. Curr Opin Cell Biol. 2003 Apr;15(2):221-31. PubmedID: 12648679 ; DOI: 10.1016/S0955-0674(03)00017-6 ;

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

This is the model described in: Bacterial adaptation through distributed sensing of metabolic fluxes
Oliver Kotte, Judith B Zaugg and Matthias Heinemann; Mol Sys Biol 2010; 6 :355. doi: 10.1038/msb.2010.10 ;
Abstract:
The recognition of carbon sources and the regulatory adjustments to recognized changes are of particular importance for bacterial survival in fluctuating environments. Despite a thorough knowledge base of Escherichia coli's central metabolism and its regulation, fundamental aspects of the employed sensing and regulatory adjustment mechanisms remain unclear. In this paper, using a differential equation model that couples enzymatic and transcriptional regulation of E. coli's central metabolism, we show that the interplay of known interactions explains in molecular-level detail the system-wide adjustments of metabolic operation between glycolytic and gluconeogenic carbon sources. We show that these adaptations are enabled by an indirect recognition of carbon sources through a mechanism we termed distributed sensing of intracellular metabolic fluxes. This mechanism uses two general motifs to establish flux-signaling metabolites, whose bindings to transcription factors form flux sensors. As these sensors are embedded in global feedback loop architectures, closed-loop self-regulation can emerge within metabolism itself and therefore, metabolic operation may adapt itself autonomously (not requiring upstream sensing and signaling) to fluctuating carbon sources.

In its current form this SBML model is parametrized for the glucose to acetate transition and to simulate the extended diauxic shift as shown in figure 3 and scenario 6 of the attached matlab file. In this scenario the cells first are grown from an OD600 (BM) of 0.03 with a starting glucose concentration of 0.5 g/l for 8.15 h (29340 sec). Then a medium containing 5 g/l acetate is inoculated with these cells to an OD600 of 0.03 and grown for another 19.7 hours (70920 sec). Finally the cells are shifted to a medium containing both glucose and acetate at a concentration of 3 g/l with a starting OD600 of 0.0005.
The shifts where implemented using events triggering at the times determined by the parameters shift1 and shift2 (in hours). To simulate other scenarios the initial conditions need to be changed as described in the supplemental materials ( supplement 1 )
The original SBML model and the MATLAB file used for the calculations can be down loaded as supplementary materials of the publication from the MSB website. ( supplement 2 ).

The units of the external metabolites are in [g/l], those of the biomass in optical density,OD ₆₀₀ , taken as dimensionless, and [micromole/(gramm dry weight)] for all intracellular metabolites. As the latter cannot be implemented in SBML, it was chosen to be micromole only and the units of the parameters are left mostly undefined.

The model is according to the paper Which Model to Use for Cortical Spiking Neurons? Figure1(N) rebound burst has been reproduced by MathSBML. The ODE and the parameters values are taken from the a paper Simple Model of Spiking Neurons The original format of the models are encoded in the MATLAB format existed in the ModelDB with Accession number 39948

Figure1 are the simulation results of the same model with different choices of parameters and different stimulus function or events. a=0.03; b=0.25; c=-52; d=0;V=-64; u=b*V;

This a model from the article:
A kinetic study of a ternary cycle between adenine nucleotides.
Valero E, Varón R, García-Carmona F FEBS J. [2006 Aug;273(15):3598-613 16884499 ,
Abstract:
In the present paper, a kinetic study is made of the behavior of a moiety-conserved ternary cycle between the adenine nucleotides. The system contains the enzymes S-acetyl coenzyme A synthetase, adenylate kinase and pyruvate kinase, and converts ATP into AMP, then into ADP and finally back to ATP. L-Lactate dehydrogenase is added to the system to enable continuous monitoring of the progress of the reaction. The cycle cannot work when the only recycling substrate in the reaction medium is AMP. A mathematical model is proposed whose kinetic behavior has been analyzed both numerically by integration of the nonlinear differential equations describing the kinetics of the reactions involved, and analytically under steady-state conditions, with good agreement with the experimental results being obtained. The data obtained showed that there is a threshold value of the S-acetyl coenzyme A synthetase/adenylate kinase ratio, above which the cycle stops because all the recycling substrate has been accumulated as AMP, never reaching the steady state. In addition, the concept of adenylate energy charge has been applied to the system, obtaining the enabled values of the rate constants for a fixed adenylate energy charge value and vice versa.

Kongas2007 - Creatine Kinase in energy metabolic signaling in muscle

This model is described in the article:

Creatine kinase in energy metabolic signaling in muscle

Olav Kongas and Johannes H. G. M. van Beek

Available from Nature Precedings

Abstract:

There has been much debate on the mechanism of regulation of mitochondrial ATP synthesis to balance ATP consumption during changing cardiac workloads. A key role of creatine kinase (CK) isoenzymes in this regulation of oxidative phosphorylation and in intracellular energy transport had been proposed, but has in the mean time been disputed for many years. It was hypothesized that high-energy phosphorylgroups are obligatorily transferred via CK; this is termed the phosphocreatine shuttle. The other important role ascribed to the CK system is its ability to buffer ADP concentration in cytosol near sites of ATP hydrolysis.

Almost all of the experiments to determine the role of CK had been done in the steady state, but recently the dynamic response of oxidative phosphorylation to quick changes in cytosolic ATP hydrolysis has been assessed at various levels of inhibition of CK. Steady state models of CK function in energy transfer existed but were unable to explain the dynamic response with CK inhibited.

The aim of this study was to explain the mode of functioning of the CK system in heart, and in particular the role of different CK isoenzymes in the dynamic response to workload steps. For this purpose we used a mathematical model of cardiac muscle cell energy metabolism containing the kinetics of the key processes of energy production, consumption and transfer pathways. The model underscores that CK plays indeed a dual role in the cardiac cells. The buffering role of CK system is due to the activity of myofibrillar CK (MMCK) while the energy transfer role depends on the activity of mitochondrial CK (MiCK). We propose that this may lead to the differences in regulation mechanisms and energy transfer modes in species with relatively low MiCK activity such as rabbit in comparison with species with high MiCK activity such as rat.

The model needed modification to explain the new type of experimental data on the dynamic response of the mitochondria. We submit that building a Virtual Muscle Cell is not possible without continuous experimental tests to improve the model. In close interaction with experiments we are developing a model for muscle energy metabolism and transport mediated by the creatine kinase isoforms which now already can explain many different types of experiments.

The model has been designed according to the spirit of the paper. The list of rate in the appendix has been corrected as follow:

d[ATP]/dt = (-Vhyd -Vmmck +Jatp) / Vcyt
d[ADP]/dt = ( Vhyd +Vmmck +Jadp) / Vcyt
d[PCr]/dt = ( Vmmck +Jpcr ) / Vcyt
d[Cr]/dt = (-Vmmck +Jpcr ) / Vcyt
d[Pi]/dt = ( Vhyd + Jpi ) / Vcyt
d[ATPi]/dt = (+Vsyn -Vmick -Jatp) / Vims
d[ADPi]/dt = (-Vsyn +Vmick -Jadp) / Vims
d[PCri]/dt = ( Vmick -Jpcr ) / Vims
d[Cri]/dt = (-Vmick -Jpcr ) / Vims
d[Pii]/dt = (-Vsyn -Jpi ) / Vims

This model is hosted on BioModels Database and identified by: BIOMD0000000041 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This model is automatically converted from the Model BIOMD0000000188 by using libsbml . According to the terms of use , this generated model is not related with Model BIOMD0000000188 any more.

This is model in continous darkness (DD) described in the article Toward a detailed computational model for the mammalian circadian clock

This model features the full interlocked negative and positive regulation of Per,Cry,Bmal and REV-ERBalpha. The model exhibits robust oscillations quite independent of the initial conditions for teh parameters given. Each species is assigned zero as initial value, and the graph started at time=120h.

Simulation results could be reproduced using Copasi 4.0.19(development) and roadRunner online.

This a model from the article:
A Hierarchical Whole-div Modeling Approach Elucidates the Link between in Vitro Insulin Signaling and in Vivo Glucose Homeostasis.
Nyman E, Brannmark C, Palmer R, Brugard J, Nystrom FH, Stralfors P, Cedersund G. J Biol Chem. 2011 Jul 22;286(29):26028-41. 21572040 ,
Abstract:
Type 2 diabetes is a metabolic disease that profoundly affects energy homeostasis. The disease involves failure at several levels and subsystems and is characterized by insulin resistance in target cells and tissues (i.e. by impaired intracellular insulin signaling). We have previously used an iterative experimental-theoretical approach to unravel the early insulin signaling events in primary human adipocytes. That study, like most insulin signaling studies, is based on in vitro experimental examination of cells, and the in vivo relevance of such studies for human beings has not been systematically examined. Herein, we develop a hierarchical model of the adipose tissue, which links intracellular insulin control of glucose transport in human primary adipocytes with whole-div glucose homeostasis. An iterative approach between experiments and minimal modeling allowed us to conclude that it is not possible to scale up the experimentally determined glucose uptake by the isolated adipocytes to match the glucose uptake profile of the adipose tissue in vivo. However, a model that additionally includes insulin effects on blood flow in the adipose tissue and GLUT4 translocation due to cell handling can explain all data, but neither of these additions is sufficient independently. We also extend the minimal model to include hierarchical dynamic links to more detailed models (both to our own models and to those by others), which act as submodules that can be turned on or off. The resulting multilevel hierarchical model can merge detailed results on different subsystems into a coherent understanding of whole-div glucose homeostasis. This hierarchical modeling can potentially create bridges between other experimental model systems and the in vivo human situation and offers a framework for systematic evaluation of the physiological relevance of in vitro obtained molecular/cellular experimental data.

This model is according to the paper Toward a detailed computational model for the mammalian circadian clock . In this model only interlocked negative and positive regulation of Per, Cry, Bmal gene are involved. Some initial values were not provided, therefore they were chosen to fit the curve from the paper.

Figure2A re-produced by Copasi 4.0.19 and roadRunner online.

This a model from the article:
Mathematical model of binding of albumin-bilirubin complex to the surface of carbon pyropolymer.
Nikolaev AV, Rozhilo YA, Starozhilova TK, Sarnatskaya VV, Yushko LA, Mikhailovskii SV, Kholodov AS, Lobanov AI. Bull Exp Biol Med 2005 Sep;140(3):365-9. 16307060 ,
Abstract:
We proposed a mathematical model and estimated the parameters of adsorption of albumin-bilirubin complex to the surface of carbon pyropolymer. Design data corresponded to the results of experimental studies. Our findings indicate that modeling of this process should take into account fractal properties of the surface of carbon pyropolymer.

This a model from the article:
Modeling the insulin-glucose feedback system: the significance of pulsatile insulin secretion.
Tolic IM, Mosekilde E, Sturis J. J Theor Biol 2000 Dec 7;207(3):361-75 11082306 ,
Abstract:
A mathematical model of the insulin-glucose feedback regulation in man is used to examine the effects of an oscillatory supply of insulin compared to a constant supply at the same average rate. We show that interactions between the oscillatory insulin supply and the receptor dynamics can be of minute significance only. It is possible, however, to interpret seemingly conflicting results of clinical studies in terms of their different experimental conditions with respect to the hepatic glucose release. If this release is operating near an upper limit, an oscillatory insulin supply will be more efficient in lowering the blood glucose level than a constant supply. If the insulin level is high enough for the hepatic release of glucose to nearly vanish, the opposite effect is observed. For insulin concentrations close to the point of inflection of the insulin-glucose dose-response curve an oscillatory and a constant insulin infusion produce similar effects. Copyright 2000 Academic Press.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Tolic IM, Mosekilde E, Sturis J. (2000) - version=1.0

The model reproduces the time profiles of the different species depicted in Fig 3a of the paper. Model successfully reproduced using MathSBML.

This is the model of IL13 induced signalling in L1236 cells described in the article:
Dynamic Mathematical Modeling of IL13-Induced Signaling in Hodgkin and Primary Mediastinal B-Cell Lymphoma Allows Prediction of Therapeutic Targets.
Raia V, Schilling M, Böhm M, Hahn B, Kowarsch A, Raue A, Sticht C, Bohl S, Saile M, Möller P, Gretz N, Timmer J, Theis F, Lehmann WD, Lichter P and Klingmüller U. Cancer Res. 2011 Feb 1;71(3):693-704. PubmedID: 21127196 ; DOI: 10.1158/0008-5472.CAN-10-2987
Abstract:
Primary mediastinal B-cell lymphoma (PMBL) and classical Hodgkin lymphoma (cHL) share a frequent constitutive activation of JAK (Janus kinase)/STAT signaling pathway. Because of complex, nonlinear relations within the pathway, key dynamic properties remained to be identified to predict possible strategies for intervention. We report the development of dynamic pathway models based on quantitative data collected on signaling components of JAK/STAT pathway in two lymphoma-derived cell lines, MedB-1 and L1236, representative of PMBL and cHL, respectively. We show that the amounts of STAT5 and STAT6 are higher whereas those of SHP1 are lower in the two lymphoma cell lines than in normal B cells. Distinctively, L1236 cells harbor more JAK2 and less SHP1 molecules per cell than MedB-1 or control cells. In both lymphoma cell lines, we observe interleukin-13 (IL13)-induced activation of IL4 receptor α, JAK2, and STAT5, but not of STAT6. Genome-wide, 11 early and 16 sustained genes are upregulated by IL13 in both lymphoma cell lines. Specifically, the known STAT-inducible negative regulators CISH and SOCS3 are upregulated within 2 hours in MedB-1 but not in L1236 cells. On the basis of this detailed quantitative information, we established two mathematical models, MedB-1 and L1236 model, able to describe the respective experimental data. Most of the model parameters are identifiable and therefore the models are predictive. Sensitivity analysis of the model identifies six possible therapeutic targets able to reduce gene expression levels in L1236 cells and three in MedB-1. We experimentally confirm reduction in target gene expression in response to inhibition of STAT5 phosphorylation, thereby validating one of the predicted targets.

All concentrations in the model, apart from IL13, are in molecules/cell. IL13 is given in ng/ml. As the cell volume is not explicitely given in the article, it is just approximately derived from the MW of IL13 (15.8 kDa) and the conversion factor 3.776 molecules IL13/cell = 1 ng/ml to be around 100 fl.

SBML model exported from PottersWheel on 2010-08-10 12:14:57.
Inline follows the original matlab code:

% PottersWheel model definition file

function m = Raia2010_IL13_L1236()

m             = pwGetEmptyModel();

%% Meta information

m.ID          = 'Raia2010_IL13_L1236';
m.name        = 'Raia2010_IL13_L1236';
m.description = '';
m.authors     = {'Raia et al'};
m.dates       = {'2010'};
m.type        = 'PW-2-0-47';

%% X: Dynamic variables
% m = pwAddX(m, ID, startValue, type, minValue, maxValue, unit, compartment, name, description, typeOfStartValue)

m = pwAddX(m, 'Rec'         ,              1.8, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'Rec_i'       , 118.598421286338, 'global',  0.001, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'IL13_Rec'    ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'p_IL13_Rec'  ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'p_IL13_Rec_i',                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'JAK2'        ,               24, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'pJAK2'       ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'SHP1'        ,              9.4, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'STAT5'       ,              209, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'pSTAT5'      ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'CD274mRNA'   ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');


%% R: Reactions
% m = pwAddR(m, reactants, products, modifiers, type, options, rateSignature, parameters, description, ID, name, fast, compartments, parameterTrunks, designerPropsR, stoichiometry, reversible)

m = pwAddR(m, {'Rec'         }, {'IL13_Rec'    }, {'IL13stimulation'}, 'C' , [] , 'k1 * m1 * r1 * 3.776', {'Kon_IL13Rec'             });
m = pwAddR(m, {'Rec'         }, {'Rec_i'       }, {                 }, 'MA', [] , []                    , {'Rec_intern'              });
m = pwAddR(m, {'Rec_i'       }, {'Rec'         }, {                 }, 'MA', [] , []                    , {'Rec_recycle'             });
m = pwAddR(m, {'IL13_Rec'    }, {'p_IL13_Rec'  }, {'pJAK2'          }, 'E' , [] , []                    , {'Rec_phosphorylation'     });
m = pwAddR(m, {'JAK2'        }, {'pJAK2'       }, {'IL13_Rec'       }, 'E' , [] , []                    , {'JAK2_phosphorylation'    });
m = pwAddR(m, {'JAK2'        }, {'pJAK2'       }, {'p_IL13_Rec'     }, 'E' , [] , []                    , {'JAK2_phosphorylation'    });
m = pwAddR(m, {'p_IL13_Rec'  }, {'p_IL13_Rec_i'}, {                 }, 'MA', [] , []                    , {'pRec_intern'             });
m = pwAddR(m, {'p_IL13_Rec_i'}, {              }, {                 }, 'MA', [] , []                    , {'pRec_degradation'        });
m = pwAddR(m, {'pJAK2'       }, {'JAK2'        }, {'SHP1'           }, 'E' , [] , []                    , {'pJAK2_dephosphorylation' });
m = pwAddR(m, {'STAT5'       }, {'pSTAT5'      }, {'pJAK2'          }, 'E' , [] , []                    , {'STAT5_phosphorylation'   });
m = pwAddR(m, {'pSTAT5'      }, {'STAT5'       }, {'SHP1'           }, 'E' , [] , []                    , {'pSTAT5_dephosphorylation'});
m = pwAddR(m, {              }, {'CD274mRNA'   }, {'pSTAT5'         }, 'C' , [] , 'm1*k1'               , {'CD274mRNA_production'    });



%% C: Compartments
% m = pwAddC(m, ID, size,  outside, spatialDimensions, name, unit, constant)

m = pwAddC(m, 'cell', 1);


%% K: Dynamical parameters
% m = pwAddK(m, ID, value, type, minValue, maxValue, unit, name, description)

m = pwAddK(m, 'Kon_IL13Rec'             , 0.00174086832237195, 'global', 1e-009, 1000);
m = pwAddK(m, 'Rec_phosphorylation'     , 9.07540737285078   , 'global', 1e-009, 1000);
m = pwAddK(m, 'pRec_intern'             , 0.324132341358502  , 'global', 1e-009, 1000);
m = pwAddK(m, 'pRec_degradation'        , 0.417538218767296  , 'global', 1e-009, 1000);
m = pwAddK(m, 'Rec_intern'              , 0.259685756311325  , 'global', 1e-009, 1000);
m = pwAddK(m, 'Rec_recycle'             , 0.00392430355501153, 'global', 1e-009, 1000);
m = pwAddK(m, 'JAK2_phosphorylation'    , 0.300019047540849  , 'global', 1e-009, 1000);
m = pwAddK(m, 'pJAK2_dephosphorylation' , 0.0981610557569751 , 'global', 1e-009, 1000);
m = pwAddK(m, 'STAT5_phosphorylation'   , 0.00426766529531612, 'global', 1e-009, 1000);
m = pwAddK(m, 'pSTAT5_dephosphorylation', 0.0116388587580445 , 'global', 1e-009, 1000);
m = pwAddK(m, 'CD274mRNA_production'    , 0.0115927572109515 , 'global', 1e-009, 1000);


%% U: Driving input
% m = pwAddU(m, ID, uType, uTimes, uValues, compartment, name, description, u2Values, alternativeIDs, designerProps)

m = pwAddU(m, 'IL13stimulation', 'steps', [-100 0]  , [0 1]  , [], [], [], [], {}, [], 'protein.generic');


%% Default sampling time points
m.t = 0:1:120;


%% Y: Observables
% m = pwAddY(m, rhs, ID, scalingParameter, errorModel, noiseType, unit, name, description, alternativeIDs, designerProps)

m = pwAddY(m, 'Rec + IL13_Rec + p_IL13_Rec'         , 'RecSurf_obs'  , 'scale_RecSurf'  , '0.1 * y + 0.1 * max(y)');
m = pwAddY(m, 'IL13_Rec + p_IL13_Rec + p_IL13_Rec_i', 'IL13-cell_obs', 'scale_IL13-cell', '0.15 * y + 0.05 * max(y)');
m = pwAddY(m, 'p_IL13_Rec + p_IL13_Rec_i'           , 'pIL4Ra_obs'   , 'scale_pIL4Ra'   , '0.10 * y + 0.15 * max(y)');
m = pwAddY(m, 'pJAK2'                               , 'pJAK2_obs'    , 'scale_pJAK2'    , '0.1 * y + 0.1 * max(y)');
m = pwAddY(m, 'CD274mRNA'                           , 'CD274mRNA_obs', 'scale_CD274mRNA', '0.1 * y + 0.1 * max(y)');
m = pwAddY(m, 'pSTAT5'                              , 'pSTAT5_obs'   , 'scale_pSTAT5'   , '0.1 * y + 0.1 * max(y)');


%% S: Scaling parameters
% m = pwAddS(m, ID, value, type, minValue, maxValue, unit, name, description)

m = pwAddS(m, 'scale_pJAK2'    , 0.469836894150194, 'global',  0.001, 10000);
m = pwAddS(m, 'scale_pIL4Ra'   ,  1.80002942264669, 'global',  0.001, 10000);
m = pwAddS(m, 'scale_RecSurf'  ,                 1,    'fix', 0.0001, 10000);
m = pwAddS(m, 'scale_IL13-cell',  174.726805005048, 'global',  0.001, 10000);
m = pwAddS(m, 'scale_CD274mRNA', 0.110568221201943, 'global',  0.001, 10000);
m = pwAddS(m, 'scale_pSTAT5'   ,                 1,    'fix',  0.001, 10000);


%% Designer properties (do not modify)
m.designerPropsM = [1 1 1 0 0 0 400 250 600 400 1 1 1 0 0 0 0];

The model reproduces Fig 2B, D, F, and 2H. The dynamics correspond to a stimulus of 1 U/ml of thrombin which is equal to 0.01 uM. Phosphorylated MLC is the sum of pMLC (s359) and ppMLC (s360). A slight discrepancy in peak values of species between the figure in the paper and simulation result might be due to different initial conditions in the two sets. The model was successfully tested on MathSBML. It is possible to simulate the model on other software that do not support "Events" at this time by removing the "listOfEvents" and substituting a value of 0.01 for thrombin (s2). This does not change the model very much. With the latter format, the model was also successfully tested on Copasi.

This model is from the article:
The auxin signalling network translates dynamic input into robust patterning at the shoo t apex.
Vernoux T, Brunoud G, Farcot E, Morin V, Van den Daele H, Legrand J, Oliva M, Das P, Larrieu A, Wells D , Guédon Y, Armitage L, Picard F, Guyomarc'h S, Cellier C, Parry G, Koumproglou R, Doonan JH, Estelle M , Godin C, Kepinski S, Bennett M, De Veylder L, Traas J. Mol Syst Biol. 2011 Jul 5;7:508. 21734647 ,
Abstract:
The plant hormone auxin is thought to provide positional information for patterning during development. It is still unclear, however, precisely how auxin is distributed across tissues and how the hormone is sensed in space and time. The control of gene expression in response to auxin involves a complex netwo rk of over 50 potentially interacting transcriptional activators and repressors, the auxin response fac tors (ARFs) and Aux/IAAs. Here, we perform a large-scale analysis of the Aux/IAA-ARF pathway in the sho ot apex of Arabidopsis, where dynamic auxin-based patterning controls organogenesis. A comprehensive ex pression map and full interactome uncovered an unexpectedly simple distribution and structure of this p athway in the shoot apex. A mathematical model of the Aux/IAA-ARF network predicted a strong buffering capacity along with spatial differences in auxin sensitivity. We then tested and confirmed these predic tions using a novel auxin signalling sensor that reports input into the signalling pathway, in conjunct ion with the published DR5 transcriptional output reporter. Our results provide evidence that the auxin signalling network is essential to create robust patterns at the shoot apex.

Note:

Figure 3 of the supplementary material of the reference article has been reproduced here. Time evolution of all the variables in the model are plotted, under the influence of a step input of auxin level (auxin=5, when time>1000; 0.11, otherwise). pi_A is varied between 0 and 2 by steps of 0.1.

This is the model of the minmal 2 feedback switch described in the article:
Synthetic conversion of a graded receptor signal into a tunable, reversible switch.
Santhosh Palani and Casim A. Sarkar, 2011, Molecular Systems Biology 7:480; doi: 10.1038/msb.2011.13

The ability to engineer an all-or-none cellular response to a given signaling ligand is important in applications ranging from biosensing to tissue engineering. However, synthetic gene network switches have been limited in their applicability and tunability due to their reliance on specific components to function. Here, we present a strategy for reversible switch design that instead relies only on a robust, easily constructed network topology with two positive feedback loops and we apply the method to create highly ultrasensitive (nH420), bistable cellular responses to a synthetic ligand/receptor complex. Independent modulation of the two feedback strengths enables rational tuning and some decoupling of steady-state (ultrasensitivity, signal amplitude, switching threshold, and bistability) and kinetic (rates of system activation and deactivation) response properties. Our integrated computational and synthetic biology approach elucidates design rules for building cellular switches with desired properties, which may be of utility in engineering signal-transduction pathways.

This model is parametrised for a transcription factor and receptor feedback strength of 3, TFs = 3 and Rs = 3. To reproduce figure 1 E, the parameters TFs and Rs have to be varied accordingly.

Nomenclature for the model:
L : Ligand
R : Receptor
C : Ligand-Receptor Complex
I : Inactive Transcription Factor
X : C bound to I
A : Active Transcription Factor

The model reproduces Fig 6 of the paper. The stoichiometry and rate of reactions involving uptake of metabolites from extracellular medium have been changed corresponding to Yvol (ratio of extracellular volume to cytosolic volume) mentioned in the publication. The extracellular and cytosolic compartments have been set to 1. Concentration of extracellular glucose, GlcX, is set to 6.7 according to the equation for cellular glucose uptake rate in Table 7 of the paper. The model was successfully tested on MathSBML and Jarnac

This model is from the article:
Mechanistic explanations for counter-intuitive phosphorylation dynamics of the insulin receptor and insulin receptor substrate-1 in response to insulin in murine adipocytes.
Nyman E, Fagerholm S, Jullesson D, Strålfors P, Cedersund G. FEBS J. 2012 Jan 16. 22248283 ,
Abstract:
Insulin signaling through insulin receptor (IR) and insulin receptor substrate-1 (IRS1) is important for insulin control of target cells. We have previously demonstrated a rapid and simultaneous overshoot behavior in the phosphorylation dynamics of IR and IRS1 in human adipocytes. Herein, we demonstrate that in murine adipocytes a similar overshoot behavior is not simultaneous for IR and IRS1. The peak of IRS1 phosphorylation, which is a direct consequence of the phosphorylation and the activation of IR, occurs earlier than the peak of IR phosphorylation. We used a conclusive modeling framework to unravel the mechanisms behind this counter-intuitive order of phosphorylation. Through a number of rejections, we demonstrate that two fundamentally different mechanisms may create the reversed order of peaks: (i) two pools of phosphorylated IR, where a large pool of internalized IR peaks late, but phosphorylation of IRS1 is governed by a small plasma membrane-localized pool of IR with an early peak, or (ii) inhibition of the IR-catalyzed phosphorylation of IRS1 by negative feedback. Although (i) may explain the reversed order, this two-pool hypothesis alone requires extensive internalization of IR, which is not supported by experimental data. However, with the additional assumption of limiting concentrations of IRS1, (i) can explain all data. Also, (ii) can explain all available data. Our findings illustrate how modeling can potentiate reasoning, to help draw nontrivial conclusions regarding competing mechanisms in signaling networks. Our work also reveals new differences between human and murine insulin signaling. Database The mathematical model described here has been submitted to the Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/nyman/index.html free of charge.

This model is according to the paper Reduced-order modeling of biochemical networks: application to the GTPase-cycle signalling module by Maurya et al 2006.The figure 4c is reproduced by Copasi 4.0.19 (development) .It is three-dimensional logarithmic plots show the output of simulations of Z at various concentrations of R and GAP.

This is the model of the in vitro DNA oscillator called oligator with the optmized set of parameters described in the article:
Programming an in vitro DNA oscillator using a molecular networking strategy.
Montagne K, Plasson R, Sakai Y, Fujii T, Rondelez Y. Mol Syst Biol. 2011 Feb 1;7:466. PubmedID: 21283142 , Doi: 10.1038/msb.2010.120

Abstract:
Living organisms perform and control complex behaviours by using webs of chemical reactions organized in precise networks. This powerful system concept, which is at the very core of biology, has recently become a new foundation for bioengineering. Remarkably, however, it is still extremely difficult to rationally create such network architectures in artificial, non-living and well-controlled settings. We introduce here a method for such a purpose, on the basis of standard DNA biochemistry. This approach is demonstrated by assembling de novo an efficient chemical oscillator: we encode the wiring of the corresponding network in the sequence of small DNA templates and obtain the predicted dynamics. Our results show that the rational cascading of standard elements opens the possibility to implement complex behaviours in vitro. Because of the simple and well-controlled environment, the corresponding chemical network is easily amenable to quantitative mathematical analysis. These synthetic systems may thus accelerate our understanding of the underlying principles of biological dynamic modules.

The model reproduces the time courses in fig 2B. The parameter identifiers of the reaction constants are not the same as in the supplemental material, but are just called kXd and kXr for the forward and backwards constant of reaction X respectively.

Note: This is the current model for the Hedgehog signaling pathway. The best data for mechanism of signaling has been worked out in Drosophila, so this model is based largely on Drosophila data. Hedgehog target genes vary from tissue to tissue, so the identities of individual target genes have not been listed. The main difference between the Drosophila and mammalian Hedgehog signaling pathways is the fact that there are three mammalian homologs of Cubitus interruptus, Gli1 Gli2 and Gli3. Some or all of the mammalian homologs may be proteolytically processed, but the data are controversial. There are two mammalian Ptc genes and three mammalian Hedgehog genes as well. The pathway for Sonic Hedgehog appears to be most similar to the Drosophila hedgehog pathway. Eg: 11731473 , 11861165 , 12200154 & 14738752 .

Note: Model of the Calvin cycle and the related end-product pathways to starch and sucrose synthesis by Hahn (1986, [click here for abstract] ).

The parameter values are taken from Hahn (1984, [click here for abstract] ). The initial metabolite values are chosen from the data set of Zhu et al. (2007, DOI:10.1104/pp.107.103713 ). A detailed description of all modifications is given in the model described by Arnold and Nikoloski (2011, PMID:22001849 .

Model reproduces Fig 4 of the paper. For fraction of phosphorylated protein, W_star, the model reproduces panel b in the same figure. Model successfully tested on MathSBML and Jarnac.

This is model is according to the paper Modelling the actions of chaperones and their role in ageing. This is a stochastic model coded in SBML. Figure 2A and Figure2B has been reproduced by Gillespie2 and Copasi4.0.19(development).

The model reproduces FIG 11A and FIG 11B of the paper. However, please note that FIG 11B is a plot of normalised amounts versus time. The "stoichiometry" field has been used to convert fluxes from membrane species to volume species. The value of 0.0009967 is a product of (Surface to Volume_M*(1/Avagadro's number)*1E21. 0.6 is the surface to volume ratio of the plasma membrane, 1E21 is required for a unit surface to volume ratio and the Avagadro's number is present in the denominator to convert molecules to moles. The model was successfully tested using MathSBML and SBML ODESolver.
All the kinetic laws have the unit items per second , which requires the one reaction taking place in the cytoplasm - IP3Phosphatase - to include an explicit conversion factor both in the kinetic law and the stoichiometry of IP3_C . The kinetic law is multiplied and the stoichiometry divided by the number of molecules per micro-mole. This conversion factor is only required for correct units and can be replaced by 1, if it should lead to numerical problems.

Goldbeter1991 - Min Mit Oscil

Minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase.

This model has been generated by MathSBML 2.4.6 (14-January-2005) 14-January-2005 18:33:39.806932.

This model is described in the article:

A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase.

Goldbeter A.

Proc. Natl. Acad. Sci. U.S.A. 1991; 88(20):9107-11

Abstract:

A minimal model for the mitotic oscillator is presented. The model, built on recent experimental advances, is based on the cascade of post-translational modification that modulates the activity of cdc2 kinase during the cell cycle. The model pertains to the situation encountered in early amphibian embryos, where the accumulation of cyclin suffices to trigger the onset of mitosis. In the first cycle of the bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation, and in the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. That cyclin activates cdc2 kinase while the kinase triggers the degradation of cyclin has suggested that oscillations may originate from such a negative feedback loop [Félix, M. A., Labbé, J. C., Dorée, M., Hunt, T. & Karsenti, E. (1990) Nature (London) 346, 379-382]. This conjecture is corroborated by the model, which indicates that sustained oscillations of the limit cycle type can arise in the cascade, provided that a threshold exists in the activation of cdc2 kinase by cyclin and in the activation of cyclin proteolysis by cdc2 kinase. The analysis shows how miototic oscillations may readily arise from time lags associated with these thresholds and from the delayed negative feedback provided by cdc2-induced cyclin degradation. A mechanism for the origin of the thresholds is proposed in terms of the phenomenon of zero-order ultrasensitivity previously described for biochemical systems regulated by covalent modification.

This model is hosted on BioModels Database and identified by: BIOMD0000000003 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This a model from the article:
Stress-specific response of the p53-Mdm2 feedback loop
Alexander Hunziker, Mogens H Jensen and Sandeep Krishna BMC Systems Biology 2010, Jul 12;4(1):94 20624280 ,
Abstract:
ABSTRACT: BACKGROUND: The p53 signalling pathway has hundreds of inputs and outputs. It can trigger cellular senescence, cell-cycle arrest and apoptosis in response to diverse stress conditions, including DNA damage, hypoxia and nutrient deprivation. Signals from all these inputs are channeled through a single node, the transcription factor p53. Yet, the pathway is flexible enough to produce different downstream gene expression patterns in response to different stresses. RESULTS: We construct a mathematical model of the negative feedback loop involving p53 and its inhibitor, Mdm2, at the core of this pathway, and use it to examine the effect of different stresses that trigger p53. In response to DNA damage, hypoxia, etc., the model exhibits a wide variety of specific output behaviour -- steady states with low or high levels of p53 and Mdm2, as well as spiky oscillations with low or high average p53 levels. CONCLUSIONS: We show that even a simple negative feedback loop is capable of exhibiting the kind of flexible stress-specific response observed in the p53 system. Further, our model provides a framework for predicting the differences in p53 response to different stresses and single nucleotide polymorphisms.

The parameters of the model corresponds to the resting state, with delta = 11hr ^-1 , gamma = 0.2hr ^-1 , k _t = 0.03nM ^-1 hr ^-1 and k _f = 5000nM ^-1 hr ^-1 .

To simulate different stress conditions as in figure 2A (also look at the curation figure of this model) of the reference publication, the above parameter should be changed. The parameter values corresponding to different stress conditions are shown in the following table.

Stress Condition/Parameter	delta	gamma	k _t	k _f
Nutlin	11hr ^-1	0.2hr ^-1	0.03nM ^-1 hr ^-1	500nM ^-1 hr ^-1
Oncogene	2hr ^-1	0.2hr ^-1	0.03nM ^-1 hr ^-1	5000nM ^-1 hr ^-1
DNA damage	2hr ^-1	0.5hr ^-1	0.03nM ^-1 hr ^-1	2500nM ^-1 hr ^-1
Hypoxia	2hr ^-1	0.2hr ^-1	0.01nM ^-1 hr ^-1	5000nM ^-1 hr ^-1

This a model from the article:
Evidence that calcium release-activated current mediates the biphasic electrical activity of mouse pancreatic beta-cells.
Mears D, Sheppard NF Jr, Atwater I, Rojas E, Bertram R, Sherman A. J Membr Biol 1997 Jan 1;155(1):47-59 9002424 ,
Abstract:
The electrical response of pancreatic beta-cells to step increases in glucose concentration is biphasic, consisting of a prolonged depolarization with action potentials (Phase 1) followed by membrane potential oscillations known as bursts. We have proposed that the Phase 1 response results from the combined depolarizing influences of potassium channel closure and an inward, nonselective cation current (ICRAN) that activates as intracellular calcium stores empty during exposure to basal glucose (Bertram et al., 1995). The stores refill during Phase 1, deactivating ICRAN and allowing steady-state bursting to commence. We support this hypothesis with additional simulations and experimental results indicating that Phase 1 duration is sensitive to the filling state of intracellular calcium stores. First, the duration of the Phase 1 transient increases with duration of prior exposure to basal (2.8 mM) glucose, reflecting the increased time required to fill calcium stores that have been emptying for longer periods. Second, Phase 1 duration is reduced when islets are exposed to elevated K+ to refill calcium stores in the presence of basal glucose. Third, when extracellular calcium is removed during the basal glucose exposure to reduce calcium influx into the stores, Phase 1 duration increases. Finally, no Phase 1 is observed following hyperpolarization of the beta-cell membrane with diazoxide in the continued presence of 11 mm glucose, a condition in which intracellular calcium stores remain full. Application of carbachol to empty calcium stores during basal glucose exposure did not increase Phase 1 duration as the model predicts. Despite this discrepancy, the good agreement between most of the experimental results and the model predictions provides evidence that a calcium release-activated current mediates the Phase 1 electrical response of the pancreatic beta-cell.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Mears D, Sheppard NF Jr, Atwater I, Rojas E, Bertram R, Sherman A. (1997) - version=1.0
The original CellML model was created by:
Tessa Paris
tpar054@aucklanduni.ac.uk
The University of Auckland

Note: Model of the Calvin cycle with focus on the RuBisCO reaction by Damour and Urban (2007, [for PDF click here] ).

The parameter values are partly taken from Farquhar et al. (1980, DOI:10.1007/BF00386231 ) and Urban et al. (2003, DOI:10.1093/treephys/23.5.289 ). The initial metabolite values are chosen from the data set of Zhu et al. (2007, DOI:10.1104/pp.107.103713 ). A detailed description of all modifications is given in the model described by Arnold and Nikoloski (2011, PMID:22001849 .

The model reproduces Figure 6 (a,b,c) for normal wnt signaling. Model was successfully tested on MathSBML.

The model reproduces the time profiles of Calcium in the spine and dendrites as depicted in Fig 8 and Fig 9 of the paper for CF activation.

The model was reproduced using MathSBML.

Please note that the units of volume species is molecules/micrometer cubed as against the units of microMolar given in the paper. To convert the units to microMolar multiply the species concentration by the conversion factor 1/602.

MAPK cascade on a scaffold

Citation
Levchenko, A., Bruck, J., Sternberg, P.W. (2000) .Scaffold proteins may biphasically affect the levels of mitogen-activated protein kinase signaling and reduce its threshold properties. Proc. Natl. Acad. Sci. USA 97(11):5818-5823. http://www.pnas.org/cgi/content/abstract/97/11/5818

Description
This model describes a basic 3-stage Mitogen Activated Protein Kinase (MAPK). Kinases in solution are written as K[3,J], K[2,J], K[1,J] for MAPKKK, MAPKK, and MAPK, respectively, J indicates the phosphorylation level, J=0,1 for K3 and J=0,1,2 for K2 and K1. Scaffolds have three slots, for MAPK, MAPKK, and MAPKKK, respectively. Bound and free scaffold are denoted as S[i,j,k], where i, j, and k indicate the binding of K[1,i], K[2,j] and K[3,k] in their respective slots. Here i,j=-1,0,1,or,2 and k=-1,0,or,1. A value of -1 means the slot is empty, 0 means the unphorphorylated kinase is bound, 1 means the singly phosphorylated kinase is bound, and 2 means the doubly phosphorylated kinase is bound. Thus S[1,-1,2] is a scaffold with K[3,1] bound in the first slot and K[1,2] in the third slot, while the second slot is empty.Note: Indices X[I,J,K] are translated into the unindexed variable X_I_J_K and so forth in the SBML. Negative indices are translated as mI, etc, thus S[1,-1,2] becomes S_1_m1_2.

Description

This model describes a basic 3-stage Mitogen Activated Protein Kinase (MAPK). Kinases in solution are written as K[3,J], K[2,J], K[1,J] for MAPKKK, MAPKK, and MAPK, respectively, J indicates the phosphorylation level, J=0,1 for K3 and J=0,1,2 for K2 and K1. Scaffolds have three slots, for MAPK, MAPKK, and MAPKKK, respectively. Bound and free scaffold are denoted as S[i,j,k], where i, j, and k indicate the binding of K[1,i], K[2,j] and K[3,k] in their respective slots. Here i,j=-1,0,1,or,2 and k=-1,0,or,1. A value of -1 means the slot is empty, 0 means the unphorphorylated kinase is bound, 1 means the singly phosphorylated kinase is bound, and 2 means the doubly phosphorylated kinase is bound. Thus S[1,-1,2] is a scaffold with K[3,1] bound in the first slot and K[1,2] in the third slot, while the second slot is empty.Note: Indices X[I,J,K] are translated into the unindexed variable X_I_J_K and so forth in the SBML. Negative indices are translated as mI, etc, thus S[1,-1,2] becomes S_1_m1_2.

Rate constant	Reaction
a10 = 5.	MAPKP + K[1, 2] -> K_MAPKP[1, 2]
a1 = 1.	RAFK + K[3, 0] -> K_RAFK[3, 0]
a2 = 0.5	RAFP + K[3, 1] -> K_RAFP[3, 1]
a3 = 3.3	K[2, 0] + K[3, 1] -> K_K[2, 0, 3, 1]
a4 = 10.	MEKP + K[2, 1] -> K_MEKP[2, 1]
a5 = 3.3	K[2, 1] + K[3, 1] -> K_K[2, 1, 3, 1]
a6 = 10.	MEKP + K[2, 2] -> K_MEKP[2, 2]
a7 = 20.	K[1, 0] + K[2, 2] -> K_K[1, 0, 2, 2]
a8 = 5.	MAPKP + K[1, 1] -> K_MAPKP[1, 1]
a9 = 20.	K[1, 1] + K[2, 2] -> K_K[1, 1, 2, 2]
d10 = 0.4	K_MAPKP[1, 2] -> MAPKP + K[1, 2]
d1 = 0.4	K_RAFK[3, 0] -> RAFK + K[3, 0]
d1a = 0	S_RAFK[0, 0, 0] -> RAFK + S[0, 0, 0]
d1a = 0	S_RAFK[0, -1, 0] -> RAFK + S[0, -1, 0]
d1a = 0	S_RAFK[0, 1, 0] -> RAFK + S[0, 1, 0]
d1a = 0	S_RAFK[0, 2, 0] -> RAFK + S[0, 2, 0]
d1a = 0	S_RAFK[-1, 0, 0] -> RAFK + S[-1, 0, 0]
d1a = 0	S_RAFK[1, 0, 0] -> RAFK + S[1, 0, 0]
d1a = 0	S_RAFK[-1, -1, 0] -> RAFK + S[-1, -1, 0]
d1a = 0	S_RAFK[-1, 1, 0] -> RAFK + S[-1, 1, 0]
d1a = 0	S_RAFK[1, -1, 0] -> RAFK + S[1, -1, 0]
d1a = 0	S_RAFK[1, 1, 0] -> RAFK + S[1, 1, 0]
d1a = 0	S_RAFK[-1, 2, 0] -> RAFK + S[-1, 2, 0]
d1a = 0	S_RAFK[1, 2, 0] -> RAFK + S[1, 2, 0]
d1a = 0	S_RAFK[2, 0, 0] -> RAFK + S[2, 0, 0]
d1a = 0	S_RAFK[2, -1, 0] -> RAFK + S[2, -1, 0]
d1a = 0	S_RAFK[2, 1, 0] -> RAFK + S[2, 1, 0]
d1a = 0	S_RAFK[2, 2, 0] -> RAFK + S[2, 2, 0]
d2 = 0.5	K_RAFP[3, 1] -> RAFP + K[3, 1]
d3 = 0.42	K_K[2, 0, 3, 1] -> K[2, 0] + K[3, 1]
d4 = 0.8	K_MEKP[2, 1] -> MEKP + K[2, 1]
d5 = 0.4	K_K[2, 1, 3, 1] -> K[2, 1] + K[3, 1]
d6 = 0.8	K_MEKP[2, 2] -> MEKP + K[2, 2]
d7 = 0.6	K_K[1, 0, 2, 2] -> K[1, 0] + K[2, 2]
d8 = 0.4	K_MAPKP[1, 1] -> MAPKP + K[1, 1]
d9 = 0.6	K_K[1, 1, 2, 2] -> K[1, 1] + K[2, 2]
k10 = 0.1	K_MAPKP[1, 2] -> MAPKP + K[1, 1]
k1 = 0.1	K_RAFK[3, 0] -> RAFK + K[3, 1]
k1 = 0.1	S_RAFK[0, 0, 0] -> RAFK + S[0, 0, 1]
k1 = 0.1	S_RAFK[0, -1, 0] -> RAFK + S[0, -1, 1]
k1 = 0.1	S_RAFK[0, 1, 0] -> RAFK + S[0, 1, 1]
k1 = 0.1	S_RAFK[0, 2, 0] -> RAFK + S[0, 2, 1]
k1 = 0.1	S_RAFK[-1, 0, 0] -> RAFK + S[-1, 0, 1]
k1 = 0.1	S_RAFK[1, 0, 0] -> RAFK + S[1, 0, 1]
k1 = 0.1	S_RAFK[-1, -1, 0] -> RAFK + S[-1, -1, 1]
k1 = 0.1	S_RAFK[-1, 1, 0] -> RAFK + S[-1, 1, 1]
k1 = 0.1	S_RAFK[1, -1, 0] -> RAFK + S[1, -1, 1]
k1 = 0.1	S_RAFK[1, 1, 0] -> RAFK + S[1, 1, 1]
k1 = 0.1	S_RAFK[-1, 2, 0] -> RAFK + S[-1, 2, 1]
k1 = 0.1	S_RAFK[1, 2, 0] -> RAFK + S[1, 2, 1]
k1 = 0.1	S_RAFK[2, 0, 0] -> RAFK + S[2, 0, 1]
k1 = 0.1	S_RAFK[2, -1, 0] -> RAFK + S[2, -1, 1]
k1 = 0.1	S_RAFK[2, 1, 0] -> RAFK + S[2, 1, 1]
k1 = 0.1	S_RAFK[2, 2, 0] -> RAFK + S[2, 2, 1]
k1a = 100	RAFK + S[0, 0, 0] -> S_RAFK[0, 0, 0]
k1a = 100	RAFK + S[0, -1, 0] -> S_RAFK[0, -1, 0]
k1a = 100	RAFK + S[0, 1, 0] -> S_RAFK[0, 1, 0]
k1a = 100	RAFK + S[0, 2, 0] -> S_RAFK[0, 2, 0]
k1a = 100	RAFK + S[-1, 0, 0] -> S_RAFK[-1, 0, 0]
k1a = 100	RAFK + S[1, 0, 0] -> S_RAFK[1, 0, 0]
k1a = 100	RAFK + S[-1, -1, 0] -> S_RAFK[-1, -1, 0]
k1a = 100	RAFK + S[-1, 1, 0] -> S_RAFK[-1, 1, 0]
k1a = 100	RAFK + S[1, -1, 0] -> S_RAFK[1, -1, 0]
k1a = 100	RAFK + S[1, 1, 0] -> S_RAFK[1, 1, 0]
k1a = 100	RAFK + S[-1, 2, 0] -> S_RAFK[-1, 2, 0]
k1a = 100	RAFK + S[1, 2, 0] -> S_RAFK[1, 2, 0]
k1a = 100	RAFK + S[2, 0, 0] -> S_RAFK[2, 0, 0]
k1a = 100	RAFK + S[2, -1, 0] -> S_RAFK[2, -1, 0]
k1a = 100	RAFK + S[2, 1, 0] -> S_RAFK[2, 1, 0]
k1a = 100	RAFK + S[2, 2, 0] -> S_RAFK[2, 2, 0]
k2 = 0.1	K_RAFP[3, 1] -> RAFP + K[3, 0]
k3 = 0.1	K_K[2, 0, 3, 1] -> K[2, 1] + K[3, 1]
k3 = 0.1	S[0, 0, 1] -> S[0, 1, 1]
k3 = 0.1	S[-1, 0, 1] -> S[-1, 1, 1]
k3 = 0.1	S[1, 0, 1] -> S[1, 1, 1]
k3 = 0.1	S[2, 0, 1] -> S[2, 1, 1]
k4 = 0.1	K_MEKP[2, 1] -> MEKP + K[2, 0]
k5 = 0.1	K_K[2, 1, 3, 1] -> K[2, 2] + K[3, 1]
k5a = 0.1	S[0, 1, 1] -> S[0, 2, 1]
k5a = 0.1	S[-1, 1, 1] -> S[-1, 2, 1]
k5a = 0.1	S[1, 1, 1] -> S[1, 2, 1]
k5a = 0.1	S[2, 1, 1] -> S[2, 2, 1]
k6 = 0.1	K_MEKP[2, 2] -> MEKP + K[2, 1]
k7 = 0.1	K_K[1, 0, 2, 2] -> K[1, 1] + K[2, 2]
k7 = 0.1	S[0, 2, 0] -> S[1, 2, 0]
k7 = 0.1	S[0, 2, -1] -> S[1, 2, -1]
k7 = 0.1	S[0, 2, 1] -> S[1, 2, 1]
k8 = 0.1	K_MAPKP[1, 1] -> MAPKP + K[1, 0]
k9 = 0.1	K_K[1, 1, 2, 2] -> K[1, 2] + K[2, 2]
k9a = 0.1	S[1, 2, 0] -> S[2, 2, 0]
k9a = 0.1	S[1, 2, -1] -> S[2, 2, -1]
k9a = 0.1	S[1, 2, 1] -> S[2, 2, 1]
koff = 0.5	S[0, 0, 0] -> K[1, 0] + S[-1, 0, 0]
koff = 0.5	S[0, 0, 0] -> K[2, 0] + S[0, -1, 0]
koff = 0.5	S[0, 0, 0] -> K[3, 0] + S[0, 0, -1]
koff = 0.5	S[0, 0, -1] -> K[1, 0] + S[-1, 0, -1]
koff = 0.5	S[0, 0, 1] -> K[1, 0] + S[-1, 0, 1]
koff = 0.5	S[0, 0, -1] -> K[2, 0] + S[0, -1, -1]
koff = 0.5	S[0, 0, 1] -> K[2, 0] + S[0, -1, 1]
koff = 0.5	S[0, -1, 0] -> K[1, 0] + S[-1, -1, 0]
koff = 0.5	S[0, 1, 0] -> K[1, 0] + S[-1, 1, 0]
koff = 0.5	S[0, -1, 0] -> K[3, 0] + S[0, -1, -1]
koff = 0.5	S[0, 1, 0] -> K[3, 0] + S[0, 1, -1]
koff = 0.5	S[0, -1, -1] -> K[1, 0] + S[-1, -1, -1]
koff = 0.5	S[0, -1, 1] -> K[1, 0] + S[-1, -1, 1]
koff = 0.5	S[0, 1, -1] -> K[1, 0] + S[-1, 1, -1]
koff = 0.5	S[0, 1, 1] -> K[1, 0] + S[-1, 1, 1]
koff = 0.5	S[0, 2, 0] -> K[1, 0] + S[-1, 2, 0]
koff = 0.5	S[0, 2, 0] -> K[3, 0] + S[0, 2, -1]
koff = 0.5	S[0, 2, -1] -> K[1, 0] + S[-1, 2, -1]
koff = 0.5	S[0, 2, 1] -> K[1, 0] + S[-1, 2, 1]
koff = 0.5	S[-1, 0, 0] -> K[2, 0] + S[-1, -1, 0]
koff = 0.5	S[1, 0, 0] -> K[2, 0] + S[1, -1, 0]
koff = 0.5	S[-1, 0, 0] -> K[3, 0] + S[-1, 0, -1]
koff = 0.5	S[1, 0, 0] -> K[3, 0] + S[1, 0, -1]
koff = 0.5	S[-1, 0, -1] -> K[2, 0] + S[-1, -1, -1]
koff = 0.5	S[-1, 0, 1] -> K[2, 0] + S[-1, -1, 1]
koff = 0.5	S[1, 0, -1] -> K[2, 0] + S[1, -1, -1]
koff = 0.5	S[1, 0, 1] -> K[2, 0] + S[1, -1, 1]
koff = 0.5	S[-1, -1, 0] -> K[3, 0] + S[-1, -1, -1]
koff = 0.5	S[-1, 1, 0] -> K[3, 0] + S[-1, 1, -1]
koff = 0.5	S[1, -1, 0] -> K[3, 0] + S[1, -1, -1]
koff = 0.5	S[1, 1, 0] -> K[3, 0] + S[1, 1, -1]
koff = 0.5	S[-1, 2, 0] -> K[3, 0] + S[-1, 2, -1]
koff = 0.5	S[1, 2, 0] -> K[3, 0] + S[1, 2, -1]
koff = 0.5	S[2, 0, 0] -> K[2, 0] + S[2, -1, 0]
koff = 0.5	S[2, 0, 0] -> K[3, 0] + S[2, 0, -1]
koff = 0.5	S[2, 0, -1] -> K[2, 0] + S[2, -1, -1]
koff = 0.5	S[2, 0, 1] -> K[2, 0] + S[2, -1, 1]
koff = 0.5	S[2, -1, 0] -> K[3, 0] + S[2, -1, -1]
koff = 0.5	S[2, 1, 0] -> K[3, 0] + S[2, 1, -1]
koff = 0.5	S[2, 2, 0] -> K[3, 0] + S[2, 2, -1]
kon = 10	K[1, 0] + S[-1, 0, 0] -> S[0, 0, 0]
kon = 10	K[1, 0] + S[-1, 0, -1] -> S[0, 0, -1]
kon = 10	K[1, 0] + S[-1, 0, 1] -> S[0, 0, 1]
kon = 10	K[1, 0] + S[-1, -1, 0] -> S[0, -1, 0]
kon = 10	K[1, 0] + S[-1, 1, 0] -> S[0, 1, 0]
kon = 10	K[1, 0] + S[-1, -1, -1] -> S[0, -1, -1]
kon = 10	K[1, 0] + S[-1, -1, 1] -> S[0, -1, 1]
kon = 10	K[1, 0] + S[-1, 1, -1] -> S[0, 1, -1]
kon = 10	K[1, 0] + S[-1, 1, 1] -> S[0, 1, 1]
kon = 10	K[1, 0] + S[-1, 2, 0] -> S[0, 2, 0]
kon = 10	K[1, 0] + S[-1, 2, -1] -> S[0, 2, -1]
kon = 10	K[1, 0] + S[-1, 2, 1] -> S[0, 2, 1]
kon = 10	K[2, 0] + S[0, -1, 0] -> S[0, 0, 0]
kon = 10	K[2, 0] + S[0, -1, -1] -> S[0, 0, -1]
kon = 10	K[2, 0] + S[0, -1, 1] -> S[0, 0, 1]
kon = 10	K[2, 0] + S[-1, -1, 0] -> S[-1, 0, 0]
kon = 10	K[2, 0] + S[1, -1, 0] -> S[1, 0, 0]
kon = 10	K[2, 0] + S[-1, -1, -1] -> S[-1, 0, -1]
kon = 10	K[2, 0] + S[-1, -1, 1] -> S[-1, 0, 1]
kon = 10	K[2, 0] + S[1, -1, -1] -> S[1, 0, -1]
kon = 10	K[2, 0] + S[1, -1, 1] -> S[1, 0, 1]
kon = 10	K[2, 0] + S[2, -1, 0] -> S[2, 0, 0]
kon = 10	K[2, 0] + S[2, -1, -1] -> S[2, 0, -1]
kon = 10	K[2, 0] + S[2, -1, 1] -> S[2, 0, 1]
kon = 10	K[3, 0] + S[0, 0, -1] -> S[0, 0, 0]
kon = 10	K[3, 0] + S[0, -1, -1] -> S[0, -1, 0]
kon = 10	K[3, 0] + S[0, 1, -1] -> S[0, 1, 0]
kon = 10	K[3, 0] + S[0, 2, -1] -> S[0, 2, 0]
kon = 10	K[3, 0] + S[-1, 0, -1] -> S[-1, 0, 0]
kon = 10	K[3, 0] + S[1, 0, -1] -> S[1, 0, 0]
kon = 10	K[3, 0] + S[-1, -1, -1] -> S[-1, -1, 0]
kon = 10	K[3, 0] + S[-1, 1, -1] -> S[-1, 1, 0]
kon = 10	K[3, 0] + S[1, -1, -1] -> S[1, -1, 0]
kon = 10	K[3, 0] + S[1, 1, -1] -> S[1, 1, 0]
kon = 10	K[3, 0] + S[-1, 2, -1] -> S[-1, 2, 0]
kon = 10	K[3, 0] + S[1, 2, -1] -> S[1, 2, 0]
kon = 10	K[3, 0] + S[2, 0, -1] -> S[2, 0, 0]
kon = 10	K[3, 0] + S[2, -1, -1] -> S[2, -1, 0]
kon = 10	K[3, 0] + S[2, 1, -1] -> S[2, 1, 0]
kon = 10	K[3, 0] + S[2, 2, -1] -> S[2, 2, 0]
kpoff = 0.05	S[0, 0, 1] -> K[3, 1] + S[0, 0, -1]
kpoff = 0.05	S[0, 1, 0] -> K[2, 1] + S[0, -1, 0]
kpoff = 0.05	S[0, 1, -1] -> K[2, 1] + S[0, -1, -1]
kpoff = 0.05	S[0, 1, 1] -> K[2, 1] + S[0, -1, 1]
kpoff = 0.05	S[0, -1, 1] -> K[3, 1] + S[0, -1, -1]
kpoff = 0.05	S[0, 1, 1] -> K[3, 1] + S[0, 1, -1]
kpoff = 0.05	S[0, 2, 0] -> K[2, 2] + S[0, -1, 0]
kpoff = 0.05	S[0, 2, -1] -> K[2, 2] + S[0, -1, -1]
kpoff = 0.05	S[0, 2, 1] -> K[2, 2] + S[0, -1, 1]
kpoff = 0.05	S[0, 2, 1] -> K[3, 1] + S[0, 2, -1]
kpoff = 0.05	S[1, 0, 0] -> K[1, 1] + S[-1, 0, 0]
kpoff = 0.05	S[1, 0, -1] -> K[1, 1] + S[-1, 0, -1]
kpoff = 0.05	S[1, 0, 1] -> K[1, 1] + S[-1, 0, 1]
kpoff = 0.05	S[-1, 0, 1] -> K[3, 1] + S[-1, 0, -1]
kpoff = 0.05	S[1, 0, 1] -> K[3, 1] + S[1, 0, -1]
kpoff = 0.05	S[1, -1, 0] -> K[1, 1] + S[-1, -1, 0]
kpoff = 0.05	S[1, 1, 0] -> K[1, 1] + S[-1, 1, 0]
kpoff = 0.05	S[-1, 1, 0] -> K[2, 1] + S[-1, -1, 0]
kpoff = 0.05	S[1, 1, 0] -> K[2, 1] + S[1, -1, 0]
kpoff = 0.05	S[1, -1, -1] -> K[1, 1] + S[-1, -1, -1]
kpoff = 0.05	S[1, -1, 1] -> K[1, 1] + S[-1, -1, 1]
kpoff = 0.05	S[1, 1, -1] -> K[1, 1] + S[-1, 1, -1]
kpoff = 0.05	S[1, 1, 1] -> K[1, 1] + S[-1, 1, 1]
kpoff = 0.05	S[-1, 1, -1] -> K[2, 1] + S[-1, -1, -1]
kpoff = 0.05	S[-1, 1, 1] -> K[2, 1] + S[-1, -1, 1]
kpoff = 0.05	S[1, 1, -1] -> K[2, 1] + S[1, -1, -1]
kpoff = 0.05	S[1, 1, 1] -> K[2, 1] + S[1, -1, 1]
kpoff = 0.05	S[-1, -1, 1] -> K[3, 1] + S[-1, -1, -1]
kpoff = 0.05	S[-1, 1, 1] -> K[3, 1] + S[-1, 1, -1]
kpoff = 0.05	S[1, -1, 1] -> K[3, 1] + S[1, -1, -1]
kpoff = 0.05	S[1, 1, 1] -> K[3, 1] + S[1, 1, -1]
kpoff = 0.05	S[1, 2, 0] -> K[1, 1] + S[-1, 2, 0]
kpoff = 0.05	S[-1, 2, 0] -> K[2, 2] + S[-1, -1, 0]
kpoff = 0.05	S[1, 2, 0] -> K[2, 2] + S[1, -1, 0]
kpoff = 0.05	S[1, 2, -1] -> K[1, 1] + S[-1, 2, -1]
kpoff = 0.05	S[1, 2, 1] -> K[1, 1] + S[-1, 2, 1]
kpoff = 0.05	S[-1, 2, -1] -> K[2, 2] + S[-1, -1, -1]
kpoff = 0.05	S[-1, 2, 1] -> K[2, 2] + S[-1, -1, 1]
kpoff = 0.05	S[1, 2, -1] -> K[2, 2] + S[1, -1, -1]
kpoff = 0.05	S[1, 2, 1] -> K[2, 2] + S[1, -1, 1]
kpoff = 0.05	S[-1, 2, 1] -> K[3, 1] + S[-1, 2, -1]
kpoff = 0.05	S[1, 2, 1] -> K[3, 1] + S[1, 2, -1]
kpoff = 0.05	S[2, 0, 0] -> K[1, 2] + S[-1, 0, 0]
kpoff = 0.05	S[2, 0, -1] -> K[1, 2] + S[-1, 0, -1]
kpoff = 0.05	S[2, 0, 1] -> K[1, 2] + S[-1, 0, 1]
kpoff = 0.05	S[2, 0, 1] -> K[3, 1] + S[2, 0, -1]
kpoff = 0.05	S[2, -1, 0] -> K[1, 2] + S[-1, -1, 0]
kpoff = 0.05	S[2, 1, 0] -> K[1, 2] + S[-1, 1, 0]
kpoff = 0.05	S[2, 1, 0] -> K[2, 1] + S[2, -1, 0]
kpoff = 0.05	S[2, -1, -1] -> K[1, 2] + S[-1, -1, -1]
kpoff = 0.05	S[2, -1, 1] -> K[1, 2] + S[-1, -1, 1]
kpoff = 0.05	S[2, 1, -1] -> K[1, 2] + S[-1, 1, -1]
kpoff = 0.05	S[2, 1, 1] -> K[1, 2] + S[-1, 1, 1]
kpoff = 0.05	S[2, 1, -1] -> K[2, 1] + S[2, -1, -1]
kpoff = 0.05	S[2, 1, 1] -> K[2, 1] + S[2, -1, 1]
kpoff = 0.05	S[2, -1, 1] -> K[3, 1] + S[2, -1, -1]
kpoff = 0.05	S[2, 1, 1] -> K[3, 1] + S[2, 1, -1]
kpoff = 0.05	S[2, 2, 0] -> K[1, 2] + S[-1, 2, 0]
kpoff = 0.05	S[2, 2, 0] -> K[2, 2] + S[2, -1, 0]
kpoff = 0.05	S[2, 2, -1] -> K[1, 2] + S[-1, 2, -1]
kpoff = 0.05	S[2, 2, 1] -> K[1, 2] + S[-1, 2, 1]
kpoff = 0.05	S[2, 2, -1] -> K[2, 2] + S[2, -1, -1]
kpoff = 0.05	S[2, 2, 1] -> K[2, 2] + S[2, -1, 1]
kpoff = 0.05	S[2, 2, 1] -> K[3, 1] + S[2, 2, -1]
kpon = 0	K[1, 1] + S[-1, 0, 0] -> S[1, 0, 0]
kpon = 0	K[1, 1] + S[-1, 0, -1] -> S[1, 0, -1]
kpon = 0	K[1, 1] + S[-1, 0, 1] -> S[1, 0, 1]
kpon = 0	K[1, 1] + S[-1, -1, 0] -> S[1, -1, 0]
kpon = 0	K[1, 1] + S[-1, 1, 0] -> S[1, 1, 0]
kpon = 0	K[1, 1] + S[-1, -1, -1] -> S[1, -1, -1]
kpon = 0	K[1, 1] + S[-1, -1, 1] -> S[1, -1, 1]
kpon = 0	K[1, 1] + S[-1, 1, -1] -> S[1, 1, -1]
kpon = 0	K[1, 1] + S[-1, 1, 1] -> S[1, 1, 1]
kpon = 0	K[1, 1] + S[-1, 2, 0] -> S[1, 2, 0]
kpon = 0	K[1, 1] + S[-1, 2, -1] -> S[1, 2, -1]
kpon = 0	K[1, 1] + S[-1, 2, 1] -> S[1, 2, 1]
kpon = 0	K[1, 2] + S[-1, 0, 0] -> S[2, 0, 0]
kpon = 0	K[1, 2] + S[-1, 0, -1] -> S[2, 0, -1]
kpon = 0	K[1, 2] + S[-1, 0, 1] -> S[2, 0, 1]
kpon = 0	K[1, 2] + S[-1, -1, 0] -> S[2, -1, 0]
kpon = 0	K[1, 2] + S[-1, 1, 0] -> S[2, 1, 0]
kpon = 0	K[1, 2] + S[-1, -1, -1] -> S[2, -1, -1]
kpon = 0	K[1, 2] + S[-1, -1, 1] -> S[2, -1, 1]
kpon = 0	K[1, 2] + S[-1, 1, -1] -> S[2, 1, -1]
kpon = 0	K[1, 2] + S[-1, 1, 1] -> S[2, 1, 1]
kpon = 0	K[1, 2] + S[-1, 2, 0] -> S[2, 2, 0]
kpon = 0	K[1, 2] + S[-1, 2, -1] -> S[2, 2, -1]
kpon = 0	K[1, 2] + S[-1, 2, 1] -> S[2, 2, 1]
kpon = 0	K[2, 1] + S[0, -1, 0] -> S[0, 1, 0]
kpon = 0	K[2, 1] + S[0, -1, -1] -> S[0, 1, -1]
kpon = 0	K[2, 1] + S[0, -1, 1] -> S[0, 1, 1]
kpon = 0	K[2, 1] + S[-1, -1, 0] -> S[-1, 1, 0]
kpon = 0	K[2, 1] + S[1, -1, 0] -> S[1, 1, 0]
kpon = 0	K[2, 1] + S[-1, -1, -1] -> S[-1, 1, -1]
kpon = 0	K[2, 1] + S[-1, -1, 1] -> S[-1, 1, 1]
kpon = 0	K[2, 1] + S[1, -1, -1] -> S[1, 1, -1]
kpon = 0	K[2, 1] + S[1, -1, 1] -> S[1, 1, 1]
kpon = 0	K[2, 1] + S[2, -1, 0] -> S[2, 1, 0]
kpon = 0	K[2, 1] + S[2, -1, -1] -> S[2, 1, -1]
kpon = 0	K[2, 1] + S[2, -1, 1] -> S[2, 1, 1]
kpon = 0	K[2, 2] + S[0, -1, 0] -> S[0, 2, 0]
kpon = 0	K[2, 2] + S[0, -1, -1] -> S[0, 2, -1]
kpon = 0	K[2, 2] + S[0, -1, 1] -> S[0, 2, 1]
kpon = 0	K[2, 2] + S[-1, -1, 0] -> S[-1, 2, 0]
kpon = 0	K[2, 2] + S[1, -1, 0] -> S[1, 2, 0]
kpon = 0	K[2, 2] + S[-1, -1, -1] -> S[-1, 2, -1]
kpon = 0	K[2, 2] + S[-1, -1, 1] -> S[-1, 2, 1]
kpon = 0	K[2, 2] + S[1, -1, -1] -> S[1, 2, -1]
kpon = 0	K[2, 2] + S[1, -1, 1] -> S[1, 2, 1]
kpon = 0	K[2, 2] + S[2, -1, 0] -> S[2, 2, 0]
kpon = 0	K[2, 2] + S[2, -1, -1] -> S[2, 2, -1]
kpon = 0	K[2, 2] + S[2, -1, 1] -> S[2, 2, 1]
kpon = 0	K[3, 1] + S[0, 0, -1] -> S[0, 0, 1]
kpon = 0	K[3, 1] + S[0, -1, -1] -> S[0, -1, 1]
kpon = 0	K[3, 1] + S[0, 1, -1] -> S[0, 1, 1]
kpon = 0	K[3, 1] + S[0, 2, -1] -> S[0, 2, 1]
kpon = 0	K[3, 1] + S[-1, 0, -1] -> S[-1, 0, 1]
kpon = 0	K[3, 1] + S[1, 0, -1] -> S[1, 0, 1]
kpon = 0	K[3, 1] + S[-1, -1, -1] -> S[-1, -1, 1]
kpon = 0	K[3, 1] + S[-1, 1, -1] -> S[-1, 1, 1]
kpon = 0	K[3, 1] + S[1, -1, -1] -> S[1, -1, 1]
kpon = 0	K[3, 1] + S[1, 1, -1] -> S[1, 1, 1]
kpon = 0	K[3, 1] + S[-1, 2, -1] -> S[-1, 2, 1]
kpon = 0	K[3, 1] + S[1, 2, -1] -> S[1, 2, 1]
kpon = 0	K[3, 1] + S[2, 0, -1] -> S[2, 0, 1]
kpon = 0	K[3, 1] + S[2, -1, -1] -> S[2, -1, 1]
kpon = 0	K[3, 1] + S[2, 1, -1] -> S[2, 1, 1]
kpon = 0	K[3, 1] + S[2, 2, -1] -> S[2, 2, 1]

Variable	IC	ODE
MAPKP	0.3	MAPKP'[t] == -(a8MAPKP[t]K[1, 1][t]) - a10MAPKP[ t]K[1, 2][t] + d8K_MAPKP[1, 1][t] + k8K_MAPKP[ 1, 1][t] + d10K_MAPKP[1, 2][t] + k10K_MAPKP[1, 2][t]
MEKP	0.2	MEKP'[t] == -(a4MEKP[t]K[2, 1][t]) - a6MEKP[t] K[2, 2][t] + d4K_MEKP[2, 1][t] + k4K_MEKP[2, 1][t] + d6K_MEKP[2, 2][t] + k6K_MEKP[2, 2] [t]
RAFK	0.1	RAFK'[t] == -(a1RAFK[t]K[3, 0][t]) + d1K_RAFK[3, 0][t] + k1K_RAFK[3, 0][t] - k1aRAFK[t]S[-1, -1, 0][t] - k1aRAFK[t]S[-1, 0, 0][t] - k1aRAFK[t]S[-1, 1, 0][t] - k1aRAFK[t]S[-1, 2, 0][t] - k1aRAFK[t]S[0, -1, 0][t] - k1a* RAFK[t]S[0, 0, 0][t] - k1aRAFK[t]S[0, 1, 0][t] - k1aRAFK[t]S[0, 2, 0][t] - k1aRAFK[t]S[1, -1, 0][t] - k1aRAFK[t]S[1, 0, 0][t] - k1aRAFK[t]S[1, 1, 0][t] - k1aRAFK[t]S[1, 2, 0][t] - k1aRAFK[t]S[2, -1, 0][t] - k1a RAFK[t]S[2, 0, 0][t] - k1aRAFK[t]S[2, 1, 0][t] - k1aRAFK[t]S[2, 2, 0][t] + d1aS_RAFK[-1, -1, 0][t] + k1S_RAFK[-1, -1, 0][t] + d1aS_RAFK[-1, 0, 0][t] + k1S_RAFK[-1, 0, 0][t] + d1aS_RAFK[-1, 1, 0][t] + k1S_RAFK[ -1, 1, 0][t] + d1aS_RAFK[-1, 2, 0][t] + k1S_RAFK[-1, 2, 0][t] + d1aS_RAFK[0, -1, 0][t] + k1S_RAFK[0, -1, 0][t] + d1aS_RAFK[ 0, 0, 0][t] + k1S_RAFK[0, 0, 0][t] + d1aS_RAFK[0, 1, 0][t] + k1S_RAFK[0, 1, 0][ t] + d1aS_RAFK[0, 2, 0][t] + k1S_RAFK[0, 2, 0][t] + d1aS_RAFK[1, -1, 0][t] + k1S_RAFK[ 1, -1, 0][t] + d1aS_RAFK[1, 0, 0][t] + k1S_RAFK[1, 0, 0][t] + d1aS_RAFK[1, 1, 0][ t] + k1S_RAFK[1, 1, 0][t] + d1aS_RAFK[1, 2, 0][t] + k1S_RAFK[1, 2, 0][t] + d1aS_RAFK[ 2, -1, 0][t] + k1S_RAFK[2, -1, 0][t] + d1aS_RAFK[2, 0, 0][t] + k1S_RAFK[2, 0, 0][ t] + d1aS_RAFK[2, 1, 0][t] + k1S_RAFK[2, 1, 0][t] + d1aS_RAFK[2, 2, 0][t] + k1*S_RAFK[ 2, 2, 0][t]
RAFP	0.3	RAFP'[t] == -(a2RAFP[t]K[3, 1][t]) + d2K_RAFP[3, 1][t] + k2K_RAFP[3, 1][t]
K[1, 0]	0.4	(K[1, 0])'[t] == -(a7K[1, 0][t]K[2, 2][t]) + d7K_K[1, 0, 2, 2][t] + k8K_MAPKP[1, 1][t] - konK[1, 0][t]S[-1, -1, -1][t] - konK[1, 0][t]S[-1, -1, 0][t] - konK[1, 0][t]S[-1, -1, 1][t] - konK[1, 0][t]S[-1, 0, -1][t] - konK[1, 0][t]S[-1, 0, 0][t] - konK[1, 0][t]S[-1, 0, 1][t] - konK[1, 0][t]S[-1, 1, -1][t] - konK[1, 0][t]S[-1, 1, 0][t] - konK[1, 0][t]S[-1, 1, 1][t] - konK[1, 0][t]S[-1, 2, -1][t] - konK[1, 0][t]S[-1, 2, 0][t] - konK[1, 0][t]S[-1, 2, 1][t] + koffS[0, -1, -1][t] + koffS[0, -1, 0][t] + koffS[0, -1, 1][t] + koffS[0, 0, -1][t] + koffS[0, 0, 0][t] + koff S[0, 0, 1][t] + koffS[0, 1, -1][t] + koffS[0, 1, 0][t] + koffS[0, 1, 1][t] + koffS[0, 2, -1][t] + koffS[0, 2, 0] [t] + koffS[0, 2, 1][t]
K[1, 1]	0	(K[1, 1])'[t] == -(a8MAPKP[t]K[1, 1][t]) - a9K[1, 1][t]K[2, 2][t] + k7K_K[1, 0, 2, 2][t] + d9K_K[1, 1, 2, 2][t] + d8* K_MAPKP[1, 1][t] + k10K_MAPKP[1, 2][t] - kponK[ 1, 1][t]S[-1, -1, -1][t] - kponK[1, 1][t]S[-1, -1, 0][t] - kponK[1, 1][t]S[-1, -1, 1][t] - kponK[1, 1][t]S[-1, 0, -1][t] - kponK[ 1, 1][t]S[-1, 0, 0][t] - kponK[1, 1][t]S[-1, 0, 1][t] - kponK[1, 1][t]S[-1, 1, -1][t] - kponK[1, 1][t]S[-1, 1, 0][t] - kponK[1, 1][t]S[-1, 1, 1][t] - kponK[1, 1][t]S[-1, 2, -1][t] - kponK[1, 1][t]S[-1, 2, 0][t] - kponK[1, 1][t]S[-1, 2, 1][t] + kpoffS[ 1, -1, -1][t] + kpoffS[1, -1, 0][t] + kpoffS[1, -1, 1][t] + kpoffS[1, 0, -1][t] + kpoffS[1, 0, 0][t] + kpoffS[1, 0, 1][t] + kpoffS[1, 1, -1][t] + kpoffS[1, 1, 0][t] + kpoffS[1, 1, 1][t] + kpoff* S[1, 2, -1][t] + kpoffS[1, 2, 0][t] + kpoffS[1, 2, 1][t]
K[1, 2]	0	(K[1, 2])'[t] == -(a10MAPKP[t]K[1, 2][t]) + k9K_K[1, 1, 2, 2][t] + d10K_MAPKP[1, 2][t] - kponK[1, 2][t]S[-1, -1, -1][t] - kponK[ 1, 2][t]S[-1, -1, 0][t] - kponK[1, 2][t]S[-1, -1, 1][t] - kponK[1, 2][t]S[-1, 0, -1][t] - kponK[1, 2][t]S[-1, 0, 0][t] - kponK[1, 2][t]S[-1, 0, 1][t] - kponK[1, 2][t]S[-1, 1, -1][t] - kponK[1, 2][t]S[-1, 1, 0][t] - kponK[1, 2][t]S[-1, 1, 1][t] - kponK[1, 2][t]S[-1, 2, -1][t] - kponK[1, 2][t]S[-1, 2, 0][t] - kponK[1, 2][t]S[-1, 2, 1][t] + kpoffS[2, -1, -1][t] + kpoffS[2, -1, 0][t] + kpoffS[2, -1, 1][t] + kpoffS[2, 0, -1][t] + kpoffS[2, 0, 0][t] + kpoffS[2, 0, 1][t] + kpoffS[2, 1, -1][t] + kpoffS[2, 1, 0][t] + kpoffS[2, 1, 1][t] + kpoffS[2, 2, -1][t] + kpoffS[2, 2, 0][t] + kpoffS[2, 2, 1][t]
K[2, 0]	0.2	(K[2, 0])'[t] == -(a3K[2, 0][t]K[3, 1][t]) + d3K_K[2, 0, 3, 1][t] + k4K_MEKP[2, 1][t] - konK[2, 0][t]S[-1, -1, -1][t] - konK[2, 0][t]S[-1, -1, 0][t] - konK[2, 0][t]S[-1, -1, 1][t] + koffS[-1, 0, -1][t] + koffS[-1, 0, 0][t] + koffS[-1, 0, 1][t] - konK[2, 0][t]S[0, -1, -1][t] - konK[2, 0][t]S[0, -1, 0][t] - konK[2, 0][t]S[0, - 1, 1][t] + koffS[0, 0, -1][t] + koffS[0, 0, 0][t] + koffS[0, 0, 1][t] - konK[ 2, 0][t]S[1, -1, -1][t] - konK[2, 0][t]S[1, -1, 0][t] - konK[2, 0][t]S[1, -1, 1][t] + koffS[1, 0, -1][t] + koffS[1, 0, 0] [t] + koffS[1, 0, 1][t] - konK[2, 0][t]S[ 2, -1, -1][t] - konK[2, 0][t]S[2, -1, 0][t] - konK[2, 0][t]S[2, -1, 1][t] + koffS[2, 0, -1][t] + koffS[2, 0, 0][t] + koff S[2, 0, 1][t]
K[2, 1]	0	(K[2, 1])'[t] == -(a4MEKP[t]K[2, 1][t]) - a5K[2, 1][t]K[3, 1][t] + k3K_K[2, 0, 3, 1][t] + d5K_K[2, 1, 3, 1][t] + d4* K_MEKP[2, 1][t] + k6K_MEKP[2, 2][t] - kponK[2, 1][t]S[-1, -1, -1][t] - kponK[2, 1][t]S[-1, -1, 0][t] - kponK[2, 1][t]S[-1, -1, 1][t] + kpoffS[-1, 1, -1][t] + kpoffS[-1, 1, 0][t] + kpoffS[-1, 1, 1][t] - kponK[2, 1][t]S[0, -1, -1][t] - kponK[2, 1][t]S[0, -1, 0][t] - kponK[2, 1][t]S[0, -1, 1][t] + kpoffS[0, 1, -1][t] + kpoffS[0, 1, 0][t] + kpoffS[0, 1, 1][t] - kponK[2, 1][t]S[1, -1, -1][t] - kponK[2, 1][t]S[1, -1, 0][t] - kponK[2, 1][t]S[1, -1, 1][t] + kpoffS[1, 1, -1][t] + kpoffS[1, 1, 0][t] + kpoffS[1, 1, 1][t] - kponK[2, 1][t]S[2, -1, -1][t] - kponK[2, 1][t]S[2, -1, 0][t] - kponK[2, 1][t]S[2, -1, 1][t] + kpoffS[2, 1, -1][t] + kpoffS[2, 1, 0][t] + kpoff*S[2, 1, 1][t]
K[2, 2]	0	(K[2, 2])'[t] == -(a6MEKP[t]K[2, 2][t]) - a7K[1, 0][t]K[2, 2][t] - a9K[1, 1][t]K[2, 2][t] + d7K_K[1, 0, 2, 2][t] + k7K_K[ 1, 0, 2, 2][t] + d9K_K[1, 1, 2, 2][t] + k9K_K[1, 1, 2, 2][t] + k5K_K[2, 1, 3, 1][t] + d6K_MEKP[2, 2][t] - kponK[2, 2][t]S[-1, -1, -1][t] - kponK[2, 2][t]S[-1, -1, 0][t] - kponK[2, 2][t]S[-1, -1, 1][t] + kpoffS[-1, 2, -1][t] + kpoffS[-1, 2, 0][t] + kpoffS[-1, 2, 1][t] - kponK[2, 2][t]S[0, -1, -1][t] - kponK[2, 2][t]S[0, -1, 0][t] - kponK[2, 2][t]S[0, -1, 1][t] + kpoffS[0, 2, -1][t] + kpoffS[0, 2, 0][t] + kpoffS[0, 2, 1][t] - kponK[2, 2][t]S[1, -1, -1][t] - kponK[2, 2][t]S[1, -1, 0][t] - kponK[2, 2][t]S[1, -1, 1][t] + kpoffS[1, 2, -1][t] + kpoffS[1, 2, 0][t] + kpoffS[1, 2, 1][t] - kponK[2, 2][t]S[2, -1, -1][t] - kponK[2, 2][t]S[2, -1, 0][t] - kponK[2, 2][t]S[2, -1, 1][t] + kpoffS[2, 2, -1][t] + kpoffS[2, 2, 0][t] + kpoffS[2, 2, 1][t]
K[3, 0]	0.3	(K[3, 0])'[t] == -(a1RAFK[t]K[3, 0][t]) + d1K_RAFK[3, 0][t] + k2K_RAFP[3, 1][t] - konK[3, 0][t]S[-1, -1, -1][t] + koffS[-1, -1, 0][t] - konK[3, 0][t]S[-1, 0, -1][t] + koffS[-1, 0, 0][t] - konK[3, 0][t]S[-1, 1, -1][t] + koffS[-1, 1, 0][t] - kon K[3, 0][t]S[-1, 2, -1][t] + koffS[-1, 2, 0] [t] - konK[3, 0][t]S[0, -1, -1][t] + koff* S[0, -1, 0][t] - konK[3, 0][t]S[0, 0, -1][ t] + koffS[0, 0, 0][t] - konK[3, 0][t]S[0, 1, -1][t] + koffS[0, 1, 0][t] - konK[ 3, 0][t]S[0, 2, -1][t] + koffS[0, 2, 0][t] - konK[3, 0][t]S[1, -1, -1][t] + koffS[1, -1, 0][t] - konK[3, 0][t]S[1, 0, -1][t] + koffS[1, 0, 0][t] - konK[3, 0][t]S[1, 1, -1][t] + koffS[1, 1, 0][t] - konK[ 3, 0][t]S[1, 2, -1][t] + koffS[1, 2, 0][t] - konK[3, 0][t]S[2, -1, -1][t] + koffS[2, -1, 0][t] - konK[3, 0][t]S[2, 0, -1][t] + koffS[2, 0, 0][t] - konK[3, 0][t]S[2, 1, -1][t] + koffS[2, 1, 0][t] - konK[ 3, 0][t]S[2, 2, -1][t] + koff*S[2, 2, 0][t]
K[3, 1]	0	(K[3, 1])'[t] == -(a2RAFP[t]K[3, 1][t]) - a3K[2, 0][t]K[3, 1][t] - a5K[2, 1][t]K[3, 1][t] + d3K_K[2, 0, 3, 1][t] + k3K_K[ 2, 0, 3, 1][t] + d5K_K[2, 1, 3, 1][t] + k5K_K[2, 1, 3, 1][t] + k1K_RAFK[3, 0][t] + d2K_RAFP[3, 1][t] - kponK[3, 1][t] S[-1, -1, -1][t] + kpoffS[-1, -1, 1][t] - kponK[3, 1][t]S[-1, 0, -1][t] + kpoffS[-1, 0, 1][t] - kponK[3, 1][t]S[-1, 1, -1][t] + kpoffS[-1, 1, 1][t] - kponK[3, 1][t]S[- 1, 2, -1][t] + kpoffS[-1, 2, 1][t] - kponK[3, 1][t]S[0, -1, -1][t] + kpoffS[0, -1, 1][t] - kponK[3, 1][t]S[0, 0, -1][t] + kpoffS[0, 0, 1][t] - kponK[3, 1][t]S[0, 1, -1][t] + kpoffS[0, 1, 1][t] - kpon K[3, 1][t]S[0, 2, -1][t] + kpoffS[0, 2, 1][ t] - kponK[3, 1][t]S[1, -1, -1][t] + kpoff* S[1, -1, 1][t] - kponK[3, 1][t]S[1, 0, -1][ t] + kpoffS[1, 0, 1][t] - kponK[3, 1][t]S[ 1, 1, -1][t] + kpoffS[1, 1, 1][t] - kponK[3, 1][t]S[1, 2, -1][t] + kpoffS[1, 2, 1][t] - kponK[3, 1][t]S[2, -1, -1][t] + kpoffS[2, -1, 1][t] - kponK[3, 1][t]S[ 2, 0, -1][t] + kpoffS[2, 0, 1][t] - kponK[3, 1][t]S[2, 1, -1][t] + kpoffS[2, 1, 1][t] - kponK[3, 1][t]S[2, 2, -1][t] + kpoff*S[2, 2, 1][t]
K_K[1, 0, 2, 2]	0	(K_K[1, 0, 2, 2])'[t] == a7K[1, 0][t]K[2, 2][t] - d7K_K[1, 0, 2, 2][t] - k7K_K[ 1, 0, 2, 2][t]
K_K[1, 1, 2, 2]	0	(K_K[1, 1, 2, 2])'[t] == a9K[1, 1][t]K[2, 2][t] - d9K_K[1, 1, 2, 2][t] - k9K_K[ 1, 1, 2, 2][t]
K_K[2, 0, 3, 1]	0	(K_K[2, 0, 3, 1])'[t] == a3K[2, 0][t]K[3, 1][t] - d3K_K[2, 0, 3, 1][t] - k3K_K[ 2, 0, 3, 1][t]
K_K[2, 1, 3, 1]	0	(K_K[2, 1, 3, 1])'[t] == a5K[2, 1][t]K[3, 1][t] - d5K_K[2, 1, 3, 1][t] - k5K_K[ 2, 1, 3, 1][t]
K_MAPKP[1, 1]	0	(K_MAPKP[1, 1])'[t] == a8MAPKP[t]K[1, 1][t] - d8K_MAPKP[1, 1][t] - k8K_MAPKP[1, 1][t]
K_MAPKP[1, 2]	0	(K_MAPKP[1, 2])'[t] == a10MAPKP[t]K[1, 2][t] - d10K_MAPKP[1, 2][t] - k10K_MAPKP[1, 2][t]
K_MEKP[2, 1]	0	(K_MEKP[2, 1])'[t] == a4MEKP[t]K[2, 1][t] - d4K_MEKP[2, 1][t] - k4K_MEKP[2, 1][t]
K_MEKP[2, 2]	0	(K_MEKP[2, 2])'[t] == a6MEKP[t]K[2, 2][t] - d6K_MEKP[2, 2][t] - k6K_MEKP[2, 2][t]
K_RAFK[3, 0]	0	(K_RAFK[3, 0])'[t] == a1RAFK[t]K[3, 0][t] - d1K_RAFK[3, 0][t] - k1K_RAFK[3, 0][t]
K_RAFP[3, 1]	0	(K_RAFP[3, 1])'[t] == a2RAFP[t]K[3, 1][t] - d2K_RAFP[3, 1][t] - k2K_RAFP[3, 1][t]
S[-1, -1, -1]	0.1	(S[-1, -1, -1])'[t] == -(konK[1, 0][t]S[-1, -1, -1][t]) - kponK[1, 1][t]S[-1, -1, -1][ t] - kponK[1, 2][t]S[-1, -1, -1][t] - kon* K[2, 0][t]S[-1, -1, -1][t] - kponK[2, 1][t]S[- 1, -1, -1][t] - kponK[2, 2][t]S[-1, -1, -1] [t] - konK[3, 0][t]S[-1, -1, -1][t] - kpon K[3, 1][t]S[-1, -1, -1][t] + koffS[-1, -1, 0][t] + kpoffS[-1, -1, 1][t] + koffS[-1, 0, -1][t] + kpoffS[-1, 1, -1][t] + kpoffS[-1, 2, -1][t] + koffS[0, -1, -1][t] + kpoffS[1, -1, -1][t] + kpoff*S[2, -1, -1][t]
S[-1, -1, 0]	0	(S[-1, -1, 0])'[t] == konK[3, 0][t]S[-1, -1, -1][t] - koffS[-1, -1, 0][t] - k1aRAFK[t]* S[-1, -1, 0][t] - konK[1, 0][t]S[-1, -1, 0] [t] - kponK[1, 1][t]S[-1, -1, 0][t] - kpon* K[1, 2][t]S[-1, -1, 0][t] - konK[2, 0][t]S[-1, -1, 0][t] - kponK[2, 1][t]S[-1, -1, 0][t] - kponK[2, 2][t]S[-1, -1, 0][t] + koffS[- 1, 0, 0][t] + kpoffS[-1, 1, 0][t] + kpoffS[-1, 2, 0][t] + koffS[0, -1, 0][t] + kpoffS[1, -1, 0][t] + kpoffS[2, -1, 0][t] + d1aS_RAFK[-1, -1, 0][t]
S[-1, -1, 1]	0	(S[-1, -1, 1])'[t] == kponK[3, 1][t]S[-1, - 1, -1][t] - kpoffS[-1, -1, 1][t] - konK[1, 0][t]S[-1, -1, 1][t] - kponK[1, 1][t]S[-1, -1, 1][t] - kponK[1, 2][t]S[-1, -1, 1][t] - konK[2, 0][t]S[-1, -1, 1][t] - kponK[2, 1][t]S[-1, -1, 1][t] - kponK[2, 2][t]S[-1, -1, 1][t] + koffS[-1, 0, 1][t] + kpoffS[-1, 1, 1][t] + kpoffS[-1, 2, 1][t] + koffS[0, -1, 1][t] + kpoffS[1, -1, 1][t] + kpoffS[2, -1, 1][t] + k1S_RAFK[-1, -1, 0][t]
S[-1, 0, -1]	0	(S[-1, 0, -1])'[t] == konK[2, 0][t]S[-1, -1, -1][t] - koffS[-1, 0, -1][t] - konK[1, 0][t]S[-1, 0, -1][t] - kponK[1, 1][t]S[-1, 0, -1][t] - kponK[1, 2][t]S[-1, 0, -1][t] - konK[3, 0][t]S[-1, 0, -1][t] - kponK[3, 1][t]S[-1, 0, -1][t] + koffS[-1, 0, 0][t] + kpoffS[-1, 0, 1][t] + koffS[0, 0, - 1][t] + kpoffS[1, 0, -1][t] + kpoffS[2, 0, -1][t]
S[-1, 0, 0]	0	(S[-1, 0, 0])'[t] == konK[2, 0][t]S[-1, -1, 0][t] + konK[3, 0][t]S[-1, 0, -1][t] - 2koffS[-1, 0, 0][t] - k1aRAFK[t]S[-1, 0, 0][t] - konK[1, 0][t]S[-1, 0, 0][t] - kponK[1, 1][t]S[-1, 0, 0][t] - kponK[1, 2][t]S[-1, 0, 0][t] + koffS[0, 0, 0][t] + kpoffS[1, 0, 0][t] + kpoffS[2, 0, 0][t] + d1aS_RAFK[-1, 0, 0][t]
S[-1, 0, 1]	0	(S[-1, 0, 1])'[t] == konK[2, 0][t]S[-1, -1, 1][t] + kponK[3, 1][t]S[-1, 0, -1][t] - k3S[-1, 0, 1][t] - koffS[-1, 0, 1][t] - kpoffS[-1, 0, 1][t] - konK[1, 0][t]S[- 1, 0, 1][t] - kponK[1, 1][t]S[-1, 0, 1][t] - kponK[1, 2][t]S[-1, 0, 1][t] + koffS[0, 0, 1][t] + kpoffS[1, 0, 1][t] + kpoff S[2, 0, 1][t] + k1*S_RAFK[-1, 0, 0][t]
S[-1, 1, -1]	0	(S[-1, 1, -1])'[t] == kponK[2, 1][t]S[-1, - 1, -1][t] - kpoffS[-1, 1, -1][t] - konK[1, 0][t]S[-1, 1, -1][t] - kponK[1, 1][t]S[-1, 1, -1][t] - kponK[1, 2][t]S[-1, 1, -1][t] - konK[3, 0][t]S[-1, 1, -1][t] - kponK[3, 1][t]S[-1, 1, -1][t] + koffS[-1, 1, 0][t] + kpoffS[-1, 1, 1][t] + koffS[0, 1, - 1][t] + kpoffS[1, 1, -1][t] + kpoffS[2, 1, -1][t]
S[-1, 1, 0]	0	(S[-1, 1, 0])'[t] == kponK[2, 1][t]S[-1, -1, 0][t] + konK[3, 0][t]S[-1, 1, -1][t] - koffS[-1, 1, 0][t] - kpoffS[-1, 1, 0][t] - k1aRAFK[t]S[-1, 1, 0][t] - konK[1, 0][ t]S[-1, 1, 0][t] - kponK[1, 1][t]S[-1, 1, 0][t] - kponK[1, 2][t]S[-1, 1, 0][t] + koffS[0, 1, 0][t] + kpoffS[1, 1, 0][t] + kpoffS[2, 1, 0][t] + d1aS_RAFK[-1, 1, 0][t]
S[-1, 1, 1]	0	(S[-1, 1, 1])'[t] == kponK[2, 1][t]S[-1, -1, 1][t] + k3S[-1, 0, 1][t] + kponK[3, 1][t]S[-1, 1, -1][t] - k5aS[-1, 1, 1][t] - 2kpoffS[-1, 1, 1][t] - konK[1, 0][t]S[ -1, 1, 1][t] - kponK[1, 1][t]S[-1, 1, 1][t] - kponK[1, 2][t]S[-1, 1, 1][t] + koffS[0, 1, 1][t] + kpoffS[1, 1, 1][t] + kpoff* S[2, 1, 1][t] + k1*S_RAFK[-1, 1, 0][t]
S[-1, 2, -1]	0	(S[-1, 2, -1])'[t] == kponK[2, 2][t]S[-1, - 1, -1][t] - kpoffS[-1, 2, -1][t] - konK[1, 0][t]S[-1, 2, -1][t] - kponK[1, 1][t]S[-1, 2, -1][t] - kponK[1, 2][t]S[-1, 2, -1][t] - konK[3, 0][t]S[-1, 2, -1][t] - kponK[3, 1][t]S[-1, 2, -1][t] + koffS[-1, 2, 0][t] + kpoffS[-1, 2, 1][t] + koffS[0, 2, - 1][t] + kpoffS[1, 2, -1][t] + kpoffS[2, 2, -1][t]
S[-1, 2, 0]	0	(S[-1, 2, 0])'[t] == kponK[2, 2][t]S[-1, -1, 0][t] + konK[3, 0][t]S[-1, 2, -1][t] - koffS[-1, 2, 0][t] - kpoffS[-1, 2, 0][t] - k1aRAFK[t]S[-1, 2, 0][t] - konK[1, 0][ t]S[-1, 2, 0][t] - kponK[1, 1][t]S[-1, 2, 0][t] - kponK[1, 2][t]S[-1, 2, 0][t] + koffS[0, 2, 0][t] + kpoffS[1, 2, 0][t] + kpoffS[2, 2, 0][t] + d1aS_RAFK[-1, 2, 0][t]
S[-1, 2, 1]	0	(S[-1, 2, 1])'[t] == kponK[2, 2][t]S[-1, -1, 1][t] + k5aS[-1, 1, 1][t] + kponK[3, 1][t]S[-1, 2, -1][t] - 2kpoffS[-1, 2, 1][ t] - konK[1, 0][t]S[-1, 2, 1][t] - kponK[ 1, 1][t]S[-1, 2, 1][t] - kponK[1, 2][t]S[-1, 2, 1][t] + koffS[0, 2, 1][t] + kpoff* S[1, 2, 1][t] + kpoffS[2, 2, 1][t] + k1S_RAFK[-1, 2, 0][t]
S[0, -1, -1]	0	(S[0, -1, -1])'[t] == konK[1, 0][t]S[-1, -1, -1][t] - koffS[0, -1, -1][t] - konK[2, 0][t]S[0, -1, -1][t] - kponK[2, 1][t]S[0, -1, -1][t] - kponK[2, 2][t]S[0, -1, -1][t] - konK[3, 0][t]S[0, -1, -1][t] - kponK[3, 1][t]S[0, -1, -1][t] + koffS[0, -1, 0][t] + kpoffS[0, -1, 1][t] + koffS[0, 0, - 1][t] + kpoffS[0, 1, -1][t] + kpoffS[0, 2, -1][t]
S[0, -1, 0]	0	(S[0, -1, 0])'[t] == konK[1, 0][t]S[-1, -1, 0][t] + konK[3, 0][t]S[0, -1, -1][t] - 2koffS[0, -1, 0][t] - k1aRAFK[t]S[0, -1, 0][t] - konK[2, 0][t]S[0, -1, 0][t] - kponK[2, 1][t]S[0, -1, 0][t] - kponK[2, 2][t]S[0, -1, 0][t] + koffS[0, 0, 0][t] + kpoffS[0, 1, 0][t] + kpoffS[0, 2, 0][t] + d1aS_RAFK[0, -1, 0][t]
S[0, -1, 1]	0	(S[0, -1, 1])'[t] == konK[1, 0][t]S[-1, -1, 1][t] + kponK[3, 1][t]S[0, -1, -1][t] - koffS[0, -1, 1][t] - kpoffS[0, -1, 1][t] - konK[2, 0][t]S[0, -1, 1][t] - kponK[2, 1][t]S[0, -1, 1][t] - kponK[2, 2][t]S[0, -1, 1][t] + koffS[0, 0, 1][t] + kpoff S[0, 1, 1][t] + kpoffS[0, 2, 1][t] + k1S_RAFK[0, -1, 0][t]
S[0, 0, -1]	0	(S[0, 0, -1])'[t] == konK[1, 0][t]S[-1, 0, -1][t] + konK[2, 0][t]S[0, -1, -1][t] - 2koffS[0, 0, -1][t] - konK[3, 0][t]S[0, 0, -1][t] - kponK[3, 1][t]S[0, 0, -1][t] + koffS[0, 0, 0][t] + kpoffS[0, 0, 1] [t]
S[0, 0, 0]	0	(S[0, 0, 0])'[t] == konK[1, 0][t]S[-1, 0, 0][t] + konK[2, 0][t]S[0, -1, 0][t] + konK[3, 0][t]S[0, 0, -1][t] - 3koffS[0, 0, 0][t] - k1aRAFK[t]S[0, 0, 0][t] + d1a*S_RAFK[0, 0, 0][t]
S[0, 0, 1]	0	(S[0, 0, 1])'[t] == konK[1, 0][t]S[-1, 0, 1][t] + konK[2, 0][t]S[0, -1, 1][t] + kponK[3, 1][t]S[0, 0, -1][t] - k3S[0, 0, 1][t] - 2koffS[0, 0, 1][t] - kpoffS[0, 0, 1][t] + k1*S_RAFK[0, 0, 0][t]
S[0, 1, -1]	0	(S[0, 1, -1])'[t] == konK[1, 0][t]S[-1, 1, -1][t] + kponK[2, 1][t]S[0, -1, -1][t] - koffS[0, 1, -1][t] - kpoffS[0, 1, -1][t] - konK[3, 0][t]S[0, 1, -1][t] - kponK[3, 1][t]S[0, 1, -1][t] + koffS[0, 1, 0][t] + kpoffS[0, 1, 1][t]
S[0, 1, 0]	0	(S[0, 1, 0])'[t] == konK[1, 0][t]S[-1, 1, 0][t] + kponK[2, 1][t]S[0, -1, 0][t] + konK[3, 0][t]S[0, 1, -1][t] - 2koffS[0, 1, 0][t] - kpoffS[0, 1, 0][t] - k1a RAFK[t]S[0, 1, 0][t] + d1aS_RAFK[0, 1, 0][t]
S[0, 1, 1]	0	(S[0, 1, 1])'[t] == konK[1, 0][t]S[-1, 1, 1][t] + kponK[2, 1][t]S[0, -1, 1][t] + k3S[0, 0, 1][t] + kponK[3, 1][t]S[0, 1, -1][t] - k5aS[0, 1, 1][t] - koffS[0, 1, 1][t] - 2kpoffS[0, 1, 1][t] + k1 S_RAFK[0, 1, 0][t]
S[0, 2, -1]	0	(S[0, 2, -1])'[t] == konK[1, 0][t]S[-1, 2, -1][t] + kponK[2, 2][t]S[0, -1, -1][t] - k7S[0, 2, -1][t] - koffS[0, 2, -1][t] - kpoffS[0, 2, -1][t] - konK[3, 0][t]S[0, 2, -1][t] - kponK[3, 1][t]S[0, 2, -1][t] + koffS[0, 2, 0][t] + kpoff*S[0, 2, 1] [t]
S[0, 2, 0]	0	(S[0, 2, 0])'[t] == konK[1, 0][t]S[-1, 2, 0][t] + kponK[2, 2][t]S[0, -1, 0][t] + konK[3, 0][t]S[0, 2, -1][t] - k7S[0, 2, 0][t] - 2koffS[0, 2, 0][t] - kpoffS[0, 2, 0][t] - k1aRAFK[t]S[0, 2, 0][t] + d1a*S_RAFK[0, 2, 0][t]
S[0, 2, 1]	0	(S[0, 2, 1])'[t] == konK[1, 0][t]S[-1, 2, 1][t] + kponK[2, 2][t]S[0, -1, 1][t] + k5aS[0, 1, 1][t] + kponK[3, 1][t]S[0, 2, -1][t] - k7S[0, 2, 1][t] - koffS[0, 2, 1][t] - 2kpoffS[0, 2, 1][t] + k1 S_RAFK[0, 2, 0][t]
S[1, -1, -1]	0	(S[1, -1, -1])'[t] == kponK[1, 1][t]S[-1, - 1, -1][t] - kpoffS[1, -1, -1][t] - konK[2, 0][t]S[1, -1, -1][t] - kponK[2, 1][t]S[1, -1, -1][t] - kponK[2, 2][t]S[1, -1, -1][t] - konK[3, 0][t]S[1, -1, -1][t] - kponK[3, 1][t]S[1, -1, -1][t] + koffS[1, -1, 0][t] + kpoffS[1, -1, 1][t] + koffS[1, 0, - 1][t] + kpoffS[1, 1, -1][t] + kpoffS[1, 2, -1][t]
S[1, -1, 0]	0	(S[1, -1, 0])'[t] == kponK[1, 1][t]S[-1, -1, 0][t] + konK[3, 0][t]S[1, -1, -1][t] - koffS[1, -1, 0][t] - kpoffS[1, -1, 0][t] - k1aRAFK[t]S[1, -1, 0][t] - konK[2, 0][ t]S[1, -1, 0][t] - kponK[2, 1][t]S[1, -1, 0][t] - kponK[2, 2][t]S[1, -1, 0][t] + koffS[1, 0, 0][t] + kpoffS[1, 1, 0][t] + kpoffS[1, 2, 0][t] + d1aS_RAFK[1, -1, 0][t]
S[1, -1, 1]	0	(S[1, -1, 1])'[t] == kponK[1, 1][t]S[-1, -1, 1][t] + kponK[3, 1][t]S[1, -1, -1][t] - 2kpoffS[1, -1, 1][t] - konK[2, 0][t]S[1, -1, 1][t] - kponK[2, 1][t]S[1, -1, 1][t] - kponK[2, 2][t]S[1, -1, 1][t] + koffS[1, 0, 1][t] + kpoffS[1, 1, 1][t] + kpoff* S[1, 2, 1][t] + k1*S_RAFK[1, -1, 0][t]
S[1, 0, -1]	0	(S[1, 0, -1])'[t] == kponK[1, 1][t]S[-1, 0, -1][t] + konK[2, 0][t]S[1, -1, -1][t] - koffS[1, 0, -1][t] - kpoffS[1, 0, -1][t] - konK[3, 0][t]S[1, 0, -1][t] - kponK[3, 1][t]S[1, 0, -1][t] + koffS[1, 0, 0][t] + kpoffS[1, 0, 1][t]
S[1, 0, 0]	0	(S[1, 0, 0])'[t] == kponK[1, 1][t]S[-1, 0, 0][t] + konK[2, 0][t]S[1, -1, 0][t] + konK[3, 0][t]S[1, 0, -1][t] - 2koffS[1, 0, 0][t] - kpoffS[1, 0, 0][t] - k1a RAFK[t]S[1, 0, 0][t] + d1aS_RAFK[1, 0, 0][t]
S[1, 0, 1]	0	(S[1, 0, 1])'[t] == kponK[1, 1][t]S[-1, 0, 1][t] + konK[2, 0][t]S[1, -1, 1][t] + kponK[3, 1][t]S[1, 0, -1][t] - k3S[1, 0, 1][t] - koffS[1, 0, 1][t] - 2kpoffS[1, 0, 1][t] + k1*S_RAFK[1, 0, 0][t]
S[1, 1, -1]	0	(S[1, 1, -1])'[t] == kponK[1, 1][t]S[-1, 1, -1][t] + kponK[2, 1][t]S[1, -1, -1][t] - 2kpoffS[1, 1, -1][t] - konK[3, 0][t]S[1, 1, -1][t] - kponK[3, 1][t]S[1, 1, -1][t] + koffS[1, 1, 0][t] + kpoffS[1, 1, 1] [t]
S[1, 1, 0]	0	(S[1, 1, 0])'[t] == kponK[1, 1][t]S[-1, 1, 0][t] + kponK[2, 1][t]S[1, -1, 0][t] + konK[3, 0][t]S[1, 1, -1][t] - koffS[1, 1, 0][t] - 2kpoffS[1, 1, 0][t] - k1aRAFK[t]* S[1, 1, 0][t] + d1a*S_RAFK[1, 1, 0][t]
S[1, 1, 1]	0	(S[1, 1, 1])'[t] == kponK[1, 1][t]S[-1, 1, 1][t] + kponK[2, 1][t]S[1, -1, 1][t] + k3S[1, 0, 1][t] + kponK[3, 1][t]S[1, 1, -1][t] - k5aS[1, 1, 1][t] - 3kpoffS[1, 1, 1][t] + k1*S_RAFK[1, 1, 0][t]
S[1, 2, -1]	0	(S[1, 2, -1])'[t] == kponK[1, 1][t]S[-1, 2, -1][t] + k7S[0, 2, -1][t] + kponK[2, 2][t]S[1, -1, -1][t] - k9aS[1, 2, -1][t] - 2kpoffS[1, 2, -1][t] - konK[3, 0][t]S[ 1, 2, -1][t] - kponK[3, 1][t]S[1, 2, -1][t] + koffS[1, 2, 0][t] + kpoffS[1, 2, 1] [t]
S[1, 2, 0]	0	(S[1, 2, 0])'[t] == kponK[1, 1][t]S[-1, 2, 0][t] + k7S[0, 2, 0][t] + kponK[2, 2] [t]S[1, -1, 0][t] + konK[3, 0][t]S[1, 2, - 1][t] - k9aS[1, 2, 0][t] - koffS[1, 2, 0][t] - 2kpoffS[1, 2, 0][t] - k1aRAFK[t]* S[1, 2, 0][t] + d1a*S_RAFK[1, 2, 0][t]
S[1, 2, 1]	0	(S[1, 2, 1])'[t] == kponK[1, 1][t]S[-1, 2, 1][t] + k7S[0, 2, 1][t] + kponK[2, 2] [t]S[1, -1, 1][t] + k5aS[1, 1, 1][t] + kponK[3, 1][t]S[1, 2, -1][t] - k9aS[1, 2, 1][t] - 3kpoffS[1, 2, 1][t] + k1S_RAFK[1, 2, 0][t]
S[2, -1, -1]	0	(S[2, -1, -1])'[t] == kponK[1, 2][t]S[-1, - 1, -1][t] - kpoffS[2, -1, -1][t] - konK[2, 0][t]S[2, -1, -1][t] - kponK[2, 1][t]S[2, -1, -1][t] - kponK[2, 2][t]S[2, -1, -1][t] - konK[3, 0][t]S[2, -1, -1][t] - kponK[3, 1][t]S[2, -1, -1][t] + koffS[2, -1, 0][t] + kpoffS[2, -1, 1][t] + koffS[2, 0, - 1][t] + kpoffS[2, 1, -1][t] + kpoffS[2, 2, -1][t]
S[2, -1, 0]	0	(S[2, -1, 0])'[t] == kponK[1, 2][t]S[-1, -1, 0][t] + konK[3, 0][t]S[2, -1, -1][t] - koffS[2, -1, 0][t] - kpoffS[2, -1, 0][t] - k1aRAFK[t]S[2, -1, 0][t] - konK[2, 0][ t]S[2, -1, 0][t] - kponK[2, 1][t]S[2, -1, 0][t] - kponK[2, 2][t]S[2, -1, 0][t] + koffS[2, 0, 0][t] + kpoffS[2, 1, 0][t] + kpoffS[2, 2, 0][t] + d1aS_RAFK[2, -1, 0][t]
S[2, -1, 1]	0	(S[2, -1, 1])'[t] == kponK[1, 2][t]S[-1, -1, 1][t] + kponK[3, 1][t]S[2, -1, -1][t] - 2kpoffS[2, -1, 1][t] - konK[2, 0][t]S[2, -1, 1][t] - kponK[2, 1][t]S[2, -1, 1][t] - kponK[2, 2][t]S[2, -1, 1][t] + koffS[2, 0, 1][t] + kpoffS[2, 1, 1][t] + kpoff* S[2, 2, 1][t] + k1*S_RAFK[2, -1, 0][t]
S[2, 0, -1]	0	(S[2, 0, -1])'[t] == kponK[1, 2][t]S[-1, 0, -1][t] + konK[2, 0][t]S[2, -1, -1][t] - koffS[2, 0, -1][t] - kpoffS[2, 0, -1][t] - konK[3, 0][t]S[2, 0, -1][t] - kponK[3, 1][t]S[2, 0, -1][t] + koffS[2, 0, 0][t] + kpoffS[2, 0, 1][t]
S[2, 0, 0]	0	(S[2, 0, 0])'[t] == kponK[1, 2][t]S[-1, 0, 0][t] + konK[2, 0][t]S[2, -1, 0][t] + konK[3, 0][t]S[2, 0, -1][t] - 2koffS[2, 0, 0][t] - kpoffS[2, 0, 0][t] - k1a RAFK[t]S[2, 0, 0][t] + d1aS_RAFK[2, 0, 0][t]
S[2, 0, 1]	0	(S[2, 0, 1])'[t] == kponK[1, 2][t]S[-1, 0, 1][t] + konK[2, 0][t]S[2, -1, 1][t] + kponK[3, 1][t]S[2, 0, -1][t] - k3S[2, 0, 1][t] - koffS[2, 0, 1][t] - 2kpoffS[2, 0, 1][t] + k1*S_RAFK[2, 0, 0][t]
S[2, 1, -1]	0	(S[2, 1, -1])'[t] == kponK[1, 2][t]S[-1, 1, -1][t] + kponK[2, 1][t]S[2, -1, -1][t] - 2kpoffS[2, 1, -1][t] - konK[3, 0][t]S[2, 1, -1][t] - kponK[3, 1][t]S[2, 1, -1][t] + koffS[2, 1, 0][t] + kpoffS[2, 1, 1] [t]
S[2, 1, 0]	0	(S[2, 1, 0])'[t] == kponK[1, 2][t]S[-1, 1, 0][t] + kponK[2, 1][t]S[2, -1, 0][t] + konK[3, 0][t]S[2, 1, -1][t] - koffS[2, 1, 0][t] - 2kpoffS[2, 1, 0][t] - k1aRAFK[t]* S[2, 1, 0][t] + d1a*S_RAFK[2, 1, 0][t]
S[2, 1, 1]	0	(S[2, 1, 1])'[t] == kponK[1, 2][t]S[-1, 1, 1][t] + kponK[2, 1][t]S[2, -1, 1][t] + k3S[2, 0, 1][t] + kponK[3, 1][t]S[2, 1, -1][t] - k5aS[2, 1, 1][t] - 3kpoffS[2, 1, 1][t] + k1*S_RAFK[2, 1, 0][t]
S[2, 2, -1]	0	(S[2, 2, -1])'[t] == kponK[1, 2][t]S[-1, 2, -1][t] + k9aS[1, 2, -1][t] + kponK[2, 2][t]S[2, -1, -1][t] - 2kpoffS[2, 2, -1][ t] - konK[3, 0][t]S[2, 2, -1][t] - kponK[ 3, 1][t]S[2, 2, -1][t] + koffS[2, 2, 0][t] + kpoff*S[2, 2, 1][t]
S[2, 2, 0]	0	(S[2, 2, 0])'[t] == kponK[1, 2][t]S[-1, 2, 0][t] + k9aS[1, 2, 0][t] + kponK[2, 2][t]S[2, -1, 0][t] + konK[3, 0][t]S[2, 2, -1][t] - koffS[2, 2, 0][t] - 2* kpoffS[2, 2, 0][t] - k1aRAFK[t]S[2, 2, 0][t] + d1aS_RAFK[2, 2, 0][t]
S[2, 2, 1]	0	(S[2, 2, 1])'[t] == kponK[1, 2][t]S[-1, 2, 1][t] + k9aS[1, 2, 1][t] + kponK[2, 2][t]S[2, -1, 1][t] + k5aS[2, 1, 1][t] + kponK[3, 1][t]S[2, 2, -1][t] - 3kpoff S[2, 2, 1][t] + k1*S_RAFK[2, 2, 0][t]
S_RAFK[-1, -1, 0]	0	(S_RAFK[-1, -1, 0])'[t] == k1aRAFK[t]S[-1, -1, 0][t] - d1aS_RAFK[-1, -1, 0][t] - k1 S_RAFK[-1, -1, 0][t]
S_RAFK[-1, 0, 0]	0	(S_RAFK[-1, 0, 0])'[t] == k1aRAFK[t]S[-1, 0, 0][t] - d1aS_RAFK[-1, 0, 0][t] - k1S_RAFK[ -1, 0, 0][t]
S_RAFK[-1, 1, 0]	0	(S_RAFK[-1, 1, 0])'[t] == k1aRAFK[t]S[-1, 1, 0][t] - d1aS_RAFK[-1, 1, 0][t] - k1S_RAFK[ -1, 1, 0][t]
S_RAFK[-1, 2, 0]	0	(S_RAFK[-1, 2, 0])'[t] == k1aRAFK[t]S[-1, 2, 0][t] - d1aS_RAFK[-1, 2, 0][t] - k1S_RAFK[ -1, 2, 0][t]
S_RAFK[0, -1, 0]	0	(S_RAFK[0, -1, 0])'[t] == k1aRAFK[t]S[0, -1, 0][t] - d1aS_RAFK[0, -1, 0][t] - k1S_RAFK[ 0, -1, 0][t]
S_RAFK[0, 0, 0]	0	(S_RAFK[0, 0, 0])'[t] == k1aRAFK[t]S[0, 0, 0][t] - d1aS_RAFK[0, 0, 0][t] - k1S_RAFK[ 0, 0, 0][t]
S_RAFK[0, 1, 0]	0	(S_RAFK[0, 1, 0])'[t] == k1aRAFK[t]S[0, 1, 0][t] - d1aS_RAFK[0, 1, 0][t] - k1S_RAFK[ 0, 1, 0][t]
S_RAFK[0, 2, 0]	0	(S_RAFK[0, 2, 0])'[t] == k1aRAFK[t]S[0, 2, 0][t] - d1aS_RAFK[0, 2, 0][t] - k1S_RAFK[ 0, 2, 0][t]
S_RAFK[1, -1, 0]	0	(S_RAFK[1, -1, 0])'[t] == k1aRAFK[t]S[1, -1, 0][t] - d1aS_RAFK[1, -1, 0][t] - k1S_RAFK[ 1, -1, 0][t]
S_RAFK[1, 0, 0]	0	(S_RAFK[1, 0, 0])'[t] == k1aRAFK[t]S[1, 0, 0][t] - d1aS_RAFK[1, 0, 0][t] - k1S_RAFK[ 1, 0, 0][t]
S_RAFK[1, 1, 0]	0	(S_RAFK[1, 1, 0])'[t] == k1aRAFK[t]S[1, 1, 0][t] - d1aS_RAFK[1, 1, 0][t] - k1S_RAFK[ 1, 1, 0][t]
S_RAFK[1, 2, 0]	0	(S_RAFK[1, 2, 0])'[t] == k1aRAFK[t]S[1, 2, 0][t] - d1aS_RAFK[1, 2, 0][t] - k1S_RAFK[ 1, 2, 0][t]
S_RAFK[2, -1, 0]	0	(S_RAFK[2, -1, 0])'[t] == k1aRAFK[t]S[2, -1, 0][t] - d1aS_RAFK[2, -1, 0][t] - k1S_RAFK[ 2, -1, 0][t]
S_RAFK[2, 0, 0]	0	(S_RAFK[2, 0, 0])'[t] == k1aRAFK[t]S[2, 0, 0][t] - d1aS_RAFK[2, 0, 0][t] - k1S_RAFK[ 2, 0, 0][t]
S_RAFK[2, 1, 0]	0	(S_RAFK[2, 1, 0])'[t] == k1aRAFK[t]S[2, 1, 0][t] - d1aS_RAFK[2, 1, 0][t] - k1S_RAFK[ 2, 1, 0][t]
S_RAFK[2, 2, 0]	0	(S_RAFK[2, 2, 0])'[t] == k1aRAFK[t]S[2, 2, 0][t] - d1aS_RAFK[2, 2, 0][t] - k1S_RAFK[ 2, 2, 0][t]

Generated by Cellerator Version 1.0 update 2.1203 using Mathematica 4.2 for Mac OS X (June 4, 2002), December 4, 2002 15:06:10, using (PowerMac,PowerPC,Mac OS X,MacOSX,Darwin)

author=B.E.Shapiro

The model is according to the paper Which Model to Use for Cortical Spiking Neurons? Figure1(K) resonator has been reproduced by MathSBML. The ODE and the parameters values are taken from the a paper Simple Model of Spiking Neurons The original format of the models are encoded in the MATLAB format existed in the ModelDB with Accession number 39948

Figure1 are the simulation results of the same model with different choices of parameters and different stimulus function or events. a=0.1; b=0.26; c=-60; d=-1; V=-62; u=b*V;

SBML level 2 code originaly generated for the JWS Online project by Jacky Snoep using PySCeS
Run this model online at http://jjj.biochem.sun.ac.za
To cite JWS Online please refer to: Olivier, B.G. and Snoep, J.L. (2004) Web-based modelling using JWS Online , Bioinformatics, 20:2143-2144

BioModels Curation : The model reproduces Fig 3 of the publication. By substituting a value of 1.4 for Tex it is possible to reproduce Fig 3C and 3D(iii), Fig 3A and 3D(i), are obtained by setting Tex=0. Also, note that the tryptophan concentrations have been normalized by 82 micromolar in the figures; the normalized concetrations can be obtained via the parameters To/s/t_norm. The model was successfully tested on MathSBML and Copasi.

The model reproduces the time profile of cytoplasmic Calcium as depicted in Fig 3 of the paper. Model successfully reproduced using Jarnac and MathSBML.

This model was successfully tested on Jarnac and MathSBML. The model reproduces the time profile of "Open Probability" of the receptor as shown in Figure 4 of the publication. The value of calcium ion concentration "c" in this model is 10 microM.

Leloup and Goldbeter, 1998

This model was created after the article by Leloup and Goldbeter, J Biol Rhythms 1998, Vol:13(1),pp70-87, pubmedID: 9486845
A Model for Circadian Rhythms in Drosophila Incorporating the Formation of a Complex between the PER and TIM Proteins
The parameters and initial concentrations are taken to reproduce figs. 4 D,E,F in the publication.
For a simulation without light dependent degradation of TIM_pp, change the the parameter v_dT_fac to 1.
The light/dark phases length can be set using the parameter l_d .

This a model from the article:
Mathematical model of the morphogenesis checkpoint in budding yeast.
Ciliberto A, Novak B, Tyson JJ J. Cell Biol. [2003 Dec; Volume: 163 (Issue: 6 )] Page info: 1243-54 14691135 ,
Abstract:
The morphogenesis checkpoint in budding yeast delays progression through the cell cycle in response to stimuli that prevent bud formation. Central to the checkpoint mechanism is Swe1 kinase: normally inactive, its activation halts cell cycle progression in G2. We propose a molecular network for Swe1 control, based on published observations of budding yeast and analogous control signals in fission yeast. The proposed Swe1 network is merged with a model of cyclin-dependent kinase regulation, converted into a set of differential equations and studied by numerical simulation. The simulations accurately reproduce the phenotypes of a dozen checkpoint mutants. Among other predictions, the model attributes a new role to Hsl1, a kinase known to play a role in Swe1 degradation: Hsl1 must also be indirectly responsible for potent inhibition of Swe1 activity. The model supports the idea that the morphogenesis checkpoint, like other checkpoints, raises the cell size threshold for progression from one phase of the cell cycle to the next.

The model reproduces Fig 3 of the paper.

Note: Model of the Calvin cycle and the related end-product pathways to starch and sucrose synthesis by Laisk et al. (2006, DOI:10.1007/s11120-006-9109-1 ) and the personally provided implementation to Laisk et al. (2009, DOI:10.1007/978-1-4020-9237-4_13 ).

A reduced version of the published model is implemented (light-dependent reactions are taken out). The parameter values are widely taken from Laisk et al. (1989, [click here for PDF] ). The initial metabolite values are chosen from the data set of Zhu et al. (2007, DOI:10.1104/pp.107.103713 ). A detailed description of all modifications is given in the model described by Arnold and Nikoloski (2011, PMID:22001849 .

This is the model of atorvastatin metabolism in hepaitc cells described in the article:
A systems biology approach to dynamic modeling and inter-subject variability of statin pharmacokinetics in human hepatocytes
Joachim Bucher , Stephan Riedmaier , Anke Schnabel , Katrin Marcus , Gabriele Vacun , Thomas S Weiss , Wolfgang E Thasler , Andreas K Nussler , Ulrich M Zanger and Matthias Reuss. BMC Systems Biology 2011, 5:66. DOI: 10.1186/1752-0509-5-66

Abstract:
Background:
The individual character of pharmacokinetics is of great importance in the risk assessment of new drug leads in pharmacological research. Amongst others, it is severely influenced by the properties and inter-individual variability of the enzymes and transporters of the drug detoxification system of the liver. Predicting individual drug biotransformation capacity requires quantitative and detailed models.
Results:
In this contribution we present the de novo deterministic modeling of atorvastatin biotransformation based on comprehensive published knowledge on involved metabolic and transport pathways as well as physicochemical properties. The model was evaluated in primary human hepatocytes and parameter identifiability analysis was performed under multiple experimental constraints. Dynamic simulations of atorvastatin biotransformation considering the inter-individual variability of the two major involved enzymes CYP3A4 and UGT1A3 based on quantitative protein expression data in a large human liver bank (n=150) highlighted the variability in the individual biotransformation profiles and therefore also points to the individuality of pharmacokinetics.
Conclusions:
A dynamic model for the biotransformation of atorvastatin has been developed using quantitative metabolite measurements in primary human hepatocytes. The model comprises kinetics for transport processes and metabolic enzymes as well as population liver expression data allowing us to assess the impact of inter-individual variability of concentrations of key proteins. Application of computational tools for parameter sensitivity analysis enabled us to considerably improve the validity of the model and to create a consistent framework for precise computer-aided simulations in toxicology.

The model is parameterized for patient 1 and reproduces the time courses in figure 2 of the article.

PLoS ONE (2008), p. e1555

In-Silicio Modeling of the Mitotic Spindle Assembly Checkpoint

Bashar Ibrahim, Stephan Diekmann, Eberhard Schmitt, Peter Dittrich

	article	model
[O-Mad2]	1.5e-7 M	1.3e-7 M
[BubR1:Bub3]	1.30e-7 M	1.27e-7 M
k _-4	0.01 M ^-1 s ^-1	0.02 M ^-1 s ^-1
k _-5	0.1 M ^-1 s ^-1	0.2 M ^-1 s ^-1

This is the model of IL13 induced signalling in MedB-1 cell described in the article:
Dynamic Mathematical Modeling of IL13-Induced Signaling in Hodgkin and Primary Mediastinal B-Cell Lymphoma Allows Prediction of Therapeutic Targets.
Raia V, Schilling M, Böhm M, Hahn B, Kowarsch A, Raue A, Sticht C, Bohl S, Saile M, Möller P, Gretz N, Timmer J, Theis F, Lehmann WD, Lichter P and Klingmüller U. Cancer Res. 2011 Feb 1;71(3):693-704. PubmedID: 21127196 ; DOI: 10.1158/0008-5472.CAN-10-2987
Abstract:
Primary mediastinal B-cell lymphoma (PMBL) and classical Hodgkin lymphoma (cHL) share a frequent constitutive activation of JAK (Janus kinase)/STAT signaling pathway. Because of complex, nonlinear relations within the pathway, key dynamic properties remained to be identified to predict possible strategies for intervention. We report the development of dynamic pathway models based on quantitative data collected on signaling components of JAK/STAT pathway in two lymphoma-derived cell lines, MedB-1 and L1236, representative of PMBL and cHL, respectively. We show that the amounts of STAT5 and STAT6 are higher whereas those of SHP1 are lower in the two lymphoma cell lines than in normal B cells. Distinctively, L1236 cells harbor more JAK2 and less SHP1 molecules per cell than MedB-1 or control cells. In both lymphoma cell lines, we observe interleukin-13 (IL13)-induced activation of IL4 receptor α, JAK2, and STAT5, but not of STAT6. Genome-wide, 11 early and 16 sustained genes are upregulated by IL13 in both lymphoma cell lines. Specifically, the known STAT-inducible negative regulators CISH and SOCS3 are upregulated within 2 hours in MedB-1 but not in L1236 cells. On the basis of this detailed quantitative information, we established two mathematical models, MedB-1 and L1236 model, able to describe the respective experimental data. Most of the model parameters are identifiable and therefore the models are predictive. Sensitivity analysis of the model identifies six possible therapeutic targets able to reduce gene expression levels in L1236 cells and three in MedB-1. We experimentally confirm reduction in target gene expression in response to inhibition of STAT5 phosphorylation, thereby validating one of the predicted targets.

All concentrations in the model, apart from IL13, are in molecules/cell. IL13 is given in ng/ml. As the cell volume is not explicitely given in the article, it is just approximately derived from the MW of IL13 () and the conversion factor 2.265 molecules IL13/cell = 1 ng/ml to be around 60 fl.

SBML model exported from PottersWheel on 2010-08-10 12:14:57.
Inline follows the original matlab code:

% PottersWheel model definition file

function m = Raia2010_IL13_MedB1()

m             = pwGetEmptyModel();

%% Meta information

m.ID          = 'Raia2010_IL13_MedB1';
m.name        = 'Raia2010_IL13_MedB1';
m.description = '';
m.authors     = {'Raia et al'};
m.dates       = {'2010'};
m.type        = 'PW-2-0-47';

%% X: Dynamic variables
% m = pwAddX(m, ID, startValue, type, minValue, maxValue, unit, compartment, name, description, typeOfStartValue)

m = pwAddX(m, 'Rec'         ,              1.3, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'Rec_i'       , 113.193916718733, 'global',  0.001, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'IL13_Rec'    ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'p_IL13_Rec'  ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'p_IL13_Rec_i',                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'JAK2'        ,              2.8, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'pJAK2'       ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'SHP1'        ,               91, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'STAT5'       ,              165, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'pSTAT5'      ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'SOCS3mRNA'   ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'DecoyR'      ,             0.34, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'IL13_DecoyR' ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'SOCS3'       ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');
m = pwAddX(m, 'CD274mRNA'   ,                0, 'fix'   , 1e-006, 10000, 'molecules/cell (x 1000)', 'cell', []  , []  , []             , []  , 'protein.generic');


%% R: Reactions
% m = pwAddR(m, reactants, products, modifiers, type, options, rateSignature, parameters, description, ID, name, fast, compartments, parameterTrunks, designerPropsR, stoichiometry, reversible)

m = pwAddR(m, {'Rec'         }, {'IL13_Rec'    }, {'IL13stimulation'   }, 'C' , [] , 'k1 * m1 * r1 * 2.265'        , {'Kon_IL13Rec'                             });
m = pwAddR(m, {'Rec'         }, {'Rec_i'       }, {                    }, 'MA', [] , []                            , {'Rec_intern'                              });
m = pwAddR(m, {'Rec_i'       }, {'Rec'         }, {                    }, 'MA', [] , []                            , {'Rec_recycle'                             });
m = pwAddR(m, {'IL13_Rec'    }, {'p_IL13_Rec'  }, {'pJAK2'             }, 'E' , [] , []                            , {'Rec_phosphorylation'                     });
m = pwAddR(m, {'JAK2'        }, {'pJAK2'       }, {'IL13_Rec','SOCS3'  }, 'C' , [] , 'k1 * m1 * r1 / (1 + k2 * m2)', {'JAK2_phosphorylation','JAK2_p_inhibition'});
m = pwAddR(m, {'JAK2'        }, {'pJAK2'       }, {'p_IL13_Rec','SOCS3'}, 'C' , [] , 'k1 * m1 * r1 / (1 + k2 * m2)', {'JAK2_phosphorylation','JAK2_p_inhibition'});
m = pwAddR(m, {'p_IL13_Rec'  }, {'p_IL13_Rec_i'}, {                    }, 'MA', [] , []                            , {'pRec_intern'                             });
m = pwAddR(m, {'p_IL13_Rec_i'}, {              }, {                    }, 'MA', [] , []                            , {'pRec_degradation'                        });
m = pwAddR(m, {'pJAK2'       }, {'JAK2'        }, {'SHP1'              }, 'E' , [] , []                            , {'pJAK2_dephosphorylation'                 });
m = pwAddR(m, {'STAT5'       }, {'pSTAT5'      }, {'pJAK2'             }, 'E' , [] , []                            , {'STAT5_phosphorylation'                   });
m = pwAddR(m, {'pSTAT5'      }, {'STAT5'       }, {'SHP1'              }, 'E' , [] , []                            , {'pSTAT5_dephosphorylation'                });
m = pwAddR(m, {'DecoyR'      }, {'IL13_DecoyR' }, {'IL13stimulation'   }, 'C' , [] , 'k1 * m1 * r1 * 2.265'        , {'DecoyR_binding'                          });
m = pwAddR(m, {              }, {'SOCS3mRNA'   }, {'pSTAT5'            }, 'C' , [] , 'm1*k1'                       , {'SOCS3mRNA_production'                    });
m = pwAddR(m, {              }, {'SOCS3'       }, {'SOCS3mRNA'         }, 'C' , [] , 'm1*k1/(k2+m1)'               , {'SOCS3_translation','SOCS3_accumulation'  });
m = pwAddR(m, {'SOCS3'       }, {              }, {                    }, 'MA', [] , []                            , {'SOCS3_degradation'                       });
m = pwAddR(m, {              }, {'CD274mRNA'   }, {'pSTAT5'            }, 'C' , [] , 'm1*k1'                       , {'CD274mRNA_production'                    });



%% C: Compartments
% m = pwAddC(m, ID, size,  outside, spatialDimensions, name, unit, constant)

m = pwAddC(m, 'cell', 1);


%% K: Dynamical parameters
% m = pwAddK(m, ID, value, type, minValue, maxValue, unit, name, description)

m = pwAddK(m, 'Kon_IL13Rec'             , 0.00341992477561527  , 'global', 1e-009, 1000);
m = pwAddK(m, 'Rec_phosphorylation'     , 999.630699390459     , 'global', 1e-009, 1000);
m = pwAddK(m, 'pRec_intern'             , 0.152540135862128    , 'global', 1e-009, 1000);
m = pwAddK(m, 'pRec_degradation'        , 0.17292753960894     , 'global', 1e-009, 1000);
m = pwAddK(m, 'Rec_intern'              , 0.103345784175639    , 'global', 1e-009, 1000);
m = pwAddK(m, 'Rec_recycle'             , 0.00135598001330518  , 'global', 1e-009, 1000);
m = pwAddK(m, 'JAK2_phosphorylation'    , 0.157057142470047    , 'global', 1e-009, 1000);
m = pwAddK(m, 'pJAK2_dephosphorylation' , 0.000621906059346898 , 'global', 1e-009, 1000);
m = pwAddK(m, 'STAT5_phosphorylation'   , 0.0382596267705733   , 'global', 1e-009, 1000);
m = pwAddK(m, 'pSTAT5_dephosphorylation', 0.000343391620492938 , 'global', 1e-009, 1000);
m = pwAddK(m, 'SOCS3mRNA_production'    , 0.00215826062955433  , 'global', 1e-009, 1000);
m = pwAddK(m, 'DecoyR_binding'          , 0.000124391087466499 , 'global', 1e-009, 1000);
m = pwAddK(m, 'JAK2_p_inhibition'       , 0.0168267797836881   , 'global', 1e-009, 1000);
m = pwAddK(m, 'SOCS3_translation'       , 11.9086462945188     , 'global', 1e-009, 1000);
m = pwAddK(m, 'SOCS3_accumulation'      , 3.70803336415341     , 'global', 1     , 1000);
m = pwAddK(m, 'SOCS3_degradation'       , 0.0429185935645562   , 'global', 1e-009, 1000);
m = pwAddK(m, 'CD274mRNA_production'    , 8.21752278733562e-005, 'global', 1e-009, 1000);


%% U: Driving input
% m = pwAddU(m, ID, uType, uTimes, uValues, compartment, name, description, u2Values, alternativeIDs, designerProps)

m = pwAddU(m, 'IL13stimulation', 'steps', [-100 0]  , [0 1]  , [], [], [], [], {}, [], 'protein.generic');


%% Default sampling time points
m.t = 0:1:120;


%% Y: Observables
% m = pwAddY(m, rhs, ID, scalingParameter, errorModel, noiseType, unit, name, description, alternativeIDs, designerProps)

m = pwAddY(m, 'Rec + IL13_Rec + p_IL13_Rec'                       , 'RecSurf_obs'  , 'scale_RecSurf'  , '0.10 * y + 0.1 * max(y)');
m = pwAddY(m, 'IL13_Rec + p_IL13_Rec + p_IL13_Rec_i + IL13_DecoyR', 'IL13-cell_obs', 'scale_IL13-cell', '0.15 * y + 0.05 * max(y)');
m = pwAddY(m, 'p_IL13_Rec + p_IL13_Rec_i'                         , 'pIL4Ra_obs'   , 'scale_pIL4Ra'   , '0.1 * y + 0.15 * max(y)');
m = pwAddY(m, 'pJAK2'                                             , 'pJAK2_obs'    , 'scale_pJAK2'    , '0.15 * y + 0.1 * max(y)');
m = pwAddY(m, 'SOCS3mRNA'                                         , 'SOCS3mRNA_obs', 'scale_SOCS3mRNA', '0.1 * y + 0.1 * max(y)');
m = pwAddY(m, 'CD274mRNA'                                         , 'CD274mRNA_obs', 'scale_CD274mRNA', '0.1 * y + 0.1 * max(y)');
m = pwAddY(m, 'SOCS3'                                             , 'SOCS3_obs'    , 'scale_SOCS3'    , '0.1 * y + 0.15 * max(y)');
m = pwAddY(m, 'pSTAT5'                                            , 'pSTAT5_obs'   , 'scale_pSTAT5'   , '0.15 * y + 0.1 * max(y)');


%% S: Scaling parameters
% m = pwAddS(m, ID, value, type, minValue, maxValue, unit, name, description)

m = pwAddS(m, 'scale_pJAK2'    , 1.39039557075997, 'global', 0.001, 10000);
m = pwAddS(m, 'scale_pIL4Ra'   , 1.88700484471494, 'global', 0.001, 10000);
m = pwAddS(m, 'scale_RecSurf'  ,                1,    'fix', 0.001, 10000);
m = pwAddS(m, 'scale_IL13-cell', 5.56750251420935, 'global', 0.001, 10000);
m = pwAddS(m, 'scale_SOCS3mRNA', 17.6699101927908, 'global', 0.001, 10000);
m = pwAddS(m, 'scale_CD274mRNA', 2.48547378765387, 'global', 0.001, 10000);
m = pwAddS(m, 'scale_pSTAT5'   ,                1,    'fix', 0.001, 10000);
m = pwAddS(m, 'scale_SOCS3'    ,                1,    'fix', 0.001, 10000);


%% Designer properties (do not modify)
m.designerPropsM = [1 1 1 0 0 0 400 250 600 400 1 1 1 0 0 0 0];

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2011 The BioModels.net Team.
For more information see the terms of use .
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Nov��re N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

This model is from the article:
Mathematical modeling and analysis of insulin clearance in vivo.
Koschorreck M, Gilles ED. BMC Syst Biol. 2008 May 13;2:43. 18477391 ,
Abstract:
BACKGROUND: Analyzing the dynamics of insulin concentration in the blood is necessary for a comprehensive understanding of the effects of insulin in vivo. Insulin removal from the blood has been addressed in many studies. The results are highly variable with respect to insulin clearance and the relative contributions of hepatic and renal insulin degradation. RESULTS: We present a dynamic mathematical model of insulin concentration in the blood and of insulin receptor activation in hepatocytes. The model describes renal and hepatic insulin degradation, pancreatic insulin secretion and nonspecific insulin binding in the liver. Hepatic insulin receptor activation by insulin binding, receptor internalization and autophosphorylation is explicitly included in the model. We present a detailed mathematical analysis of insulin degradation and insulin clearance. Stationary model analysis shows that degradation rates, relative contributions of the different tissues to total insulin degradation and insulin clearance highly depend on the insulin concentration. CONCLUSION: This study provides a detailed dynamic model of insulin concentration in the blood and of insulin receptor activation in hepatocytes. Experimental data sets from literature are used for the model validation. We show that essential dynamic and stationary characteristics of insulin degradation are nonlinear and depend on the actual insulin concentration.

This a model from the article:
Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors.
Schoeberl B ,Eichler-Jonsson C ,Gilles ED ,Müller G Nat. Biotechnol. [2002 Apr; Volume: 20 (Issue: 4 )]: 370-5 11923843 ,
Abstract:
We present a computational model that offers an integrated quantitative, dynamic, and topological representation of intracellular signal networks, based on known components of epidermal growth factor (EGF) receptor signal pathways. The model provides insight into signal-response relationships between the binding of EGF to its receptor at the cell surface and the activation of downstream proteins in the signaling cascade. It shows that EGF-induced responses are remarkably stable over a 100-fold range of ligand concentration and that the critical parameter in determining signal efficacy is the initial velocity of receptor activation. The predictions of the model agree well with experimental analysis of the effect of EGF on two downstream responses, phosphorylation of ERK-1/2 and expression of the target gene, c-fos.

The initial model was constructed by Ken Lau from the matlab source code
This model does not exactly reproduce the results given in the original publication. It has, though, the same reaction graph and gives very similar time courses for the conditions depicted in the article.

Several corrections were applied to the parameters described in the paper's supplementary materials. Some parameter names were replaced by the corresponding identical ones: k(r)26 by k(r)18, k(r)27 by k(r)19, k(r)30 by k(r)20, k(r)38 by k(r)24, k(r)39 by k(r)37, k(r)46 by k(r)44, k51 by k49, k(r)54 by k(r)52 and k62 by k62. In particular the parameter values described in the column "remark" of supplementary table1 override the values explicitely written in the numerical columns:

name value value

in suppl. used

kr16 0.055 0.275

k30 7.9e6 2.1e6 as k20

kr30 0.3 0.4 as kr24

k38 3e7 1e7 as k20

kr38 0.055 0.55 as kr24

k52 1.1e5 5.34e7

k5 was used for v116, v119, v122 and v125 in addition of v107, v110 and v113 as listed in the legend of supplementary figure 2. k5 is calculated using th eformula from the matlab file not given in the supplements.

All rate constants were rescaled to minutes (k[min] = 60*k[sec]) and all second order rate constants additionally to molecules/cell with a cell volume of 1 picolitre (k[molecs/cell] = k[M]/(Vc*Na), with Vc=1e-12 l and Na = 6e23).
The association constant of internalized EGF was rescaled to molecules/endosome using an endosomal volume of 4.3 al (= 4.3*10 ^-18 litre).
The extracellular EGF concentration was converted to molecules per picolitre with a MW of 6045 Da.

[ng/ml] [numb/pl]

50 4962

0.5 49.6

0.125 12.4

With the initial conditions given in the paper, the results could not be reproduced at all. Therefore the initial conditions used in the matlab file were adopted for SHC (1.01 * 10 ⁵ instead of 1.01 * 10 ⁶ ) and Ras_GDP. (7.2 * 10 ⁴ instead of 1.14 * 10 ⁷ )

Another model from Hormone induced Calcium Oscillations in Liver Cells Can Be Explained by a Simply One Pool Model. Anatomy of a single Ca2+ spike. Figure4A has been simulated by COPASI4.0.20(development). However, the simulated figure is slightly different from the paper, single spike of Ca2+ is around "6" time arbitrary units instead "9" time arbitrary units displayed in the paper.

This a model from the article:
Modelling the dynamics of the yeast pheromone pathway.
Kofahl B, Klipp E Yeast [2004 Jul; Volume: 21 (Issue: 10 )] Page info: 831-50 15300679 ,
Abstract:
We present a mathematical model of the dynamics of the pheromone pathways in haploid yeast cells of mating type MATa after stimulation with pheromone alpha-factor. The model consists of a set of differential equations and describes the dynamics of signal transduction from the receptor via several steps, including a G protein and a scaffold MAP kinase cascade, up to changes in the gene expression after pheromone stimulation in terms of biochemical changes (complex formations, phosphorylations, etc.). The parameters entering the models have been taken from the literature or adapted to observed time courses or behaviour. Using this model we can follow the time course of the various complex formation processes and of the phosphorylation states of the proteins involved. Furthermore, we can explain the phenotype of more than a dozen well-characterized mutants and also the graded response of yeast cells to varying concentrations of the stimulating pheromone.

The model was updated on 21 ^st October 2010, by Vijayalakshmi Chelliah.
The following changes were made: 1) The model has been converted to SBML l2v4. 2) The model has been recurated and the curation figure was updated (units are in nanoMolar; but the publication has units in microMolar). Simulations were done using Copasi v4.6 (Build 32). 3) Notes have been added. 4) Annotation for one of the species has been corrected (Complex M).

The following are the four major differences between the original publication by Kofahl et al and the model that actually is able to replicate the results as depicted in the publication (those corrections have been made in agreement with the authors):
1. Bar1 is the inactive protease present inside the cell but the publication wrongly mentions that Bar1 is also the protease that is present on the extracellular surface.
The model correctly names the protease in it's different forms by calling inactive Bar1 within the cell as Bar1, active Bar1 within the cell as Bar1a and extracellular Bar1 as Bar1aex
2. The initial amount of Alpha-factor is given as 1000nM but the model uses a value of 100nM.
3. The value of the paramenter k8 is given as 0.33 but the model uses a value of 0.033.
4. The value of the paramenter k41 is given as 0.002 but the model uses a value of 0.02.

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/).(http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2010 The BioModels.net Team.
For more information see the terms of use .
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

This model is from the article:
Experimental and in silico analyses of glycolytic flux control in bloodstream form Trypanosoma brucei.
Albert MA, Haanstra JR, Hannaert V, Van Roy J, Opperdoes FR, Bakker BM, Michels PA. J Biol Chem 2005 Aug 5;280(31):28306-15. 15955817 ,
Abstract:
A mathematical model of glycolysis in bloodstream form Trypanosoma brucei was developed previously on the basis of all available enzyme kinetic data (Bakker, B. M., Michels, P. A. M., Opperdoes, F. R., and Westerhoff, H. V. (1997) J. Biol. Chem. 272, 3207-3215). The model predicted correctly the fluxes and cellular metabolite concentrations as measured in non-growing trypanosomes and the major contribution to the flux control exerted by the plasma membrane glucose transporter. Surprisingly, a large overcapacity was predicted for hexokinase (HXK), phosphofructokinase (PFK), and pyruvate kinase (PYK). Here, we present our further analysis of the control of glycolytic flux in bloodstream form T. brucei. First, the model was optimized and extended with recent information about the kinetics of enzymes and their activities as measured in lysates of in vitro cultured growing trypanosomes. Second, the concentrations of five glycolytic enzymes (HXK, PFK, phosphoglycerate mutase, enolase, and PYK) in trypanosomes were changed by RNA interference. The effects of the knockdown of these enzymes on the growth, activities, and levels of various enzymes and glycolytic flux were studied and compared with model predictions. Data thus obtained support the conclusion from the in silico analysis that HXK, PFK, and PYK are in excess, albeit less than predicted. Interestingly, depletion of PFK and enolase had an effect on the activity (but not, or to a lesser extent, expression) of some other glycolytic enzymes. Enzymes located both in the glycosomes (the peroxisome-like organelles harboring the first seven enzymes of the glycolytic pathway of trypanosomes) and in the cytosol were affected. These data suggest the existence of novel regulatory mechanisms operating in trypanosome glycolysis.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2012 The BioModels.net Team.
For more information see the terms of use .
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

This particular version of the model has been translated from equations 1a-1j (Drosophila).

This model according to the paper A Theoretical Framework for Specificity in Cell Signalling The model is "basic architecture" of Figure2A. Figure2B, Figure2C have been reproduced by MathSBML. The reproduced figures are slightly different from the original ones in the paper, the peak of [x2] is higher than 1 and is not decreasing dramatically when [x0]=0. And I think maybe the author shift the or scale the curves.

The model is according to the paper Endothelin Action on Pituitary Lactotrophs: One Receptor, Many GTP-Binding Proteins Figure 1 has been simulated by MathSBML. The figure for the [Ca2+]i and [Ca2+]ER have been normalized in the paper.Original model comes from http://www.math.fsu.edu/~bertram/software/pituitary

The units for parameters and species are varied from one to another, so I omit the unit definition here . Conductances in pS; currents in fA; Ca concentrations in uM; time in ms

This a model from the article:
Modelling the onset of Type 1 diabetes: can impaired macrophage phagocytosis make the difference between health and disease?
Maree AF, Kublik R, Finegood DT, Edelstein-Keshet L. Philos Transact A Math Phys Eng Sci. 2006 May 15;364(1842):1267-82. 16608707 ,
Abstract:
A wave of apoptosis (programmed cell death) occurs normally in pancreatic beta-cells of newborn mice. We previously showed that macrophages from non-obese diabetic (NOD) mice become activated more slowly and engulf apoptotic cells at a lower rate than macrophages from control (Balb/c) mice. It has been hypothesized that this low clearance could result in secondary necrosis, escalating inflammation and self-antigen presentation that later triggers autoimmune, Type 1 diabetes (T1D). We here investigate whether this hypothesis could offer a reasonable and parsimonious explanation for onset of T1D in NOD mice. We quantify variants of the Copenhagen model (Freiesleben De Blasio et al. 1999 Diabetes 48, 1677), based on parameters from NOD and Balb/c experimental data. We show that the original Copenhagen model fails to explain observed phenomena within a reasonable range of parameter values, predicting an unrealistic all-or-none disease occurrence for both strains. However, if we take into account that, in general, activated macrophages produce harmful cytokines only when engulfing necrotic (but not apoptotic) cells, then the revised model becomes qualitatively and quantitatively reasonable. Further, we show that known differences between NOD and Balb/c mouse macrophage kinetics are large enough to account for the fact that an apoptotic wave can trigger escalating inflammatory response in NOD, but not Balb/c mice. In Balb/c mice, macrophages clear the apoptotic wave so efficiently, that chronic inflammation is prevented.

This a model from the article:
PI3K-dependent cross-talk interactions converge with Ras as quantifiable inputs integrated by Erk.
Wang CC, Cirit M, Haugh JM Mol. Syst. Biol. 2009;5:246. 19225459 ,
Abstract:
Although it is appreciated that canonical signal-transduction pathways represent dominant modes of regulation embedded in larger interaction networks, relatively little has been done to quantify pathway cross-talk in such networks. Through quantitative measurements that systematically canvas an array of stimulation and molecular perturbation conditions, together with computational modeling and analysis, we have elucidated cross-talk mechanisms in the platelet-derived growth factor (PDGF) receptor signaling network, in which phosphoinositide 3-kinase (PI3K) and Ras/extracellular signal-regulated kinase (Erk) pathways are prominently activated. We show that, while PI3K signaling is insulated from cross-talk, PI3K enhances Erk activation at points both upstream and downstream of Ras. The magnitudes of these effects depend strongly on the stimulation conditions, subject to saturation effects in the respective pathways and negative feedback loops. Motivated by those dynamics, a kinetic model of the network was formulated and used to precisely quantify the relative contributions of PI3K-dependent and -independent modes of Ras/Erk activation.

This model is parameterized with the median of the estimated parameters given in the supplementary material of the original publication's (doi: 10.1038/msb.2009.4 ) supplement on pages 8 and 9.

The model should reproduce the figure 2F of the article.

The equation 7 has been split into equations 7a-7c, in order to take into account the different flux rates of Lysine and CML formation from Schiff.

The model was tested in Jarnac (SBML L2 V1) and Copasi (SBML L2 V3).

This file describes the SBML version of the mathematical model in the following journal article: Linking Pulmonary Oxygen Uptake, Muscle Oxygen Utilization and Cellular Metabolism during Exercise, Ann Biomed Eng. 2007 Jun;35(6):956-69. (Pubmed ID: 17380394). This mathematical model simulates oxygen transport and metabolism in skeletal muscle in response to a step change from a warm-up steady state to a higher work rate corresponding to exercise at different levels of intensity: moderate (M), heavy (H) and very heavy (VH). The model parameter values are listed in the tables of this article. The parameter values that are independent of the exercise level are reported in Table 2. The parameter values that depend on the exercise level are reported in Tables 1A, 3 and 4. The model simulations (Figures 2, 3, 4 and 5) were obtained for a representative subject with a set of parameter values different from those in Table 1A, 3 and 4. In the sbml model, these model parameters are used to simulate exercise at a very heavy (VH) intensity for the representative subject. Additionally, the parameter values needed to simulate exercise at moderate (M) and heavy (H) intensity are reported in the list of parameters of the file. The model simulates dynamics of (1) the concentrations of free (F) and total (T) oxygen concentration in blood (CFcap, CTcap) and tissue (CFtis, CTtis), Adenosine Triphosphate (ATP), Adenosine Diphosphate (ADP), Phosphocreatine (PCr) and Creatine (Cr); (2) the metabolic flux of oxidative phosphorylation, creatine kinase and ATPase; (3) the oxygen uptake in blood and oxygen transport rate from blood to tissue during exercise. The simulation also computes muscle oxygen saturation (StO2m) and relative muscle oxygen saturation (RStO2m) in order to compare simulated and experimental responses of human muscle oxygenation during exercise. The model was successfully tested with Roadrunner of the Systems Biology Workbench (SBW). The model simulations obtained with Roadrunner match those obtained with the mathematical model represented in Fortran and Matlab for relative and absolute tolerance smaller than 10-7.

To allow for simulations at varying levels of exercise, the parameter exercise_level was introduced. A value of 1 means medium, 2 heavy and 3 very heavy exercise. Setting this parameter assigns the parameters Vmax , KatpaseE , dQMm and tauQm with the relevant parameters. The warmup steady state is influenced by the parameter changes for this representative subject and the model has to be brought into steady state after each change of exercise level.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2010 The BioModels Team.
For more information see the terms of use .
To cite BioModels Database, please use Le Nov��re N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

Kholodenko2000 - MAPK feedback

Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades.

This model is described in the article:

Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades.

Kholodenko BN

Eur. J. Biochem. 2000; 267(6):1583-8

Abstract:

Functional organization of signal transduction into protein phosphorylation cascades, such as the mitogen-activated protein kinase (MAPK) cascades, greatly enhances the sensitivity of cellular targets to external stimuli. The sensitivity increases multiplicatively with the number of cascade levels, so that a tiny change in a stimulus results in a large change in the response, the phenomenon referred to as ultrasensitivity. In a variety of cell types, the MAPK cascades are imbedded in long feedback loops, positive or negative, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. Here we demonstrate that a negative feedback loop combined with intrinsic ultrasensitivity of the MAPK cascade can bring about sustained oscillations in MAPK phosphorylation. Based on recent kinetic data on the MAPK cascades, we predict that the period of oscillations can range from minutes to hours. The phosphorylation level can vary between the base level and almost 100% of the total protein. The oscillations of the phosphorylation cascades and slow protein diffusion in the cytoplasm can lead to intracellular waves of phospho-proteins.

This model is hosted on BioModels Database and identified by: BIOMD0000000010 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This model encoded according to the paper Cross-talk and decision making in MAP kinase pathways. Supplementary Figure 2 has been reproduced by COPASI4.0.20 (development) using parameter scan method. You probably need to uncheck "always use initial conditions" in copasi when you simulate for the second run in order to get the figure. S1 scale from 0 to 12. Keep in mind that the y axis is the fractions of excited X3 and Y3, meaning that X3P and Y3P are normalized by total concentration X3T and Y3T.

The results from modeling the pathway in Supplementary Figure1a, including both activation and inhibition. According to the paper, the value of ka and kd should in the orange region (ka belongs [0,1], kd belongs [1,10]) so assigned ka=0, kd=1.

The author made the simplifying assumption that the interactions between the pathways are symmetric. Thus the k12xy=k12yx=ka, k33xy=k33yx=kd.

NFkB model M(39,65,90) - most complex model

This is a model of NFkB pathway functioning from hierarchy of models of decreasing complexity, created to demonstrate application of model reduction methods proposed in

Robust simplifications of multiscale biochemical networks.
Radulescu O, Gorban A., Zinovyev A., Lilienbaum. A. BMC Syst Biol 2008:2:86 18854041 ,
Abstract:
BACKGROUND: Cellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions. In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In systems biology we also need to compare models or to couple them as parts of larger models. In these situations reduction to a common level of complexity is needed. RESULTS: We propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as "pseudo-monomolecular" subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in 1. Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model. The methods are demonstrated for simple examples and for a more complex model of NF-kappaB pathway. CONCLUSION: Our approach allows critical parameter identification and produces hierarchies of models. Hierarchical modeling is important in "middle-out" approaches when there is need to zoom in and out several levels of complexity. Critical parameter identification is an important issue in systems biology withpotential applications to biological control and therapeutics. Our approach also deals naturally with the presence of multiple time scales, which is a general property of systems biology models.

The models are provided in CellDesigner v3.5 format. The name of the model M(x,y,z) should be deciphered as following:

x - number of species y - number of reactions z - number of parameters

Simulation protocol: The model can be simulated in CellDesigner directly, or in any simulator supporting events. The simulation period should be set up in 40 hours (t=144000 sec). The 'signal' event applies signal to the pathway at the moment t=20 hours=72000 sec. This model reproduces Figure 7c (M(39,65,90)) of the publication.

For additional information please contact Andrei.Zinovyev at curie.fr

This model is from the article:
Quantitative analysis of transient and sustained transforming growth factor-β signaling dynamics.
Zhike Zi, Zipei Feng, Douglas A Chapnick, Markus Dahl, Difan Deng, Edda Klipp, Aristidis Moustakas & Xuedong Liu Molecular Systems Biology 2011 May 24;7:492. 21613981 ,
Abstract:
Mammalian cells can decode the concentration of extracellular transforming growth factor-β (TGF-β) and transduce this cue into appropriate cell fate decisions. How variable TGF-β ligand doses quantitatively control intracellular signaling dynamics and how continuous ligand doses are translated into discontinuous cellular fate decisions remain poorly understood. Using a combined experimental and mathematical modeling approach, we discovered that cells respond differently to continuous and pulsating TGF-β stimulation. The TGF-β pathway elicits a transient signaling response to a single pulse of TGF-β stimulation, whereas it is capable of integrating repeated pulses of ligand stimulation at short time interval, resulting in sustained phospho-Smad2 and transcriptional responses. Additionally, the TGF-β pathway displays different sensitivities to ligand doses at different time scales. While ligand-induced short-term Smad2 phosphorylation is graded, long-term Smad2 phosphorylation is switch-like to a small change in TGF-β levels. Correspondingly, the short-term Smad7 gene expression is graded, while long-term PAI-1 gene expression is switch-like, as is the long-term growth inhibitory response. Our results suggest that long-term switch-like signaling responses in the TGF-β pathway might be critical for cell fate determination.

Note:

Developer of the model: Zhike Zi

Reference: Zi Z. et al., Quantitative Analysis of Transient and Sustained Transforming Growth Factor-beta Signaling Dynamics, Molecular Systems Biology, 2011

1. The global parameter that set the type of stimulation

(a) for sustained TGF-beta stimulation: set stimulation_type = 1.

(b) for single pulse of TGF-beta stimulation: set stimulation_type = 2.

parameter "single_pulse_duration" is for the duration of stimulation, for example,

single_pulse_duration = 0.5, for 0.5 min (30 seconds) of TGF-beta stimulation.

*Note: make sure that the time course cover the time point when the event is triggered.

change the trigger of event "single_pulse_TGF_beta_washout"

from

"and(eq(stimulation_type, 2), eq(time, single_pulse_duration))" (for SBML-SAT)

"and(eq(stimulation_type, 2), gt(time, single_pulse_duration))" (for COPASI)

2. Notes for TGF-beta dose in terms of molecules per cell

(a) The following equation applies for conversion of TGF-beta dose in molecules per cell

TGF_beta_dose_mol_per_cell = initial TGF_beta_ex*1e-9*Vmed*6e23

(b) for standard experimental setup 1e6 cells in 2 mL medium

0.001 nM initial TGF_beta_ex is approximately equal to the dose of 1200 TGF-beta molecules/cell

0.050 nM initial TGF_beta_ex is approximately equal to the dose of 60000 TGF-beta molecules/cell

(c) For 1e6 cells in 10 mL medium, please change the initial compartment size of Vmed and the corresponding assignment rule for Vmed.

initial Vmed = 1e-8 (1e6 cells in 10 mL medium)

Vmed = 0.010/(1e6*exp(log(1.45)*time/1440)) (1e6 cells in 10 mL medium)

3. Please note that this model contains events and the medium compartment size is varied.

4. For the model simulation in SBML-SAT, please remove initialAssignments and save it as SBML Level 2 Verion 1 file.

This a model from the article:
Applications of metabolic modelling to plant metabolism.
Poolman MG ,Assmus HE, Fell DA J. Exp. Bot. [2004 May; Volume: 55 (Issue: 400 )]: 1177-86 15073223 ,
Abstract:
In this paper some of the general concepts underpinning the computer modelling of metabolic systems are introduced. The difference between kinetic and structural modelling is emphasized, and the more important techniques from both, along with the physiological implications, are described. These approaches are then illustrated by descriptions of other work, in which they have been applied to models of the Calvin cycle, sucrose metabolism in sugar cane, and starch metabolism in potatoes.

This model describes the non oxidative Calvin cycle as depicted in Poolman et al; J Exp Bot (2004) 55:1177-1186, fig 2. Reaction E20: E4P + F6P ↔ S7P + GAP, is depicted in the figure, but not included in the model. The light reaction: ADP + P _i → ATP, is included in the model, but only mentioned in the figure caption. The parameters and initial concentrations are the same as in Poolman, 1999, Computer Modelling Applied to the Calvin Cycle, PhD Thesis, Oxford Brookes University, Appendix A (available at at http://mudshark.brookes.ac.uk/index.php/Publications/Theses/Mark )

© Mark Poolman (mgpoolman@brookes.ac.uk) 1995-2002
Based on a description by Pettersson 1988, Eur. J. Biochem. 175, 661-672
Differences are:
1 - Reactions assumed by Pettersson to be in equilibrium have fast mass action kinetics.
2 - Introduction of the parameter PGAxpMult to modulate PGA export through TPT.
3 - Introduction of Starch phosphorylase reaction.
This file may be freely copied or translated into other formats provided:
1 - This notice is reproduced in its entirety
2 - Published material making use of (information gained from) this model cites at least:
(a) Poolman, 1999, Computer Modelling Applied to the Calvin Cycle, PhD Thesis, Oxford Brookes University
(b) Poolman, Fell, and Thomas. 2000, Modelling Photosynthesis and its control, J. Exp. Bot. 51, 319-328
or
(c) Poolman et al. 2001, Computer modelling and experimental evidence for two steady states in the photosynthetic Calvin cycle. Eur. J. Biochem. 268, 2810-2816
Further related information may be found at http://mudshark.brookes.ac.uk .

Note:

The paper describes three models 1) Zero-dimensional Bone Model without Tumou r, 2) Zero-dimensional Bone Model with Tumour and 3) Zero-dimensional Bone Model with Tumour and Drug Treatment. This model corresponds to the Zero-dimensional Bo ne Model with Tumour and Drug Treatment.

Typos in the publication:

Equation (4): The first term should be (β1/α1)^(g12/Γ) and not (β2/α2)^(g12/Γ)

Equation (14): The first term should be (β1/α1)^(((g12/(1+r12))/Γ) and not (β2/α2)^(((g12/(1+r12))/Γ)

Equation (13): The first term should be (β1/α1)^((1-g22+r22)/Γ) and not (β1/α1)^((1-g22-r22)/Γ)

All these corrections has been implemented in the model, with the authors agreement.

Beyond these, there are several mismatches between the equation numbers that are mentioned in for each equation and the reference that has been made to these equations in the figure legend.

This model is from the article:
Cooperation and Competition in the Evolution of ATP-Producing Pathways
Thomas Pfeiffer, Stefan Schuster, Sebastian Bonhoeffer Science 2001 Apr; Volume:292 (Issue:5516); Page info:504-7 11283355 ,
Abstract:
Heterotrophic organisms generally face a trade-off between rate and yield of adenosine triphosphate (ATP) production. This trade-off may result in an evolutionary dilemma, because cells with a higher rate but lower yield of ATP production may gain a selective advantage when competing for shared energy resources. Using an analysis of model simulations and biochemical observations, we show that ATP production with a low rate and high yield can be viewed as a form of cooperative resource use and may evolve in spatially structured environments. Furthermore, we argue that the high ATP yield of respiration may have facilitated the evolutionary transition from unicellular to undifferentiated multicellular organisms.

Note:

This model reproduces the competition and invasion described in Supplemental Figure 2.

This model is described in the paper Toward a detailed computational model for the mammalian circadian clock . In this model only interlocked negative and positive regulation of Per, Cry, Bmal gene are involved. Some initial values were not provided, therefore they were chosen to fit the curves from the paper.

Figure2C is re-produced by odeSolver.

This model is from the article:
Modelling the Role of the Hsp70/Hsp90 System in the Maintenance of Protein Homeostasis
Proctor CJ, Lorimer IAJ PLoS ONE 2011; 6(7): e22038. doi:10.1371/journal.pone.0022038 ,
Abstract:
Neurodegeneration is an age-related disorder which is characterised by the accumulation of aggregated protein and neuronal cell death. There are many different neurodegenerative diseases which are classified according to the specific proteins involved and the regions of the brain which are affected. Despite individual differences, there are common mechanisms at the sub-cellular level leading to loss of protein homeostasis. The two central systems in protein homeostasis are the chaperone system, which promotes correct protein folding, and the cellular proteolytic system, which degrades misfolded or damaged proteins. Since these systems and their interactions are very complex, we use mathematical modelling to aid understanding of the processes involved. The model developed in this study focuses on the role of Hsp70 (IPR00103) and Hsp90 (IPR001404) chaperones in preventing both protein aggregation and cell death. Simulations were performed under three different conditions: no stress; transient stress due to an increase in reactive oxygen species; and high stress due to sustained increases in reactive oxygen species. The model predicts that protein homeostasis can be maintained during short periods of stress. However, under long periods of stress, the chaperone system becomes overwhelmed and the probability of cell death pathways being activated increases. Simulations were also run in which cell death mediated by the JNK (P45983) and p38 (Q16539) pathways was inhibited. The model predicts that inhibiting either or both of these pathways may delay cell death but does not stop the aggregation process and that eventually cells die due to aggregated protein inhibiting proteasomal function. This problem can be overcome if the sequestration of aggregated protein into inclusion bodies is enhanced. This model predicts responses to reactive oxygen species-mediated stress that are consistent with currently available experimental data. The model can be used to assess specific interventions to reduce cell death due to impaired protein homeostasis.

Note:

Simulations were performed under three different conditions: 1) normal condition (no stress), 2) moderate stress due to an increase in reactive oxygen species (ROS) i.e. ROS levels were increased by a factor of 4 at time=4hours for a period of 1 hour (not 2 hours as mentioned in the figure 5 legend of the reference publication. This is a typo in the paper and is clarified by the author) and 3) high stress due to sustained increase in reactive oxygen species (ROS) (here ROS increases with time).

The model that corresponds to the normal condition is submitted as a main model in the BioModels Database. The other two models, that corresponds to the moderate stress conditions and high stress conditions are available in SBML format as supporting files [go to Curation tab].

Supplementary figures S3 (normal condition), S4 (moderate stress condition) and S6 (high stress condition) are reproduced here.

This mechanistic model describes the activation of immediate early genes such as cFos after EGF or heregulin (HRG) stimulation of the MAPK pathway. Phosphorylated cFos is a key transcription factor triggering downstream cascades of cell fate determination. The model can explain how the switch-like response of p-cFos emerges from the spatiotemporal dynamics. This mechanistic model comprises the explicit reaction kinetics of the signal transduction pathway, the transcriptional and the posttranslational feedback and feedforward loops. In the below article, two different mechanistic models have been studied, the first one based on previously known interactions but failing to account for the experimental data and the second one including additional interactions which were discovered and confirmed by new experiments. The mechanistic model encoded here is the second one, the extended and at the time of creation most complete model of cell fate decision making in response to different doses of EGF or HRG stimulation. The encoded parameter set corresponds to 10mM HRG stimulation as shown in Fig.1 of the article. The Supplementary Methods of the article provide further parameter sets that allow simulations for different ligands and different doses. A corresponding core model is available from http://www.ebi.ac.uk/biomodels/ as MODEL1003170000.

Ligand-specific c-Fos expression emerges from the spatiotemporal control of ErbB network dynamics.
Takashi Nakakuki(1), Marc R. Birtwistle(2,3,4), Yuko Saeki(1,5), Noriko Yumoto(1,5), Kaori Ide(1), Takeshi Nagashima(1,5), Lutz Brusch(6), Babatunde A. Ogunnaike(3), Mariko Hatakeyama(1,5), and Boris N. Kholodenko(2,4); Cell In Press, online 20 May 2010 , doi: 10.1016/j.cell.2010.03.054
(1) RIKEN Advanced Science Institute, Computational Systems Biology Research Group, Advanced Computational Sciences Department, 1-7-22 Tsurumi-ku, Yokohama, Kanagawa, 230-0045, Japan
(2) Systems Biology Ireland, University College Dublin, Belfield, Dublin 4, Ireland
(3) University of Delaware, Department of Chemical Engineering, 150 Academy St., Newark, DE 19716, USA
(4) Thomas Jefferson University, Department of Pathology, Anatomy, and Cell Biology, 1020 Locust Street, Philadelphia, PA 19107, USA
(5) RIKEN Research Center for Allergy and Immunology, Laboratory for Cellular Systems Modeling, 1-7-22 Tsurumi-ku, Yokohama, 230-0045, Japan
(6) Dresden University of Technology, Center for Information Services and High Performance Computing, 01062 Dresden, Germany

This a model from the article:
How yeast cells synchronize their glycolytic oscillations: a perturbation analytic treatment
Bier M, Bakker BM, Westerhoff HV. Biophys. J 2000 Mar;78(3):1087-93. 10692299 ,
Abstract:
Of all the lifeforms that obtain their energy from glycolysis, yeast cells are among the most basic. Under certain conditions the concentrations of the glycolytic intermediates in yeast cells can oscillate. Individual yeast cells in a suspension can synchronize their oscillations to get in phase with each other. Although the glycolytic oscillations originate in the upper part of the glycolytic chain, the signaling agent in this synchronization appears to be acetaldehyde, a membrane-permeating metabolite at the bottom of the anaerobic part of the glycolytic chain. Here we address the issue of how a metabolite remote from the pacemaking origin of the oscillation may nevertheless control the synchronization. We present a quantitative model for glycolytic oscillations and their synchronization in terms of chemical kinetics. We show that, in essence, the common acetaldehyde concentration can be modeled as a small perturbation on the "pacemaker" whose effect on the period of the oscillations of cells in the same suspension is indeed such that a synchronization develops.

The model is described in the paper by Wu and Chang (2006). Diethyl pyrocarbonate, a histidine-modifying agent, directly stimulates activity of ATP-sensitive potassium channels in pituitary GH3 cells. Biochem Pharmacol. 71(5): 615-23.

The unit of time is ms, and the simulation time is 80 s, that is 8e4 ms. Therfore, you probably need to increase the maximum steps for your simulator.

The figure 7 has been reproduced by MathSBML. Application of DEPC as indicated at horizontal bar was mimicked by an increase of maximal conductance of Katp-channels from 500 to 530 ps at t=30 s.

This a model from the article:
A theoretical study on activation of transcription factor modulated by intracellular Ca2+ oscillations.
Zhu CL, Zheng Y, Jia Y Biophys. Chem. [2007 Aug:129(1):49-55 17560007 ,
Abstract:
This work presents both deterministic and stochastic models of genetic expression modulated by intracellular calcium (Ca2+) oscillations, based on macroscopic differential equations and chemical Langevin equations, respectively. In deterministic case, the oscillations of intracellular Ca2+ decrease the effective Ca2+ threshold for the activation of transcriptional activator (TF-A). The average activation of TF-A increases with the increase of the average amplitude of intracellular Ca2+ oscillations, but decreases with the increase of the period of intracellular Ca2+ oscillations, which are qualitatively consistent with the experimental results on the gene expression in lymphocytes. In stochastic case, it is found that a large internal fluctuation of the biochemical reaction can enhance gene expression efficiency specifically at a low level of external stimulations or at a small rate of TF-A dimer phosphorylation activated by Ca2+, which reduces the threshold of the average intracellular Ca2+ concentration for gene expression.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2009 The BioModels Team.
For more information see the terms of use .
To cite BioModels Database, please use Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M.(2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

The model reproduces Fig 2 , Fig3A and Fig 3B of the paper. The ODE for x1(gp180) and x3 (gp 130) is wrong and the authors have communicated to the curator that the species ought to have a constant value. There are a few other differences from the paper and these were made in consultation with the authors. Model was successfully tested on MathSBML.

The model reproduces the calcium oscillation dependent activation-deactivation kinetics of nuclear factor of activated T cells (NFAT) as depicted in Fig 4a of the paper. A simple algorithm in the events section takes care of the calcium oscillation. The model was successfully tested on MathSBML.

The model reproduces the compartmental model for Ran transport as depicted in Fig 3 of the paper. Model reproduced using MathSBML.

The model reproduces the time profile of species depicted in Figure 12a and 12 b. The authors communicated to the curator that there is a typo in the paper, the values of kd1 and kd2 are reversed. Model successfully reproduced using MathSBML.

This a model from the article:
Glucose sensing in the pancreatic beta cell: a computational systems analysis.
Fridlyand LE, Philipson LH. Theor Biol Med Model. 2010 May 24;7:15. 20497556 ,
Abstract:
BACKGROUND: Pancreatic beta-cells respond to rising blood glucose by increasing oxidative metabolism, leading to an increased ATP/ADP ratio in the cytoplasm. This leads to a closure of KATP channels, depolarization of the plasma membrane, influx of calcium and the eventual secretion of insulin. Such mechanism suggests that beta-cell metabolism should have a functional regulation specific to secretion, as opposed to coupling to contraction. The goal of this work is to uncover contributions of the cytoplasmic and mitochondrial processes in this secretory coupling mechanism using mathematical modeling in a systems biology approach. METHODS: We describe a mathematical model of beta-cell sensitivity to glucose. The cytoplasmic part of the model includes equations describing glucokinase, glycolysis, pyruvate reduction, NADH and ATP production and consumption. The mitochondrial part begins with production of NADH, which is regulated by pyruvate dehydrogenase. NADH is used in the electron transport chain to establish a proton motive force, driving the F1F0 ATPase. Redox shuttles and mitochondrial Ca2+ handling were also modeled. RESULTS: The model correctly predicts changes in the ATP/ADP ratio, Ca2+ and other metabolic parameters in response to changes in substrate delivery at steady-state and during cytoplasmic Ca2+ oscillations. Our analysis of the model simulations suggests that the mitochondrial membrane potential should be relatively lower in beta cells compared with other cell types to permit precise mitochondrial regulation of the cytoplasmic ATP/ADP ratio. This key difference may follow from a relative reduction in respiratory activity. The model demonstrates how activity of lactate dehydrogenase, uncoupling proteins and the redox shuttles can regulate beta-cell function in concert; that independent oscillations of cytoplasmic Ca2+ can lead to slow coupled metabolic oscillations; and that the relatively low production rate of reactive oxygen species in beta-cells under physiological conditions is a consequence of the relatively decreased mitochondrial membrane potential. CONCLUSION: This comprehensive model predicts a special role for mitochondrial control mechanisms in insulin secretion and ROS generation in the beta cell. The model can be used for testing and generating control hypotheses and will help to provide a more complete understanding of beta-cell glucose-sensing central to the physiology and pathology of pancreatic beta-cells.

This model was taken from the Vcell MathModel directory and was converted to SBML

This a model from the article:
On the encoding and decoding of calcium signals in hepatocytes
Ann Zahle Larsen, Lars Folke Olsen and Ursula Kummera Biophysical Chemistry Volume 107, Issue 1, 1 January 2004, Pages 83-99 14871603 ,
Abstract:
Many different agonists use calcium as a second messenger. Despite intensive research in intracellular calcium signalling it is an unsolved riddle how the different types of information represented by the different agonists, is encoded using the universal carrier calcium. It is also still not clear how the information encoded is decoded again into the intracellular specific information at the site of enzymes and genes. After the discovery of calcium oscillations, one likely mechanism is that information is encoded in the frequency, amplitude and waveform of the oscillations. This hypothesis has received some experimental support. However, the mechanism of decoding of oscillatory signals is still not known. Here, we study a mechanistic model of calcium oscillations, which is able to reproduce both spiking and bursting calcium oscillations. We use the model to study the decoding of calcium signals on the basis of co-operativity of calcium binding to various proteins. We show that this co-operativity offers a simple way to decode different calcium dynamics into different enzyme activities.

Note:

This model corresponds to the improved model eqn 1-7, as described by Larsen et al., 2004 implemented to investigate how the cell can decode different oscillations. This is done by introducing 2 more variables Enzyme and Product in addition to the 5 variables G-alpha, PLC, Ca_cyt, Ca_ER and Ca_mit receptor-operated model described in the first part of the paper. The receptor-operated model is itself a modified version of the model described in Kummer 2000 (PMID: 10968983 )

Biomodels Curation The model simulates the flux values as given for "kinetic model" in Table 1 of the paper. The model was successfully tested on Jarnac.

The model reproduces Fig 2B of the paper. Model successfully reproduced using MathSBML.

This model is according to the paper Cellular consequences of HEGR mutations in the long QT syndrome: precursors to sudden cardiac death. The author used Markovian model of cardiac Ikr in the paper. Figure4B in the paper has been reproduced using CellDesigner3.5.1. The cell is depolarized to the indicated test potential for 250ms (from 50ms to 300ms) from a holding potential of -40mV and then repolarized to -40mV. Change the value for vtest from -30,-20,-10,0,10,20,30,40 for each simulation in order to produce the different cureve in the paper.

This a model from the article:
Network-level analysis of light adaptation in rod cells under normal and altered conditions.
Dell'Orco D, Schmidt H, Mariani S, Fanelli F Mol Biosyst 2009 Oct; 5(10):1232-46 19756313 ,
Abstract:
Photoreceptor cells finely adjust their sensitivity and electrical response according to changes in light stimuli as a direct consequence of the feedback and regulation mechanisms in the phototransduction cascade. In this study, we employed a systems biology approach to develop a dynamic model of vertebrate rod phototransduction that accounts for the details of the underlying biochemistry. Following a bottom-up strategy, we first reproduced the results of a robust model developed by Hamer et al. (Vis. Neurosci., 2005, 22(4), 417), and then added a number of additional cascade reactions including: (a) explicit reactions to simulate the interaction between the activated effector and the regulator of G-protein signalling (RGS); (b) a reaction for the reformation of the G-protein from separate subunits; (c) a reaction for rhodopsin (R) reconstitution from the association of the opsin apoprotein with the 11-cis-retinal chromophore; (d) reactions for the slow activation of the cascade by opsin. The extended network structure successfully reproduced a number of experimental conditions that were inaccessible to prior models. With a single set of parameters the model was able to predict qualitative and quantitative features of rod photoresponses to light stimuli ranging over five orders of magnitude, in normal and altered conditions, including genetic manipulations of the cascade components. In particular, the model reproduced the salient dynamic features of the rod from Rpe65(-/-) animals, a well established model for Leber congenital amaurosis and vitamin A deficiency. The results of this study suggest that a systems-level approach can help to unravel the adaptation mechanisms in normal and in disease-associated conditions on a molecular basis.

Note:

Figure 7 of the reference is reproduced here. Each plot is obtained by increasing flash strength. More details about generating the plots can be obtained from the comments in the curation figure (go to curation tab).

The model is according to the paper Which Model to Use for Cortical Spiking Neurons? Figure1(O) threshold variability has been reproduced by MathSBML. The ODE and the parameters values are taken from the a paper Simple Model of Spiking Neurons The original format of the models are encoded in the MATLAB format existed in the ModelDB with Accession number 39948

Figure1 are the simulation results of the same model with different choices of parameters and different stimulus function or events.a=0.03; b=0.25; c=-60; d=4; V=-64; u=b*V;

This model reproduces figure 5 and figure 4(B)of the paper, with Kinh represented by [G-GTP]. We arbitrarily chosed to set the initial concentration of D to 31 micorMolar based on legend of figure 4. [R] was not given anywhere in the paper and was chosen to calibrate the sigmoid response to an increased [GTP]. THe figure 5 in the model was successfully simulated on COPASI 4.0 ,the figure 4(B) was sucessfully simulated on both COPASI and SBML_odeSolver.

There are two curves for Kinh in the absence and presence of NaCl in the figure obtained from simulations of the model using parameters of set C and set D.Here in the model the initial value given is from set D.The parameters in set C :k7=0.5, k10=1.0,k5=0.1,the others are the same with set D.

The model reproduces the time profiles of Total Smad2 in the nucleus as well as the cytoplasm as depicted in 2D and also the other time profiles as depicted in Fig 2. Two parameters that are not present in the paper are introduced here for illustration purposes and they are Total Smad2n and Total Smad2c. The term kr_EE*LRC_EE has not been included in the ODE's for T1R_surf, T2R_surf and TGFbeta in the paper but is included in this model. MathSBML was used to reproduce the simulation result.

This model represents a concentration gradient of RanGTP across the nuclear envelope. This gradient is generated by distribution of regulators of RanGTPase. We have taken a log linear plot of graphs generated by GENESIS and compared with the experimental graphs.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2008 The BioModels Team.
For more information see the terms of use .

The model reproduces the plots in Figures 1 and 2. Note that the units of the time scale "A" are not right in the paper, it was corrected by the curator. Model successfully tested on MathSBML.

The model reproduces the time profiles of Golgi Ras-GTP and plasma membrane Ras-GTP, subjected to a palmitoylation rate of 0.00015849 second inverse. This is depicted in Fig 5a and 5b for various palmitolylation rates, however the value used in this model is not present in the figure in the paper but corresponds to Fig S2 of the supplement. Model successfully reproduced using MathSBML. Please note that the units of volumetric species in this model are molecules/micrometer cubed, to convert this to microMolar as given in the paper, multiply the simulation result by 1/602.

The model corresponds to the schema 3 of Markevich et al 2004, as described in the figure 2 and the supplementary table S2. Phosphorylations follow distributive random kinetics, while dephosphorylations follow an ordered mechanism. The phosphorylations are modeled with three elementary reactions:
E+S<=>ES->E+P
The dephosphorylations are modeled with five elementary reactions:
E+S<=>ES->EP<=>E+P
The model reproduces figure 5 in the main article.

described in: Pharmacokinetic-pharmacodynamic modeling of caffeine: Tolerance to pressor effects
Shi J, Benowitz NL, Denaro CP and Sheiner LB. ; Clin. Pharmacol. Ther. 1993 Jan;53(1):6-14. PMID: 8422743 ;
Abstract:
We propose a parametric pharmacokinetic-pharmacodynamic model for caffeine that quantifies the development of tolerance to the pressor effect of the drug and characterizes the mean behavior and inter-individual variation of both pharmacokinetics and pressor effect. Our study in a small group of subjects indicates that acute tolerance develops to the pressor effect of caffeine and that both the pressor effect and tolerance occur after some time delay relative to changes in plasma caffeine concentration. The half-life of equilibration of effect with plasma caffeine concentration is about 20 minutes. The half-life of development and regression of tolerance is estimated to be about 1 hour, and the model suggests that tolerance, at its fullest, causes more than a 90 percent reduction of initial (nontolerant) effect. Whereas tolerance to the pressor effect of caffeine develops in habitual coffee drinkers, the pressor response is regained after relatively brief periods of abstinence. Because of the rapid development and regression of tolerance, the pressor response to caffeine depends on how much caffeine is consumed, the schedule of consumption, and the elimination half-life of caffeine.

Caffeine intake in this version is modelled as cups of coffee drunk at regular intervals (parameter t_interval ). The amount of caffeine per cup is determined by the parameter cupsize . The div weight of the person drinking is given by the parameter divweight .
The even coffee cup occures delayed to the drinking of each cup, as the availability of the caffeine in the digestive tract is assumed to be delayed to the ingestion by the time t_lag .

This is model according to the paper "A Molecular Network That Produces Spontaneous Oscillations in Excitalbe Cells of Dictyostelium. Figure 3 has been reproduced by Copasi 4.0.20(development) ". However four of the parameters have been changed , see details in notes.

Mosca2012 - Central Carbon Metabolism Regulated by AKT

The role of the PI3K/Akt/PKB signalling pathway in oncogenesis has been extensively investigated and altered expression or mutations of many components of this pathway have been implicated in human cancers. Indeed, expression of constitutively active forms of Akt/PKB can prevent cell death upon growth factor withdrawal. PI3K/Akt/mTOR-mediated survival relies on a profound metabolic adaptation, including aerobic glycolysis. Here, the link between the PI3K/Akt/mTOR pathway, glycolysis, lactic acid production and nucleotide biosynthesis has been modelled, considering two states - high and low PI3K/Akt/mTOR activity. The high PI3K/Akt/mTOR activity represents cancer cell line where PI3K/Akt/mTOR promotes a high rate of glucose metabolism (condition H) and the low PI3K/Akt/mTOR activity is characterised by a lower glycolytic rate due to a reduced PI3K/Akt/mTOR signal (condition L). This model corresponds to the high PI3K/Akt/mTOR signal (condition H).

This model is described in the article:

Computational Modelling of the Metabolic States Regulated by the Kinase Akt.

Mosca E, Alfieri R, Maj C, Bevilacqua A, Canti G, Milanesi L.

Frontiers in Systems Biology. 2012 Oct 13

Abstract:

Signal transduction pathways and gene regulation determine a major reorganization of metabolic activities in order to support cell proliferation. Protein Kinase B (PKB), also known as Akt, participates in the PI3K/Akt/mTOR pathway, a master regulator of aerobic glycolysis and cellular biosynthesis, two activities shown by both normal and cancer proliferating cells. Not surprisingly considering its relevance for cellular metabolism, Akt/PKB is often found hyperactive in cancer cells. In the last decade, many efforts have been made to improve the understanding of the control of glucose metabolism and the identification of a therapeutic window between proliferating cancer cells and proliferating normal cells. In this context, we have modelled the link between the PI3K/Akt/mTOR pathway, glycolysis, lactic acid production and nucleotide biosynthesis. We used a computational model in order to compare two metabolic states generated by the specific variation of the metabolic fluxes regulated by the activity of the PI3K/Akt/mTOR pathway. One of the two states represented the metabolism of a growing cancer cell characterised by aerobic glycolysis and cellular biosynthesis, while the other state represented the same metabolic network with a reduced glycolytic rate and a higher mitochondrial pyruvate metabolism, as reported in literature in relation to the activity of the PI3K/Akt/mTOR. Some steps that link glycolysis and pentose phosphate pathway revealed their importance for controlling the dynamics of cancer glucose metabolism.

This model is hosted on BioModels Database and identified by: BIOMD0000000426 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

The model reproduces the time evolution of several species as depicted in Fig 4 of the paper. Events have been used to reset cell mass when the value of M-phase promoting factor (MPF) decreases through 0.1. The model was successfully tested on Cell Designer.

The model reproduces the kinetics of the nuclear factor of activated cells (NFAT) as depicted in Figure 3a of the paper. Model was successfully tested on Jarnac and MathSBML

Tyson1991 - Cell Cycle 2 var

Mathematical model of the interactions of cdc2 and cyclin.

Description taken from the original Cellerator version of the model ( Tyson (1991, 2 variables) at http://www.cellerator.org ).

This model is described in the article:

Modeling the cell division cycle: cdc2 and cyclin interactions.

Tyson JJ.

Proc. Natl. Acad. Sci. U.S.A. 1991; 88(16); 7328-32

Abstract:

This is a two variable reduction of the larger 6-variable model published in the same paper. The equations are:

u'= k4(v-u)(alpha+u^2)-k6*u
v'=kappa-k6*u
z= v-u
with kappa = k1[aa]/[CT]

In the present implementation, an additional variable z is introduced with z = v-u is made, so that the different variables be interpreted as follows:

u=[activeMPF]/[CT]
v=([cyclin]+[preMPF]+[activeMPF])/[CT]
z=([ cyclin]+[preMPF])/[CT]
with [CT]=[CDC2]+{CDC2P]+[preMPF]+[aMPF].

The reactions included are only to show the flows between z and u, and do not influence the species, as they all are set to boundaryCondition=True , meaning, that they are only determined by the rate rules (explicit differential equations) and assignment rules.

If you set boundaryCondition=False and remove the rate rules for v, u and the the assignment rule for z, you get the more symmetrical, but equivalent, version from the Cellerator repository:

u'= k4*z*(alpha+u^2)-k6*u
z'=kappa-z*(alpha+u^2)

This model is hosted on BioModels Database and identified by: BIOMD0000000006 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This model is according to the paper Signal-induced Ca2+ oscillations: Properties of a model based on Ca2+-induced Ca2+ release. Figure4B in the paper has been reproduced by RoadRunner and MathSBML. Damped Ca2+ oscillations elicited by a transient pulse of InsP3 applied intracellularly to a resting, non-oscillatory cell.

This is the Dynamical model of nuclear division cycles during early embryogenesis of Drosophila, without StringT regulation. so ksstg=kdstg=0. Figure1B has been simulated by MathSBML. Curator changed model from only one compartment into two compartments according to the paper. Detail explaination of the models are in the supplement information of the paper.The author didn't specify which compartment Xm, Stgm, Xp are located, we assume that they locate in cytoplasm.

Some of the parameter values for the equations are dimensionless parameters.

Note: Model of the Calvin cycle and the related end-product pathways to starch and sucrose synthesis and photorespiration by Zhu et al. (2007, DOI:10.1104/pp.107.103713 ) and the personally provided implementation.

The parameter values are partly taken from Pettersson and Ryde-Pettersson (1988, DOI:10.1111/j.1432-1033.1988.tb14242.x ). The initial metabolite values are chosen from the data set of Zhu et al. (2007, DOI:10.1104/pp.107.103713 ). A detailed description of all modifications is given in the model described by Arnold and Nikoloski (2011, PMID:22001849 .

This a model from the article:
Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data.
Yildirim N, Mackey MC Biophys. J. 2003 12719218 ,
Abstract:
A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; beta-galactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose interactions with the lac repressor; and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the transcription and translation process. We have paid particular attention to the estimation of the parameters in the model. We have tested our model against two sets of beta-galactosidase activity versus time data, as well as a set of data on beta-galactosidase activity during periodic phosphate feeding. In all three cases we find excellent agreement between the data and the model predictions. Analytical and numerical studies also indicate that for physiologically realistic values of the external lactose and the bacterial growth rate, a regime exists where there may be bistable steady-state behavior, and that this corresponds to a cusp bifurcation in the model dynamics.

The model reproduces the time profile of beta-galactosidase activity as shown in Fig 3 of the paper. The delay functions for transcription (M) and translation (B and P) have been implemented by introducing intermediates ( I1, I2 and I3) in the reaction scheme which then give their respective products (I1-> M, I2 ->B and I3 ->P) after an appropriate length of time. The steady state values, attained upon simulation of model equations, for Allolactose (A), mRNA (M), beta-galactosidase (B), Lactose (L), and Permease (P) match with those predicted by the paper. The model was successfully tested on Jarnac, MathSBML and COPASI

Novak1997 - Cell Cycle

Modeling the control of DNA replication in fission yeast.

This model is described in the article:

Modeling the control of DNA replication in fission yeast.

Novak B., Tyson JJ.

Proc. Natl. Acad. Sci. U.S.A. 1997:94(17):9147-52

Abstract:

A central event in the eukaryotic cell cycle is the decision to commence DNA replication (S phase). Strict controls normally operate to prevent repeated rounds of DNA replication without intervening mitoses ("endoreplication") or initiation of mitosis before DNA is fully replicated ("mitotic catastrophe"). Some of the genetic interactions involved in these controls have recently been identified in yeast. From this evidence we propose a molecular mechanism of "Start" control in Schizosaccharomyces pombe. Using established principles of biochemical kinetics, we compare the properties of this model in detail with the observed behavior of various mutant strains of fission yeast: wee1(-) (size control at Start), cdc13Delta and rum1(OP) (endoreplication), and wee1(-) rum1Delta (rapid division cycles of diminishing cell size). We discuss essential features of the mechanism that are responsible for characteristic properties of Start control in fission yeast, to expose our proposal to crucial experimental tests.

This model is hosted on BioModels Database and identified by: BIOMD0000000007 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

The model reproduces Fig 3 of the paper. Model successfully reproduced using MathSBML and Jarnac.

The model reproduces block A of Fig 5 and also Fig 3 (without the inclusion of Tg action). The model was successfully tested on MathSBML

This a model from the article:
Modeling of bone formation and resorption mediated by parathyroid hormone: response to estrogen/PTH therapy.
Rattanakul C, Lenbury Y, Krishnamara N, Wollkind DJ. Biosystems 2003:70(1):55-72. 12753937 ,
Abstract:
Bone, a major reservoir of div calcium, is under the hormonal control of the parathyroid hormone (PTH). Several aspects of its growth, turnover, and mechanism, occur in the absence of gonadal hormones. Sex steroids such as estrogen, nonetheless, play an important role in bone physiology, and are extremely essential to maintain bone balance in adults. In order to provide a basis for understanding the underlying mechanisms of bone remodeling as it is mediated by PTH, we propose here a mathematical model of the process. The nonlinear system model is then utilized to study the temporal effect of PTH as well as the action of estrogen replacement therapy on bone turnover. Analysis of the model is done on the assumption, supported by reported clinical evidence, that the process is characterized by highly diversified dynamics, which warrants the use of singular perturbation arguments. The model is shown to exhibit limit cycle behavior, which can develop into chaotic dynamics for certain ranges of the system's parametric values. Effects of estrogen and PTH administrations are then investigated by extending on the core model. Analysis of the model seems to indicate that the paradoxical observation that intermittent PTH administration causes net bone deposition while continuous administration causes net bone loss, and certain other reported phenomena may be attributed to the highly diversified dynamics which characterizes this nonlinear remodeling process.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: rattananakul, lenbury, krishnamara, wollkind. (2003) - version01
The original CellML model was created by:
Lloyd, Catherine, May
c.lloyd@auckland.ac.nz
The University of Auckland
Auckland Bioengineering Institute

This is the standard model described in the article:
Systems analysis of effector caspase activation and its control by X-linked inhibitor of apoptosis protein.
Rehm M, Huber HJ, Dussmann H, Prehn JH. EMBO J. 2006 Sep 20;25(18):4338-49. Epub 2006 Aug 24. PMID: 16932741 , doi: 10.1038/sj.emboj.7601295 ;
Abstract:
Activation of effector caspases is a final step during apoptosis. Single-cell imaging studies have demonstrated that this process may occur as a rapid, all-or-none response, triggering a complete substrate cleavage within 15 min. Based on biochemical data from HeLa cells, we have developed a computational model of apoptosome-dependent caspase activation that was sufficient to remodel the rapid kinetics of effector caspase activation observed in vivo. Sensitivity analyses predicted a critical role for caspase-3-dependent feedback signalling and the X-linked-inhibitor-of-apoptosis-protein (XIAP), but a less prominent role for the XIAP antagonist Smac. Single-cell experiments employing a caspase fluorescence resonance energy transfer substrate verified these model predictions qualitatively and quantitatively. XIAP was predicted to control this all-or-none response, with concentrations as high as 0.15 microM enabling, but concentrations >0.30 microM significantly blocking substrate cleavage. Overexpression of XIAP within these threshold concentrations produced cells showing slow effector caspase activation and submaximal substrate cleavage. Our study supports the hypothesis that high levels of XIAP control caspase activation and substrate cleavage, and may promote apoptosis resistance and sublethal caspase activation in vivo.

This model is slightly altered from the description in the article. Cytochrome C and SMAC release from the mitochondrion is modelled as simple first order kinetics, giving the same form as the (integrated) equations in the supplement of the article. The apoptosome formation is modelled equally - and independent of the Cytochrome C release. The speed is either limited by the Apaf1 or ProCaspase9 concentration, whichever is higher, symbolised via the parameter with the ID apolim .
Also, once the substrate concentration falls below 1 percent, the event Production_Breakdown is triggered, leading to a breakdown of XIAP and procaspase3 production and turning off of the enhanced/proteosomal degradation (degradation rate for reactions 38,39,40,43,44,46,48,50,51 changes from 0.0347 to 0.0058).

Originally created by libAntimony v1.3 (using libSBML 3.4.1)

This is the full model (eq. 1 and 2) of the voltage oscillations in barnacle muscle fibers described in the article:
Voltage oscillations in the barnacle giant muscle fiber.
Morris C, Lecar H. Biophys J. 1981 Jul;35(1):193-213. PubmedID: 7260316 ; DOI: 10.1016/S0006-3495(81)84782-0
Abstract:
Barnacle muscle fibers subjected to constant current stimulation produce a variety of types of oscillatory behavior when the internal medium contains the Ca++ chelator EGTA. Oscillations are abolished if Ca++ is removed from the external medium, or if the K+ conductance is blocked. Available voltage-clamp data indicate that the cell's active conductance systems are exceptionally simple. Given the complexity of barnacle fiber voltage behavior, this seems paradoxical. This paper presents an analysis of the possible modes of behavior available to a system of two noninactivating conductance mechanisms, and indicates a good correspondence to the types of behavior exhibited by barnacle fiber. The differential equations of a simple equivalent circuit for the fiber are dealt with by means of some of the mathematical techniques of nonlinear mechanics. General features of the system are (a) a propensity to produce damped or sustained oscillations over a rather broad parameter range, and (b) considerable latitude in the shape of the oscillatory potentials. It is concluded that for cells subject to changeable parameters (either from cell to cell or with time during cellular activity), a system dominated by two noninactivating conductances can exhibit varied oscillatory and bistable behavior.

The model consists of the differential equations (1) and (2) given on pages 195 and 196 of the article. There is one typo in the equation for I in (1), g _L (V _L ) should be g _L (V - V _L ). This was changed in the SBML file. As there are no current values given, for reproducing the time courses in figure 6 an applied current of 50 uA was assumed. The legend for the broken and the full line in this figure seems to be confounded in the article.

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

This a model from the article:
Modelling the Role of UCH-L1 on Protein Aggregation in Age-Related Neurodegeneration.
Proctor CJ, Tangeman PJ, Ardley HC. PLoS One. 2010 Oct 6;5(10):e13175 20949132 ,
Abstract:
Overexpression of the de-ubiquitinating enzyme UCH-L1 leads to inclusion formation in response to proteasome impairment. These inclusions contain components of the ubiquitin-proteasome system and α-synuclein confirming that the ubiquitin-proteasome system plays an important role in protein aggregation. The processes involved are very complex and so we have chosen to take a systems biology approach to examine the system whereby we combine mathematical modelling with experiments in an iterative process. The experiments show that cells are very heterogeneous with respect to inclusion formation and so we use stochastic simulation. The model shows that the variability is partly due to stochastic effects but also depends on protein expression levels of UCH-L1 within cells. The model also indicates that the aggregation process can start even before any proteasome inhibition is present, but that proteasome inhibition greatly accelerates aggregation progression. This leads to less efficient protein degradation and hence more aggregation suggesting that there is a vicious cycle. However, proteasome inhibition may not necessarily be the initiating event. Our combined modelling and experimental approach show that stochastic effects play an important role in the aggregation process and could explain the variability in the age of disease onset. Furthermore, our model provides a valuable tool, as it can be easily modified and extended to incorporate new experimental data, test hypotheses and make testable predictions.

Note:

Typos in the publication:

Equation (4): The first term should be (β1/α1)^(g12/Γ) and not (β2/α2)^(g12/Γ)

Equation (14): The first term should be (β1/α1)^(((g12/(1+r12))/Γ) and not (β2/α2)^(((g12/(1+r12))/Γ)

Equation (13): The first term should be (β1/α1)^((1-g22+r22)/Γ) and not (β1/α1)^((1-g22-r22)/Γ)

All these corrections has been implemented in the model, with the authors agreement.

Beyond these, there are several mismatches between the equation numbers that are mentioned in for each equation and the reference that has been made to these equations in the figure legend.

This model is from the article:
On the encoding and decoding of calcium signals in hepatocytes
Ann Zahle Larsen, Lars Folke Olsen and Ursula Kummera Biophysical Chemistry Volume 107, Issue 1, 1 January 2004, Pages 83-99 14871603 ,
Abstract:
Many different agonists use calcium as a second messenger. Despite intensive research in intracellular calcium signalling it is an unsolved riddle how the different types of information represented by the different agonists, is encoded using the universal carrier calcium. It is also still not clear how the information encoded is decoded again into the intracellular specific information at the site of enzymes and genes. After the discovery of calcium oscillations, one likely mechanism is that information is encoded in the frequency, amplitude and waveform of the oscillations. This hypothesis has received some experimental support. However, the mechanism of decoding of oscillatory signals is still not known. Here, we study a mechanistic model of calcium oscillations, which is able to reproduce both spiking and bursting calcium oscillations. We use the model to study the decoding of calcium signals on the basis of co-operativity of calcium binding to various proteins. We show that this co-operativity offers a simple way to decode different calcium dynamics into different enzyme activities.

Note:

This model corresponds to the 5 variable receptor-operated model, as described by Larsen et al., 2004. This model is a modified version of the model described in Kummer 2000 (PMID: 10968983 )

This is the reduced model (model 8) described in: Dynamics within the CD95 death-inducing signaling complex decide life and death of cells.
Leo Neumann, Carina Pforr, Joel Beaudouin, Alexander Golks, Peter H. Krammer, Inna N. Lavrik and Roland Eils (German Cancer Research Center (DKFZ), http://www.dkfz.de ); Mol Sys Biol 2010; 6 :352. doi: 10.1038/msb.2010.6 ;

Abstract:
This study explores the dilemma in cellular signaling that triggering of CD95 (Fas/APO-1) in some situations results in cell death and in others leads to the activation of NF-κB. We established an integrated kinetic mathematical model for CD95-mediated apoptotic and NF-κB signaling. Systematic model reduction resulted in a surprisingly simple model well approximating experimentally observed dynamics. The model postulates a new link between c-FLIP _L cleavage in the death-inducing signaling complex (DISC) and the NF-κB pathway. We validated experimentally that CD95 stimulation resulted in an interaction of p43-FLIP with the IKK complex followed by its activation. Furthermore, we showed that the apoptotic and NF-κB pathways diverge already at the DISC. Model and experimental analysis of DISC formation showed that a subtle balance of c-FLIP _L and procaspase-8 determines life/death decisions in a nonlinear manner. We present an integrated model describing the complex dynamics of CD95-mediated apoptosis and NF-κB signaling.

The original was taken from the MSB article supplementary material site msb20106-s2.xml . All the species ids were changed since the model was not a valid SBML with its original ids - Lukas.

Notes added to the species [L] (the initial concentration of Anti-CD95), regarding changes to be made in the initial concentration of [L], to obtain figure 5D.

The model reproduces Fig 6B of the paper for model 6. The model was reproduced using XPP.

This a model from the article:
Mathematical model of paracrine interactions between osteoclasts and osteoblasts predicts anabolic action of parathyroid hormone on bone.
Komarova SV. Endocrinology. 2005 Aug;146(8):3589-95. 15860557 ,
Abstract:
To restore falling plasma calcium levels, PTH promotes calcium liberation from bone. PTH targets bone-forming cells, osteoblasts, to increase expression of the cytokine receptor activator of nuclear factor kappaB ligand (RANKL), which then stimulates osteoclastic bone resorption. Intriguingly, whereas continuous administration of PTH decreases bone mass, intermittent PTH has an anabolic effect on bone, which was proposed to arise from direct effects of PTH on osteoblastic bone formation. However, antiresorptive therapies impair the ability of PTH to increase bone mass, indicating a complex role for osteoclasts in the process. We developed a mathematical model that describes the actions of PTH at a single site of bone remodeling, where osteoclasts and osteoblasts are regulated by local autocrine and paracrine factors. It was assumed that PTH acts only to increase the production of RANKL by osteoblasts. As a result, PTH stimulated osteoclasts upon application, followed by compensatory osteoblast activation due to the coupling of osteoblasts to osteoclasts through local paracrine factors. Continuous PTH administration resulted in net bone loss, because bone resorption preceded bone formation at all times. In contrast, over a wide range of model parameters, short application of PTH resulted in a net increase in bone mass, because osteoclasts were rapidly removed upon PTH withdrawal, enabling osteoblasts to rebuild the bone. In excellent agreement with experimental findings, increase in the rate of osteoclast death abolished the anabolic effect of PTH on bone. This study presents an original concept for the regulation of bone remodeling by PTH, currently the only approved anabolic treatment for osteoporosis.

The model reproduces Figures 1B and 2A of the reference publication. To obtain the figures 1B, the parameter g21 needs changes. To obtain the figures 1A, the parameters g21, g12 and k2 need to changed. For details look at the curation tab.

The initial concentration of Osteoclasts (x1) is corrected to 1.06066 from 10.06066.

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: CellMLdetails
The original CellML model was created by:
Lloyd, Catherine, May
c.lloyd@auckland.ac.nz
The University of Auckland
The Bioengineering Institute

Sarma2012 - Interaction topologies of MAPK cascade (M4_K2_USEQ)

The paper presents the various interaction topologies between the kinases and phosphatases of MAPK cascade. They are represented as M1, M2, M3 and M4. The kinases of the cascades are MKKK, MKK and MK, and Phos1, Phos2 and Phos3 are phosphatases of the system. All three kinases in a M1 type network have specific phosphatases Phos1, Phos2 and Phos3 for the dephosphorylation process. In a M2 type system, kinases MKKK and MKK are dephosphorylated by Phos1 and MK is dephosphorylated by Phos2. The architecture of system like M3 is such that MKKK gets dephosphorylated by Phos1, whereas Phos2 dephosphorylates both MKK and MK. Finally, the MAPK cascade exhibiting more complex design of interaction such as M4 is such that MKKK and MKK are dephosphorylated by Phos1 whereas MKK and MK are dephosphorylated by Phos2. In addition, as it is plausible that the kinases can sequester their respective phosphatases by binding to them, this is considered in the design of the systems (PSEQ-sequestrated system; USEQ-Unsequestrated system). The robustness of different interaction designs of the systems is checked, considering both MichaelisMenten type kinetics (K1) and elementary mass action kinetics (K2). In the living systems, the MAPK cascade transmit both short and long duration signals where short duration signals trigger proliferation and long duration signals trigger cell differentiation. These signal variants are considered to interpret the systems behaviour. It is also tested how the robustness and signal response behaviour of K2 models are affected when K2 assumes quasi steady state (QSS). The combinations of the above variants resulted in 40 models (MODEL1204280001-40). All these 40 models are available from BioModels Database .

This model [ MODEL1204280020 - M4_K2_USEQ] correspond to type M4 with mass-action kinetics K2, in USEQ (Unsequestrated ) condition.

This model is described in the article:

Different designs of kinase-phosphatase interactions and phosphatase sequestration shapes the robustness and signal flow in the MAPK cascade.

Sarma U, Ghosh I.

BMC Syst Biol. 2012 Jul 2;6(1):82.

Abstract:

This model is hosted on BioModels Database and identified by: BIOMD0000000430 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

This is an SBML version of the folate cycle model model from:
A mathematical model of the folate cycle: new insights into folate homeostasis.
Nijhout HF, Reed MC, Budu P, Ulrich CM J. Biol. Chem.,2004, 279 (53),55008-16
pubmedID: 15496403
Abstract:
A mathematical model is developed for the folate cycle based on standard biochemical kinetics. We use the model to provide new insights into several different mechanisms of folate homeostasis. The model reproduces the known pool sizes of folate substrates and the fluxes through each of the loops of the folate cycle and has the qualitative behavior observed in a variety of experimental studies. Vitamin B(12) deficiency, modeled as a reduction in the V(max) of the methionine synthase reaction, results in a secondary folate deficiency via the accumulation of folate as 5-methyltetrahydrofolate (the "methyl trap"). One form of homeostasis is revealed by the fact that a 100-fold up-regulation of thymidylate synthase and dihydrofolate reductase (known to occur at the G(1)/S transition) dramatically increases pyrimidine production without affecting the other reactions of the folate cycle. The model also predicts that an almost total inhibition of dihydrofolate reductase is required to significantly inhibit the thymidylate synthase reaction, consistent with experimental and clinical studies on the effects of methotrexate. Sensitivity to variation in enzymatic parameters tends to be local in the cycle and inversely proportional to the number of reactions that interconvert two folate substrates. Another form of homeostasis is a consequence of the nonenzymatic binding of folate substrates to folate enzymes. Without folate binding, the velocities of the reactions decrease approximately linearly as total folate is decreased. In the presence of folate binding and allosteric inhibition, the velocities show a remarkable constancy as total folate is decreased.
This model was encoded by Michal Galdzicki from a MatLab file send to him by Prof. Michael Reed. There some differences in this model compared to the one described in the article, possible due to typos in the publication:
1) reaction NE (THF + H2CO <=> 5,10-CH2-THF) in the article has H2C=O as a reactant and is mentioned to display pseudo first order mass action kinetics, while in the matlab file formic acid, also used in reaction FTS, is included in the rate law for the forward reaction.
2) the reaction MS is modeled after Reed et al. 2004, which is not explicitly mentioned in the article, although Kd and the parameters from Reed et al. 2004 are given.
3) in the kinetic law of the SHTM reaction (THF + Ser <=> 5,10-CH2-THF + Gly), there are separate values given for Km,Gly and Km,5,10-CH2-THF in the article. in the matlab file and the SBML model Km,Ser and Km,THF are used instead of Km,Gly and Km,5,10-CH2-THF for the backwards reaction.

This model is the 4-step model from the article:
Onset dynamics of type A botulinum neurotoxin-induced paralysis.
Lebeda FJ, Adler M, Erickson K, Chushak Y J Pharmacokinet Pharmacodyn 2008 Jun; 35(3): 251-67 18551355 ,
Abstract:
Experimental studies have demonstrated that botulinum neurotoxin serotype A (BoNT/A) causes flaccid paralysis by a multi-step mechanism. Following its binding to specific receptors at peripheral cholinergic nerve endings, BoNT/A is internalized by receptor-mediated endocytosis. Subsequently its zinc-dependent catalytic domain translocates into the neuroplasm where it cleaves a vesicle-docking protein, SNAP-25, to block neurally evoked cholinergic neurotransmission. We tested the hypothesis that mathematical models having a minimal number of reactions and reactants can simulate published data concerning the onset of paralysis of skeletal muscles induced by BoNT/A at the isolated rat neuromuscular junction (NMJ) and in other systems. Experimental data from several laboratories were simulated with two different models that were represented by sets of coupled, first-order differential equations. In this study, the 3-step sequential model developed by Simpson (J Pharmacol Exp Ther 212:16-21,1980) was used to estimate upper limits of the times during which anti-toxins and other impermeable inhibitors of BoNT/A can exert an effect. The experimentally determined binding reaction rate was verified to be consistent with published estimates for the rate constants for BoNT/A binding to and dissociating from its receptors. Because this 3-step model was not designed to reproduce temporal changes in paralysis with different toxin concentrations, a new BoNT/A species and rate (k(S)) were added at the beginning of the reaction sequence to create a 4-step scheme. This unbound initial species is transformed at a rate determined by k(S) to a free species that is capable of binding. By systematically adjusting the values of k(S), the 4-step model simulated the rapid decline in NMJ function (k(S) >or= 0.01), the less rapid onset of paralysis in mice following i.m. injections (k (S) = 0.001), and the slow onset of the therapeutic effects of BoNT/A (k(S) < 0.001) in man. This minimal modeling approach was not only verified by simulating experimental results, it helped to quantitatively define the time available for an inhibitor to have some effect (t(inhib)) and the relation between this time and the rate of paralysis onset. The 4-step model predicted that as the rate of paralysis becomes slower, the estimated upper limits of (t(inhib)) for impermeable inhibitors become longer. More generally, this modeling approach may be useful in studying the kinetics of other toxins or viruses that invade host cells by similar mechanisms, e.g., receptor-mediated endocytosis.

Model updated by Viji on 07/09/2010.

This model is the extended model of BIOMD0000000267 , which itself is the reduced form of the model developed by Simpson 1980; PMID 6243359

Note: Model of the Calvin cycle with focus on the RuBisCO reaction by Schultz (2003, DOI:10.1071/FP02146 ).

The model reproduces Fig 6B of the paper for model 3. The model was reproduced using XPP.

This model was taken from the Vcell MathModel directory and was converted to SBML

This is the single input module, SIM, described in the article:
Network motifs in the transcriptional regulation network of Escherichia coli
Shai S. Shen-Orr, Ron Milo, Shmoolik Mangan, Uri Alon, Nat Genet 2002 31:64-68; PMID: 11967538 ; DOI: 10.1038/ng881 ;

This model reproduces the SIM timecourse presented in Figure 2b. All species and parameters in the model are dimensionless.

This is the compartmental model for L-Dopa/Benserazide pharmacokinetics as described in the article:
A pharmacokinetic model to predict the PK interaction of L-dopa and benserazide in rats.
Grange S, Holford NH and Guentert TW. Pharm Res. 2001 AUg; 18(8):1174-84 11587490

Abstract:

The volumes and variables in this model are taken for a rat with 0.25 kg. The inital dose for L_Dopa (L_Dopa_per_kg_rat) and Benserazide (Benserazide_per_kg_rat) are to be given in umole per kg. 80 mg/kg L-Dopa correspond to 404 umol/kg, 20 mg/kg benserazide to 78 umol/kg. To change the model to a different mass of rat the compartment volumes, and the parameters rat_div_mass and Q have to changed accordingly.

Note:

The model has three species (A-dopa, A_B, A_M) whose initial concentrations are calculated from a listOfInitialAssignments . While running for the first time the time-course (24hrs) for this model in COPASI (up to version 4.6, Build 33), the resulting graph displays only straight lines for all the species. Any subsequent runs should provide proper plots (i.e. without making any change to the model, just by clicking the "run" button again).

The above issue is caused by some initial assignments which are not calculated when COPASI imports the file. This issue should not be present in newer releases of COPASI.

Copyright:

Achcar2012 - Glycolysis in bloodstream form T. brucei

Kinetic models of metabolism require quantitative knowledge of detailed kinetic parameters. However, the knowledge about these parameters is often uncertain. An analysis of the effect of parameter uncertainties on a particularly well defined example of a quantitative metablic model, the model of glycolysis in bloodstream form Trypanosoma brucei , has been presented here.

This model is described in the article:

Dynamic modelling under uncertainty: the case of Trypanosoma brucei energy metabolism.

Achcar F, Kerkhoven EJ; SilicoTryp Consortium, Bakker BM, Barrett MP, Breitling R.

PLoS Comput Biol. 2012 Jan; 8(1):e1002352.

Abstract:

Kinetic models of metabolism require detailed knowledge of kinetic parameters. However, due to measurement errors or lack of data this knowledge is often uncertain. The model of glycolysis in the parasitic protozoan Trypanosoma brucei is a particularly well analysed example of a quantitative metabolic model, but so far it has been studied with a fixed set of parameters only. Here we evaluate the effect of parameter uncertainty. In order to define probability distributions for each parameter, information about the experimental sources and confidence intervals for all parameters were collected. We created a wiki-based website dedicated to the detailed documentation of this information: the SilicoTryp wiki (http://silicotryp.ibls.gla.ac.uk/wiki/Glycolysis). Using information collected in the wiki, we then assigned probability distributions to all parameters of the model. This allowed us to sample sets of alternative models, accurately representing our degree of uncertainty. Some properties of the model, such as the repartition of the glycolytic flux between the glycerol and pyruvate producing branches, are robust to these uncertainties. However, our analysis also allowed us to identify fragilities of the model leading to the accumulation of 3-phosphoglycerate and/or pyruvate. The analysis of the control coefficients revealed the importance of taking into account the uncertainties about the parameters, as the ranking of the reactions can be greatly affected. This work will now form the basis for a comprehensive Bayesian analysis and extension of the model considering alternative topologies.

This model is hosted on BioModels Database and identified by: BIOMD0000000428 .

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models .

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

This is an SBML implementation the model of negative feedback oscillator (figure 2a) described in the article:
Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell.
Tyson JJ, Chen KC, Novak B. Curr Opin Cell Biol. 2003 Apr;15(2):221-31. PubmedID: 12648679 ; DOI: 10.1016/S0955-0674(03)00017-6 ;

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

This a model from the article:
A kinetic model of the branch-point between the methionine and threonine biosynthesis pathways in Arabidopsis thaliana.
Curien G, Ravanel S, Dumas R Eur. J. Biochem. 2003 Dec; Volume: 270 (Issue: 23 )]:4615-27 14622248 ,
Abstract:
This work proposes a model of the metabolic branch-point between the methionine and threonine biosynthesis pathways in Arabidopsis thaliana which involves kinetic competition for phosphohomoserine between the allosteric enzyme threonine synthase and the two-substrate enzyme cystathionine gamma-synthase. Threonine synthase is activated by S-adenosylmethionine and inhibited by AMP. Cystathionine gamma-synthase condenses phosphohomoserine to cysteine via a ping-pong mechanism. Reactions are irreversible and inhibited by inorganic phosphate. The modelling procedure included an examination of the kinetic links, the determination of the operating conditions in chloroplasts and the establishment of a computer model using the enzyme rate equations. To test the model, the branch-point was reconstituted with purified enzymes. The computer model showed a partial agreement with the in vitro results. The model was subsequently improved and was then found consistent with flux partition in vitro and in vivo. Under near physiological conditions, S-adenosylmethionine, but not AMP, modulates the partition of a steady-state flux of phosphohomoserine. The computer model indicates a high sensitivity of cystathionine flux to enzyme and S-adenosylmethionine concentrations. Cystathionine flux is sensitive to modulation of threonine flux whereas the reverse is not true. The cystathionine gamma-synthase kinetic mechanism favours a low sensitivity of the fluxes to cysteine. Though sensitivity to inorganic phosphate is low, its concentration conditions the dynamics of the system. Threonine synthase and cystathionine gamma-synthase display similar kinetic efficiencies in the metabolic context considered and are first-order for the phosphohomoserine substrate. Under these conditions outflows are coordinated.

Biomodels Curation The model simulates the flux for TS and CGS under conditions given in Table 2 and reproduces the dotted lines given in Table 3 of the paper. There is a typo in the equation for the apparent specificity constant for Phser, Kts (equation13). This was changed after communication with the authors to be: Kts = 5.9E-4+6.2E-2*pow(AdoMet,2.9)/(pow(32,2.9)+pow(AdoMet,2.9)). The model was successfully tested on Jarnac and Copasi. Due to a suggestion from Pedro Mendez the parameter AdoMet, TS and CGS where made constant species.

SBML creators: Armando Reyes-Palomares * , Raul Montañez *, Carlos Rodriguez-Caso +, Francisca Sanchez-Jimenez * , Miguel A. Medina *

http://asp.uma.es

In silico analysis of arginine catabolism as a source of nitric oxide or polyamines in endothelial cells.
Montañez, R et al.: Amino Acids. 2008 Feb;34(2):223-9.
The model reproduces the dynamical behavior of the arginine catabolism and transport in relation to the nitric oxide production. In this model there are some additions and corrections to the publication. All perturbations and analysis have produced results very close to the published experiments. The model was successfully tested on CoPaSi v.4.4 (build 26).

Erratum: parameters values modificated respect to the publication to reach the steady-state:

Kmodc=90 µM (60 µM in the paper)

Kiornhat (is equivalent to the parameter Kmefflhat Eq ) = 360 µM (380 µM in the paper)

The model reproduces the time profile of Open probability of the ryanodine receptor as shown in Fig 2A and 2B of the paper. The model was successfully tested on MathSBML and Jarnac.

This a model from the article:
Isoform switching facilitates period control in the Neurospora crassa circadian clock.
Akman OE, Locke JC, Tang S, Carré I, Millar AJ, Rand DA Mol. Syst. Biol. 2008;Vol 4: 164 18277380 ,
Abstract:
A striking and defining feature of circadian clocks is the small variation in period over a physiological range of temperatures. This is referred to as temperature compensation, although recent work has suggested that the variation observed is a specific, adaptive control of period. Moreover, given that many biological rate constants have a Q(10) of around 2, it is remarkable that such clocks remain rhythmic under significant temperature changes. We introduce a new mathematical model for the Neurospora crassa circadian network incorporating experimental work showing that temperature alters the balance of translation between a short and long form of the FREQUENCY (FRQ) protein. This is used to discuss period control and functionality for the Neurospora system. The model reproduces a broad range of key experimental data on temperature dependence and rhythmicity, both in wild-type and mutant strains. We present a simple mechanism utilising the presence of the FRQ isoforms (isoform switching) by which period control could have evolved, and argue that this regulatory structure may also increase the temperature range where the clock is robustly rhythmic.

BioSystems (2007), doi:10.1016/j.biosystems.2008.06.007

In-silico study of kinetochore control, amplification, and inhibition effects in MCC assembly

Bashar Ibrahim, Eberhard Schmitt, Peter Dittrich, Stephan Diekmann
This is the kinetochore dependent MCC model (KDM) from the article. For the kinetochore independent MCC model (KIM) replace u*k4f in R4 by k4f and u*k5f in R5 by k5f .

The model reproduces Fig 2A of the paper. Model successfully reproduced using Jarnac and MathSBML.

Notes from the original DOCQS curator:
In this version of the CDK2/Cyclin A complex activation there is discrepancy in the first curve which plots the binding reaction of CDK2 and Cyclin A expressed in E. coli. With the published rate constants the simulation does not match the published graph (Fig.1B) in Morris MC. et al. J Biol Chem. 277(26):23847-53 .

Notes from BioModels DB curator:
Although the parameters are those reported in the table I for CDK2/Cyclin A, the total fluorescence follows exactly the curve reported in the paper for CDK2/Cyclin H in figure 1B. Either the plot legend or the table is wrong.

Model is according to the paper Contribution of Persistent Na+ Current and M-Type K+ Current to Somatic Bursting in CA1 Pyramidal Cell: Combined Experimental. Figure6Da has been reproduced by MathSBML. The original model from ModelDB. http://senselab.med.yale.edu/modeldb/

Biomodels Curation The model reproduces the time series depicted in Fig 2 of the paper. Also, by varying the values of Vmax for the second kinase (k5) the time series of X3P as shown in Fig3 can be reproduced. The model was successfully tested on MathSBML and Jarnac.

The model reproduces the temporal evolution of Glycogen phosphorylase for a vale of Vm5=30 as depicted in Fig 1a of the paper. The model makes use of calcium oscillations from the Borghans model to stimulate the activation of glycogen phosphorylase. Hence, this is a simple extension of the Borghans model. The model was succesfully tested on MathSBML and Jarnac.

VmGLT	97.264	mmol/min
VmGLK	226.45
VmPGI	339.667
VmPFK	182.903
VmALD	322.258
VmGAPDH_f	1184.52
VmGAPDH_r	6549.68
VmPGK	1306.45
VmPGM	2525.81
VmENO	365.806
VmPYK	1088.71
VmPDC	174.194
VmG3PDH	70.15

name	value	value
	in suppl.	used
kr16	0.055	0.275
k30	7.9e6	2.1e6	as k20
kr30	0.3	0.4	as kr24
k38	3e7	1e7	as k20
kr38	0.055	0.55	as kr24
k52	1.1e5	5.34e7