BioModels for E. coli

BIOMD0000000301
Friedland2009_Ara_RTC3_counter

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 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.



BIOMD0000000066
Chassagnole2001_Threonine Synthesis

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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

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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



BIOMD0000000067
Fung2005_Metabolic_Oscillator

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.



BIOMD0000000571
Nishio2008 - Design of the phosphotransferase system for enhanced glucose uptake in E. coli.
Nishio2008 - Design of the phosphotransferase system for enhanced glucose uptake in E. coli.

This model is described in the article:

Nishio Y, Usuda Y, Matsui K, Kurata H.
Mol. Syst. Biol. 2008; 4: 160

Abstract:

The phosphotransferase system (PTS) is the sugar transportation machinery that is widely distributed in prokaryotes and is critical for enhanced production of useful metabolites. To increase the glucose uptake rate, we propose a rational strategy for designing the molecular architecture of the Escherichia coli glucose PTS by using a computer-aided design (CAD) system and verified the simulated results with biological experiments. CAD supports construction of a biochemical map, mathematical modeling, simulation, and system analysis. Assuming that the PTS aims at controlling the glucose uptake rate, the PTS was decomposed into hierarchical modules, functional and flux modules, and the effect of changes in gene expression on the glucose uptake rate was simulated to make a rational strategy of how the gene regulatory network is engineered. Such design and analysis predicted that the mlc knockout mutant with ptsI gene overexpression would greatly increase the specific glucose uptake rate. By using biological experiments, we validated the prediction and the presented strategy, thereby enhancing the specific glucose uptake rate.

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.



BIOMD0000000507
Gardner2000 - genetic toggle switch in E.coli
Gardner2000 - genetic toggle switch in E.coli

The behaviour of the genetic toggle switch and the conditions for bistability has been studies using a synthetic, bistable gene circuit.

This model is described in the article:

Gardner TS, Cantor CR, Collins JJ
Nature. 2000 Jan 20;403(6767):339-42.

Abstract:

It has been proposed' that gene-regulatory circuits with virtually any desired property can be constructed from networks of simple regulatory elements. These properties, which include multistability and oscillations, have been found in specialized gene circuits such as the bacteriophage lambda switch and the Cyanobacteria circadian oscillator. However, these behaviours have not been demonstrated in networks of non-specialized regulatory components. Here we present the construction of a genetic toggle switch-a synthetic, bistable gene-regulatory network-in Escherichia coli and provide a simple theory that predicts the conditions necessary for bistability. The toggle is constructed from any two repressible promoters arranged in a mutually inhibitory network. It is flipped between stable states using transient chemical or thermal induction and exhibits a nearly ideal switching threshold. As a practical device, the toggle switch forms a synthetic, addressable cellular memory unit and has implications for biotechnology, biocomputing and gene therapy.

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.



BIOMD0000000639
Thiaville2016 - Wild type folate pathway model with proposed PanB reaction
Thiaville2016 - Wild type folate pathway model with proposed PanB reaction
This is a wild type E. coli model, and is one amongst the three models described in the paper. The other two models are MODEL1602280002 (wild type with PanB over expression) and MODEL1602280003 (wild type with PanB over expression and THF regulation). 

This model is described in the article:

Thiaville JJ, Frelin O, García-Salinas C, Harrison K, Hasnain G, Horenstein NA, Díaz de la Garza RI, Henry CS, Hanson AD, de Crécy-Lagard V.
Front Microbiol 2016; 7: 431

Abstract:

Tetrahydrofolate (THF) and its one-carbon derivatives, collectively termed folates, are essential cofactors, but are inherently unstable. While it is clear that chemical oxidation can cleave folates or damage their pterin precursors, very little is known about enzymatic damage to these molecules or about whether the folate biosynthesis pathway responds adaptively to damage to its end-products. The presence of a duplication of the gene encoding the folate biosynthesis enzyme 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (FolK) in many sequenced bacterial genomes combined with a strong chromosomal clustering of the folK gene with panB, encoding the 5,10-methylene-THF-dependent enzyme ketopantoate hydroxymethyltransferase, led us to infer that PanB has a side activity that cleaves 5,10-methylene-THF, yielding a pterin product that is recycled by FolK. Genetic and metabolic analyses of Escherichia coli strains showed that overexpression of PanB leads to accumulation of the likely folate cleavage product 6-hydroxymethylpterin and other pterins in cells and medium, and-unexpectedly-to a 46% increase in total folate content. In silico modeling of the folate biosynthesis pathway showed that these observations are consistent with the in vivo cleavage of 5,10-methylene-THF by a side-activity of PanB, with FolK-mediated recycling of the pterin cleavage product, and with regulation of folate biosynthesis by folates or their damage products.

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.



BIOMD0000000404
Bray1993_chemotaxis

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 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.



BIOMD0000000217
Bruggeman2005_AmmoniumAssimilation

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.

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.



BIOMD0000000316
Shen-Orr2002_FeedForward_AND_gate

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.



BIOMD0000000317
Shen-Orr2002_Single_Input_Module

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;

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 SIM timecourse presented in Figure 2b. All species and parameters in the model are dimensionless.



BIOMD0000000425
Tan2012 - Antibiotic Treatment, Inoculum Effect
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:

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.

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.



BIOMD0000000458
Smallbone2013 - Serine biosynthesis
Smallbone2013 - Serine biosynthesis

Kinetic modelling of metabolic pathways in application to Serine biosynthesis.

This model is described in the article:

Kieran Smallbone, Natalie J. Stanford
Methods in Molecular Biology. 2013; 985:113-121

Abstract:

In this chapter, we describe the steps needed to create a kinetic model of a metabolic pathway using kinetic data from both experimental measurements and literature review. Our methodology is presented by using the example of serine biosynthesis in E. coli.

As there are no plots to be reproduced as curation figure, table 6 and 7 that corresponds to steady state concentration of metabolite and steady state fluxes of reactions has been reproduced.

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.



BIOMD0000000469
Smallbone2013 - E.coli metabolic model with linlog rate law
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BIOMD0000000565
Machado2014 - Curcumin production pathway in Escherichia coli
Machado2014 - Curcumin production pathway in Escherichia coli

This model is described in the article:

Machado D, Rodrigues LR, Rocha I.
BioSystems 2014 Nov; 125: 16-21

Abstract:

Curcumin is a natural compound obtained from turmeric, and is well known for its pharmacological effects. In this work, we design a heterologous pathway for industrial production of curcumin in Escherichia coli. A kinetic model of the pathway is then developed and connected to a kinetic model of the central carbon metabolism of E. coli. This model is used for optimization of the mutant strain through a rational design approach, and two manipulation targets are identified for overexpression. Dynamic simulations are then performed to compare the curcumin production profiles of the different mutant strains. Our results show that it is possible to obtain a significant improvement in the curcumin production rates with the proposed mutants. The kinetic model here developed can be an important framework to optimize curcumin production at an industrial scale and add value to its biomedical potential.

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.



BIOMD0000000038
Rohwer2000_Phosphotransferase_System

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



BIOMD0000000200
Bray1995_chemotaxis_receptorlinkedcomplex

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.



BIOMD0000000244
Kotte2010_Ecoli_Metabolic_Adaption

This is the model described in: Bacterial adaptation through distributed sensing of metabolic fluxes
Oliver Kotte, Judith B Zaugg and Matthias Heinemann;Mol Sys Biol2010;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,OD600, 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.

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.



BIOMD0000000222
Singh2006_TCA_Ecoli_glucose

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 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.



BIOMD0000000012
Elowitz2000 - Repressilator
Elowitz2000 - Repressilator

This model 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 the appropriate parameter values this system oscillates.

This model is described in the article:

Elowitz MB, Leibler S.
Nature. 2000 Jan; 403(6767):335-338

Abstract:

Networks of interacting biomolecules carry out many essential functions in living cells, but the 'design principles' underlying the functioning of such intracellular networks remain poorly understood, despite intensive efforts including quantitative analysis of relatively simple systems. Here we present a complementary approach to this problem: the design and construction of a synthetic network to implement a particular function. We used three transcriptional repressor systems that are not part of any natural biological clock to build an oscillating network, termed the repressilator, in Escherichia coli. The network periodically induces the synthesis of green fluorescent protein as a readout of its state in individual cells. The resulting oscillations, with typical periods of hours, are slower than the cell-division cycle, so the state of the oscillator has to be transmitted from generation to generation. This artificial clock displays noisy behaviour, possibly because of stochastic fluctuations of its components. Such 'rational network design may lead both to the engineering of new cellular behaviours and to an improved understanding of naturally occurring networks.

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 provided a corrected version generated by SBMLeditor on Sun Aug 20 00:44:05 BST 2006. This removed the EmptySet species. Ran fine on COPASI 4.0 build 18.

Bruce Shapiro revised the model with SBMLeditor on 23 October 2006 20:39 PST. This defines 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.

Moreover, the equations used in this model were clarified, cf. below.

The equations given in box 1 of 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: ? = 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

? in the equations should be in units of rescaled proteins per promotor and cell, and ? 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 ? and ? 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, ? 1/2,mRNA : 2 min
protein half life, ? 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 ): ? 1/2,mRNA /ln(2) = 2.89 min
mRNA decay rate ( kd_mRNA ): ln(2)/ ? 1/2,mRNA = 0.347 min -1
protein decay rate ( kd_prot ): ln(2)/ ? 1/2,prot
transcription rate ( a_tr ): tps_active*60 = 29.97 transcripts/min
transcription rate (repressed) ( a0_tr ): tps_repr*60 = 0.03 transcripts/min
translation rate ( k_tl ): eff*kd_mRNA = 6.93 proteins/(mRNA*min)
? : a_tr*eff*? 1/2,prot /(ln(2)*K M ) = 216.4 proteins/(promotor*cell*Km)
? 0 : a0_tr*eff*? 1/2,prot /(ln(2)*K M ) = 0.2164 proteins/(promotor*cell*Km)
? : 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 ).

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.



BIOMD0000000221
Singh2006_TCA_Ecoli_acetate

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.


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: 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.



BIOMD0000000065
Yildirim2003_Lac_Operon

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

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.



BIOMD0000000296
Balagaddé2008_E_coli_Predator_Prey

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 103 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 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.



BIOMD0000000062
Bhartiya2003_Tryptophan_operon

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.

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.



BIOMD0000000051
Chassagnole2002_Carbon_Metabolism

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.

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


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: 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.



BIOMD0000000480
Carbo2013 - Mucosal Immune Response during H.pylori Infection


BIOMD0000000470
Smallbone2013 - E.coli metabolic model with modular rate law
-