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BIOMD0000000035 - Vilar2002_Oscillator

 

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Reference Publication
Publication ID: 11972055
Vilar JM, Kueh HY, Barkai N, Leibler S.
Mechanisms of noise-resistance in genetic oscillators.
Proc. Natl. Acad. Sci. U.S.A. 2002 Apr; 99(9): 5988-5992
Howard Hughes Medical Institute, Department of Molecular Biology and Physics, Princeton University, Princeton, NJ 08544, USA.  [more]
Model
Original Model: BIOMD0000000035.origin
Submitter: Nicolas Le Novère
Submission ID: MODEL6619651140
Submission Date: 13 Sep 2005 14:54:33 UTC
Last Modification Date: 03 Jun 2013 14:58:11 UTC
Creation Date: 30 Jun 2005 11:20:37 UTC
Encoders:  Nicolas Le Novère
   Bruce Shapiro
set #1
bqbiol:hasTaxon Taxonomy cellular organisms
set #2
bqbiol:isVersionOf Gene Ontology regulation of circadian rhythm
Notes

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] == -(deltaA*A[t]) - gammaA*A[t]*DA[t] + thetaA*DAp[ t] - gammaR*A[t]*DR[t] + thetaR*DRp[t] + betaA*MA[t] -  gammaC*A[t]*R[t]
C 0 C'[t] == -(deltaA*C[t]) + gammaC*A[t]*R[t]
DA 1 DA'[t] == -(gammaA*A[t]*DA[t]) + thetaA*DAp[t]
DAp 0 DAp'[t] == gammaA*A[t]*DA[t] - thetaA*DAp[t]
DR 1 DR'[t] == -(gammaR*A[t]*DR[t]) + thetaR*DRp[t]
DRp 0 DRp'[t] == gammaR*A[t]*DR[t] - thetaR*DRp[t]
MA 0 MA'[t] == alphaA*DA[t] + alphaAp*DAp[t] - deltaMA*MA[t]
MR 0 MR'[t] == alphaR*DR[t] + alphaRp*DRp[t] - deltaMR*MR[t]
R 0 R'[t] == deltaA*C[t] + betaR*MR[t] - deltaR*R[t] -  gammaC*A[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 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.

Model
Publication ID: 11972055 Submission Date: 13 Sep 2005 14:54:33 UTC Last Modification Date: 03 Jun 2013 14:58:11 UTC Creation Date: 30 Jun 2005 11:20:37 UTC
Mathematical expressions
Reactions
Reaction1 Reaction2 Reaction3 Reaction4
Reaction5 Reaction6 Reaction7 Reaction8
Reaction9 Reaction10 Reaction11 Reaction12
Reaction13 Reaction14 Reaction15 Reaction16
Physical entities
Compartments Species
deterministicOscillator EmptySet A C
DA DAp DR
DRp MA MR
R    
Reactions (16)
 
 Reaction1 [A] + [R] → [C];  
 
 Reaction2 [A] → [EmptySet];  
 
 Reaction3 [C] → [R];  
 
 Reaction4 [R] → [EmptySet];  
 
 Reaction5 [A] + [DA] → [DAp];  
 
 Reaction6 [DAp] → [A] + [DA];  
 
 Reaction7 [DA] → [DA] + [MA];  
 
 Reaction8 [DAp] → [DAp] + [MA];  
 
 Reaction9 [MA] → [EmptySet];  
 
 Reaction10 [MA] → [A] + [MA];  
 
 Reaction11 [A] + [DR] → [DRp];  
 
 Reaction12 [DRp] → [A] + [DR];  
 
 Reaction13 [DR] → [DR] + [MR];  
 
 Reaction14 [DRp] → [DRp] + [MR];  
 
 Reaction15 [MR] → [EmptySet];  
 
 Reaction16 [MR] → [MR] + [R];  
 
   Spatial dimensions: 3.0  Compartment size: 1.0
 
   EmptySet
Compartment: deterministicOscillator
Initial amount: 0.0
 
 A
Compartment: deterministicOscillator
Initial amount: 0.0
 
 C
Compartment: deterministicOscillator
Initial amount: 0.0
 
   DA
Compartment: deterministicOscillator
Initial amount: 1.0
 
   DAp
Compartment: deterministicOscillator
Initial amount: 0.0
 
   DR
Compartment: deterministicOscillator
Initial amount: 1.0
 
   DRp
Compartment: deterministicOscillator
Initial amount: 0.0
 
 MA
Compartment: deterministicOscillator
Initial amount: 0.0
 
 MR
Compartment: deterministicOscillator
Initial amount: 0.0
 
 R
Compartment: deterministicOscillator
Initial amount: 0.0
 
Reaction1 (1)
 
   gammaC
Value: 2.0
Constant
 
Reaction2 (1)
 
   deltaA
Value: 1.0
Constant
 
Reaction3 (1)
 
   deltaA
Value: 1.0
Constant
 
Reaction4 (1)
 
   deltaR
Value: 0.2
Constant
 
Reaction5 (1)
 
   gammaA
Value: 1.0
Constant
 
Reaction6 (1)
 
   thetaA
Value: 50.0
Constant
 
Reaction7 (1)
 
   alphaA
Value: 50.0
Constant
 
Reaction8 (1)
 
   alphaAp
Value: 500.0
Constant
 
Reaction9 (1)
 
   deltaMA
Value: 10.0
Constant
 
Reaction10 (1)
 
   betaA
Value: 50.0
Constant
 
Reaction11 (1)
 
   gammaR
Value: 1.0
Constant
 
Reaction12 (1)
 
   thetaR
Value: 100.0
Constant
 
Reaction13 (1)
 
   alphaR
Value: 0.01
Constant
 
Reaction14 (1)
 
   alphaRp
Value: 50.0
Constant
 
Reaction15 (1)
 
   deltaMR
Value: 0.5
Constant
 
Reaction16 (1)
 
   betaR
Value: 5.0
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000035

Curator's comment: (updated: 27 Aug 2009 14:33:03 GMT)

Figure 2AB reproduced with Copasi 4.5 (build 30).

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