Vilar2002_Oscillator

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.