ABSTRACT:
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.
Nicolas Le Novère 
