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]

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