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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 . T…
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