In Drosophila, circadian oscillations in the levels of two proteins, PER and TIM, result from the negative feedback exerted by a PER-TIM complex on the expression of the per and tim genes which code for these proteins. per (Mp) and tim (Mt) are synthesized in the nucleus and transferred into the cytoson, where they accumulate at the maximum rates vsp and vst, respectively, and are degraded enzymatically at maximum rates vmp and vmt, with Michaelis constants Kmp and Kmt. The rates of synthesis of the PER and TIM proteins, respectively proportional to Mp and Mt, are characterized by the apparent first-order rate constants ksp and kst. Parameters Vip, Vit and Kip, Kit (i = 1,..4) denote the maximum rates and Michaelis constants of the kinase(s) and phosphatase(s) involved in the reversible phosphorylation of P0(T0) into P1(T1), and P1(T1) into P2(T2), respectively. The fully phosphorylated forms (P2 and T2) are degraded by enzymes of maximum rate Vdp, Vdt, and Michaelis constants Kdp, Kdt, and reversibly form a complex C (with forward and reverse rate constants k3, k4) which is transported into the nucleus at a rate characterized by the apparent first-order rate constant k1. Transport of the nuclear form of the PER-TIM complex (Cn) into the cytosol is characterized by the apparent first-order rate constant k2. The negative feedback exerted by the nuclear PER-TIM complex on per and tim transcription is described by an equation of the Hill type, in which n denotes the degree of cooperativity, and KIp and KIt the thresholds constants for repression.
Leloup JC, Goldbeter A (1999) Chaos and birhythmicity in a model for circadian oscillations of the PER and TIM proteins in Drosophila, J Theor Biol 198:445-459, http://www.sciencedirect.com/.
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