Stochastic models for circadian oscillations: Emergence of a biological rhythm

Nearly all living organisms display circadian oscillations characterized by a period close to 24 h. These rhythms originate from the negative autoregulation of gene expression. Deterministic models based on such genetic regulatory processes account for the occurrence of circadian rhythms in constant environmental conditions (e.g., constant darkness), for entrainment of these rhythms by light-dark cycles, and for their phase-shifting by light pulses. When the numbers of protein and mRNA molecules involved in the oscillations are small, as may occur in cellular conditions, it becomes necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. We address the effect of molecular noise by considering the stochastic version of a core deterministic model previously proposed for circadian oscillations of the PER protein and its mRNA in Drosophila. The model is based on cooperative repression of the per gene by the PER protein. Numerical simulations of the stochastic version of the model are performed by means of the Gillespie method. The predictions of the stochastic approach compare well with those of the deterministic model with respect to both sustained oscillations of the limit cycle type and the influence of the proximity from a bifurcation point below which the system evolves to a stable steady state. Stochastic simulations indicate that robust circadian oscillations can emerge at the cellular level, even when the maximum numbers of mRNA and protein molecules involved in the oscillations are of the order of only a few tens or hundreds. The stochastic simulations also reproduce the evolution toward a strange attractor in conditions where an extended version of the deterministic model admits chaotic behavior. These results show how regulatory feedback processes at the cellular level allow the emergence of a coherent biological rhythm out of molecular noise. (C) 2004 Wiley Periodicals, Inc.