Deterministic and Stochastic Models Analyze the Robustness of Circadian Rhythms

Abstract

The Drosophila circadian oscillator shows a robust property to environmental changes, internal variations, and fluctuations, where two interlocked negative feedback loops play a major role for oscillation [1, 2]. The PER-TIM loop is activated by dCLK-CYC and repressed by PER-TIM, whereas the dCLK loop is repressed by dCLK-CYC and activated by PER-TIM. Not only the molecular architecture, but also the parameters provide the robust property to the oscillator. However, the intrinsic mechanism of how the clock system acquires the robust oscillator remains to be elucidated. In this paper, we aim at understanding how critical the values of parameters is for producing the robust oscillator using a deterministic model, and how the probabilistic fluctuations involve the stable oscillation using a stochastic model [5]. In the deterministic model, we classified the various parameter combinations that produced the cycle of 24 hours. The robust properties depended on the values of the parameters. In the stochastic model, the proper use of fluctuation could make stable oscillations.