Sinusoidal regulation reduces circadian period variability

The rhythms transmitted from the circadian clock inevitably fluctuate because of molecular noise. The level of period fluctuations, observed not in the circadian clock, but in the output system that receives the transmitted rhythm, varies according to the organism and cell type, ranging from 0.5% to 10%. However, it remains unclear how the signal transduction involved in this transmission affects the fluctuations in the oscillation period of the output system. To address this, we investigated a coupled system consisting of a circadian clock and its output. We numerically and analytically demonstrated that the rhythmic regulation through which the clock controls downstream gene expression affects the level of fluctuations in the output system. Moreover, Gibbs sampling based on the analytically obtained fluctuation formula confirmed that the sine-wave-like regulatory functions effectively minimized the fluctuation of the output system. These theoretical insights provide new perspectives on signal transduction as a denoising mechanism embodied in the circadian system.