Sinusoidal regulation denoises circadian machinery

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. Author summaryRecent single-cell observations have revealed that individual cells exhibit circadian rhythms with intrinsic variability. In particular, the period fluctuation, evaluated using the coefficient of variation (CV), was studied. In this study, we investigated how signal transduction from the central clock affects period fluctuations in the output system. We identified a key factor influencing these fluctuations: the waveform of the regulatory function by which the circadian clock governs the downstream output. We numerically demonstrated that the fluctuations vary widely depending on the regulatory function and that the sinusoidal function significantly reduced fluctuations in the output system. Furthermore, Gibbs sampling revealed that sine-like regulatory functions effectively minimized fluctuations. These findings suggest a preference for near-sinusoidal waveforms in the regulation of circadian rhythms.