Waveform distortion for temperature compensation and synchronization in circadian rhythms: An approach based on the renormalization group method

Numerous biological processes accelerate as temperatures increase, but the period of circadian rhythms remains constant, known as temperature compensation, while synchronizing with the 24h light-dark cycle. We theoretically explore the possible relevance of waveform distortions in circadian gene-protein dynamics to the temperature compensation and synchronization. Our analysis of the Goodwin model provides a coherent explanation of most of temperature compensation hypotheses. Using the renormalization group method, we analytically demonstrate that the decreasing phase of circadian protein oscillations should lengthen with increasing temperature, leading to waveform distortions to maintain a stable period. This waveform-period correlation also occurs in other oscillators like Lotka-Volterra, van der Pol models, and a realistic model for mammalian circadian rhythms. A reanalysis of known data nicely confirms our findings on waveform distortion and its impact on synchronization range. Thus we conclude that circadian rhythm waveforms are fundamental to both temperature compensation and synchronization.