Robust entrainment of circadian oscillators requires specific phase response curves

TL;DR

This paper investigates how the shape of phase response curves (PRCs) influences the robustness of circadian clocks to environmental fluctuations, revealing evolutionary adaptations for maintaining accurate biological timekeeping.

Contribution

It establishes a general relationship between PRC shape and robustness of circadian entrainment, supported by analysis of experimental PRCs across multiple organisms.

Findings

PRC shape determines stability and phase shift robustness

Experimental PRCs suggest convergent evolution towards optimal PRC shapes

Theoretical models link PRC curvature to entrainment robustness

Abstract

The circadian clocks keeping time of day in many living organisms rely on self-sustained biochemical oscillations which can be entrained by external cues, such as light, to the 24-hour cycle induced by Earth rotation. However, environmental cues are unreliable due to the variability of habitats, weather conditions or cue-sensing mechanisms among individuals. A tempting hypothesis is that circadian clocks have evolved so as to be robust to fluctuations in daylight or other cues when entrained by the day/night cycle. To test this hypothesis, we analyze the synchronization behavior of weakly and periodically forced oscillators in terms of their phase response curve (PRC), which measures phase changes induced by a perturbation applied at different phases. We establish a general relationship between, on the one side, the robustness of key entrainment properties such as stability and phase shift and, on the other side, the shape of the PRC as characterized by a specific curvature or the existence of a dead zone. This result can be applied to computational models of circadian clocks where it accounts for the disparate robustness properties of various forcing schemes. Finally, the analysis of PRCs measured experimentally in several organisms strongly suggests a case of convergent evolution toward an optimal strategy for maintaining a clock that is accurate and robust to environmental fluctuations.