Robust entrainment of circadian oscillators requires specific phase response curves

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.

References in corpus (2)

• Oscillations in the expression of a self-repressed gene induced by a slow transcriptional dynamics
• A robust two-gene oscillator at the core of Ostreococcus tauri circadian clock

Cited by in corpus (8)

• Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems
• Circadian clocks optimally adapt to sunlight for reliable synchronization
• Switching between oscillations and homeostasis in competing negative and positive feedback motifs
• Period Robustness and Entrainability of the Kai System to Changing Nucleotide Concentrations
• Robustness of clocks to input noise
• Optimal entrainment of circadian clocks in the presence of noise
• Entrainment of noise-induced and limit cycle oscillators under weak noise
• Sensitivity analysis of circadian entrainment in the space of phase response curves