Circadian clocks optimally adapt to sunlight for reliable synchronization

TL;DR

This paper analytically investigates how circadian clocks balance entrainability and regularity, revealing that an optimal dead zone in response to sunlight enhances synchronization with the day-night cycle.

Contribution

The study introduces a variational method to derive the optimal phase-response curve, showing that dead zones are essential for circadian clocks to adapt effectively to sunlight.

Findings

Dead zones appear only with realistic solar input patterns.

Optimal circadian clocks include dead zones for better adaptation.

Simple sine models cannot produce dead zones.

Abstract

Circadian oscillation provides selection advantages through synchronization to the daylight cycle. However, a reliable clock must be designed through two conflicting properties: entrainability to synchronize internal time with periodic stimuli such as sunlight, and regularity to oscillate with a precise period. These two aspects do not easily coexist because better entrainability favors higher sensitivity, which may sacrifice the regularity. To investigate conditions for satisfying the two properties, we analytically calculated the optimal phase-response curve with a variational method. Our result indicates an existence of a dead zone, i.e., a time period during which input stimuli neither advance nor delay the clock. A dead zone appears only when input stimuli obey the time course of actual solar radiation but a simple sine curve cannot yield a dead zone. Our calculation demonstrates that every circadian clock with a dead zone is optimally adapted to the daylight cycle.