Reciprocity Between Robustness of Period and Plasticity of Phase in Biological Clocks

TL;DR

This paper reveals a reciprocal relationship between the robustness of circadian clock periods and the plasticity of their phases, showing that adaptations in one aspect influence the other through a linear negative correlation.

Contribution

It demonstrates a fundamental reciprocity mechanism between period robustness and phase plasticity in biological clocks, supported by theoretical models and biological implications.

Findings

Higher period robustness correlates with greater phase plasticity.

Changes in period and phase follow a linear negative relationship.

The adaptation mechanism involves a buffer molecule affecting the limit cycle.

Abstract

Circadian clocks exhibit the robustness of period and plasticity of phase against environmental changes such as temperature and nutrient conditions. Thus far, however, it is unclear how both are simultaneously achieved. By investigating distinct models of circadian clocks, we demonstrate reci- procity between robustness and plasticity: higher robustness in the period implies higher plasticity in the phase, where changes in period and in phase follow a linear relationship with a negative coef- ficient. The robustness of period is achieved by the adaptation on the limit cycle via a concentration change of a buffer molecule, whose temporal change leads to a phase shift following a shift of the limit-cycle orbit in phase space. Generality of reciprocity in clocks with the adaptation mechanism is confirmed with theoretical analysis of simple models, while biological significance is discussed.