Robustness of clocks to input noise

TL;DR

This paper compares the robustness of limit-cycle oscillators and hourglass models in biological clocks under noisy input conditions, showing limit-cycle oscillators are more reliable in high-noise environments.

Contribution

It introduces a comparative analysis of different biological clock models, demonstrating the superior noise resilience of limit-cycle oscillators over hourglass models.

Findings

Limit-cycle oscillators outperform hourglass models under high input noise.

All models are equally informative at low noise levels.

The universality of results is confirmed using the Stuart-Landau model.

Abstract

To estimate the time, many organisms, ranging from cyanobacteria to animals, employ a circadian clock which is based on a limit-cycle oscillator that can tick autonomously with a nearly 24h period. Yet, a limit-cycle oscillator is not essential for knowing the time, as exemplified by bacteria that possess an 'hourglass': a system that when forced by an oscillatory light input exhibits robust oscillations from which the organism can infer the time, but that in the absence of driving relaxes to a stable fixed point. Here, using models of the Kai system of cyanobacteria, we compare a limit- cycle oscillator with two hourglass models, one that without driving relaxes exponentially and one that does so in an oscillatory fashion. In the limit of low input-noise, all three systems are equally informative on time, yet in the regime of high input-noise the limit-cycle oscillator is far superior. The same behavior is found in the Stuart-Landau model, indicating that our result is universal.