Enhanced entrainability of genetic oscillators by period mismatch

TL;DR

This study demonstrates that period mismatch in genetic oscillators enhances their ability to synchronize with external signals, suggesting biological systems may exploit this mismatch for improved function.

Contribution

The paper reveals that period mismatch actively improves entrainability in genetic oscillators, a novel insight into the functional benefits of multiple feedback loops.

Findings

Period mismatch enhances oscillator entrainability.

Optimal period ratio aligns with experimental observations.

Active benefits of period mismatch increase oscillator efficiency.

Abstract

Biological oscillators coordinate individual cellular components so that they function coherently and collectively. They are typically composed of multiple feedback loops, and period mismatch is unavoidable in biological implementations. We investigated the advantageous effect of this period mismatch in terms of a synchronization response to external stimuli. Specifically, we considered two fundamental models of genetic circuits: smooth- and relaxation oscillators. Using phase reduction and Floquet multipliers, we numerically analyzed their entrainability under different coupling strengths and period ratios. We found that a period mismatch induces better entrainment in both types of oscillator; the enhancement occurs in the vicinity of the bifurcation on their limit cycles. In the smooth oscillator, the optimal period ratio for the enhancement coincides with the experimentally observed ratio, which suggests biological exploitation of the period mismatch. Although the origin of multiple feedback loops is often explained as a passive mechanism to ensure robustness against perturbation, we study the active benefits of the period mismatch, which include increasing the efficiency of the genetic oscillators. Our findings show a qualitatively different perspective for both the inherent advantages of multiple loops and their essentiality.