A mechanism for the generation of robust circadian oscillations through ultransensitivity and differential binding affinity

TL;DR

This paper presents a minimal analytical model of cyanobacterial circadian oscillations, highlighting how ultrasensitivity and differential binding affinity contribute to robustness and stability under varying nutrient conditions.

Contribution

The study introduces a minimal, analytically tractable model incorporating key biophysical features of the KaiABC system, elucidating mechanisms for robust circadian oscillations.

Findings

Ultrasensitivity and differential binding affinity promote robust oscillations.

Biological clocks can maintain a stable period across nutrient variations.

Entropy production alone may not indicate oscillation quality.

Abstract

Biochemical circadian rhythm oscillations play an important role in many signalling mechanisms. In this work, we explore some of the biophysical mechanisms responsible for sustaining robust oscillations by constructing a minimal but analytically tractable model of the circadian oscillations in the KaiABC protein system found in the cyanobacteria $S. \ elongatus$. In particular, our minimal model explicitly accounts for two experimentally characterized biophysical features of the KaiABC protein system, namely, a differential binding affinity and an ultrasensitive response. Our analytical work shows how these mechanisms might be crucial for promoting robust oscillations even in sub optimal nutrient conditions. Our analytical and numerical work also identifies mechanisms by which biological clocks can stably maintain a constant time period under a variety of nutrient conditions. Finally, our work also explores the thermodynamic costs associated with the generation of robust sustained oscillations and shows that the net rate of entropy production alone might not be a good figure of merit to asses the quality of oscillations.