Robust oscillations in multi-cyclic models of biochemical clocks

TL;DR

This paper investigates how biochemical clocks maintain robust oscillations despite stochastic fluctuations by analyzing complex Markov models with multiple cycles, revealing that higher energy budgets enhance robustness and degeneracy.

Contribution

It extends previous models to include multiple small cycles, providing analytical predictions for oscillation period and coherence, and shows high energy budgets improve robustness.

Findings

High energy budgets lead to degeneracy in network topologies regarding oscillation properties.

Analytical predictions match numerical simulations, confirming the theory.

Multiple cycles can be effectively mapped to single-cycle models for analysis.

Abstract

Organisms often use cyclic changes in the concentrations of chemicals species to precisely time biological functions. Underlying these biochemical clocks are chemical reactions and transport processes, which are inherently stochastic. Understanding the physical basis for robust biochemical oscillations in the presence of fluctuations has thus emerged as an important problem. In a previous paper [C. del Junco and S. Vaikuntanathan, Phys. Rev. E 101, 012410 (2020)], we explored this question using the non-equilibrium statistical mechanics of single-ring Markov state models of biochemical networks that support oscillations. Our finding was that they can exploit non-equilibrium driving to robustly maintain the period and coherence of oscillations in the presence of randomness in the rates. Here, we extend our work to Markov state models consisting of a large cycle decorated with multiple small cycles. These additional cycles are intended to represent alternate pathways that the oscillator may take as it fluctuates about its average path. Combining a mapping to single-cycle networks based on first passage time distributions with our previously developed theory, we are able to make analytical predictions for the period and coherence of oscillations in these networks. One implication of our predictions is that a high energy budget can make different network topologies and arrangements of rates degenerate as far as the period and coherence of oscillations is concerned. Excellent agreement between analytical and numerical results confirms that this is the case. Our results suggest that biochemical oscillators can be more robust to fluctuations in the path of the oscillator when they have a high energy budget.