The free energy cost of accurate biochemical oscillations

TL;DR

This paper reveals a universal relationship between thermodynamic cost and accuracy in biochemical oscillations, showing that energy dissipation limits phase fluctuations across different systems.

Contribution

It demonstrates that phase diffusion in biochemical oscillations inversely relates to free energy dissipation, providing a unified analytical and experimental framework.

Findings

Phase diffusion constant inversely proportional to free energy dissipation per period.

Multiple irreversible cycles drive oscillations, hydrolyzing ATP.

Number of coherent periods scales with energy consumed per cycle.

Abstract

Oscillation is an important cellular process that regulates timing of different vital life cycles. However, in the noisy cellular environment, oscillations can be highly inaccurate due to phase fluctuations. It remains poorly understood how biochemical circuits suppress phase fluctuations and what is the incurred thermodynamic cost. Here, we study four different types of biochemical oscillations representing three basic oscillation motifs shared by all known oscillatory systems. We find that the phase diffusion constant follows the same inverse dependence on the free energy dissipation per period for all systems studied. This relationship between the phase diffusion and energy dissipation is shown analytically in a model of noisy oscillation. Microscopically, we find that the oscillation is driven by multiple irreversible cycles that hydrolyze the fuel molecules such as ATP; the number of phase coherent periods is proportional to the free energy consumed per period. Experimental evidence in support of this universal relationship and testable predictions are also presented.