Quantifying fluctuations in reversible enzymatic cycles and clocks

TL;DR

This paper analyzes fluctuations in reversible biochemical cycles, providing analytical tools and linking cycle timing precision to thermodynamic principles, thereby enhancing understanding of molecular noise in biological systems.

Contribution

It introduces a unified approach to quantify fluctuations in reversible enzymatic cycles and connects these fluctuations to thermodynamic uncertainty relations.

Findings

Equivalence of two classical definitions of the randomness parameter in reversible cycles

Analytical solutions for the moments of the stochastic period

Thermodynamic uncertainty relation constrains cycle timing precision

Abstract

Biochemical reactions are fundamentally noisy at a molecular scale. This limits the precision of reaction networks, but also allows fluctuation measurements which may reveal the structure and dynamics of the underlying biochemical network. Here, we study non-equilibrium reaction cycles, such as the mechanochemical cycle of molecular motors, the phosphorylation cycle of circadian clock proteins, or the transition state cycle of enzymes. Fluctuations in such cycles may be measured using either of two classical definitions of the randomness parameter, which we show to be equivalent in general microscopically reversible cycles. We define a stochastic period for reversible cycles and present analytical solutions for its moments. Furthermore, we associate the two forms of the randomness parameter with the thermodynamic uncertainty relation, which sets limits on the timing precision of the cycle in terms of thermodynamic quantities. Our results should prove useful also for the study of temporal fluctuations in more general networks.