Quantifying fluctuations in reversible enzymatic cycles and clocks

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.

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Cited by in corpus (15)

• Hysteretic thermodynamic uncertainty relation for systems with broken time-reversal symmetry
• The Thermodynamic Uncertainty Relation in Biochemical Oscillations
• Phase transition in thermodynamically consistent biochemical oscillators
• Nonreciprocal Ising model
• Universal minimal cost of coherent biochemical oscillations
• Dynamical phase transitions in the nonreciprocal Ising model
• High chemical affinity increases the robustness of biochemical oscillations
• Precision and dissipation of a stochastic Turing pattern
• Optimal time estimation and the clock uncertainty relation for stochastic processes
• Robust oscillations in multi-cyclic models of biochemical clocks
• Subharmonic oscillations in stochastic systems under periodic driving
• Oscillations in feedback driven systems: thermodynamics and noise
• Stochastic thermodynamics of chemical reactions coupled to finite reservoirs: A case study for the Brusselator
• A case study of thermodynamic bounds for chemical kinetics
• Using precision coefficients on recurrence times and integrated currents to lower bound the average dissipation rate