Stochastic Thermodynamics of Cooperative Biomolecular Machines: Fluctuation Relations and Hidden Detailed Balance Breaking

TL;DR

This paper develops a stochastic thermodynamics framework to analyze fluctuation relations in cooperative biomolecular machines, revealing how hidden detailed balance breaking affects entropy production and first-passage time fluctuations.

Contribution

It introduces a general condition for fluctuation theorem validity in systems with hidden processes and characterizes the impact of hidden detailed balance breaking on thermodynamic signatures.

Findings

First-passage time fluctuation theorem holds when hidden flux is zero.

Violation of the theorem indicates hidden detailed balance breaking.

Local detailed balance breakdown explains fluctuation theorem violations.

Abstract

We examine a biomolecular machine involving a driven, observable process coupled to a hidden process in a kinetically cooperative manner. A stochastic thermodynamics framework is employed to analyze a fluctuation theorem for the first-passage time of the observable process under nonequilibrium steady-state conditions. Based on a generic kinetic model, we demonstrate that, along first-passage trajectories, entropy production remains constant when the changes in stochastic entropy and free energy of the machine are balanced, which corresponds to zero net hidden flux through the initial state manifold. Under this condition, which we define quite generally, this first-passage time fluctuation theorem can be established, with its violation serving as an experimentally detectable signature of hidden detailed balance breaking (which we subsequently characterize). In addition, using an enzymatic model, we show that the violation of our first-passage time fluctuation theorem can be thought of as a consequence of the breakdown of local detailed balance in the steps linking coarse-grained states that correspond to the initial and intermediate state manifolds. In the absence of hidden current, the fluctuation theorem is restored, and a mesoscopic local detailed balance condition can be established, which has implications for the thermodynamic analysis of driven, coarse-grained systems. This work sheds significant light on the unique connections between stochastic thermodynamic quantities and kinetic measurements in complex cooperative networks.