First-Passage Time Fluctuation Theorem and Thermodynamic Bound in Cooperative Biomolecular Networks

TL;DR

This paper investigates a fluctuation theorem for the first-passage time in cooperative biomolecular networks, revealing conditions for its validity and deriving thermodynamic bounds, with implications for understanding nonequilibrium thermodynamics in biological systems.

Contribution

It introduces a fluctuation theorem applicable to cooperative biomolecular networks and derives a thermodynamic bound on the kinetic branching ratio, supported by a novel pathway analysis technique.

Findings

Fluctuation theorem holds when hidden currents are absent.

Violation indicates hidden detailed balance breaking.

Derived thermodynamic bound constrains kinetic branching ratios.

Abstract

A fluctuation theorem is examined for the first-passage time of a biomolecular machine (e.g., a motor protein or an enzyme) in a nonequilibrium steady-state. For such machines in which the driven, observable process is coupled to a hidden process in a kinetically cooperative fashion, the entropy produced along first-passage trajectories is no longer constant, resulting in a breakdown of this expression. Here, we consider the canonical model for this type of system, a kinetic scheme for conformation-modulated single-enzyme catalysis (a type of continuous-time Markov process with relevance to $\beta$-galactosidase and human glucokinase), as we explore this fluctuation theorem in cooperative biomolecular networks. Kinetic evaluations are performed using a novel, efficient pathway analysis technique, allowing us to attain surprising and concise results from complex calculations. We find that in the absence of hidden current, a fluctuation theorem can be established for the first-passage time of the observable process, and we demonstrate that this dramatic reduction is a general feature applicable to a wide variety of cooperative networks. The validity of this expression can be experimentally tested, with its violation serving as a unique signature of hidden detailed balance breaking. In addition, we obtain a remarkably compact exact expression for the integrated correction to this first-passage time fluctuation theorem, as well as the general form, revealing a thermodynamic bound on the kinetic branching ratio (a measure of directionality defined as the ratio of the forward observable process probability to the backward one). These results provide detailed insight into the rich connections between dynamic measurements and the underlying nonequilibrium thermodynamics for cooperative biomolecular machines.