On the First-Passage Time Fluctuation Theorem in Complex Biomolecular Networks (2501.09087v1)

Abstract: A fluctuation theorem is examined for the first-passage time of a biomolecular machine 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 uniform, resulting in a breakdown of this relation. Here, we consider the canonical model for this type of system, a kinetic scheme for conformation-modulated single-enzyme catalysis, as we (i) determine the circumstances under which this fluctuation theorem can be restored; (ii) assess what its violation reveals about the hidden dynamics; and (iii) characterize the general form of the deviation from this relation. Kinetic evaluations are performed using a novel, efficient pathway analysis technique, allowing us to attain some surprising and fairly straightforward results from relatively complex calculations. We find that in the absence of hidden current, a fluctuation theorem can be written for the first-passage time of the observable process, and we demonstrate that this is a general feature applicable to a wide variety of complex networks. The validity of this relation can be experimentally tested, with its violation serving as a 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, which indicates that the kinetic branching ratio, defined as the ratio of the forward observable process probability to the backward one, is bounded by the entropy production associated with the first-passage work (i.e., the work applied along a first-passage trajectory). These results provide detailed insight into the rich connections between dynamic measurements and the underlying nonequilibrium thermodynamics in complex biomolecular networks.

• The paper examines the first-passage time fluctuation theorem in complex biomolecular networks and shows how its failure can detect hidden detailed balance breaking.
• A key finding provides an exact expression showing the kinetic branching ratio is limited by first-passage work-associated entropy production.
• The study bridges experimental kinetics and nonequilibrium thermodynamics, offering an analytical method to detect hidden dynamics in biomolecular systems.

Overview of First-Passage Time Fluctuation Theorem in Complex Biomolecular Networks

The paper "On the First-Passage Time Fluctuation Theorem in Complex Biomolecular Networks" by D. Evan Piephoff and Jianshu Cao rigorously examines the fluctuation theorem for first-passage time concerning biomolecular machines, particularly those operating under nonequilibrium steady-state (NESS) conditions. The primary focus is on systems where the observable process is kinetically coupled to a hidden process, challenging traditional entropy production paradigms.

The paper dissects the canonical model of conformation-modulated single-enzyme catalysis, representing a continuous-time Markov chain of both theoretical and experimental interest. The authors explore specific conditions under which the first-passage time fluctuation theorem can be maintained, the insights gleaned from its failure, and the general nature of deviations from expected relations in these complex biomolecular settings.

Key Findings and Methodological Approach

Piephoff and Cao employ a novel and efficient pathway analysis technique that simplifies into the transition rate matrix method, enabling them to navigate intricate calculations with surprising clarity. A critical revelation is that a fluctuation theorem that maintains validity in the absence of a hidden current in the observable process can be applied to a diverse array of complex networks. This theorem restoration is experimentally testable; its failure indicates hidden detailed balance breaking, providing a direct observable signature of such disruptions.

Remarkably, the authors derive a compact exact expression for the integrated correction to this first-passage time fluctuation theorem. It reveals the kinetic branching ratio, defined as the observational process's forward to backward probability, is restricted by the first-passage work-associated entropy production. Notably, the kinetic branching ratio cannot surpass this thermodynamic limit, aligning with intuitive understanding but within the context of hidden dynamics.

Implications and Future Directions

This paper bridges experimental kinetic observations with underlying nonequilibrium thermodynamic principles in complex biomolecular networks. The findings emphasize the nuances involved when an observable biomolecular process operates in tandem with hidden dynamics, challenging assumptions of uniform entropy distribution along first-passage trajectories.

The implications for biomolecular and enzymatic studies are vast. By providing an analytical lens to detect nonequilibrium hidden dynamics, the paper sets forth a paradigm where such intricate couplings become crucial experimental markers. Scientists can leverage these theoretical insights in practical settings, exploring conditions under which traditional entropy-centric narratives align or conflict with observable results.

Future research, as indicated by the authors, will focus on demystifying this signature of hidden detailed balance breaking. Additionally, the aim will be to establish broader applicability across more generalized driven processes interfaced with concealed dynamics, enriched by stochastic thermodynamics frameworks. Such expansions promise significant contributions to the field, enhancing the understanding of biomolecular machine operations within living systems, providing clarity to their thermodynamic characterization under NESS.