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

Using a pathway analysis technique, a dynamic fluctuation relation is derived for a kinetically cooperative biomolecular machine (e.g., an enzyme or a motor protein). This new relation indicates that, in the absence of hidden current, a fluctuation theorem can be established for the first-passage time of the observable process, and we show that this dramatic reduction is a general feature applicable to a wide variety of cooperative networks. This first-passage time fluctuation theorem can be experimentally tested, with its violation serving as a signature of hidden detailed balance breaking. Importantly, we obtain a compact exact expression for the integrated correction to this fluctuation theorem, as well as the general single-loop form, revealing a thermodynamic bound on the kinetic branching ratio (a measure of directionality defined as the forward-to-backward observable process probability ratio). These results provide detailed insight into the rich connections between dynamic measurements and the underlying nonequilibrium thermodynamics for cooperative biomolecular machines.