Fluctuations, Responses and Energetics of Molecular Motors

TL;DR

This paper introduces a new equality linking energy dissipation to the violation of the fluctuation-response relation in nonequilibrium systems, with applications to molecular motors like kinesin.

Contribution

It provides a comprehensive explanation of the fluctuation-response relation, its violation, and a novel equality connecting these to energy dissipation in molecular motor models.

Findings

Derived a new equality relating energy dissipation to FRR violation.

Applied the theory to predict a time constant for KIF1A kinesin.

Discussed experimental implications for molecular motor studies.

Abstract

A novel equality relating the rate of energy dissipation to a degree of violation of the fluctuation-response relation (FRR) in nonequilibrium Langevin systems is described. The FRR is a relation between the correlation function of the fluctuations and the response function of macroscopic variables. Although it has been established that the FRR holds in equilibrium, physical significance of violation of the FRR in nonequilibrium systems has been under debate. Recently, the authors have found that an extent of the FRR violation is related in a simple equality to the rate of energy dissipation into the environment in nonequilibrium Langevin systems. In this paper, we fully explain the FRR, the FRR violation, and the new equality with regard to a Langevin model termed a Brownian motor model, which is considered as a simple model of a biological molecular motor. Furthermore, applications of our result to experimental studies of molecular motors are discussed, and, as an illustration, we predict the value of a new time constant regarding the motion of a KIF1A, which is a kind of single-headed kinesin.