Energy Transfer in a Molecular Motor in Kramers' Regime

TL;DR

This paper develops a comprehensive theoretical framework for analyzing energy transfer in molecular motors modeled as overdamped Brownian particles in multidimensional tilted periodic potentials, covering various regimes and coupling strengths.

Contribution

It introduces a unified analytical approach using a master equation to describe energy transfer, drift, and diffusion in molecular motors across different regimes and potential complexities.

Findings

Derived explicit expressions for hopping rates, drift, and diffusion.

Established the validity of generalized detailed balance and Onsager relations.

Provided insights into energy transfer mechanisms in non-separable potentials.

Abstract

We present a theoretical treatment of energy transfer in a molecular motor described in terms of overdamped Brownian motion on a multidimensional tilted periodic potential. The tilt acts as a thermodynamic force driving the system out of equilibrium and, for non-separable potentials, energy transfer occurs between degrees of freedom. For deep potential wells, the continuous theory transforms to a discrete master equation that is tractable analytically. We use this master equation to derive formal expressions for the hopping rates, drift, diffusion, efficiency and rate of energy transfer in terms of the thermodynamic force. These results span both strong and weak coupling between degrees of freedom, describe the near and far from equilibrium regimes, and are consistent with generalized detailed balance and the Onsager relations. We thereby derive a number of diverse results for molecular motors within a single theoretical framework.