Thermal Fluctuation Statistics in a Molecular Motor Described by a Multidimensional Master Equation

TL;DR

This paper models thermal fluctuations in a molecular motor using a multidimensional master equation, revealing how energy transfer correlations and coupling strength influence fluctuation statistics and motor behavior.

Contribution

It introduces a multidimensional master equation framework to analyze thermal fluctuations and correlations in molecular motors, including formal expressions and simulations for different coupling regimes.

Findings

Fluctuation statistics reveal different operating regimes.

Strong coupling simplifies to a one-dimensional description.

Simulations match theoretical predictions across regimes.

Abstract

We present a theoretical investigation of thermal fluctuation statistics in a molecular motor. Energy transfer in the motor is described using a multidimensional discrete master equation with nearest-neighbor hopping. In this theory, energy transfer leads to statistical correlations between thermal fluctuations in different degrees of freedom. For long times, the energy transfer is a multivariate diffusion process with a constant drift and diffusion. The fluctuations and drift align in the strong-coupling limit enabling a one-dimensional description along the coupled coordinate. We derive formal expressions for the probability distribution and simulate single trajectories of the system in the near and far from equilibrium limits both for strong and weak coupling. Our results show that the hopping statistics provide an opportunity to distinguish different operating regimes.