A Reversibility Parameter for a Markovian Stepper

TL;DR

This paper introduces a reversibility parameter for molecular motors based on the characteristic distance, which helps determine whether the motor's motion is reversible or not, even with limited observational data.

Contribution

It proposes a Langevin model with a hidden degree of freedom to relate the characteristic distance to the reversibility of molecular motors.

Findings

The ratio of characteristic distance to step size equals one for one-dimensional dominant paths.

Deviations from unity indicate branched dominant paths.

The parameter can assess motor reversibility from restricted observations.

Abstract

Recent experimental studies on the stepwize motion of biological molecular motors have revealed that the ``characteristic distance'' of a step is usually less than the actual step size. This observation implies that the detailed-balance condition for kinetic rates of steps is violated in these motors. In this letter, in order to clarify the significance of the characteristic distance, we study a Langevin model of a molecular motor with a hidden degree of freedom. We find that the ratio of the characteristic distance to the step size is equal to unity if the dominant paths in the state space are one dimensional, while it deviates from unity if the dominant paths are branched. Therefore, this parameter can be utilized to determine the reversibility of a motor even under a restricted observation.