A reversibility parameter for a Markovian stepper

¹ Department of Human and Artificial Intelligent Systems, University of Fukui - Fukui 910-8507, Japan
² College of Science, Ibaraki University - Mito 310-8512, Japan

Received: 18 September 2006
Accepted: 16 April 2007

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.