Diffusion Enhancement of Brownian Motors Revealed by a Solvable Model

TL;DR

This paper introduces a solvable model demonstrating how diffusion enhancement in molecular motors occurs, showing that the diffusion coefficient increases when waiting and stepping times are comparable, relevant to biological rotary motors.

Contribution

The paper presents a new solvable model that explains diffusion enhancement in molecular motors through a random walk framework with exponential waiting times.

Findings

Diffusion coefficient increases when waiting and stepping times are comparable.

The model accurately describes diffusion enhancement observed in biological rotary motors.

Waiting time distribution is key to understanding diffusion behavior in molecular motors.

Abstract

A solvable model is proposed and analyzed to reveal the mechanism underlying the diffusion enhancement recently reported for a model of molecular motors and predicted to be observed in the biological rotary motor $\rm F_1$-ATPase. It turns out that the diffusion enhancement for the present model can approximately described by a random walk in which the waiting time for a step to occur is exponentially distributed and it takes nonzero time to proceed forward by the step. It is shown that the diffusion coefficient of such a random walk can significantly be increased when the average waiting time is comparable to the average stepping time.