General relation between drift velocity and dispersion of a molecular motor

TL;DR

This paper derives an upper bound relating the drift velocity and diffusion coefficient of a molecular motor modeled as a particle on a periodic lattice, aiding in estimating internal states and force limits.

Contribution

It provides a simple proof of a theorem linking drift velocity and diffusion in molecular motors, establishing an upper bound useful for estimating motor properties.

Findings

The ratio V/D is bounded above by 2N/d.

The relation helps estimate the minimal internal states of the motor.

It allows approximation of the maximal force exerted by the motor.

Abstract

We model a processive linear molecular motor as a particle diffusing in a one-dimensional periodic lattice with arbitrary transition rates between its sites. We present a relatively simple proof of a theorem which states that the ratio of the drift velocity V to the diffusion coefficient D has the upper bound 2N/d, where N is the number of nodes in an elementary cell and d denotes its length. This relation can be used to estimate the minimal value of internal states of the motor and the maximal value of the so called Einstein force, which approximately equals to the maximal force exerted by a molecular motor.