Efficiency of molecular machines with continuous phase space

TL;DR

This paper analyzes the efficiency of molecular machines modeled as Brownian particles in tilted periodic potentials, deriving efficiency at maximum power and comparing coupled and loosely coupled systems.

Contribution

It introduces a method to evaluate power and efficiency of molecular machines with continuous phase space, including explicit calculations for 2-D models.

Findings

Efficiency at maximum power depends on coupling strength.

Loosely coupled machines have lower efficiency at maximum power.

Explicit formulas for efficiency in simple and broad models.

Abstract

We consider a molecular machine described as a Brownian particle diffusing in a tilted periodic potential. We evaluate the absorbed and released power of the machine as a function of the applied molecular and chemical forces, by using the fact that the times for completing a cycle in the forward and the backward direction have the same distribution, and that the ratio of the corresponding splitting probabilities can be simply expressed as a function of the applied force. We explicitly evaluate the efficiency at maximum power for a simple sawtooth potential. We also obtain the efficiency at maximum power for a broad class of 2-D models of a Brownian machine and find that loosely coupled machines operate with a smaller efficiency at maximum power than their strongly coupled counterparts.