Chemically driven motility of Brownian particles

A simple model is devised to show that an enzymatic Brownian particle in a static electric field can undergo directional movement when coupled with a nonequilibrium chemical reaction which the particle catalyzes, if at least one of the intermediate states of the catalytic cycle is charged. The direction of the movement depends not only on the asymmetry of the electric field, but also on the direction of the chemical reaction and the mechanism of the catalytic cycle. The Brownian particle can also move against an external load and thus do mechanical work. This study suggests that enzyme molecules could be separated based on their enzymatic activities. The formalism developed in this paper can be extended and applied to biological motors.