A simple model is devised to show that an enzymatic Brownian particle
in a static electric field can undergo directional movement when coupl
ed with a nonequilibrium chemical reaction which the particle catalyze
s, if at least one of the intermediate states of the catalytic cycle i
s charged. The direction of the movement depends not only on the asymm
etry of the electric field, but also on the direction of the chemical
reaction and the mechanism of the catalytic cycle. The Brownian partic
le 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.