Maximal force exerted by a molecular motor.

We consider a particle diffusing in a one-dimensional periodic lattice with arbitrary transition rates between nearest-neighbor sites. We show rigorously 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. Applying this result to a model of a molecular motor introduced by Fisher and Kolomeisky [Proc. Natl. Acad. Sci. USA 96, 6597 (1999)] we show that the so called Einstein force, which sets the lower bound for the force exerted by a molecular motor, is bounded from above by 2k(B)TN/d irrespective of the actual values of the jump rates between internal states of the motor.