Asymmetric cycling and biased movement of Brownian particles in fluctuating symmetric potentials

Brownian particles can be induced to undergo biased movement by a fluctuating periodic potential, if the potential within each period is asymmetric. In this Letter, we show that similar phenomenon can be obtained even when the periodic potential is symmetric, if (i) there are at least three states for the potential to fluctuate, (ii) the extrema of the nonflat potentials are properly shifted, and (iii) the potential is fluctuating among the states in a cyclic way. We found that biased movement occurs only when net cycling is present and the direction of the movement is closely related to that of the net cycling, similar to the movement of a chemically driven enzyme particle in a static periodic potential. The formalism and the model can be used in studying the movement of a bead on a microtubule filament powered by a single one-headed kinesin. [S0031-9007(97)04385-8].