The diffusion of a molecular motor in the presence of a constant external force is considered on the basis of a simple theoretical model. The motor is represented by a Brownian particle moving in a series of parabolic potentials placed periodically on a line, and the potential is switched stochastically from one parabola to another by a chemical reaction, which corresponds to the hydrolysis or synthesis of adenosine triphosphate (ATP) in motor proteins. It is found that the diffusion coefficient as a function of the force exhibits peaks. The mechanism of this diffusion enhancement and the possibility of observing it in F 1 -ATPase, a biological rotary motor, are discussed.

A solvable model is proposed and analyzed to reveal the mechanism underlying the diffusion enhancement recently reported for a model of molecular motors and predicted to be observed in the biological rotary motor F1-ATPase. It turns out that the diffusion enhancement for the present model can approximately described by a random walk in which the waiting time for a step to occur is exponentially distributed and it takes nonzero time to proceed forward by the step. It is shown that the diffusion coefficient of such a random walk can significantly be increased when the average waiting time is comparable to the average stepping time.

Diffusion enhancement is a phenomenon in which the diffusion coefficient of a system is increased by an external force and it becomes larger than that of the force-free diffusion in thermal equilibrium. It is known that this phenomenon occurs for a Brownian particle in a periodic potential under a constant external force. Recently, it was found that diffusion enhancement also occurred in a biological molecular motor, whose moving part could move itself by switching the potentials generated by the other parts. It was shown that the diffusion coefficient exhibited peaks as a function of a constant external force. Here, we report the occurrence of an additional peak and investigate the condition governing its appearance.

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