Abstract
One-dimensional hopping model is useful to describe the motion of microscopic particle in thermal noise environment, such as motor proteins. Recent experiments about the new generation of light-driven rotary molecular motors found that, the motor in state i can jump forward to state i+1 or i+2, or backward to state i-1 or i-2 directly. In this paper, such modified periodic one-dimensional hopping model of arbitrary period N is studied mathematically. The mean velocity, effective diffusion constant, and mean dwell time in one single cycle are obtained. Corresponding results are illustrated and verified by being applied to a type of synthetic rotary molecular motors.
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