Abstract
Focusing on the directed transport phenomena of the two-headed molecular motor, we adopt power function as the damping kernel function of general Langevin equation due to the power-law memory characteristics of cytosol in biological cells and present the model of fractional coupling Brownian motor in overdamped condition in this paper. We also discuss the influences of fractional order and coupling factor on the transport speed. From the simulation results there are found the directed transport phenomena and the inverse transport which is not seen in the conventional Brownian motor, in the overdamped fractional coupling Brownian motor. When the noise density is fixed, the generalized stochastic resonance appears when transport speed varies with the fractional order and coupling factor. In particular, the results reveal that the magnitude and direction of the directional flow are controlled by coupling the noise with the interaction force between the two heads, which is the movement characteristic of the two-headed molecular motor in the memory ratchet, rather than of the single-headed motor.
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