Optimal number of disperse states in the model of Brownian motors

An N-state discrete model for studying the directed motion of a molecular motor is proposed, where the distribution of the states is used to describe the asymmetry of a ratchet potential. The whole system flashes between the potential on and off, and the particle transits asymmetrically in the forward and backward directions along the track. The current, diffusion constant, Peclet number and efficiency are calculated by solving numerically the master equation. The results show that the current direction of the Brownian motor can be reversed due to competition between the potential flashing and the particle asymmetrical transiting. Under some conditions, we can find an optimal number of discrete states, which maximizes the current.