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Motivated by a biased diffusion of molecular motors with the bias dependenton the state of the substrate, we investigate a random walk on aone-dimensional lattice that contains weak links (called "bridges'') which areaffected by the walker. Namely, a bridge is destroyed with probability p whenthe walker crosses it; the walker is not allowed to cross it again and thisleads to a directed motion. The velocity of the walker is determinedanalytically for equidistant bridges. The special case of p=1 is more tractable-- both the velocity and the diffusion constant are calculated for uncorrelatedlocations of bridges, including periodic and random distributions.Comment: 11 pages, 7 figure

“Burnt-bridge” mechanism of molecular motor motion