  Motivated by a biased diffusion of molecular motors with the bias dependent
on the state of the substrate, we investigate a random walk on a
one-dimensional lattice that contains weak links (called "bridges'') which are
affected by the walker. Namely, a bridge is destroyed with probability p when
the walker crosses it; the walker is not allowed to cross it again and this
leads to a directed motion. The velocity of the walker is determined
analytically for equidistant bridges. The special case of p=1 is more tractable
-- both the velocity and the diffusion constant are calculated for uncorrelated
locations of bridges, including periodic and random distributions.
