  Dynamic properties of molecular motors that fuel their motion by actively
interacting with underlying molecular tracks are studied theoretically via
discrete-state stochastic ``burnt-bridge'' models. The transport of the
particles is viewed as an effective diffusion along one-dimensional lattices
with periodically distributed weak links. When an unbiased random walker passes
the weak link it can be destroyed (``burned'') with probability p, providing a
bias in the motion of the molecular motor. A new theoretical approach that
allows one to calculate exactly all dynamic properties of motor proteins, such
as velocity and dispersion, at general conditions is presented. It is found
that dispersion is a decreasing function of the concentration of bridges, while
the dependence of dispersion on the burning probability is more complex. Our
calculations also show a gap in dispersion for very low concentrations of weak
links which indicates a dynamic phase transition between unbiased and biased
diffusion regimes. Theoretical findings are supported by Monte Carlo computer
simulations.
