  Transport of molecular motors, stimulated by interactions with specific links
between consecutive binding sites (called ``bridges''), is investigated
theoretically by analyzing discrete-state stochastic ``burnt-bridge'' models.
When an unbiased diffusing particle crosses the bridge, the link can be
destroyed (``burned'') with a probability $p$, creating a biased directed
motion for the particle. It is shown that for probability of burning $p=1$ the
system can be mapped into one-dimensional single-particle hopping model along
the periodic infinite lattice that allows one to calculate exactly all dynamic
properties. For general case of $p<1$ a new theoretical method is developed,
and dynamic properties are computed explicitly. Discrete-time and
continuous-time dynamics, periodic and random distribution of bridges and
different burning dynamics are analyzed and compared. Theoretical predictions
are supported by extensive Monte Carlo computer simulations. Theoretical
results are applied for analysis of the experiments on collagenase motor
proteins.
