  Molecular motors interacting with cytoskeletal filaments undergo peculiar
random walks consisting of alternating sequences of directed movements along
the filaments and diffusive motion in the surrounding solution. An ensemble of
motors is studied which interacts with a single filament in two and three
dimensions. The time evolution of the probability distribution for the bound
and unbound motors is determined analytically. The diffusion of the motors is
strongly enhanced parallel to the filament. The analytical expressions are in
excellent agreement with the results of Monte Carlo simulations.
