  Movements of molecular motors on cytoskeletal filaments are described by
directed walks on a line. Detachment from this line is allowed to occur with a
small probability. Motion in the surrounding fluid is described by symmetric
random walks. Effects of detachment and reattachment are calculated by an
analytical solution of the master equation. Results are obtained for the
fraction of bound motors, their average velocity and displacement. Enclosing
the system in a finite geometry (tube, slab) leads to an experimentally
realizable problem, that is studied in a continuum description and also
numerically in a lattice simulation.
