  The flow of motor proteins on a filamental track is modelled within the the
framework of lattice driven diffusive systems. Motors, considered as hopping
particles, perform a highly biased asymmetric exclusion process when bound to
the filament. With a certain rate, they detach from the filament and execute
unbiased random walk in the bulk which is considered as a closed cubic
compartment. Motors are injected (extracted) from the leftmost (rightmost) site
of the filament located along the symmetry axis of the compartment. We explore
the transport properties of this system and investigate the bulk-boundary
interplay on the system stationary states. It is shown that the detachment rate
notably affects the system properties. In particular and in contrast to ASEP,
it is shown that the density profile of bound particles exhibit different types
of non monotonic behaviours when the detachment rate varies. It is shown that
in certain situations, the density profile of the filament consists of
coexisting high and low regions.
