Filament based intracellular transport involves the collective action of
molecular motor proteins. Experimental evidences suggest that microtubule (MT)
filament bound motor proteins such as {\it kinesins} weakly interact among
themselves during transport and with the surrounding cellular environment.
Motivated by these observations we study a driven lattice gas model for
collective unidirectional transport of molecular motors on open filament, which
incorporates the short-range interactions between the motors on filaments and
couples the transport process on filament with surrounding cellular environment
through adsorption-desorption Langmuir (LK) kinetics of the motors. We analyse
this model within the framework of a Mean Field (MF) theory in the limit of
{\it weak} interactions between the motors. We point to the mapping of this
model with the non-conserved version of Katz-Lebowitz-Spohn (KLS) model. The
system exhibits rich phase behavior with variety of inhomogeneous phases
including localized shocks in the bulk of the filament. We obtain the steady
state density and current profiles and analyse their variation as function of
the strength of interaction. We compare these MF results with Monte Carlo
simulations and find that the MF analysis shows reasonably good agreement as
long as the motors are weakly interacting. We also construct the
non-equilibrium MF phase diagram.Comment: 4 figure
