  Many biological processes are supported by special molecules, called motor
proteins or molecular motors, that transport cellular cargoes along linear
protein filaments and can reversibly associate to their tracks. Stimulated by
these observations, we developed a theoretical model for collective dynamics of
biological molecular motors that accounts for local association/dissociation
events. In our approach, the particles interacting only via exclusion move
along a lattice in the preferred direction, while the reversible associations
are allowed at the specific site far away from the boundaries. Considering the
association/dissociation site as a local defect, the inhomogeneous system is
approximated as two coupled homogeneous sub-lattices. This allows us to obtain
a full description of stationary dynamics in the system. It is found that the
number and nature of steady-state phases strongly depend on the values of
association and dissociation transition rates. Microscopic arguments to explain
these observations, as well as biological implications, are also discussed.
Theoretical predictions agree well with extensive Monte Carlo computer
simulations.
