Self-organized density patterns of molecular motors in arrays of cytoskeletal filaments

The stationary states of systems with many molecular motors are studied theoretically for uniaxial and centered (asterlike) arrangements of cytoskeletal filaments using Monte Carlo simulations and a two-state model. Mutual exclusion of motors from binding sites of the filaments is taken into account. For small overall motor concentration, the density profiles are exponential and algebraic in uniaxial and centered filament systems, respectively. For uniaxial systems, exclusion leads to the coexistence of regions of high and low densities of bound motors corresponding to motor traffic jams, which grow upon increasing the overall motor concentration. These jams are insensitive to the motor behavior at the end of the filament. In centered systems, traffic jams remain small and an increase in the motor concentration leads to a flattening of the profile if the motors move inwards, and to the buildup of a concentration maximum in the center of the aster if motors move outwards. In addition to motor density patterns, we also determine the corresponding patterns of the motor current.