  Biopolymers serve as one-dimensional tracks on which motor proteins move to
perform their biological roles. Motor protein phenomena have inspired
theoretical models of one-dimensional transport, crowding, and jamming.
Experiments studying the motion of Xklp1 motors on reconstituted antiparallel
microtubule overlaps demonstrated that motors recruited to the overlap walk
toward the plus end of individual microtubules and frequently switch between
filaments. We study a model of this system that couples the totally asymmetric
simple exclusion process (TASEP) for motor motion with switches between
antiparallel filaments and binding kinetics. We determine steady-state motor
density profiles for fixed-length overlaps using exact and approximate
solutions of the continuum differential equations and compare to kinetic Monte
Carlo simulations. Overlap motor density profiles and motor trajectories
resemble experimental measurements. The phase diagram of the model is similar
to the single-filament case for low switching rate, while for high switching
rate we find a new low density-high density-low density-high density phase. The
overlap center region, far from the overlap ends, has a constant motor density
as one would naively expect. However, rather than following a simple binding
equilibrium, the center motor density depends on total overlap length, motor
speed, and motor switching rate. The size of the crowded boundary layer near
the overlap ends is also dependent on the overlap length and switching rate in
addition to the motor speed and bulk concentration. The antiparallel
microtubule overlap geometry may offer a previously unrecognized mechanism for
biological regulation of protein concentration and consequent activity.
