  In intracellular transports, motor proteins transport macromolecules as
cargos to desired locations by moving on biopolymers such as microtubules.
Recent experiments suggest that cargos that can associate motor proteins during
their translocation have larger run-length, association time and can overcome
the motor traffic on microtubule tracks. Here, we model the dynamics of a cargo
that can associate at the most m free motors present on the track as obstacles
to its motion. The proposed models display competing effects of association and
crowding, leading to a peak in the run-length with the free motor density. This
result is consistent with past experimental observations. For m=2 and 3, we
show that this feature is governed by the largest eigenvalue of the transition
matrix describing the cargo dynamics. In all the above cases, free motors are
assumed to be present as stalled obstacles. We finally compare simulation
results for the run-length for general scenarios where the free motors undergo
processive motion in addition to binding and unbinding to or from the
microtubule.
