In intracellular transports, motor proteins transport macromolecules as cargos to desired locations by moving on biopolymers such as microtubules. Recent experiments suggest that, while moving in crowded environments, cargos that can associate motor proteins during their translocation have larger run-length and association time compared to free motors. Here, we model the dynamics of a cargo that can associate at the most m free motors present on the microtubule 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. For 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 on the microtubule 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.
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