Traffic Jams and Shocks of Molecular Motors inside Cellular Protrusions

Molecular motors are involved in key transport processes inside actin-based cellular protrusions. The motors carry cargo proteins to the protrusion tip which participate in regulating the actin polymerization, and play a key role in facilitating the growth and formation of such protrusions. It is observed that the motors accumulate at the tips of cellular protrusions, and in addition form aggregates that are found to drift towards the protrusion base at the rate of actin treadmilling. We present a one-dimensional driven lattice model, where motors become inactive after delivering their cargo at the tip, or by loosing their cargo to a cargo-less neighbor. The results suggest that the experimental observations may be explained by the formation of traffic jams that form at the tip. The model is solved using a novel application of mean-field and shock analysis. We find a new class of shocks that undergo intermittent collapses, and on average do not obey the Rankine-Hugoniot relation.