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We study the dynamics of membrane vesicle motor transport into dendriticspines, which are bulbous intracellular compartments in neurons that play a keyrole in transmitting signals between neurons. We consider the stochastic analogof the vesicle transport model in [Park and Fai, The Dynamics of VesiclesDriven Into Closed Constrictions by Molecular Motors. Bull. Math. Biol. 82, 141(2020)]. The stochastic version, which may be considered as an agent-basedmodel, relies mostly on the action of individual myosin motors to producevesicle motion. To aid in our analysis, we coarse-grain this agent-based modelusing a master equation combined with a partial differential equationdescribing the probability of local motor positions. We confirm throughconvergence studies that the coarse-graining captures the essential features ofbistability in velocity (observed in experiments) and waiting-timedistributions to switch between steady-state velocities. Interestingly, theseresults allow us to reformulate the translocation problem in terms of the meanfirst passage time for a run-and-tumble particle moving on a finite domain withabsorbing boundaries at the two ends. We conclude by presenting numerical andanalytical calculations of vesicle translocation.

Coarse-grained Stochastic Model of Myosin-Driven Vesicles into Dendritic Spines