  Fluid-resistance limited transport of vesicles through narrow constrictions
is a recurring theme in many biological and engineering applications. Inspired
by the motor-driven movement of soft membrane-bound vesicles into closed
neuronal dendritic spines, here we study this problem using a combination of
passive three-dimensional simulations and a simplified semi-analytical theory
for active transport of vesicles that are forced through such constrictions by
molecular motors. We show that the motion of these objects is characterized by
two dimensionless quantities related to the geometry and the strength of
forcing relative to the vesicle elasticity. We use numerical simulations to
characterize the transit time for a vesicle forced by fluid pressure through a
constriction in a channel, and find that relative to an open channel, transport
into a blind end leads to the formation of an effective lubrication layer that
strongly impedes motion. When the fluid pressure forcing is complemented by
forces due to molecular motors that are responsible for vesicle trafficking
into dendritic spines, we find that the competition between motor forcing and
fluid drag results in multistable dynamics reminiscent of the real system. Our
study highlights the role of non-local hydrodynamic effects in determining the
kinetics of vesicular transport in constricted geometries.
