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 semianalytical theory for the active transport of vesicles forced through
constrictions by molecular motors. We show that the motion of these objects is characterized
by two dimensionless quantities related to the geometry and to 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 a
smaller forward-flowing 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 nonlocal hydrodynamic effects in determining the kinetics of
vesicular transport in constricted geometries.