  Power-law dwell times have been observed for molecular motors in living
cells, but the origins of these trapped states are not known. We introduce a
minimal model of motors moving on a two-dimensional network of filaments, and
simulations of its dynamics exhibit statistics comparable to those observed
experimentally. Analysis of the model trajectories, as well as experimental
particle tracking data, reveals a state in which motors cycle unproductively at
junctions of three or more filaments. We formulate a master equation for these
junction dynamics and show that the time required to escape from this
vortex-like state can account for the power-law dwell times. We identify trends
in the dynamics with the motor valency for further experimental validation. We
demonstrate that these trends exist in individual trajectories of myosin II on
an actin network. We discuss how cells could regulate intracellular transport
and, in turn, biological function, by controlling their cytoskeletal network
structures locally.
