  Motivated by the sidewise motions of dynein motors shown in experiments, we
use a variant of the exclusion process to model the multistep dynamics of
dyneins on a cylinder with open ends. Due to the varied step sizes of the
particles in a quasi-two-dimensional topology, we observe the emergence of a
novel phase diagram depending on the various load conditions. Under high-load
conditions, our numerical findings yield results similar to the TASEP model
with the presence of all three standard TASEP phases, namely the low-density
(LD), high-density (HD), and maximal-current (MC) phases. However, for medium-
to low-load conditions, for all chosen influx and outflux rates, we only
observe the LD and HD phases, and the maximal-current phase disappears.
Further, we also measure the dynamics for a single dynein particle which is
logarithmically slower than a TASEP particle with a shorter waiting time. Our
results also confirm experimental observations of the dwell time distribution.
The dwell time distribution for dyneins is exponential in less crowded
conditions, whereas a double exponential emerges under overcrowded conditions.
