  We introduce a one-dimensional non-equilibrium lattice gas model representing
the processive motion of dynein molecular motors over the microtubule. We study
both dynamical and stationary state properties for the model consisting of
hardcore particles hopping on the lattice with variable step sizes. We find
that the stationary state gap-distribution exhibits striking peaks around gap
sizes that are multiples of the maximum step size, for both open and periodic
boundary conditions. We verified this feature using a mean-field calculation.
For open boundary conditions, we observe intriguing damped oscillator-like
distribution of particles over the lattice with a periodicity equal to the
maximum step size. To characterize transient dynamics, we measure the mean
square displacement that shows weak superdiffusive growth with exponent $\gamma
\approx 1.34$ for periodic boundary and ballistic growth ($\gamma \approx 2$)
for open boundary conditions at early times. We also study the effect of
Langmuir dynamics on the density profile.

Statistical Mechanics;Cellular Automata and Lattice Gases