  Transport of dense core vesicles (DCVs) in neurons is crucial for
distributing molecules like neuropeptides and growth factors. We studied the
experimental trajectories of dynein-driven directed movement of DCVs in the ALA
neuron C. elegans over a duration of up to 6 seconds. We analysed the DCV
movement in three strains of C. elegans: 1) with normal kinesin-1 function, 2)
with reduced function in kinesin light chain 2 (KLC-2), and 3) a null mutation
in kinesin light chain 1 (KLC-1). We find that DCVs move superdiffusively with
displacement variance $var(x) \sim t^2$ in all three strains with low reversal
rates and frequent immobilization of DCVs. The distribution of DCV
displacements fits a beta-binomial distribution with the mean and the variance
following linear and quadratic growth patterns, respectively. We propose a
simple heterogeneous random walk model to explain the observed superdiffusive
retrograde transport behaviour of DCV movement. This model involves a random
probability with the beta density for a DCV to resume its movement or remain in
the same position.
