  The origins of the large differences observed to the rates with which the
diverse particles are conveyed along axonal microtubules are still a matter of
debate in the literature. There is evidence that certain neurodegenerative
diseases may be triggered by disturbances to the related transport processes.
Motivated by this, we employ a model to investigate the mobility properties of
certain cargoes which dynamics are coupled with that of molecular motors on
crowded microtubules. For certain initial and boundary conditions, we use the
method of characteristics to resolve perturbatively the pair of equations of
the Burgers type resulting from a mean-field approach to the original
microscopic stochastic model. Extensions to the non-perturbative limits are
explored numerically. In this context, we were able to figure out conditions
under which cargos average velocities may differ up to orders of magnitude just
by changing the number of motors on the considered track. We then discuss
possibilities to connect these theoretical predictions with available
experimental data about axon transport.
