Intracellular cargo transport time statistics that result from competing transport mechanisms.

We consider intracellular transport of cargo when molecular motor-driven transport along microtubules is directed towards the target in the interior of the cell.  Diffusive motion of cargo - when the motors disengage from microtubules - allows the transport in the opposite direction, with the possibility of reaching the cell membrane.  We find that when the switching between the two transport mechanisms is rapid, the asymmetric placement of the target gives the cell a sensitive control of the mean first passage time (MFPT) for reaching the membrane as a function of the location of the source of cargo and of the asymmetry.  At lower rates of switching, we find a transition to much lower MFPTs due to the possibility of a purely diffusive escape.  Here again, the degree of asymmetry of the target placement can lead to rich phenomenology.  We map out the phase diagram for different regimes in the space of parameters and discuss other statistical quantities - such as properties of density profiles that are established due to the competition between the two transport mechanisms.