Before revision:   In particular, we find a nonlinear scaling of the mean {\em   number of particles accumulated at the tip ( tip size ) with injection rate and an associated phase transition leading to {\em pulsing states} characterized by periodic filling and emptying of the system . Moreover, we show that the ability of changing protofilaments can affect the transport efficiency. Finally, we show that the particle-direction change rate obtained from experiments is close to optimal in order to achieve efficient motor URLanelle transport in a living cell .
After revision:  In particular, we find a nonlinear scaling of the mean {\em number of particles accumulated at the tip ( tip size ) with injection rate and an associated phase transition leading to {\em pulsing states} characterized by periodic filling and emptying of the system .