  The transportation of the cargoes in biological cells is primarily driven by
the motor proteins on filamentous protein tracks. The stochastic nature of the
motion of motor protein often leads to its spontaneous detachment from the
track. Using the available experimental data, we demonstrate a tradeoff between
the speed of the motor and its rate of spontaneous detachment from the track.
Further, it is also shown that this speed-detachment relation follows a power
law where its exponent dictates the nature of the motor protein processivity.
We utilize this information to study the motion of motor protein on track using
a random-walk model. We obtain the average distance travelled in fixed duration
and average time required for covering a given distance by the motor protein.
These analyses reveal non-monotonic dependence of the motor protein speed on
its transport and, therefore, optimal motor speeds can be identified for the
time and distance controlled conditions.
