  Intracellular transport of organelles is fundamental to cell function and
health. The mounting evidence suggests that this transport is in fact
anomalous. However, the reasons for the anomaly is still under debate. We
examined experimental trajectories of organelles inside a living cell and
propose a mathematical model that describes the previously reported transition
from sub-diffusive to super-diffusive motion. In order to explain
super-diffusive behaviour at long times, we introduce non-Markovian detachment
kinetics of the cargo: the rate of detachment is inversely proportional to the
time since the last attachment. Recently, we observed the non-Markovian
detachment rate experimentally in eukaryotic cells. Here we further discuss
different scenarios of how this effective non-Markovian detachment rate could
arise. The non-Markovian model is successful in simultaneously describing the
time-averaged variance (the time-averaged mean squared displacement corrected
for directed motion), the mean first passage time of trajectories and the
multiple peaks observed in the distributions of cargo velocities. We argue that
non-Markovian kinetics could be biologically beneficial compared to the
Markovian kinetics commonly used for modelling, by increasing the average
distance the cargoes travel when a microtubule is blocked by other filaments.
In turn, sub-diffusion allows cargoes to reach neighbouring filaments with
higher probability, which promotes active motion along the microtubules.
