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Intracellular transport of organelles is fundamental to cell function andhealth. The mounting evidence suggests that this transport is in factanomalous. However, the reasons for the anomaly is still under debate. Weexamined experimental trajectories of organelles inside a living cell andpropose a mathematical model that describes the previously reported transitionfrom sub-diffusive to super-diffusive motion. In order to explainsuper-diffusive behaviour at long times, we introduce non-Markovian detachmentkinetics of the cargo: the rate of detachment is inversely proportional to thetime since the last attachment. Recently, we observed the non-Markoviandetachment rate experimentally in eukaryotic cells. Here we further discussdifferent scenarios of how this effective non-Markovian detachment rate couldarise. The non-Markovian model is successful in simultaneously describing thetime-averaged variance (the time-averaged mean squared displacement correctedfor directed motion), the mean first passage time of trajectories and themultiple peaks observed in the distributions of cargo velocities. We argue thatnon-Markovian kinetics could be biologically beneficial compared to theMarkovian kinetics commonly used for modelling, by increasing the averagedistance the cargoes travel when a microtubule is blocked by other filaments.In turn, sub-diffusion allows cargoes to reach neighbouring filaments withhigher probability, which promotes active motion along the microtubules.

Non-Markovian intracellular transport with sub-diffusion and run-length dependent detachment rate