# A stochastic model for intracellular active transport

## Abstract

We develop a stochastic model for an intracellular active transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (mean first passage time).

В We will study different biologically relevant scenarios, which include the possibility of multiple hidden targets (which breed competition), the presence of moving targets and moving obstacles. The purpose of including obstacles is to illustrate actual disruptions of the intracellular transport (which can result, for example, in several neurological disorders [1])

В From a mathematical point of view, the intracellular active transport is modelled by two independent continuous-time, discrete space Markov chains: one for the dynamics of the molecular motor in the space intervals and one for the domain of target. The process is time homogeneous and independent of the position of the molecular motor.

## References

M.A.M. Franker, C.C. Hoogenraad, Microtubule-based transport - basic mechanisms, traffic rules and role in neurological pathogenesis, Journal of Cell Science 126 2319--2329.

J.W. Lamperti, Probability: A Survey of the Mathematical Theory, John Wiley&Sons, USA, 2011.

O. Benichou et al, Intermittent search strategies, Review of Modern Physics 83 81--129.

J. Newby, P.C. Bressloff, Random intermittent search and the tug-of-war model of motor-driven transport, Journal of Stattistical Mechanics: Theory and Experiments 2010, no.04, P04014.