Directed intermittent search model of microtubule cargo transport

Introduction

Microtubule motor driven transport has been implicated in many critical processes in neurons. Examples include mRNA transport in dendrites and mitochondria transport in axons. We present a model of microtubule cargo transport that builds upon previous models by accounting for delivery of the cargo to the correct target. Using random search theory [1], we derive equations for the probability that a motor driven cargo moving along a one-dimensional track will find its target. We also derive equations for the average time to find the target, called the mean first passage time or mfpt. We then utilize a model reduction to approximate the governing system of hyperbolic master equations to a standard Fokker-Plank equation. The accuracy of our reduction can be verified by comparison to Monte-Carlo simulations. Using this reduction, we can consider a detailed biophysical model of bidirectional motor transport, known at the tug-of-war model, within the random search model. We conclude by proposing a model for ATP dependent transitions between search-oriented behavior and directed-transport-oriented behavior.