Stochastic modeling of intracellular transport in neurons

Abstract

A cell is not just a cell. It’s a factory that is manufacturing, growing, signaling, communicating, transporting, dividing, all at the same time. Molecular motors are the powerful agents that perform the long distance transport in eukaryotic cells of humans and other animals. Understanding of these transport processes is a crucial step towards developing further insights into many neuro-degenerative disorders that have plagued our species. We present a mathematical framework to analyze the intracellular transport inside a neuron. We study the transport on a parallel arrangement of microtubules inside the axon (axonal transport), as well as various tangled networks of microtubules inside the soma (somatic transport). For the former, our model captures the spatial dynamics and interactions of a motor and cargo particles, and the mean attachment time of the motor to a microtubule is computed. For the latter, we analyze the effects on the transport of particle switching at the microtubule intersections. In all cases, we have obtained the effective velocity and diffusion coefficient for the transport at the cellular scale. To validate the theoretical results for the motor attachment time, we also present a custom-built numerical scheme to efficiently simulate the mean first passage time to a small target in a multidimensional domain.