Pattern formation of microtubules and motors: inelastic interaction of polar rods

TL;DR

This paper develops a mathematical model for microtubule and motor interactions, revealing how orientational instability leads to vortex and aster formation observed in experiments.

Contribution

It introduces a new set of equations derived from a stochastic model to describe microtubule organization and instability phenomena.

Findings

Orientational instability causes vortex and aster formation.

High density and anisotropic interactions enhance pattern formation.

The model aligns with recent experimental observations.

Abstract

We derive a model describing spatio-temporal organization of an array of microtubules interacting via molecular motors. Starting from a stochastic model of inelastic polar rods with a generic anisotropic interaction kernel we obtain a set of equations for the local rods concentration and orientation. At large enough mean density of rods and concentration of motors, the model describes orientational instability. We demonstrate that the orientational instability leads to the formation of vortices and (for large density and/or kernel anisotropy) asters seen in recent experiments.