A model for the orientational ordering of the plant microtubule cortical array

TL;DR

This paper develops a continuum model explaining how plant microtubule arrays become highly aligned, based on experimental observations of microtubule interactions, and analyzes the stability of ordered and disordered states.

Contribution

It introduces a novel continuum model linking microtubule interaction dynamics to orientational order in plant cells.

Findings

Identifies a control parameter governing microtubule alignment

Analytically solves for stable ordered and isotropic phases

Determines conditions for phase stability and transition

Abstract

The plant microtubule cortical array is a striking feature of all growing plant cells. It consists of a more or less homogeneously distributed array of highly aligned microtubules connected to the inner side of the plasma membrane and oriented transversely to the cell growth axis. Here we formulate a continuum model to describe the origin of orientational order in such confined arrays of dynamical microtubules. The model is based on recent experimental observations that show that a growing cortical microtubule can interact through angle dependent collisions with pre-existing microtubules that can lead either to co-alignment of the growth, retraction through catastrophe induction or crossing over the encountered microtubule. We identify a single control parameter, which is fully determined by the nucleation rate and intrinsic dynamics of individual microtubules. We solve the model analytically in the stationary isotropic phase, discuss the limits of stability of this isotropic phase, and explicitly solve for the ordered stationary states in a simplified version of the model.