A mean-field theory approach to 3D nematic phase transitions in microtubules

TL;DR

This paper develops a 3D mean-field theory to analyze the nematic phase transition of microtubules, predicting a critical control parameter value and validating it through simulations, advancing understanding of microtubule patterning.

Contribution

The paper introduces a novel 3D mean-field model for microtubule nematic transitions, providing analytical predictions validated by simulations, and clarifies the role of zippering in phase behavior.

Findings

Critical value of G_eff = 1.56 for phase transition.

Phase transition independent of zippering effects.

Analytical estimates match simulation results.

Abstract

Microtubules are dynamic intracellular fibers that have been observed experimentally to undergo spontaneous self-alignment. We formulate a 3D mean-field theory model to analyze the nematic phase transition of microtubules growing and interacting within a 3D space then make a comparison with computational simulations. We identify a control parameter $G_\text{eff}$ and predict a unique critical value $G_\text{eff}=1.56$ for which a phase transition can occur. Furthermore, we show both analytically and using simulations that this predicted critical value does not depend on the presence of zippering. The mean-field theory developed here provides an analytical estimate of microtubule patterning characteristics without running time-consuming simulations and is a step towards bridging scales from microtubule behavior to multicellular simulations.