Microtubules are dynamic intracellular fibers that have been observed experimentally to undergo spontaneous self-alignment. We formulate a three-dimensional (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.

• Received 2 June 2023
• Accepted 16 November 2023

DOI:https://doi.org/10.1103/PhysRevE.108.064414

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society