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Updated: Jul 5, 2025

Forming, Confining, and Observing Microtubule-Based Active Nematics
Published on: January 13, 2023
Mean-field theory approach to three-dimensional nematic phase transitions in microtubules
Cameron Gibson1,2,3, Henrik Jönsson1,4,5, Tamsin A Spelman1
1Sainsbury Laboratory, University of Cambridge, Cambridge, CB2 1LR, United Kingdom.
Abstract:
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_{eff} and predict a unique critical value G_{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.
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