Topological phonon modes and their role in dynamic instability of microtubules

TL;DR

This paper investigates the vibrational properties of microtubules, revealing topological phonon modes with potential implications for their dynamic stability and edge behavior.

Contribution

It identifies topological vibrational modes in microtubules' lattice, linking phonon band topology to microtubule stability and edge localization.

Findings

Discovery of Dirac points in phonon spectrum

Phonon bands with nonzero Chern numbers

Topological edge modes observed in calculations

Abstract

Microtubules (MTs) are self-assembled hollow protein tubes playing important functions in live cells. Their building block is a protein called tubulin, which self-assembles in a particulate 2 dimensional lattice. We study the vibrational modes of this lattice and find Dirac points in the phonon spectrum. We discuss a splitting of the Dirac points that leads to phonon bands with nonzero Chern numbers, signaling the existence of topological vibrational modes localized at MTs edges, which we indeed observe after explicit calculations. Since these modes are robust against the large changes occurring at the edges during the dynamic cycle of the MTs, we can build a simple mechanical model to illustrate how they would participate in this phenomenon.