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Microtubules (MTs) are self-assembled hollow protein tubes playing importantfunctions in live cells. Their building block is a protein called tubulin,which self-assembles in a particulate 2 dimensional lattice. We study thevibrational 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 withnonzero Chern numbers, signaling the existence of topological vibrational modeslocalized at MTs edges, which we indeed observe after explicit calculations.Since these modes are robust against the large changes occurring at the edgesduring the dynamic cycle of the MTs, we can build a simple mechanical model toillustrate how they would participate in this phenomenon.

Topological phonon modes and their role in dynamic instability of microtubules