Microtubules as electron-based topological insulators

TL;DR

This paper proposes that microtubules can function as topological insulators with robust electronic boundary states, based on modeling their structure as a stack of Su-Schrieffer-Heeger chains and analyzing their electronic properties.

Contribution

It introduces a novel topological insulator model for microtubules, linking biological structure to electronic topological phases and demonstrating robustness to disorder.

Findings

Microtubules can act as topological insulators with protected boundary states.

Topological properties are robust under disordered hopping parameters.

Modeling microtubules as SSH chains explains their potential electronic behavior.

Abstract

The microtubule is a cylindrical biological polymer that plays key roles in cellular structure, transport, and signalling. In this work, based on studies of electronic properties of polyacetelene and mechanical properties of microtubules themselves (see Phys. Rev. Lett. 103, 248101), we explore the possibility that microtubules could act as topological insulators that are gapped to electronic excitations in the bulk but possess robust electronic bounds states at the tube ends. Through analyses of structural and electronic properties, we model the microtubule as a cylindrical stack of Su-Schrieffer-Heeger chains (originally proposed in the context of polyacetylene) describing electron hopping between the underlying dimerized tubulin lattice sites. We postulate that the microtubule is mostly uniform, dominated purely by GDP-bound dimers, and is capped by a disordered regime due to the presence of GTP-bound dimers as well. In the uniform region, we identify the electron hopping parameter regime in which the microtubule is a topological insulator. We then show the manner in which these topological features remain robust when the hopping parameters are disordered. We briefly mention possible biological implications for these microtubules to possess topologically robust electronic bound states.