Effects of disorder on the topological properties of microtubules

Microtubules are macromolecular polymeric structures in eukaryotic cells that play key roles in intracellular transport, motility, and structure. It has been proposed that their physical structure allows for the existence of mechanical topological edge modes (Phys. Rev. Lett. 103, 248101). In this work, we employ a model to demonstrate that the charge distribution and lattice-like configuration of the microtubule additionally allow for electronic topological edge modes. We show this by modelling the microtubule as a cylindrical stack of Su–Schrieffer–Heeger chains forming an effective one-dimensional system. Further, we illustrate the robustness of these modes to low disorder strengths, as well as a topological phase transition that sets in at larger disorder strengths. We also discuss potential implications of disorder and topological defects for the phenomenon of dynamic instability in the microtubule as well as possible ways to model it within our system.