Polymorphism in tubulin assemblies: a mechanical model

TL;DR

This paper presents a mechanical model explaining the polymorphic structures in tubulin assemblies, highlighting how lattice strain and curvature influence their formation and disassembly.

Contribution

It introduces a minimal elastic shell model linking mechanical strain and curvature to the polymorphic structures of tubulin assemblies.

Findings

Mechanical strain from lattice asymmetries causes polymorphic structures.

Spontaneous curvature determines the predominant tubular forms.

Sign change in Gaussian curvature may trigger microtubule disassembly.

Abstract

We investigate the mechanical origin of polymorphic structures in two-dimensional tubulin assemblies, of which microtubules are the best known example. These structures feature twisted ribbons, flat tubulin sheets, macrotubules, and hoops, and they spontaneously assemble depending on the chemical environment. Upon modelling tubulin aggregates as minimally anisotropic elastic shells and using a combination of numerical simulations and analytical work, we show that the mechanical strain in tubulin lattices, originating from asymmetries at the single dimer level, naturally gives rise to polymorphic assemblies, among which cylinders and other tubular structures are predominant for a wide range of values of spontaneous curvature. Furthermore, our model suggests that switching the sign of the sheets' spontaneous Gaussian curvature from positive (i.e. sphere-like) to negative (i.e. saddle-like), could provide a possible route to microtubules disassembly.