Polymorphism in tubulin assemblies: A mechanical model

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 modeling 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 the 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. Our paper sheds light on the organization of in vitro tubulin assemblies and paves the way towards a more comprehensive theory of in vivo systems, where the nonequilibrium effects resulting from the dynamic polymerization and deopolymerization of tubulin and thermal fluctuations conspire with the elastic forces described here.