Polymorphism of tubulin assemblies

Tubulin is a ubiquitous biomolecule in eukaryotes, known to assemble in a variety of 2D shapes. The most studied of such are microtubules (MTs), slender but rigid cylindrical aggregates of tubulin chains, which are found with some structural variability. Microtubules undergo constant switching between growth and shrink phases, in a process known as dynamic instability.
When suddenly switching to a shrinking state during a catastrophe, the tubulin chains, known as protofilaments, splay apart and peel off from the microtubule tip, curving outwards. A spontaneous curvature of the protofilaments is therefore hypothesized to play a part in the dynamic instability of MTs. As their mechanical properties are influenced by the environmental conditions, such curvature terms are likely also responsible for the fascinating shape variability observed for tubulin assemblies beyond cylindrical MTs: flat sheets, ribbons, macrotubules and hoops.
By modelling tubulin aggregates as continuous elastic materials, we investigate how spontaneous curvature and anisotropic elastic properties influence the resulting equilibrium shape. Interestingly, this provides an insight on the role of mechanics in microtubule catastrophe.