Tubulin: from atomistic structure to supramolecular mechanical properties

Microtubules (MTs) are fundamental structural elements in the cytoskeleton of eukaryotic cells. Their unique mechanical properties depend on the properties of the tubulin dimer, its interactions with surrounding dimers and the geometric organization within the MT. While the geometry has already been well described in experimental works, the mechanical characteristics of the dimer as well as of the individual monomers have up to date not been described. These may therefore provide new, additional insight to the microtubule tensile properties. In this paper we construct a mesoscale model of MT with a bottom-up approach. First, we evaluate the elastic constants of each of the two monomers together with the interaction force between them by means of molecular dynamics (MD) simulations carried out in an explicit water environment. Using the MD results, we model a 1 lm long MT as a cylinder constituted by interacting elastic elements and examine its properties via finite element method (FEM). The obtained results show an elastic constant value for a-tubulin of 11 N/m, while for the b-tubulin the elastic constant was measured to be 15.6 N/m. Concerning interactions between neighbouring monomers, the elastic constants along the protofilament (45 N/m for the intra-dimer interface and 18 N/m for the inter-dimer interface) are more rigid than elastic constants calculated for lateral interfaces (11 and 15 N/m). The mesoscale model provides mechanical properties of the whole MT, thus allowing the comparison with data obtained by other previous experimental and theoretical studies. We report here a Young modulus of 1.66 GPa for the MT under axial tension. In perspective our approach provides a simple tool for the analysis of MT mechanical behaviour under different conditions.