Mechanics of microtubules: effects of protofilament orientation

Microtubules are hollow cylindrical polymers of the protein tubulin that play a number of important dynamic and structural roles in eukaryotic cells. Both in vivo and in vitro microtubules can exist in several possible configurations, differing in the number of protofilaments, helical rise of tubulin dimers, and protofilament skew angle with respect to the main tube axis. Here, finite element modeling is applied to examine the mechanical response of several known microtubule types when subjected to radial deformation. The data presented here provide an important insight into microtubule stiffness and reveal that protofilament orientation does not affect radial stiffness. Rather, stiffness is primarily dependent on the effective Young's modulus of the polymerized material and the effective radius of the microtubule. These results are also directly correlated to atomic force microscopy nanoindentation measurements to allow a more detailed interpretation of previous experiments. When combined with experimental data that show a significant difference between microtubules stabilized with a slowly hydrolyzable GTP analog and microtubules stabilized with paclitaxel, the finite element data suggest that paclitaxel increases the overall radial flexibility of the microtubule wall.