Geometric Influences on Radial Indentation of Microtubules

Abstract

Microtubules assembled in vitro exist in a variety of configurations that vary in number of protofilaments, radius, and skew angle of protofilaments relative to the main microtubule axis. Such variations affect microtubule stability, energetics, and assembly/disassembly dynamics. Further, the most abundant microtubule geometries observed in vitro are influenced by assembly conditions and stabilization methods. We have studied the relationship between microtubule geometry and mechanical properties using finite element modeling (FEM). Specifically, we have examined the effects of protofilament number, microtubule radius, and protofilament skew on the radial stiffness (effective radial spring constant of the microtubule wall) of microtubules as measured in atomic force microscopy (AFM) experiments. Our previous AFM work determined that microtubules assembled in the presence of a slowly-hydrolysable GTP analog, GMPCPP, have enhanced radial stiffness relative to those stabilized with paclitaxel. We surmise that in vitro populations of GMPCPP-microtubules and paclitaxel microtubules contain distinct distributions of microtubule geometries, so we have used FEM to examine the relative effect of microtubule geometry on stiffness values we measure. Our modeling results indicate that the changes in stiffness that we have observed experimentally are not simply a result of changes in protofilament number or orientation but instead are likely due to a relative change in material properties (e.g. effective Young's modulus) of the tubulin polymers.