Buckling of microtubules under bending and torsion

Microtubules (MTs) in living cells are frequently bend, e.g., with a mean curvature of about 0.4 rad/μm in fibroblast cells [Odde et al., J. Cell Sci. 112, 3283 (1999)]. This raises a natural question whether bending buckling can occur in a MT. In this paper, an orthotropic model is developed to investigate buckling of MTs upon bending and torsion. A critical buckling curvature for a bent MT is predicted to be about 0.03 rad/μm (to which the corresponding bending moment is 0.85 nN nm), indicating that MTs in living cells are likely buckled. Buckling behavior of torsional MTs is also studied, and a critical buckling torque of 0.077 nN nm is obtained. Comparison to the results from an isotropic model shows that anisotropic properties of the MT wall have severe effect on the mechanical behavior of MTs.