Mechanics of microtubules modeled as orthotropic elastic shells with transverse shearing

Microtubules are hollow cylindrical filaments of the eukaryotic cytoskeleton characterized by extremely low shear modulus. In this paper, an orthotropic elastic shell model with transverse shearing is developed to study the effects of transverse shearing on shell-like mechanics of microtubules. The study is based on a detailed comparison between four elastic beam and shell models with and without transverse shearing. It is shown that the length-dependent flexural rigidity of microtubules predicted by the present orthotropic shell model with transverse shearing is in good agreement with known experimental data and is consistently close to that given by the Timoshenko-beam model. Our results show that transverse shearing is essential for shell-like deformation of microtubules when the axial wave-length is not extremely long (compared to the diameter of microtubules which is∼25 nm) or the circumferential wave-number is larger than unity. In particular, transverse shearing is found to significantly lower the critical pressure for buckling of a long microtubule under radial pressure and leads to an even better agreement with recently observed experimental data. These results suggest that the 2D orthotropic shell model with transverse shearing is suitable to study the shell-like mechanics of microtubules for short axial wave-length and circumferential wave-number exceeding unity.