Ph.D., Mines ParisTech                                      

Date: January, 2010

Topic: Mechanics and Materials

Advisor: Prof. Mary C. Boyce, Dean of SEAS at Columbia University

Dissertation: Micromechanical Properties of Microtubules



Prof. Martine Ben Amar Président

Prof. Mathias Brieu Rapporteur

Prof. Erwan Verron Rapporteur

Dr. Julie Diani Examinateur


Microtubules serve as one of the structural components of the cell and govern some of the important cellular functions such as mitosis and vesicular transport. Microtubules are comprised of tubulin subunits formed by α and β tubulin dimers arranged in a cylindrical hollow tube structure with a diameter of 20nm. They are typically comprised of 13 or 14 protofilaments arranged in spiral configurations. The longitudinal bonds between the tubulin dimers are much stiffer and stronger than the lateral bonds. This implies a highly anisotropic structure and mechanical properties of the microtubule. In this work, the aim is to define a complete set of elastic properties that capture the atomistic behaviour and track the deformation of the microtubules under different loading conditions. A seamless microtubule wall is represented as a two dimensional triangulated lattice of dimers from which a representative volume element is defined. A harmonic potential is adapted for the dimer–dimer interactions. Estimating the lattice elastic constants and following the methodology from the analysis of the mechanical behaviour of triangulated spectrin network of the red blood cell membrane (Arslan and Boyce, 2006); a general continuum level constitutive model of the mechanical behaviour of the microtubule lattice wall is developed. The model together with the experimental data given in the literature provides an insight to defining the mechanical properties required for the discrete numerical model of an entire microtubule created in finite element analysis medium. The three point bending simulations for a microtubule modeled using shell elements, give tube bending stiffness values that are in accordance with the experimental bending stiffness values and also reveal the mechanisms of local wall bending and shearing govern the deformation of short tubes transitioning to tube shearing and bending governing moderate length tubes and, finally, very long tubes displace by bending during the three point loading. These results uncover the importance of the anisotropic response of the tube in different loading conditions and also explain the length dependent bending stiffness reported in the literature. Furthermore, micrographs also show that shrinking ends of microtubules (due to microtubule instabilities) curl out. This implies the existence of prestress. A “connector model” is proposed to include the effect of the prestress and to capture the dynamic instabilities of microtubules during polymerization/depolymerization.