Eur. Phys. J. E (2010) 31: 215-227
https://doi.org/10.1140/epje/i2010-10562-x

Regular Article

Torsional elastic deformations of microtubules within continuous sheet model

¹ Department of Physics, University of Warwick, CV4 7AL, Coventry, UK
² Department of Experimental Oncology, University of Alberta, T6G 1Z2, Edmonton, Alberta, Canada

^* e-mail: geronimo@amu.edu.pl
^** e-mail: jtus@phys.ualberta.ca

Received: 8 June 2009
Revised: 16 November 2009
Published online: 10 March 2010

Abstract

This paper develops a rigorous analysis of the microtubule elastic deformations in terms of the torsional degrees of freedom using the helix-based cylindrical structure of this biopolymer. Methods of differential geometry and the theory of elasticity are employed in our analysis. We find equilibrium conditions and constitutive equations in the linear regime. We estimate the value of torsional rigidity for microtubules based on their structure and some experimentally known elastic properties. The paper concludes with the derivation of a bulk modulus formula for a microtubule in solution. Both the entropy change and the fluctuation of the twist angle are obtained.