The European Physical Journal E

, Volume 31, Issue 2, pp 215–227 | Cite as

Torsional elastic deformations of microtubules within continuous sheet model

Regular Article


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.


Torque Bulk Modulus Strain Tensor Tangent Plane Twist Angle 
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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • P. Chełminiak
    • 1
  • J. M. Dixon
    • 1
  • J. A. Tuszyński
    • 2
  1. 1.Department of PhysicsUniversity of WarwickCoventryUK
  2. 2.Department of Experimental OncologyUniversity of AlbertaEdmontonCanada

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