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arXiv · 1305.1049

Elasticity of cross-linked semiflexible biopolymers under tension

Alice von der Heydt·Daniel Wilkin·Panayotis Benetatos·Annette Zippelius
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Abstract

Aiming at the mechanical properties of cross-linked biopolymers, we set up and analyze a model of two weakly bending wormlike chains subjected to a tensile force, with regularly spaced inter-chain bonds (cross-links) represented by harmonic springs. Within this model, we compute the force-extension curve and the differential stiffness exactly and discuss several limiting cases. Cross-links effectively stiffen the chain pair by reducing thermal fluctuations transverse to the force and alignment direction. The extra alignment due to cross-links increases both with growing number and with growing strength of the cross-links, and is most prominent for small force f. For large f, the additional, cross-link-induced extension is subdominant except for the case of linking the chains rigidly and continuously along their contour. In this combined limit, we recover asymptotically the elasticity of a weakly bending wormlike chain without constraints, stiffened by a factor four. The increase in differential stiffness can be as large as 100% for small f or large numbers of cross-links.

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Alice von der Heydt, Daniel Wilkin, Panayotis Benetatos, Annette Zippelius. 2013-05-05. Elasticity of cross-linked semiflexible biopolymers under tension. https://doi.org/10.1103/physreve.88.032701

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