Elasticity of cross-linked semiflexible biopolymers under tension

von der Heydt, Alice; Wilkin, Daniel; Benetatos, Panayotis; Zippelius, Annette

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Elasticity of cross-linked semiflexible biopolymers under tension

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Zippelius, Annette
Fellow Group Polymers, complex fluids and disordered systems, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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von der Heydt, A., Wilkin, D., Benetatos, P., & Zippelius, A. (2013). Elasticity of cross-linked semiflexible biopolymers under tension. Physical Review E, 88: 032701, pp. 032701-01-032701-11. Retrieved from http://dx.doi.org/10.1103/PhysRevE.88.032701.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-0FAF-E

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 of 4. The increase in differential stiffness can be as large as 100% for small f or large numbers of cross-links.