title: Elasticity of cross-linked semiflexible biopolymers under tension.
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.
authors.affiliation: Institute for Theoretical Physics, Georg-August University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
authors.forename: Alice
authors.initials: A
authors.lastname: von der Heydt
authors.forename: Daniel
authors.initials: D
authors.lastname: Wilkin
authors.forename: Panayotis
authors.initials: P
authors.lastname: Benetatos
authors.forename: Annette
authors.initials: A
authors.lastname: Zippelius
mesh_terms: D001704:Biopolymers / Q000737:chemistry*; D004548:Elasticity; D016014:Linear Models; D008958:Models, Molecular
chemical_list: D001704:Biopolymers