Elasticity of cross-linked semiflexible biopolymers under tension

TL;DR

This paper models the mechanical response of cross-linked semiflexible biopolymers under tension, revealing how cross-links enhance stiffness and alignment, with exact calculations of force-extension behavior and limiting case analysis.

Contribution

It introduces an exactly solvable model of two weakly bending wormlike chains with regular cross-links, providing new insights into their elasticity and stiffness enhancement.

Findings

Cross-links increase chain stiffness by reducing thermal fluctuations.

Stiffening effect is most significant at small forces and with more or stronger cross-links.

At high forces, the elasticity approaches that of an unconstrained wormlike chain, with possible fourfold stiffening.

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.