Related Experiment Video
Updated: May 7, 2026

DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers
Published on: October 25, 2017
Elasticity of cross-linked semiflexible biopolymers under tension
Alice von der Heydt1, Daniel Wilkin, Panayotis Benetatos
1Institute for Theoretical Physics, Georg-August University of Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany.
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.
Related Concept Videos
Members Made of Elastoplastic Material
As the bending moment...
Classification and Mechanical Properties of Synthetic Polymers
Polymer Classification: Architecture
Bending of Members Made of Several Materials
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each material's...
Elastin is Responsible for Tissue Elasticity
Ligaments and tendons are made of dense regular connective tissue, but in ligaments not all fibers are parallel. Dense regular elastic tissue contains elastin fibers and...
Plastic Behavior

