Exact theory of kinkable elastic polymers

TL;DR

This paper develops an exact statistical mechanics model for elastic polymers that can undergo kinking, capturing both low-curvature elasticity and high-curvature softening observed in DNA experiments.

Contribution

It introduces a simple, exact theory of kinking in elastic polymers, extending the Wormlike Chain model to include high-curvature softening behavior.

Findings

Reproduces linear-elastic behavior at low curvature

Captures high-curvature softening in DNA cyclization

Provides a single-parameter characterization of kinking

Abstract

The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection angles, many rod systems exhibit a high-curvature softening. The signature behavior of these rod systems is a kinking transition in which the bending is localized. Recent DNA cyclization experiments by Cloutier and Widom have offered evidence that the linear-elastic bending theory fails to describe the high-curvature mechanics of DNA. Motivated by this recent experimental work, we develop a simple and exact theory of the statistical mechanics of linear-elastic polymer chains that can undergo a kinking transition. We characterize the kinking behavior with a single parameter and show that the resulting theory reproduces both the low-curvature linear-elastic behavior which is already well described by the Wormlike Chain model, as well as the high-curvature softening observed in recent cyclization experiments.