Bending elasticity of macromolecules: analytic predictions from the wormlike chain model

TL;DR

This paper analytically investigates the bending elasticity of semiflexible polymers using the wormlike chain model, providing formulas for bend angle distribution and elastic response, with applications to DNA and actin studies.

Contribution

It offers new analytical expressions for the nonlinear elastic behavior of semiflexible polymers, extending beyond the Hookean regime and validated by simulations.

Findings

Derived analytical formulas for bend angle distribution.

Validated formulas with Monte Carlo simulations.

Applicable to DNA and actin microscopic studies.

Abstract

We present a study of the bend angle distribution of semiflexible polymers of short and intermediate lengths within the wormlike chain model. This enables us to calculate the elastic response of a stiff molecule to a bending moment. Our results go beyond the Hookean regime and explore the nonlinear elastic behaviour of a single molecule. We present analytical formulae for the bend angle distribution and for the moment-angle relation. Our analytical study is compared against numerical Monte Carlo simulations. The functional forms derived here can be applied to fluorescence microscopic studies on actin and DNA. Our results are relevant to recent studies in "kinks" and cyclization in short and intermediate length DNA strands.