Elastic Rod Model of a Supercoiled DNA Molecule

TL;DR

This paper models supercoiled DNA as an elastic rod, incorporating a cutoff length scale, to quantitatively match experimental data and analyze supercoiling effects, including torque, writhe, and extension fluctuations.

Contribution

It introduces a singular elastic rod model with a cutoff for supercoiled DNA, enabling quantitative analysis and extraction of physical parameters from experiments.

Findings

The model reproduces supercoiling effects on DNA extension.

A sharp crossover regime related to plectonemic structures is identified.

Extension fluctuations are predicted and compared with preliminary data.

Abstract

We study the elastic behaviour of a supercoiled DNA molecule. The simplest model is that of a rod like chain, involving two elastic constants, the bending and the twist rigidities. We show that this model is singular and needs a small distance cut-off, which is a natural length scale giving the limit of validity of the model, of the order of the double helix pitch. The rod like chain in presence of the cutoff is able to reproduce quantitatively the experimentally observed effects of supercoiling on the elongation-force characteristics, in the small supercoiling regime. An exact solution of the model, using both transfer matrix techniques and its mapping to a quantum mechanics problem, allows to extract, from the experimental data,the value of the twist rigidity. We also analyse the variation of the torque and the writhe to twist ratio versus supercoiling, showing analytically the existence of a rather sharp crossover regime which can be related to the excitation of plectonemic-like structures. Finally we study the extension fluctuations of a stretched and supercoiled DNA molecule, both at fixed torque and at fixed supercoiling angle, and we compare the theoretical predictions to some preliminary experimental data.