Elasticity model of a supercoiled DNA molecule

TL;DR

This paper develops an elastic model for supercoiled DNA, linking physical properties to quantum analogies, addressing singularities, and aligning with experimental data to improve measurement of DNA twist rigidity.

Contribution

It introduces a novel elastic theory for supercoiled DNA, incorporating quantum path integral methods and regularization techniques to match experimental observations.

Findings

Good agreement with experimental data

Identifies singularities in the continuum limit

Provides a method to measure twist rigidity accurately

Abstract

Within a simple elastic theory, we study the elongation versus force characteristics of a supercoiled DNA molecule at thermal equilibrium in the regime of small supercoiling. The partition function is mapped to the path integral representation for a quantum charged particle in the field of a magnetic monopole with unquantized charge. We show that the theory is singular in the continuum limit and must be regularised at an intermediate length scale. We find good agreement with existing experimental data, and point out how to measure the twist rigidity accurately.