Conformations of closed DNA

TL;DR

This paper models closed DNA as an elastic rod to analyze various conformations, including circular, figure-eight, and knotted forms, and assesses their stability and energetic properties.

Contribution

It provides analytical solutions for DNA conformations with linking number constraints, including new configurations like knotted loops, advancing understanding of DNA structural behavior.

Findings

Derived explicit expressions for DNA shapes.

Identified conditions for stable and unstable conformations.

Explored effects of fluctuations on free energy.

Abstract

We examine the conformations of a model for a short segment of closed DNA. The molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number. We obtain analytic expressions leading to the spatial configuration of a family of solutions representing distortions that interpolate between the circular form of DNA and a figure-eight form that represents the onset of interwinding. We are also able to generate knotted loops. We suggest ways to use our approach to produce other configurations relevant to studies of DNA structure. The stability of the distorted configurations is assessed, along with the effects of fluctuations on the free energy of the various configurations.