An algebro-geometric model for the shape of supercoiled DNA

This article proposes a model including thermal effects for closed supercoiled DNA. Existing models include an elastic rod. Euler's elastica, ideal elastic rods on a plane, have only two kinds of closed shapes, the circle and a figure-eight, realized as minima of the Euler-Bernoulli energy. Even considering three dimensional effects, this elastica model provides much simpler shapes than observed via Atomic Force Microscope (AFM), since the minimal points of the energy are expressed by elliptic functions. In this paper, by a generalization of elastica, we obtain shapes determined by data of hyperelliptic curves, which partially reproduce the shapes and properties of the DNA. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This article proposes a model for closed supercoiled DNA that takes into account thermal effects. Existing models based on the elastic rod theory can only generate simple closed shapes, which do not match the observed shapes obtained through Atomic Force Microscopy (AFM). In this paper, a generalized elastica model using hyperelliptic curve data is introduced to better replicate the shapes and properties of DNA.