DNA toroid condensation as analytic solutions

TL;DR

This paper models DNA toroid condensation using a non-linear sigma model, providing exact solutions that align with experimental observations of toroid ground states.

Contribution

It introduces a rigorous analytical framework for DNA toroid formation, connecting classical solutions of the sigma model with experimental data.

Findings

Classical solutions exhibit toroidal forms matching experimental structures

The solutions are proven to be exact solutions of the equations of motion

Refined data mapping accounts for finite size effects

Abstract

It now becomes apparent that condensed DNA toroid which emerges in a poor solvent condition can be realised in the framework of the non-linear sigma model on a line segment. In fact, the classical solutions of the model, i.e., of the bending potential exhibit toroidal forms, and fit well with the delta-function term of the attractive interaction. The proposed theory is in good agreement with experimental observations that the toroid is the ground state. In this paper, we give a rigorous proof that the solutions are indeed the exact solutions of the equations of motion with the first derivatives of the attractive interaction term. We also show a refined mapping to experimental data, considering the finite size effects of the cross section and of the chain length.