Effect of interaction shape on the condensed DNA toroid

TL;DR

This paper explores how microscopic interactions influence the physical properties of condensed DNA toroids, predicting different scaling behaviors and explaining experimental observations of DNA toroid structures.

Contribution

It introduces a general Hamiltonian model for DNA toroids and predicts how various interactions affect their size scaling, providing insights into experimental DNA condensation.

Findings

Different interaction types lead to distinct size scaling exponents.

Yukawa interaction results in near-constant toroid size with length.

Van der Waals interactions produce a small positive size exponent.

Abstract

We investigate how different microscopic interactions between semiflexible chain segments can qualitatively alter the physical properties of the condensed toroid. We propose a general form of the Hamiltonian of the toroid and discuss its analytic properties. For different interactions, the theory predicts different scaling behaviours of the mean toroidal and cross sectional radii, $r_c$ and $r_{cross}$, as functions of the contour length L: $(r_c, r_{cross}) \sim L^{\nu(N_c)}$ with $\nu=(1/5, 2/5)$ for the van der Waals type, $\nu=(-1/3, 2/3)$ for the Coulomb type, $\nu=(-1, 1)$ for the delta function type attractions in the asymptotic limit. For the toroids with finite winding number $N_c=100 \sim 400$, we find $\nu \simeq 0$ for the Yukawa interaction with screening parameter $\kappa=0.5 \sim 1.0$, and $\nu=0.1 \sim 0.13$ for the van der Waals type interactions. These findings could provide possible explanation for the experimentally well known observation $\nu \simeq 0$ of the condensed DNA toroids. Conformational transitions are also discussed.