Topological interactions in DNA catenanes

TL;DR

This paper models the elasticity and interactions of DNA catenanes using topological invariants, deriving free energy functions and distribution predictions that align with experimental observations.

Contribution

It introduces a minimal topological model for DNA catenane elasticity and derives distribution functions matching experimental data.

Findings

An anharmonic elastic free energy grows as R^4 at large distances.

Strong repulsion at small distances between segments.

Qualitative agreement with electron micrograph data.

Abstract

The elasticity of DNA catenanes, i.e. multiply linked DNA rings, is investigated using the Gauss invariant as a minimal model for topology conservation. An effective elastic free energy as a function of the distance $R$ between segments located on different rings is obtained. An anharmonic part at large distances, growing as $R^{4}$, if $R\gg R_{G}$ ($R_{G}$ being the radius of gyration of a random walk ring) is found, while for $R\ll R_{G}$ the interaction is strongly repulsive. Treating the attractive interaction as the dominant one, distribution functions for the distance between segments located on different rings for several linking numbers are derived which are in qualitative agreement with distributions functions obtained experimentally from electron micrographs of DNA catenanes (S. D. Levene et al., Biophys.J. 69, 277, 1995).