DNA Elasticity : Topology of Self-Avoidance

TL;DR

This paper provides a theoretical analysis of DNA elasticity, focusing on the topological aspects of self-avoidance, and clarifies the relation between different elastic models, explaining phenomena like topological untwisting and free energy periodicity.

Contribution

It offers a detailed theoretical framework connecting the WLRC, WLC, and PWLC models, and introduces a new approach to approximate self-avoidance with 'south avoidance' for better understanding.

Findings

Periodic free energy in WLC model due to topological untwisting

Disappearance of periodicity when considering self-avoidance topology

Effective approximation of self-avoidance by south avoidance

Abstract

We present a theoretical treatment of DNA stretching and twisting experiments, in which we discuss global topological subtleties of self avoiding ribbons and provide an underlying justification for the worm like rod chain (WLRC) model proposed by Bouchiat and Mezard. Some theoretical points regarding the WLRC model are clarified: the writhe of open curves and the use of an adjustable cutoff parameter to ``regularise'' the model. Our treatment brings out the precise relation between the worm like chain (WLC), the paraxial worm like chain (PWLC) and the WLRC models. We describe the phenomenon of ``topological untwisting'' and the resulting collapse of link sectors in the WLC model and note that this leads to a free energy profile {\it{periodic}} in the applied link. This periodicity disappears when one takes into account the topology of self avoidance or at large stretch forces (paraxial limit). We note that the difficult nonlocal notion of self avoidance can be replaced (in an approximation) by the simpler local notion of ``south avoidance'' in the WLRC model. This gives an explanation for the efficacy of the approach of Bouchiat and Mezard in explaining the `hat curves' using the WLRC model. We propose a new class of experiments to probe the continuous transition between the periodic and aperiodic behavior of the free energy.