Gel-Electrophoresis and Diffusion of Ring-Shaped DNA

TL;DR

This paper introduces a model for the movement of ring-shaped DNA in gels, highlighting the role of hernias and tension, and compares theoretical predictions with experimental observations of DNA mobility.

Contribution

It extends reptation models by incorporating hernia-mediated motion and tension effects, providing new insights into ring DNA dynamics in gel environments.

Findings

Mobility saturates similar to linear DNA

Mobility drops exponentially with ring size in experiments

Exact solutions for steady-state and diffusion coefficient derived

Abstract

A model for the motion of ring-shaped DNA in a gel is introduced and studied by numerical simulations and a mean-field approximation. The ring motion is mediated by finger-shaped loops (hernias) that move in an amoeba-like fashion around the gel obstructions. This constitutes an extension of previous reptation tube treatments. It is shown that tension is essential for describing the dynamics in the presence of hernias. It is included in the model as long range interactions over stretched DNA regions. The mobility of ring-shaped DNA is found to saturate much as in the well-studied case of linear DNA. Experiments in polymer gels, however, show that the mobility drops exponentially with the DNA ring size. This is commonly attributed to dangling-ends in the gel that can impale the ring. The predictions of the present model are expected to apply to artificial 2D obstacle arrays (W.D. Volkmuth, R.H. Austin, Nature 358,600 (1992)) which have no dangling-ends. In the zero-field case an exact solution of the model steady-state is obtained, and quantities such as the average ring size are calculated. An approximate treatment of the ring dynamics is given, and the diffusion coefficient is derived. The model is also discussed in the context of spontaneous symmetry breaking in one dimension.