Topological Patterns in Two-dimensional Gel Electrophoresis of DNA Knots

TL;DR

This paper develops a theoretical framework to understand how DNA knot mobility in gel electrophoresis depends on gel properties, explaining observed arc patterns and predicting their shapes based on molecule length and topology.

Contribution

It introduces a new model linking gel properties and DNA topology to electrophoretic mobility, explaining arc patterns and enabling predictions for future experiments.

Findings

DNA mobility depends on gel dangling ends and physical properties.

Gel bands form characteristic arc patterns in 2D electrophoresis.

A new predictive framework for arc shapes based on molecule length and topology.

Abstract

Gel electrophoresis is a powerful experimental method to probe the topology of DNA and other biopolymers. While there is a large body of experimental work which allows us to accurately separate different topoisomers of a molecule, a full theoretical understanding of these experiments has not yet been achieved. Here we show that the mobility of DNA knots depends crucially and subtly on the physical properties of the gel, and in particular on the presence of dangling ends. The topological interactions between these and DNA molecules can be described in terms of an "entanglement number", and yield a non-monotonic mobility at moderate fields. Consequently, in two-dimensional electrophoresis, gel bands display a characteristic arc pattern; this turns into a straight line when the density of dangling ends vanishes. We also provide a novel framework to accurately predict the shape of such arcs as a function of molecule length and topological complexity, which may be used to inform future experiments.