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Topological patterns in two-dimensional gel electrophoresis of DNA knots

D. Michieletto,D. Marenduzzo,E. Orlandini

Published 2015 in Proceedings of the National Academy of Sciences of the United States of America

ABSTRACT

Significance Gel electrophoresis is a ubiquitous biophysical technique. It consists of dragging charged biopolymers through a porous gel, by applying an electric field. Because the migration speed depends on topology, this method can be used to classify DNA knots. Currently, electrophoresis relies on empirical observations, and its theoretical understanding is limited. No theory can explain why knot mobility under strong fields depends nonmonotonically on complexity. Our study reveals a possible reason: Although complex knots have a smaller size, and hence move faster through the gel, they can become severely entangled with the gel, causing longer pauses. Our results can improve the design of future electrophoresis experiments. Gel electrophoresis is a powerful experimental method to probe the topology of DNA and other biopolymers. Although there is a large body of experimental work that 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 nonmonotonic mobility at moderate fields. Consequently, in 2D 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.

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