Classification of Tangle Solutions for Integrases, A Protein Family that Changes DNA Topology

Details Classification of Tangle Solutions for Integrases, A Protein Family that Changes DNA Topology Classification of Tangle Solutions for Integrases, A Protein Family that Changes DNA Topology

2005-01-11

arxiv.org/abs/math/0501173v1

Mathematics

Geometric Topology

17 pages, 1 figure

Scientific paper

Integrase proteins acting on circular double-stranded DNA often change its topology by transforming unknotted circles into torus knots and links. Two systems of tangle equations--corresponding to the two initial DNA sequences--arise when modelling this transformation: direct and inverted. With no a priori assumptions on the constituent tangles, we utilize Dehn surgery arguments to completely classify the tangle solutions for each of the two systems. A key step is to combine work of our previous paper with recent results of Kronheimer, Mrowka, Ozsvath and Szabo, and Ernst to show a certain prime tangle must in fact be a generalized Montesinos tangle. These tangle solutions are divided into three classes, common to both systems, plus a fourth class for the inverted system that contains the sole generalized Montesinos tangle. We discuss the possible biological implications of our classification, and of this novel solution.

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