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Rational tangle surgery and Xer recombination on catenanes

Isabel K Darcy, Kai Ishihara, Ram K Medikonduri and Koya Shimokawa

Algebraic & Geometric Topology 12 (2012) 1183–1210

The protein recombinase can change the knot type of circular DNA. The action of a recombinase converting one knot into another knot is normally mathematically modeled by band surgery. Band surgeries on a 2–bridge knot N4mn1 2m yielding a (2,2k)–torus link are characterized. We apply this and other rational tangle surgery results to analyze Xer recombination on DNA catenanes using the tangle model for protein-bound DNA.

tangle, DNA topology, recombination, surgery
Mathematical Subject Classification 2000
Primary: 57M25, 92C40
Received: 29 September 2011
Revised: 2 February 2012
Accepted: 3 February 2012
Published: 28 May 2012
Isabel K Darcy
Department of Mathematics and Applied Mathematical and Computational Sciences
University of Iowa
14 MLH
Iowa City IA 52242
Kai Ishihara
Department of Mathematics
Imperial College London
London SW7 2AZ
Ram K Medikonduri
Pyxis Solutions
New York NY 10004
Koya Shimokawa
Department of Mathematics
Saitama University
Saitama 338-8570