Rational tangle surgery and Xer recombination on catenanes

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 N((4mn-1)/(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.Comment: 20 pages, 23 figure

Coloring the Mu transpososome

Isabel K. Darcy, Colin McKinney, Ram K. Medikonduri, and Travis Thompson are with the Mathematics Department, University of Iowa, Iowa City, IA 52242, USA, -- Jeff Chang, and Jesse Sweet are with the Mathematics Department, University of Texas at Austin, Austin, TX 78712, USA, -- Nathan Druivenga is with the Mathematics Department, Indiana University, Bloomington, IN 47405, USA, -- Stacy Mills is with the Mathematics Department, Florida State University, Tallahassee, FL 32306, USA, -- Junalyn Navarra-Madsen is with the Mathematics Department, Texas Woman's University, Denton, TX 76204, USA and -- Arun Ponnusamy is with Credit Suisse First, Boston, MA 02110, USABackground: Tangle analysis has been applied successfully to study proteins which bind two segments of DNA and can knot and link circular DNA. We show how tangle analysis can be extended to model any stable protein-DNA complex. -- Results: We discuss a computational method for finding the topological conformation of DNA bound within a protein complex. We use an elementary invariant from knot theory called colorability to encode and search for possible DNA conformations. We apply this method to analyze the experimental results of Pathania, Jayaram, and Harshey (Cell 2002). We show that the only topological DNA conformation bound by Mu transposase which is biologically likely is the five crossing solution found by Pathania et al (although other possibilities are discussed). -- Conclusion: Our algorithm can be used to analyze the results of the experimental technique described in Pathania et al in order to determine the topological conformation of DNA bound within a stable protein-DNA [email protected]