Topology Seminar for 3/13/2003

John Luecke
University of Texas at Austin

The Mu transpososome is a bringing-together of three separate segments of a DNA molecule.  We describe a recent experiment by Pathania, Jayaram, Harshey (Cell, Vol. 109, 425-436) which discovers the architecture of this complex (thinking of it as a 3-string tangle) by coupling it with the recombination enzyme CRE and observing the resulting knotted products which arise.  We will give a knot-theoretic analysis of the results of this experiment.  We show that there are other possible architectures, and then classify these architectures in terms of certain kinds of knotted graphs.  Using this description, we shot that the PJH solution is the only rational (3-string) tangle solution for the architecture, and furthermore show that any other solution must have at least 11 crossings (where the PJH solution has only 6).  This is joint work with Isabel Darcy and Mariel Vasquez.