Classification of Tangle Solutions for Integrases, A Protein Family that   Changes DNA Topology
  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. 
Dorothy Buck and Cynthia Verjovsky Marcotte