CLASSIFICATION OF TANGLE SOLUTIONS FOR INTEGRASES, A PROTEIN FAMILY THAT CHANGES DNA TOPOLOGY

Abstract

A generic integrase protein, when acting on circular DNA, often changes the DNA topology by transforming unknotted circles into torus knots and links. Two systems of tangle equations — corresponding to two possible orientations of two DNA subsequences — arise when modelling this transformation.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 [10] with recent results of Kronheimer, Mrowka, Ozsváth and Szabó [39] and work of Ernst [23] to show a certain prime tangle must in fact be a Montesinos tangle.These tangle solutions are divided into three classes, common to both systems, plus a fourth class for one system that contains the sole Montesinos tangle. We discuss the possible biological implications of our classification, and of this novel solution.