2005/01/11 by Dorothy Buck, Buck, Dorothy, Cynthia Verjovsky Marcotte +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Cellular transport and secretion #Geometric and Algebraic Topology #Protein Structure and Dynamics #math.GT #msc:57M #q-bio.BM
paper · pdf · doi:10.48550/arxiv.math/0501173
17 pages, 1 figure
arxiv created 2005/01/11 · arxiv updated 2009/12/01
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.