We use the tangle model to study the action of the site-specific recombinase Gin, an enzyme that can introduce topological changes on circular DNA molecules. Gin and its bound DNA are modelled as a 2-string tangle which undergoes changes during recombination, thereby changing the topology of the DNA substrate. We show that the tangles involved in the analysis are all rational tangles. This technique allows us to prove that, under the model's assumptions, there is a unique topological description of the enzymatic action. The Gin system is one of the few to date where tangle analysis can be carried out systematically and rigorously, yielding a single, biologically reasonable solution.
Preview and motivationSite-specific recombination alters the genome of an organism by moving, inserting or inverting DNA segments. When acting on circular DNA molecules, site-specific recombinases can change the topology and geometry of the molecules [25,31]. The tangle model provides mathematical tools to analyze such changes [26,27,28]. The detailed tangle formalism and an application of the model to the Tn3 resolvase system were first presented in [10].Here we analyze the enzymatic action of Gin, a site-specific recombinase encoded by bacteriophage Mu (a virus that infects bacteria). Gin inverts a DNA segment within the phage genome to extend the phage's range of infection. The phage genome contains two recombination sites that Gin recognizes, cleaves and rearranges to complete one round of recombination (Figure 1). Gin recombination is processive, i.e. it can carry out more than one recombination round while binding only once to its substrate. We study the case where, prior to recombination, the phage genome is a single circular DNA molecule, effectively the unknot in S 3 . Recombination can then be analyzed by using tangles to model an enzyme such as Gin together with the DNA bound to the enzyme (see: [29]). Tangles, defined formally below, are