The product of Xer recombination at directly repeated psi sites on a circular unknotted DNA molecule is a right-hand four-noded catenane. Here, we use tangle equations to analyze the topological changes associated with Xer recombination at psi. This mathematical method allows computation of all possible topological pathways consistent with the experimental data. We give a rigorous mathematical proof that, under reasonable biological assumptions, there are only three solutions to the tangle equations. One of the solutions corresponds to a synaptic complex with antiparallel alignment of recombination core sites, the other two correspond to parallel alignment of cores. We show that all three solutions can be unified into a single three-dimensional model for Xer recombination. Thus the three distinct mathematical solutions do not necessarily represent distinct three-dimensional pathways, and in this case the three distinct tangle solutions are different planar projections of the same three-dimensional configuration. Keywords: site-specific recombination; Xer recombination; topological mechanism; tangle equations; DNA knots
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IntroductionSite-specific recombinases catalyze the exchange of genetic material between specific sites on a DNA molecule. This recombination mediates a number of biologically important processes including: integration and excision of viral DNA into and out of its host genome; inversion of DNA segments to regulate gene expression; resolution of multimeric DNA molecules to allow proper segregation at cell division; and plasmid copy number regulation. 1,2 Recombination reactions can be divided into two stages, synapsis and strand-exchange. In the first stage, the two recombination sites are brought together by the recombinase and accessory proteins to form a specific synaptic complex. In the second stage, the DNA strands are cleaved, exchanged and religated within this synapse, to form recombinant products. When the DNA substrate is circular, topological changes associated with recombination can be observed and quantified. These topological changes can be used to infer topological details of the synaptic complex and the strand-exchange mechanism, 3,4 and can be analyzed mathematically using the tangle method (reviewed in the next section). Site-specific recombinases are divided into two families, based on sequence similarity and reaction mechanism: the tyrosine recombinases, which include Flp, Cre, Int and XerC/XerD and recombine through a Holliday junction (HJ) intermediate; 6,7 and the serine recombinases, which include Tn3 and gd resolvases, as well as DNA invertases such as Gin, and recombine via double-strand cleaved intermediates.
8Many serine recombinases display topological selectivity, i.e. they distinguish between sites in different orientations, and between inter-and intramolecular sites. These systems also display topological specificity, i.e. the topology of the substrate uniquely determines the topology of the reaction product. Topological specificity implies that...