The protein recombinase can change the knot type of circular DNA. The action of a recombinase converting one knot into another knot is normally mathematically modeled by band surgery. Band surgeries on a –bridge knot yielding a –torus link are characterized. We apply this and other rational tangle surgery results to analyze Xer recombination on DNA catenanes using the tangle model for protein-bound DNA.
"Rational tangle surgery and Xer recombination on catenanes." Algebr. Geom. Topol. 12 (2) 1183 - 1210, 2012. https://doi.org/10.2140/agt.2012.12.1183