Mariel Vázquez

Department of Mathematics,
San Francisco State University,
San Francisco CA 94132, USA.

Title: DNA unknotting and unlinking

Abstract: DNA topology is the study of knotting, linking and supercoiling of circular DNA molecules. The bacterial chromosome is circular and replication results in the formation of interlinked DNA circles. Error-free unlinking is required to ensure proper segregation at cell division. In Escherichia coli, in the absence of topo IV (the type II topoisomerase credited with chromosome unlinking), the site-specific recombination system XerCD mediates chromosome unlinking. We use knot theory, low-dimensional topology, and computer simulations to characterize the mechanism by which these enzymes simplify the topology of DNA. It has been proposed that XerCD recombination removes DNA links in a stepwise manner. Here we provide a mathematically rigorous characterization of this topological mechanism of DNA unlinking. We show that stepwise unlinking is the only possible pathway that strictly reduces the complexity of the substrates at each step and propose a topological mechanism for the unlinking reaction.

Title: DNA unknotting, topoisomerases and bacteriophages

Abstract: Type II topoisomerases simplify DNA knots and links efficiently by performing strand-passage on DNA strands. Experimental studies have shown that these enzymes simplify the topology of DNA very efficiently, however the key to this efficiency is yet to be revealed. Motivated by these experimental observations, we study random transitions of knotted polygonal chains of fixed length. We use Monte Carlo computer simulations and computational knot theory methods to model strand-passage, with and without topological biases. Unknotting patterns can assist with knot identification. We propose to apply these methods in the study of the DNA knots extracted from bacteriophage P4 capsids.