The tangle model is a mathematical method due to De Witt Sumners and Claus Ernst [Sumners et al. Quart. Rev. Biophysics 28, 3 (1995), 253 - 313], which uses knot theory and low-dimensional topology to understand the mechanisms of binding and strand-exchange by site-specific recombinases. A web description of the tangle model can be found here.

TangleSolve. While at Berkeley, I worked with an undergraduate research assistants, Yuki Saka, Wenjing Zheng and Stefanus Jasin on a computer implementation of the tangle model. The resulting software, TangleSolve, is available for use on the web or for download. A description of TangleSolve can be found in [Saka and Vazquez, 2002; Zheng et al. 2007], and on the TangleSolve website. 

I have worked on several site-specific recombination systems: 

Gin and mutant Gin, Vazquez and Sumners, 2004

Gin is a site-specific recombination system of bacteriphage Mu. Bacteriophage Mu infects a large family of bacteria, including several strains of Escherichia coli. Gin’s role in the phage’s development is to invert a segment of DNA, called the G-segment, thus extending the host range of the phage. The DNA knots and/or links produced by site-specific recombination on circular DNA substrates were characterized in Nicholas Cozzarelli’s lab in Berkeley, mainly by Roland Kanaar (Gin) and Nancy Crisona (mutant Gin).

XerC/XerD at psi, Vazquez, Colloms and Sumners, 2005

XerC and XerD are two site-specific recombinases of E. coli which act cooperatively to resolve chromosomal dimers formed by Homologous Recombination, thus allowing proper segregation at cell division. XerC/XerD act at dif sites in the E. coli chromosome, but also at other sites such as psi and cer in naturally occurring plasmids. When acting at psi sites the Xer system produces 4-crossing torus links. The experiments were done in David Sherratt’s lab (University of Oxford) by Jonathan Bath and Sean Colloms. 

FtsK-XerC/D at dif, Grainge et al. 2007

To act at dif sites, XerC and Xer D are recruited by the powerful translocase FtsK and co-localize at the septum to perform a simple recombination event turning a dimeric chromosomes into two monomers which can properly segregate at cell division. We have recently reported that this system is able to unlink replication catenanes in vivo when topoIV is inhibited. I have analyzed the mathematical pathway of unknotting. The experiments were done by Ian Grainge and Migena Bregu in Sherratt’s lab in Oxford, and I am collaborating with Koya Shimokawa (Saitama University, Japan) on the mathematical analysis.

TnpI-IRS, Zheng et al. 2007

Bacillus thuringiensis is a bacterium that produces specific toxins that are lethal to a variety of insect species, but inoffensive to most other organisms Therefore, B. thuringiensis and its toxin crystals are used in organic farming to protect crops from harmful moths and butterflies.

Transposons are segments of DNA that can move to different regions (transposition) within the genome of a single cell. Tn4430 is a transposon from from B. thuringiensis. During this process, co-integrate intermediates between the donor and target replicons are generated. Tn4430 encodes the TnpI protein, a member of the tyrosine site-specific recombinase family that catalyzes the site-specific recombination reaction used to resolve these co-integrate intermediates. In-vitro recombination reactions on circular DNA substrates with two directed repeats of the full IRS sites yield products with specific topology: all products are two-node links (Hopf Links). The DNA knots and/or links produced by TnpI recombination were characterized by Christine Galloy in Bernard Hallet’s lab (Universite Catholique de Louvain)