Solving tangle equations and the tangle model for DNA recombination

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• Mauro Mauricio (Imperial)
• Tuesday 15 May 2012, 15:00-16:00
• MR9.

If you have a question about this talk, please contact Dr Andras Juhasz.

In modelling site-specific DNA recombination, one is interested in solving certain “tangle equations” to characterise some biological processes. If the given data consists of “small” 2-bridge knots, then the problem admits a very satisfactory solution, as given by Ernst and Sumners (circa 1990). However, there are instances where one has to deal with connect-sums of 2-bridge knots, and this greatly complicates the analysis. In this talk, we will explain how tangle equations are solved. This is essentially studying a Dehn surgery problem by taking double branched covers. We will see how the work of Ernst and Sumners relied on using some Dehn surgery theorems (available at the time), and how we can use some more recent machinery to obtain some results on the connect-sums of 2-bridge knots case. These turn out to be strong enough to characterise the action of a particular protein, which we will describe.

This talk is part of the Topology Seminar series.

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