BIOLOGICAL DISTANCES ON DNA KNOTS AND LINKS: Applications to XER recombination

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Abstract
The mathematics of tangles has been very useful in studying recombinases which act processively and which require DNA to be in a certain configuration in order for the enzyme to act. Electron micrographs of the enzyme-DNA complex show the enzyme as a blob with DNA looping out of it. The configuration of the DNA within the blob cannot be determined form the electron micrographs. However, mathematics can in some cases determine the configuration of the DNA within the enzyme blob as well as the enzyme action. In this paper, several theorems used to analyze recombinase experiments are summarized. In particular Xer recombinase, an enzyme which does not act processively is analyzed. Unfortunately, for enzymes which do not act processively, infinitely many possibilities exist. Several experiments are proposed to reduce this number and to emphasize both the usefulness and limitations of tangle analysis. Although the local action cannot be mathematically determined without more biological assumptions, it is possible to determine the topology of the synaptic complex through additional biolgical experiments.

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