A Topological Characterization of Knots and Links Arising from Site-Specific Recombination

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2007

Keywords

knots, processive recombination

Abstract

We develop a topological model of knots and links arising from a single (or multiple processive) round(s) of recombination starting with an unknot, unlink, or (2, m)-torus knot or link substrate. We show that all knotted or linked products fall into a single family, and prove that the size of this family grows linearly with the cube of the minimum number of crossings. Additionally, we prove that the only possible nontrivial products of an unknot substrate are (2, m)-torus knots and links and those knots and links which consist of two non-adjacent rows of crossings. (In the special case where one row contains only two crossings, these are the well-known twist knots and links.) In the (common) case of (2, m)-torus knot or link substrates whose products have minimal crossing number m + 1, we prove that the types of products are tightly prescribed, and use this to examine previously uncharacterized experimental data. Finally, we illustrate how the model can help determine the sequence of products in multiple rounds of processive recombination.

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© 2007 Institute of Physics Publishing

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