  Site-specific recombination on supercoiled circular DNA molecules can yield a
variety of knots and catenanes. Twist knots are some of the most common
conformations of these products and they can act as substrates for further
rounds of site-specific recombination. They are also one of the simplest
families of knots and catenanes. Yet, our systematic understanding of their
implication in DNA and important cellular processes like site-specific
recombination is very limited. Here we present a topological model of
site-specific recombination characterising all possible products of this
reaction on twist knot substrates, extending previous work of Buck and Flapan.
We illustrate how to use our model to examine previously uncharacterised
experimental data. We also show how our model can help determine the sequence
of products in multiple rounds of processive recombination and distinguish
between products of processive and distributive recombination. This model
studies generic site- specific recombination on arbitrary twist knot
substrates, a subject for which there is limited global understanding. We also
provide a systematic method of applying our model to a variety of different
recombination systems.
