A note on the tangle model for DNA recombination

Abstract

The tangle model developed by Ernst and Sumners provides a rigorous framework to study processive DNA recombination. We suggest here a slight modification of that model. The tangle equations become:

$$\begin{gathered} N(S) = b(1,1), \hfill \\ N(S + M) = b(2,1), \hfill \\ N(S + M + M) = b(5,2), \hfill \\ N(S + M + M + M) = b(8,5), \hfill \\ N(S + M + M + M + M) = b(11,7), \hfill \\ \end{gathered} $$

where M is the mechanism tangle, and S is the substrate tangle, that is the sum of O (outside tangle) and P (parent tangle). The advantage of this revisited model is that it faithfully models the fact that the recombination mechanism is the same during each event of recombination. This leads to new solutions for O and P, some of which are interesting from a biological viewpoint.