Tangle solutions for composite knots: applications to Hin recombination

TL;DR

This paper extends the tangle model to composite knots, providing new mathematical constraints and applying these results to understand the action of Hin recombinase on DNA recombination processes.

Contribution

The authors generalize the tangle model to include composite knots and derive constraints on rational tangle attachments, applying these findings to model DNA recombination by Hin recombinase.

Findings

No rational tangle attachments of distance > 1 yield certain knot types.

Complete solutions to tangle equations for processive and distributive recombination.

Application of the model to biological recombination mechanisms.

Abstract

We extend the tangle model, originally developed by Ernst and Sumners, to include composite knots. We show that, for any prime tangle, there are no rational tangle attachments of distance greater than one that first yield a 4-plat and then a connected sum of 4-plats. This is done by building on results on exceptional Dehn fillings at maximal distance. We then apply our results to the action of the Hin recombinase on mutated sites. In particular, after solving the tangle equations for processive recombination, we use our work to give a complete set of solutions to the tangle equations modelling distributive recombination.