A Topological Characterization Of Knots and Links Arising From Site-Specific Recombination

TL;DR

This paper presents a topological model for knots and links resulting from site-specific recombination, revealing that all products belong to a specific family with size growing linearly with the cube of minimal crossings, and characterizing possible outcomes.

Contribution

It introduces a comprehensive topological framework for analyzing recombination products, identifying their family structure and growth, and classifying possible knot and link types from simple substrates.

Findings

All recombination products fall into a single family.

The family size grows linearly with the cube of minimal crossings.

Products from unknot substrates are classified as clasp knots/links or (2,m)-torus knots/links.

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 products of an unknot substrate are either clasp knots and links or (2,m)-torus knots and links. Finally, 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.