Tangle analysis of difference topology experiments: applications to a Mu protein-DNA complex

TL;DR

This paper introduces topological methods to analyze difference topology experiments involving 3-string tangles, specifically applied to the Mu protein-DNA complex, revealing a unique biologically relevant solution.

Contribution

It develops a novel topological framework for analyzing protein-DNA complexes using tangle equations and knotted graphs, identifying a unique rational tangle solution.

Findings

Unique rational tangle solution identified

Solution has minimal crossing number

Biologically relevant solution confirmed

Abstract

We develop topological methods for analyzing difference topology experiments involving 3-string tangles. Difference topology is a novel technique used to unveil the structure of stable protein-DNA complexes involving two or more DNA segments. We analyze such experiments for the Mu protein-DNA complex. We characterize the solutions to the corresponding tangle equations by certain knotted graphs. By investigating planarity conditions on these graphs we show that there is a unique biologically relevant solution. That is, we show there is a unique rational tangle solution, which is also the unique solution with small crossing number.