Algebraic & Geometric Topology 9 (2009) 2247–2309

DOI: 10.2140/agt.2009.9.2247

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. 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.

Keywords

3–string tangle, DNA topology, tangle method, difference topology, Mu transpososome, graph planarity, Dehn surgery, handle addition lemma

Mathematical Subject Classification

Primary: 57M25, 92C40

References

Publication

Received: 31 October 2007
Revised: 14 July 2009
Accepted: 20 July 2009
Published: 30 October 2009

Authors