#### Volume 9, issue 4 (2009)

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

### Isabel K Darcy, John Luecke and Mariel Vazquez

Algebraic & Geometric Topology 9 (2009) 2247–2309
##### 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 2000
Primary: 57M25, 92C40