Volume 9, issue 4 (2009)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
References
Publication
Received: 31 October 2007
Revised: 14 July 2009
Accepted: 20 July 2009
Published: 30 October 2009
Authors
Isabel K Darcy
Department of Mathematics
University of Iowa
Iowa City, IA 52242
USA
http://math.uiowa.edu/~idarcy
John Luecke
Department of Mathematics
The University of Texas at Austin
1 University Station C1200
Austin, TX 78712-0257
USA
Mariel Vazquez
Department of Mathematics
San Francisco State University
1600 Holloway Avenue
San Francisco, CA 94132
USA
http://math.sfsu.edu/mariel/