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Isabel K. Darcy Mathematics Department University of Iowa http://www.math.uiowa.edu/~idarcy Modeling Protein-DNA Complexes Using Tangles http://knotplot.com/zoo

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Isabel k darcy mathematics department university of iowa http www math uiowa edu idarcy l.jpg

Isabel K. Darcy

Mathematics Department

University of Iowa

http://www.math.uiowa.edu/~idarcy

Modeling Protein-DNA

Complexes Using Tangles



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Duplex DNA knots produced by Escherichia coli topoisomerase I. Dean FB, Stasiak A, Koller T, Cozzarelli NR., J Biol Chem. 1985 Apr 25;260(8):4975-83.


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C. Ernst, D. W. Sumners, A calculus for rational tangles: applications to DNA recombination, Math. Proc. Camb. Phil. Soc. 108 (1990), 489-515.

protein = three dimensional ball

protein-bound DNA = strings.

Protein-DNA complex

Heichman and Johnson


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Solving tangle equations applications to DNA recombination,


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Path of DNA within the Mu Transpososome Transposase Interactions Bridging Two Mu Ends and the Enhancer Trap Five DNA Supercoils

Shailja Pathania, Makkuni Jayaram and

Rasika M Harshey


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Interactions of Phage Mu Enhancer and Termini that Specify the Assembly of a Topologically Unique Interwrapped Transpososome

Zhiqi Yin, Asaka Suzuki, Zheng Lou,

Makkuni Jayaram and Rasika M. Harshey


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Older Model: the Assembly of a Topologically Unique Interwrapped Transpososome

Newer Model:


A difference topology experiment l.jpg
A difference topology experiment: the Assembly of a Topologically Unique Interwrapped Transpososome


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x the Assembly of a Topologically Unique Interwrapped Transpososome 2

x2

x1

x1

x3

x3

x2 + x3 = 4


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x the Assembly of a Topologically Unique Interwrapped Transpososome 2

x1

x3

x2 + x3 = 4

x1 + x3 = 3

x1 + x2 = 3

implies

x1 = 1,

x2 = 2,

x3 = 2

Thus T =


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Theorem [ the Assembly of a Topologically Unique Interwrapped Transpososome Darcy, I. K., Luecke, J., Vazquez, M., Tangle analysis of difference topology experiments: applications to a Mu protein-DNA complex]: If T is a solution to the Mu-Cre equations, and if either

1.) T is rational or split or has parallel strands or

2.) If T has fewer than 9 crossings,

Then

T =

(assuming a particular handedness of the products)


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TopoICE in the Assembly of a Topologically Unique Interwrapped Transpososome

Rob Scharein’s

KnotPlot.com


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3D visualization software to analyze topological outcomes of topoisomerase reactions

I. K. Darcy,

R. G. Scharein and A. Stasiak Nucleic Acids Research 2008 36(11):3515-3521


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Cover topoisomerase reactions: Visual presentation of knot distance metric created using the software TopoICE-X within KnotPlot. A pair of knots in this graph is connected by an edge if they can be converted into one another via a single intersegmental passage. This graph shows all mathematically possible topoisomerase reaction pathways involving small crossing knots. Darcy et al. (Nucleic Acids Res., 2008; 36: 3515–3521).


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Topoisomerase II performing a crossing change on DNA: topoisomerase reactions

Cellular roles of DNA topoisomerases: a molecular perspective, James C. Wang, Nature Reviews Molecular Cell Biology 3, 430-440 (June 2002)