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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
Isabel K. Darcy

Mathematics Department

University of Iowa

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

Modeling Protein-DNA

Complexes Using Tangles

slide3

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.

slide4

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

slide6

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

slide7

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

slide8

Older Model:

Newer Model:

slide15

x2

x2

x1

x1

x3

x3

x2 + x3 = 4

slide16

x2

x1

x3

x2 + x3 = 4

x1 + x3 = 3

x1 + x2 = 3

implies

x1 = 1,

x2 = 2,

x3 = 2

Thus T =

slide18

Theorem [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)

slide19

TopoICE in

Rob Scharein’s

KnotPlot.com

slide20

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

slide21

Cover: 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).

slide22

Topoisomerase II performing a crossing change on DNA:

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