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Modeling Protein-DNA Complexes Using Tangles: A Mathematical Analysis

Explore the intricate world of protein-DNA complexes through tangle analysis. Discover the applications of rational tangles in DNA recombination and topological outcomes of topoisomerase reactions. This study delves into the structural intricacies of protein-bound DNA strings, providing insights into the interactions and pathways within the Mu transpososome. Unravel the mathematics behind DNA topology experiments and the cellular roles of DNA topoisomerases. Visualize knot distance metrics and explore the diverse topological pathways involved in small crossing knots. The research links theory to practice, showcasing the interplay between mathematics and molecular biology.

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Modeling Protein-DNA Complexes Using Tangles: A Mathematical Analysis

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

  2. http://knotplot.com/zoo

  3. 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.

  4. 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

  5. Solving tangle equations

  6. 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

  7. 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

  8. Older Model: Newer Model:

  9. A difference topology experiment:

  10. x2 x2 x1 x1 x3 x3 x2 + x3 = 4

  11. x2 x1 x3 x2 + x3 = 4 x1 + x3 = 3 x1 + x2 = 3 implies x1 = 1, x2 = 2, x3 = 2 Thus T =

  12. 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)

  13. TopoICE in Rob Scharein’s KnotPlot.com

  14. 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

  15. 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).

  16. 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)

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