Isabel K. Darcy Mathematics Department University of Iowa idarcy ©2008 I.K. Darcy. All rights...
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Transcript of Isabel K. Darcy Mathematics Department University of Iowa idarcy ©2008 I.K. Darcy. All rights...
Isabel K. Darcy
Mathematics Department University of Iowahttp://www.math.uiowa.edu/~idarcy
©2008 I.K. Darcy. All rights reserved
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Rob Scharein’s
KnotPlot.com
http://updatecenter.britannica.com/art?assemblyId=91&type=A
Intricate Knots in Proteins: Function and EvolutionPeter Virnau, Leonid A. Mirny, and Mehran Kardar, PLoS Comput Biol. 2006 September; 2(9): e122.
Statistics of knots, geometry of conformations, and evolution of proteins.Rhonald C. Lua, Alexander Y. Grosberg PLoS Comput Biol. 2006 May;2(5)
unknot 3.1 4.1 5.2
Direct 4516 164 9 3
Center 4692 20 3 1
Random 4697 15 0 1
and more complicated knots for random closure
Many mathematicians solve equations
x + 3 = 5
x = 2 is a solution: 2 + 3 = 5
x = 1 is not a solution: 1 + 3 = 4 = 5
Solving tangle equations
A + B = C
2 + 0 = 2
2 + -2 = 0
Most tangles don’t have inverses
Some tangles (but not all) can be classified using fractions.
How to solve tangle equations
1.) Brute force
Ex: solve x + 3 = 5
1 + 3 = 5, 1 + 3 = 5, 2 + 3 = 5
How to solve tangle equations
1.) Brute force
Ex: solve x + 3 = 5
1 + 3 = 5, 1 + 3 = 5, 2 + 3 = 5
2.) Use mathematics
A protein bound to two segments of DNA can be modeled by a tangle. An electron micrograph of the Flp DNA complex is shown below:
Electron micrograph courtesy of Kenneth Human and Steve Levene
The tangle equations corresponding to the electron micrograph:
Protein-DNA complexHeichman and Johnson
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.
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
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
A difference topology experiment: