Isabel K Darcy Mathematics Department University of Iowa

Rob Scharein’s Knot. Plot. com

http: //updatecenter. britannica. com/art? assembly. Id=91&type=A

Intricate Knots in Proteins: Function and Evolution Peter Virnau, Leonid A. Mirny, and Mehran Kardar, PLo. S Comput Biol. 2006 September; 2(9): e 122.

Statistics of knots, geometry of conformations, and evolution of proteins. Rhonald C. Lua, Alexander Y. Grosberg PLo. S Comput Biol. 2006 May; 2(5) unknot 3. 1 4516 164 9 3 Center 4692 20 3 1 Random 4697 15 0 1 Direct 5. 2 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

$Some tangles (but not all) can be classified using fractions.$

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, 2 + 3 = 5

How to solve tangle equations 1. ) Brute force Ex: solve x + 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:

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

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: