The Writhe—A Macromolecular Shape Descriptor; Applications to DNA Structure

speaker: De Witt Sumners (Florida State University)

abstract: The directional writhe of a spatial closed curve is the sum of the signed crossings in the projection of the curve in the given direction. The writhe of a simple closed curve in 3-space is the average over all directions of directional writhe. We extend 1 this definition to apply to edge-oriented (each edge has an arrow on it) finite spatial graphs. This definition of writhe covers spatial polygonal arcs and non-connected graphs, and does not require the ad hoc closing of arcs to eliminate the problems posed by endpoints. This talk will discuss the properties of writhe of graphs, and the proof of writhe additivity for connected sums, with applications to DNA and RNA.

References:

1. E.J.Janse van Rensburg, E. Orlandini, D.W. Sumners, M.C. Tesi and S.G. Whittington. The writhe of a self-avoiding walk, J. Phys. A Math. Gen. 27 (1994), L333-L338.

2. E.J.Janse van Rensburg, E. Orlandini, D.W. Sumners, M.C. Tesi and S.G. Whittington. The writhe of knots in the cubic lattice, Journal of Knot Theory and Its Ramifications 6 (1997), 31-44.

3. C. Laing and D.W. Sumners, Computing the Writhe on Lattices, J. Phys A, Math. Gen. 39 (2006), 3535-3543.

4. C. Laing and D.W. Sumners. The Writhe of Oriented Polygonal Graphs, J. Knot Theory and Its Ramifications 17 (2008), 1575-1594.

5. C. Laing and D.W. Sumners. Additivity of Writhe. In preparation.

timetable:
Thu 16 Jun, 11:30 - 12:30, Aula Dini
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