Calculating the Secrets of Life: Contributions of the Mathematical Sciences to Molecular Biology (1995)
Chapter: Application of Geometry and Topology to Biology
Page 232
relaxed DNA knots is determined by crossing number; the larger the crossing number, the faster the migration. Perhaps this is because among knots of the same length with small crossing numbers, the average value of the radius of gyration (a measure of the average size) correlates strongly with crossing number. It is very curious that the crossing number, clearly an artifact of planar diagrammatic representation of knots, would have anything at all to do with the three-dimensional average knot confor-mation. What is the relationship (if any) between radius of gyration of DNA circles of fixed molecular weight and fixed knot type, crossing number, and the gel mobility of these knotted DNA circles?
Annotated Bibliography
Knot Theory
Adams, C., 1994, The Knot Book: An Elementary Introduction to Mathematical Theory of Knots, New York: W.H. Freeman.
Kauffman, L.H., 1987, On Knots, Princeton, N.J.: Princeton University Press.
Livingston, C., 1994, Knot Theory, Carus Mathematical Monograph, Vol. 24, Washington, D.C.: Mathematical Association of America.
Rolfsen, D., 1990, Knots and Links, Berkeley, Calif.: Publish or Perish, Inc.
Each of these mathematics books has an easygoing, reader-friendly style and numerous pictures, a very important commodity when one is trying to understand knot theory.
Application of Geometry and Topology to Biology
Bauer, W.R., F.H.C. Crick, and J.H. White, 1980, "Supercoiled DNA," Scientific American 243, 100-113.
This paper is a very nice introduction to the description and measurement of DNA supercoiling.
Sumners, D.W., 1987, "The role of knot theory in DNA research," pp. 297-318 in Geometry and Topology, C. McCrory and T. Shifrin (eds.), New York: Marcel Dekker.
Sumners, D.W., 1990, "Untangling DNA," The Mathematical Intelligencer 12, 71-80.
These papers are expository articles written for a mathematical audience. The first gives an overview of knot theory and DNA, and the second describes the tangle model.
Sumners, D.W. (ed.), 1994, New Scientific Applications of Geometry and Topology, Proceedings of Symposia in Applied Mathematics, Vol. 45, Providence, R.I.: American Mathematical Society.
