Mathematics of DNA

In order to perform such functions as replication and information transmission, DNA must transform itself from one form of knotting or coiling into another. The agent for these transformations are enzymes. Enzymes maintain the proper geometry and topology during the transformation and also ``cut'' the DNA strands and recombine the loose ends. Mathematics can be used to model these complicated processes.

In an article published in the May 1995 issue of the Notices of the AMS, " Lifting the Curtain: Using Topology to Probe the Hidden Action of Enzymes, " mathematician De Witt Sumners discusses these problems. Sumners has worked for a number of years with molecular biologists to help them unravel some of the mathematical problems presented by DNA structure.

``The description and quantization of the three-dimensional structure of DNA and the changes in DNA structure due to the action of these enzymes have required the serious use of geometry and topology,'' Sumners writes. ``This use of mathematics as an analytical tool is especially important because there is no experimental way to observe the dynamics of enzymatic action directly.''

A key mathematical challenge is to deduce the enzyme mechanisms from observing the changes the enzymes bring about in the geometry and topology of the DNA. ``This requires the construction of mathematical models for enzyme action and the use of these models to analyze the results of topological enzymology experiments,'' the article says. ``The entangled form of the product DNA knots and links contains information about the enzymes that made them.''

-Allyn Jackson