An upper bound for the writhing number of knotted DNA

Herman Gluck

Abstract: DNA is typically much longer than its host cell, and so must wrap and coil around itself in order to fit. The "writhing number" is a numerical measure of this wrapping and coiling, and is important to molecular biologists because it is closely connected with the interlinking of the two strands of DNA on the double helix...an interlinking which must be overcome by the action of cut-and-paste enzymes during replication/reproduction.

In this talk, I'll describe ongoing work with Jason Cantarella, the goal of which is to obtain a sharp upper bound for the writhing number in terms of length and thickness of the DNA, and to describe the patterns of coiling which achieve, or come close to, this maximum.

I'll give an overview of the project, including the ideas from electrodynamics which have given us our best hope for a solution, use videos to demonstrate the computer modelling techniques which we have found so helpful, and end by showing how to transform the problem into one which searches for the largest eigenvalues and corresponding eigenfunctions of a family of compact integral operators on Hilbert space.