Physical Knots

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The investigator and his colleagues study "Physical Knots," bridging the gap between purely topological properties of knots and links, and physically realistic systems in which properties such as thickness, curvature, repelling forces, and randomness are evident. Focus areas include: understanding how random tangling increases with filament length in different kinds of systems; determining existence, uniqueness, and geometric properties of optimal conformations of knots; modeling gel electrophoresis of knotted DNA loops; understanding how the "symmetric energy" of knots models physical behavior such as accessibility of molecules to enzymes and self-irradiation of filaments that emit; determining relationships between various knot energies; understanding how knots, such as folding proteins, form in filaments with free ends.This project contributes to the understanding of one of the fundamental ways that matter behaves: a solid object occupies space; a sheet of material separates one part of space from another; and a string tangles with itself or other strings. There is growing scientific awareness that knotting and tangling happen, and are physically important, at every scale of size, from molecules such as DNA and other polymers, to magnetic field lines in the sun. But there are many basic questions that are not yet answered: How are knots and tangles created, or destroyed, in various settings? What happens when one pulls a knot tight? Why do mathematically different kinds of knots behave the way they do in physical situations? How can we model knots on the computer, and how well do the computer simulations reflect actual behavior? The combination of importance of the phenomenon, together with substantial open questions, makes this area fascinating and valuable for research. In particular, the project seeks to contribute to areas of national interest, including increasing understanding of the behavior of DNA molecules, and helping to elucidate the process of protein folding.