RUI: Structure of Entanglement in Macromolecules

University Of St. Thomas, Saint Paul MN

Investigators

Abstract

The structures of tightly entangled tubes have been used to predict properties of entangled macromolecules, e.g. the pitch of alpha helices in proteins and the pitch of the DNA double helix. In addition, physicists have proposed that subatomic particles known as glueballs are tightly entangled QCD flux tubes. While there is a great deal of mathematical and scientific interest in these tight entanglements, explicit descriptions are unknown for all but some simple examples. In the first portion of this project, the PI, collaborators, and students determine the structure of tight knots and links by performing careful numerical simulations and using the data to provide explicit descriptions of tight configurations and their sets of tube-to-tube contacts. These configurations provide insights into how long tubes pack into small spaces, behavior seen throughout nature (e.g. in the packing of DNA in viral capsids). Entanglement can also be seen in natural materials that form open chains. The existence (or lack thereof) of entangled regions in polymeric chains, for example, raises many interesting questions regarding the complex interplay between structure and function. Recently, the discovery of knotted regions in proteins has received much attention. However, the algorithms for detecting the regions (and, thus, the definition of exactly what a knotted open chain is) vary by research group and is in much need of rigorous analysis. In the second portion of this project, the PI, collaborators, and students explore new notions of knotting in open chains that can be used to detect entangled regions in polymers and then measure the size and shape of these knotted regions. In particular, they establish a firm theoretical understanding of entanglement in open chains, use new and established spatial measurements to better understand the shapes of linked catenanes and knotted polymer chains and loops, and find connections between the structure of polymer models and those of tight knots. Knotting and tangling occur frequently in nature at every scale. For example, DNA forms knots during biological reactions and physicists conjecture that magnetic fields formed during storms on the sun can be knotted. The early proposal of Kelvin that elementary particles form knots found recent support in studies of subatomic particles known as glueballs which are hypothesized to take the shape of tightly entangled tubes. Other chain-like natural materials pack tightly as well, e.g. a large amount of DNA is packed into the head of viruses and the release of the DNA into the cell is what spearheads the infection process. The structure and function of these chains are inherently intertwined. In particular, understanding the native structure of these chains is a key step in manipulating processes, such as in creating designer plastics or identifying and killing rogue cells. The PI, collaborators, and students study two models: tight realizations of knots and knots occurring in open and closed chains. Examples of applications include predicting unidentified glueballs, describing how materials pack tightly in small spaces, and characterizing the structure of knots in open chains of protein.