The innovation engine for new materials

Leticia Torres

Leticia Torres

Major: 

Mathematics

Mentor(s): 

Eleni Panagiotou

Faculty Sponsor(s): 

Kenneth Millett

Faculty Sponsor's Department(s): 

Mathematics

Project Title: 

Linking Analysis of Knotted Proteins and Topoisomerases Illuminate Structure

Project Description: 

Proteins, large molecules composed of many amino acids, are required for the replication and regulation of the body's cells, tissues, and organs. However, little is known about the correlation between a protein’s function and its structure. Simplifying the representation of these macromolecules, they can be imagined as mathematically simple (closed or open) curves in space. This representation allows the use of knot theory to study their entanglement complexity. In this study, we analyze the linking fingerprint of proteins, a matrix representation of the molecule that encodes the linking of all its sub-chains, to identify important patterns among different proteins but having similar conformation characteristics. Using the simplified polygonal chain of knotted proteins, we analyze the local linking components and identify key features in known knotted proteins. Initial studies have identified strong linking bands as being interesting signals of possibly important regions as well as self-linking features of the local knot that appear similar to those of unknotted regions. Such bands also exist in topoisomerases, which are unknotted enzymes that regulate the overwinding or underwinding of DNA or otherwise assist in its replication. We focus on the family of methyltransferases, proteins whose function is similar and use the linking fingerprint to detect similarities in their structure.