LEAPS-MPS: DNA Knot Shadows Explorations

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This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). Recent advances at the intersection of mathematics and biology have demonstrated that topological methods can help address one of the fundamental challenges in science: how DNA functions as the building blocks of a living organism. In laboratory experiments, biologists react circular DNA substrates with proteins and capture protein signatures in the form of changes in the shape of the DNA. The mathematics of topological objects (for example, knots, links, and tangles) are then applied to these biological observations to deduce the action of proteins. The project's research objectives are to classify experimentally obtained images of products of protein-DNA interactions; to accurately model strand dynamics of protein-DNA interactions; and to share the computational tools developed in the course of this work, ultimately creating a database for mathematicians and biologists working on related scientific questions. This project is also designed to attract underrepresented students to STEM studies and careers, particularly at the intersection of mathematics and biology.To further the understanding of the dynamics of DNA topology, the PI will apply combinatorial tools to interpret 2-dimensional projections of DNA products of protein action. As DNA knots are 3-dimensional objects, some information is inevitably lost when they are projected into 2-dimensions. In previous work, the PI extended the relationship between skein relation knot quadruples of 4-plats algebraically. The overall goal of this proposed research is to extend the utility of knot quadruples with combinatorics by focusing on the 2-dimensional projections of knots with no crossing information. The proposed study will allow for the creation of quadruples that have not been categorized with previous techniques, while also refining previously found bounds on knot distances. In addition, the project will continue to pursue the PI's service mission: to support those underrepresented in STEM by creating and supporting programs that increase visibility of, and amplify the voices of, women and people of color in STEM, and create networks and community in STEM to provide opportunities to share resources.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.