Title:  Topological Metrics of Biopolymer Structure and Function
Abstract:  Proteins and other biopolymers can be represented by mathematical curves in space. Understanding the structure of such macromolecules is at the core of very important problems in biology, such as protein folding, protein aggregation and cell nucleus organization and function. The single, pairwise, or multi-chain characterization of entanglement complexity becomes rigorous in the context of mathematical topology. In this talk we will introduce a novel and general topological approach to analyze the structures of macromolecules. We will apply our methods to proteins and show that these enable us to create a new framework for understanding protein folding, which is validated by experimental data. When applied to the SARS-CoV-2 spike protein, we see that topology can predict residues where mutations can have an important impact on protein structure and possibly in viral transmissibility. These methods can thus help us understand biopolymer function and biological material properties in many contexts with the goal of their prediction and design.