Topological entanglement effects in biopolymers

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. Predicting polymer material properties based on chemical composition, density, crosslinking, or architecture requires bridging the gap between the lengthscale of chemical bonds to that of an entire polymer chain and also bridging the gap of properties of a single chain and those of a collection of chains. 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.

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