Computational geometry, Delaunay tessellations and alpha shapes for protein interactions: Exploring Coronavirus Mpro drug binding

This work discusses application of techniques of computational geometry and topological persistence to the problem of comparing drug interactions with SARS-CoV-2 main protease (Mpro). We use alpha-shape methods and Delaunay triangulations, which generalize convex hulls of point sets in 3D and are an efficient way of representing molecular shapes and between-atom relationships in proteins. Weighted Delaunay triangulations are needed to accommodate different Van der Waals radii of atoms, and formation of alpha complexes from those tessellations permit characterization of the protein pockets that enable drug binding. This work applies the tools of computational geometry to a comparative analysis of drug binding to Mpro, which is a primary target for therapeutic development against Covid-19. Mpro functions to enzymatically cleave the SARS-CoV-2 polypeptide encoded by the RNA genome into its constituent functional parts, critical for viral replication. There are nearly 300 Mpro structures deposited to the PDB with various ligands bound, including inhibitors and small molecule fragments. We also have structures of the apo- form of Mpro, with no ligand bound. Our analyses of Mpro drug binding sites from these structures reveal variations in the binding pockets that can influence specificity and strength of ligand binding ability.