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Capturing surface complementarity in proteins using unsupervised learning and robust curvature measure

The structure of a protein plays a pivotal role in determining its function. Often, the protein surface's shape and curvature dictate its nature of interaction with other proteins and biomolecules. However, marked by corrugations and roughness, a protein's surface representation poses significant challenges for its curvature‐based characterization. In the present study, we employ unsupervised machine learning to segment the protein surface into patches. To measure the surface curvature of a patch, we present an algebraic sphere fitting method that is fast, accurate, and robust. Moreover, we use local curvatures to show the existence of “shape complementarity” in protein–protein, antigen–antibody, and protein‐ligand interfaces. We believe that the current approach could help understand the relationship between protein structure and its biological function and can be used to find binding partners of a given protein.