Entanglement-based continuum conformational landscape of proteins

MotivationWith the rapid development of AI methods that predict protein structures from sequence, understanding the structure-function relation increasingly depends on quantitative structural descriptors that are both biologically meaningful and scalable to large datasets. Here, we introduce mathematical topology metrics that quantify the entanglement complexity of a tertiary protein structure while respecting uncrossability constraints. ResultsBy employing only three such metrics across all protein structures in the Protein Data Bank, we represent the proteome structural space in a continuous three-dimensional space. Distances within this space capture structural similarity and correlate with functional similarity. We find that the mathematical entanglement based landscape of protein structural space diversifies with the evolutionary expansion of protein function across species. Moreover, this continuous representation reproduces CATH classifications with high accuracy for major structural classes. These results indicate that these metrics efficiently encode structural features linked to protein function and provide a more informative description than conventional metrics. AvailabilityData used in this study are available in the Protein Data Bank. Details of the machine learning model used can be found in https://github.com/roshitac/CATH_Classification-. ContactBanu.Ozkan@asu.edu, Eleni.Panagiotou@asu.edu Supplementary informationSupplementary data are available at Journal Name online.