Topological magnitude for protein flexibility analysis

Protein flexibility is critical for structural adaptability and biological function, influencing enzymatic catalysis, molecular recognition and signal transduction. Magnitude, an invariant from category theory and algebraic topology, was initially used to measure the size of finite metric spaces and has since been extended to graphs, hypergraphs and material science. In this study, we introduce a novel method for predicting B-factors based on the magnitude of finite metric spaces. We model protein structures as finite metric spaces with biologically relevant distance functions and use magnitude to capture their geometric and topological properties, improving the prediction of B-factors, which represent atomic fluctuation. Experimental results on the superset dataset show that our method achieves a Pearson correlation coefficient (PCC) of 0.725, outperforming GNM, pfFRI, ASPH, opFRI and EH. Compared with GNM, our approach improves PCC by 28.32%, demonstrating its performance advantage. Additionally, by combining magnitude with global and local structural features, we validate the method’s robustness in blind tests, proving its effectiveness in predicting B-factors and offering a novel approach to protein dynamics analysis.