Density-driven support fields for topological stability in protein structures
TL;DR
Support Field Neural Representation Learning (SF-NRL), a topology-guided approach that integrates persistent homology(PH), spatial density estimation, and geometric deep learning to infer residue-wise support directly from protein structures, is introduced.
Abstract
We model protein structural stability as a continuous scalar quantity defined over molecular geometry, referred to as the support field. Instead of treating stability as a discrete residue annotation or an empirical score, this representation characterizes protein folds through the combined effects of geometric organization, topological persistence, and local density. Based on this idea, we introduce Support Field Neural Representation Learning (SF-NRL), a topology-guided approach that integrates persistent homology(PH), spatial density estimation, and geometric deep learning to infer residue-wise support directly from protein structures. Persistent topological features are incorporated as structural constraints that modulate local support values across the fold, enabling a continuous description of structural reliability. Across diverse protein families, the inferred support field shows consistent agreement with independent indicators of structural stability and highlights low-support regions associated with conformational flexibility and weak structural integration. By embedding protein structures into a continuous stability landscape, SF-NRL provides an interpretable representation that complements structure prediction models and facilitates systematic identification of structural cores, flexible regions, and functionally relevant motifs. These results demonstrate that topology-informed field representations offer a generalizable and practically useful approach for analyzing protein stability and fold organization.