Fast and Interpretable Estimation of Amino Acid Residue Surface Accessibility Based on Protein Contact Graph

Abstract

The solvent-accessible surface area (SASA) of amino acid residues is a crucial parameter for protein structure analysis; however, precise computational methods such as FreeSASA are computationally expensive. As an alternative, empirical approximations based on residue interaction network (RIN) graphs can offer high speed while maintaining acceptable accuracy. In this study, we propose and validate three empirical functions for estimating relative SASA—approx_sasa, surface_score, and exp_sasa—using node degree as the sole argument. We present a comparative analysis of two graph construction approaches: the classical Cα-graph (8 Å threshold) and the heavy-atom graph (HAG, 5.0 Å threshold). Parameters were calibrated on a dataset of 509 protein structures (128,794 residues) using the true relative SASA calculated by the FreeSASA library. An extended set of 11 topological features was also developed and validated. Ensemble models (Random Forest, XGBoost) achieved a best performance of MAE = 0.057 ± 0.033 and Pearson r = 0.915 ± 0.080 on HAG, outperforming graph neural networks (GCN, GAT, GraphSAGE) in this setting. The empirical formulas demonstrate extreme computational efficiency (0.008 ms per structure), ~26,000× faster than FreeSASA, making them suitable for large-scale pipelines requiring both speed and interpretability. Random Forest on HAG is recommended for applications requiring maximum accuracy, while GraphSAGE on HAG is a viable deep learning alternative.