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

Abstract

Relevance. The solvent accessible surface area (SASA) of amino acid residues is a key characteristic for protein structure analysis, but precise methods for calculating it (e.g., FreeSASA) are computationally expensive. Empirical approximations based on the res-idue interaction network (RIN) graph can provide high speed while maintaining ac-ceptable accuracy. Proposed approach. Three empirical functions for estimating relative SASA are pro-posed: approx_sasa, surface_score, and exp_sasa using the degree of the node in RIN as an argument. We present a comparative study of two approaches to graph construction: the classical Cα-graph (threshold 8 Å) and the graph of heavy atoms (Heavy-Atom Graph, HAG, threshold 5.0 Å). The parameters were calibrated on a sample of 509 protein structures (128,794 residues) from various origins using the true relative SASA calculated by the FreeSASA library. Main results. An extended set of 11 RIN topological features was developed and vali-dated, including basic node characteristics, centrality measures (betweenness, eigen-vector, closeness) and hydrophobic subgraph features. Training ensemble models (Random Forest, XGBoost) with these features made it possible to achieve: Random Forest on HAG: MAE = 0.057 ± 0.033, Pearson r = 0.915 ± 0.080 (best result), Random Forest on Cα graph: MAE = 0.066 ± 0.041, Pearson r = 0.890 ± 0.100. Comparison with GNN. We compared our approach with graph neural networks (GCN, GAT, GraphSAGE). GraphSAGE on HAG showed a result close to Random Forest: MAE = 0.0715, Pearson r = 0.8917, indicating the potential applicability of graph neural net-works when using HAG. GCN and GAT performed significantly worse (MAE = 0.14–0.15, Pearson r = 0.51–0.61). Computational efficiency. Empirical formulas are calculated in 0.008 ms per structure (~26,000× faster than FreeSASA), Random Forest in prediction mode is calculated in 36.5 ms (~6× faster than FreeSASA). HAG construction takes 21 times longer than a Cα graph (279.5 ms vs. 13.3 ms). Practical significance. The proposed empirical features are recommended for large-scale pipelines critical to speed and interpretability. Random Forest on HAG is the optimal choice for tasks that require maximum accuracy (MAE = 0.057, Pearson r = 0.915). GraphSAGE on HAG can be considered as an alternative when using deep learning.