Accurate Protein-Ligand Affinity Prediction by Modeling Molecular Interactions

Accurately predicting the binding affinity of a ligand to its protein target is a central challenge in computational drug discovery. This affinity emerges from a complex interplay of non-covalent interactions—hydrogen bonding, hydrophobic effects, and electrostatics—governed by subtle geometric and energetic trade-offs. While geometric deep learning has advanced this field, prevailing models largely refine representations for atoms or residues (nodes), leaving the crucial intermolecular interactions implicitly modeled as conduits for message passing rather than first-class learning targets. We argue that directly modeling the interaction network offers a more physically grounded alternative. We introduce PHESA (Physics-informed Hierarchical Edge-Set Attention), a framework built upon edge-set attention that: (1) treats pairwise intermolecular interactions as primary objects across two scales—the atomic level and the chemical-group level (residues and BRICS-defined motifs); and (2) injects physical priors via rich edge features and a learnable bias added to the attention logits, informed by geometric and electrostatic descriptors. On the PDBbind v2016 benchmark under stringent splits, PHESA attains state-of-the-art accuracy. On the Sequence-Identity (60%) split it reaches RMSE 1.34, Pearson 0.79, and Spearman 0.77; on the Scaffold split it achieves RMSE 1.50, Pearson 0.53, and Spearman 0.54. Without task-specific modification, the same architecture generalizes to protein-protein binding freeenergy change prediction ($\Delta \Delta G$) on SKEMPI v2.0, where it surpasses several specialized learned and physics-based baselines. Attention maps highlight chemically meaningful hydrogen-bonding, hydrophobic packing, and electrostatic patterns, providing interpretable rationales. Collectively, these results establish hierarchical, edge-centric modeling with physics-aware attention as a robust, accurate, and generalizable paradigm for learning molecular interactions.