Learning Protein-Ligand Binding in Hyperbolic Space

Abstract: Protein-ligand binding prediction is central to virtual screening and affinity ranking, two fundamental tasks in drug discovery. While recent retrieval-based methods embed ligands and protein pockets into Euclidean space for similarity-based search, the geometry of Euclidean embeddings often fails to capture the hierarchical structure and fine-grained affinity variations intrinsic to molecular interactions. In this work, we propose HypSeek, a hyperbolic representation learning framework that embeds ligands, protein pockets, and sequences into Lorentz-model hyperbolic space. By leveraging the exponential geometry and negative curvature of hyperbolic space, HypSeek enables expressive, affinity-sensitive embeddings that can effectively model both global activity and subtle functional differences-particularly in challenging cases such as activity cliffs, where structurally similar ligands exhibit large affinity gaps. Our mode unifies virtual screening and affinity ranking in a single framework, introducing a protein-guided three-tower architecture to enhance representational structure. HypSeek improves early enrichment in virtual screening on DUD-E from 42.63 to 51.44 (+20.7%) and affinity ranking correlation on JACS from 0.5774 to 0.7239 (+25.4%), demonstrating the benefits of hyperbolic geometry across both tasks and highlighting its potential as a powerful inductive bias for protein-ligand modeling.