Pocket-Surface Discrete Differential Geometry as a Leakage-Robust Feature Class for Protein-Ligand Binding Affinity Prediction.

Protein-ligand binding affinity prediction underpins structure-based drug discovery, yet random partitions of public benchmarks overestimate generalisation due to protein-family and ligand leakage, and the marginal value of explicit pocket-geometry descriptors over atom-level graph neural networks remains unclear. We computed a 59-dimensional discrete differential geometry descriptor on the ligand-aware solvent-excluded surface of 3285 PDBBind v2020 complexes, combining curvature distributions, the leading sixteen Laplace-Beltrami eigenvalues and a ten-point heat-kernel signature, and evaluated it in gradient-boosted tree pipelines across progressively stricter split regimes and two leak-proof external benchmarks, together with four mechanistically distinct injection strategies in a SchNet-style graph neural network. The descriptor lifted Pearson correlations by 0.111 on cluster-disjoint testing, 0.258 on LP-PDBBind DataSAIL S2 and 0.365 on CASF-2016, while in isolation reaching 0.456 to 0.594 on external benchmarks, on a par with X-Score and AutoDock Vina (version 1.2). TreeSHAP attribution localised the dominant signal to the heat-kernel signature. The four graph neural network injection strategies produced no statistically significant lift, indicating that distance-based message passing on atomic coordinates already captures much of the geometric content. Pocket-surface discrete differential geometry, therefore, offers an interpretable, leakage-robust and lightweight feature class for early-stage virtual screening, and motivates hybrid mesh-to-atom architectures.