CurvFlow-DTA: dual-graph discrete Ricci curvature flow for drug--target affinity prediction

Graph neural networks are widely used for drug--target affinity (DTA) prediction, and discrete Ricci curvature has recently been used to characterize molecular graph geometry. Existing curvature-aware DTA approaches mainly use static curvature on the drug graph while representing proteins primarily with sequence-derived features. This leaves pair-adaptive use of graph geometry underexplored, which may limit adaptation to unseen entities in cold-start settings relevant to practical screening. We present CurvFlow-DTA, which replaces a single static curvature representation with weighted Forman curvature flow on both molecular and protein residue--residue contact graphs. A label-independent flow trajectory is precomputed for each entity, and a pair-conditioned selector determines the horizons read by a dual-branch Flow-GINE. A frozen ESM-2 supplies residue-level representations and contact scores used to construct the protein graph. Inference requires only SMILES strings and protein sequences, without a bound complex structure. On Davis and KIBA, CurvFlow-DTA improves on the protocol-matched Ricci-GraphDTA baseline in every warm and cold-start setting. Warm-split mean squared error (MSE) decreases by 19.9% on Davis and 18.9% on KIBA. Across the six cold-start comparisons, MSE decreases by 14.3--27.4%, with higher concordance index (CI) throughout. Within our compiled set of literature baselines, CurvFlow-DTA achieves the lowest MSE on both warm benchmarks and across four out of six cold-start evaluation settings.