Protein-ligand binding affinity (PLA) prediction is critical in drug discovery. Despite the notable advancements in machine learning-based approaches, existing methods struggle to jointly characterize local geometric organization and globally coordinated cross-molecular interactions, limiting their ability to model complex binding mechanisms. Here, we propose RicciBind, a geometric representation framework that integrates curvature-guided hierarchical structure learning with optimal transport (OT)-based cross-domain alignment to model molecular interactions. Specifically, RicciBind leverages Ricci curvature to capture local interaction tightness within molecular structures, enhancing structural awareness and organizing atomic interactions into curvature-aware hierarchical representations. An OT-based cluster matching mechanism then aligns protein and ligand clusters across heterogeneous domains under geometric constraints, enabling globally consistent correspondences and revealing higher-order interaction patterns beyond local neighborhoods. By coupling curvature-guided structure encoding with OT-driven cross-domain alignment, RicciBind effectively models complex interaction semantics and substantially improves both the accuracy and interpretability of binding affinity prediction. Extensive experiments demonstrate that RicciBind achieved superior predictive performance and generalization across PLA benchmarks and virtual screening tasks. Ablation studies further confirmed the essential role of Ricci curvature in enhancing molecular interaction representations.
Predicting protein-ligand binding affinity remains intractable for multi-domain proteins, where inter-domain dynamics govern molecular recognition. Existing geometric deep learning methods typically treat proteins as monolithic static graphs, suffering from rigid-body assumptions and aleatoric noise in flexible regions. To address this, we introduced HCLBind, a self-supervised framework that decouples geometric representation learning from affinity regression. HCLBind leverages a general-to-specific pre-training paradigm on the Q-BioLiP database to learn a robust physical grammar of binding. We propose a novel hierarchical decoy strategy: the model learns local physicochemical constraints through protein coordinate perturbation in single-domain proteins and global conformational geometry through inter-domain rotation in multi-domain complexes. Our hybrid architecture integrates a domain-gated graph attention network and cross-modal attention to explicitly prioritize domain interfaces. Furthermore, we employ LoRA on protein and ligand foundation models, ensuring efficient optimization while preserving evolutionary knowledge. Experiments on PDBBind demonstrate that HCLBind effectively learns discriminative interface features and provides robust uncertainty estimation, overcoming the limitations of standard supervised learning. The code is available at https://github.com/jiankliu/HCLBind.
Accurate prediction of protein-ligand binding affinity is essential for structure-based drug discovery. Recent geometric deep learning methods have achieved promising performance by representing protein-ligand complexes as three-dimensional graphs. However, most existing approaches mainly rely on static interaction geometry from a single bound conformation, while neglecting molecular flexibility and binding-induced conformational changes. To address this limitation, we propose a curvature-informed potential energy surface (CPES) graph neural network for protein-ligand binding affinity prediction, which incorporates physics-informed curvature representations to model conformational flexibility. CPES first derives curvature spectral descriptors from the Hessian of the potential energy surface evaluated at equilibrium configurations, whose eigenvalues define the local principal curvatures of the potential energy surface. It then uses spectral cross-attention to compare the unbound ligand and protein with the bound complex, thereby capturing binding-induced changes in conformational dynamics. In parallel, hierarchical protein-ligand interaction representations are learned from static structural features through geometry-aware message passing, soft clustering, and bidirectional cross-attention. Finally, CPES fuses the curvature-informed dynamic representations with static interaction representations for affinity regression. Extensive evaluations on multiple benchmark datasets demonstrate that CPES achieves improved predictive performance and offers physical interpretability.
Quantitative estimation of protein-ligand binding affinity from three-dimensional complex structures is a fundamental task in structure-based computational chemistry and molecular modeling. Reliable prediction remains challenging because available structure-affinity data are limited, experimentally heterogeneous, conformation-dependent, and sensitive to dataset partitioning. RAVEN (Randomized Atomistic Views with Ensemble Neural Reservoirs) utilizes a multihead reservoir of independently initialized and fully frozen atomistic graph encoders to generate diverse structural projections without end-to-end optimization of the graph representation. These projections are integrated with a deterministic physicochemical interaction fingerprint and processed by heterogeneous supervised readers, including neural and tree-based regressors, whose outputs are combined through validation-based nonnegative fusion. The random reservoir expands structural feature coverage across independent encoder realizations, whereas the explicit physicochemical descriptors and heterogeneous readers contribute complementary information and distinct inductive biases. Evaluation on a similarity-isolated PDBbind 2020R1 split reconstructed using GEMS similarity resources, together with the protected CASF-2016 subset, demonstrated strong predictive performance. The results indicate that frozen multi-view graph representations, explicit physicochemical statistics, and heterogeneous model fusion provide a robust and flexible framework for protein-ligand binding-affinity prediction.