Curvature-Guided Geometric Representation for Protein-Ligand Binding Affinity Prediction

2026-06-12

AI Summary

Existing methods struggle to simultaneously capture fine-grained local geometric details and global cross-molecular cooperative interactions in protein–ligand binding, limiting the accuracy of affinity prediction. To address this challenge, this work proposes RicciBind, a novel framework that, for the first time, incorporates Ricci curvature into molecular representations to characterize the tightness of local interactions. By integrating optimal transport theory, RicciBind enforces geometrically constrained alignment between heterogeneous molecular clusters, enabling joint learning of hierarchical local structures and global interaction consistency. The method achieves significant performance gains over state-of-the-art models across multiple benchmarks for binding affinity prediction and virtual screening. Ablation studies further confirm that Ricci curvature modeling plays a pivotal role in driving these improvements.

Abstract

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.

Problem

• Protein-ligand binding affinity
• geometric representation
• molecular interactions
• local geometric organization
• cross-molecular interactions

Innovation

• Ricci curvature
• optimal transport
• geometric representation
• hierarchical structure learning
• protein-ligand binding affinity