Curvature-Informed Potential Energy Surface for Protein-Ligand Binding Affinity Prediction

2026-06-12

AI Summary

This work addresses the limitation of existing protein–ligand binding affinity prediction methods that rely predominantly on static structures and overlook molecular flexibility and binding-induced conformational changes. The authors propose a Curvature-aware Potential Energy Surface (CPES) graph neural network, which introduces—for the first time—the local principal curvature spectrum derived from the Hessian matrix of the potential energy surface as a dynamic descriptor within a deep learning framework. By integrating this dynamic information with static geometric features, the model employs a spectral cross-attention mechanism to capture conformational differences before and after binding. It further combines geometry-aware message passing with soft clustering to learn multi-scale interactions and uses bidirectional cross-attention to fuse dynamic and static representations for affinity regression. The method achieves significantly improved prediction performance across multiple benchmarks and offers physically interpretable insights into conformational changes.

Abstract

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.

Problem

• protein-ligand binding affinity
• molecular flexibility
• conformational changes
• potential energy surface
• geometric deep learning

Innovation

• curvature-informed representation
• potential energy surface
• conformational flexibility
• geometric deep learning
• spectral cross-attention