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.

翻译：准确预测蛋白质-配体结合亲和力是结构导向药物发现的关键。近年来，几何深度学习方法通过将蛋白质-配体复合物表示为三维图结构，取得了令人瞩目的性能。然而，现有方法大多仅依赖单一结合构象的静态相互作用几何，忽视了分子柔性与结合诱导的构象变化。为解决这一局限，我们提出一种基于曲率感知势能面（CPES）的图神经网络用于蛋白质-配体结合亲和力预测，该方法融合物理学启发的曲率表示来建模构象柔性。CPES首先从势能面在平衡构型处计算的Hessian矩阵中推导曲率谱描述符，其特征值定义了势能面的局部主曲率；随后利用谱交叉注意力对比未结合配体、蛋白质与结合复合物，从而捕获结合诱导的构象动力学变化。与此同时，通过几何感知消息传递、软聚类和双向交叉注意力，从静态结构特征中学习层次化蛋白质-配体相互作用表示。最后，CPES将曲率感知的动态表示与静态相互作用表示融合以进行亲和力回归。在多个基准数据集上的广泛评估表明，CPES实现了更优的预测性能，并具备物理可解释性。