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

arXiv: https://arxiv.org/abs/2606.14217 · HTML: https://mlsanity.com/paper/2606.14217/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 90 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 30 of 33)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Evaluating Protein Transfer Learning with TAPE](https://mlsanity.com/paper/1906.08230/) (2019)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [DeepDTA: Deep Drug-Target Binding Affinity Prediction](https://mlsanity.com/paper/1801.10193/) (2018)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [ATOM3D: Tasks On Molecules in Three Dimensions](https://mlsanity.com/paper/2012.04035/) (2020)
- [Molecular Geometry Pretraining with SE(3)-Invariant Denoising Distance Matching](https://mlsanity.com/paper/2206.13602/) (2022)
- [Learning Hierarchical Protein Representations via Complete 3D Graph Networks](https://mlsanity.com/paper/2207.12600/) (2022)
- [Multi-Scale Representation Learning on Proteins](https://mlsanity.com/paper/2204.02337/) (2022)
- [Learning protein sequence embeddings using information from structure](https://mlsanity.com/paper/1902.08661/) (2019)
- [A new perspective on building efficient and expressive 3D equivariant graph neural networks](https://mlsanity.com/paper/2304.04757/) (2023)
- [PotentialNet for Molecular Property Prediction](https://mlsanity.com/paper/1803.04465/) (2018)
- [Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning](https://mlsanity.com/paper/2306.01474/) (2023)
- [Integration of Pre-trained Protein Language Models into Geometric Deep Learning Networks](https://mlsanity.com/paper/2212.03447/) (2022)
- [Protein-ligand binding representation learning from fine-grained interactions](https://mlsanity.com/paper/2311.16160/) (2023)
- [ProFSA: Self-supervised Pocket Pretraining via Protein Fragment-Surroundings Alignment](https://mlsanity.com/paper/2310.07229/) (2023)
- [SS-GNN: A Simple-Structured Graph Neural Network for Affinity Prediction](https://mlsanity.com/paper/2206.07015/) (2022)

## Abstract (arXiv)

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.