# Unsupervised Protein-Ligand Binding Energy Prediction via Neural Euler's Rotation Equation

arXiv: https://arxiv.org/abs/2301.10814 · HTML: https://mlsanity.com/paper/2301.10814/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 49 references that are in the map.
- First posted on arXiv 25 Jan 2023.

## Builds on (most cited first, 18 of 18)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [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)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Analyzing Learned Molecular Representations for Property Prediction](https://mlsanity.com/paper/1904.01561/) (2019)
- [DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking](https://mlsanity.com/paper/2210.01776/) (2022)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction](https://mlsanity.com/paper/2202.05146/) (2022)
- [Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Docking](https://mlsanity.com/paper/2111.07786/) (2021)
- [ATOM3D: Tasks On Molecules in Three Dimensions](https://mlsanity.com/paper/2012.04035/) (2020)
- [Protein-Ligand Scoring with Convolutional Neural Networks](https://mlsanity.com/paper/1612.02751/) (2016)
- [Multi-Scale Representation Learning on Proteins](https://mlsanity.com/paper/2204.02337/) (2022)
- [Improved Protein-ligand Binding Affinity Prediction with Structure-Based Deep Fusion Inference](https://mlsanity.com/paper/2005.07704/) (2020)
- [When Attention Meets Fast Recurrence: Training Language Models with Reduced Compute](https://mlsanity.com/paper/2102.12459/) (2021)
- [PIGNet: A physics-informed deep learning model toward generalized drug-target interaction predictions](https://mlsanity.com/paper/2008.12249/) (2020)
- [Energy-based models for atomic-resolution protein conformations](https://mlsanity.com/paper/2004.13167/) (2020)
- [EBM-Fold: Fully-Differentiable Protein Folding Powered by Energy-based Models](https://mlsanity.com/paper/2105.04771/) (2021)

## Built on by (most cited first, 18 of 18)

- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodies](https://mlsanity.com/paper/2308.05027/) (2023)
- [Diffusion Models in textitDe Novo Drug Design](https://mlsanity.com/paper/2406.08511/) (2024)
- [Learning to design protein-protein interactions with enhanced generalization](https://mlsanity.com/paper/2310.18515/) (2023)
- [Re-Dock: Towards Flexible and Realistic Molecular Docking with Diffusion Bridge](https://mlsanity.com/paper/2402.11459/) (2024)
- [All-atom inverse protein folding through discrete flow matching](https://mlsanity.com/paper/2507.14156/) (2025)
- [An Equivariant Pretrained Transformer for Unified 3D Molecular Representation Learning](https://mlsanity.com/paper/2402.12714/) (2024)
- [A Cross-Field Fusion Strategy for Drug-Target Interaction Prediction](https://mlsanity.com/paper/2405.14545/) (2024)
- [SigmaDock: Untwisting Molecular Docking With Fragment-Based SE(3) Diffusion](https://mlsanity.com/paper/2511.04854/) (2025)
- [Tokenizing Electron Cloud in Protein-Ligand Interaction Learning](https://mlsanity.com/paper/2505.19014/) (2025)
- [Recent Developments in GNNs for Drug Discovery](https://mlsanity.com/paper/2506.01302/) (2025)
- [Multi-Modality Representation Learning for Antibody-Antigen Interactions Prediction](https://mlsanity.com/paper/2503.17666/) (2025)
- [DockGame: Cooperative Games for Multimeric Rigid Protein Docking](https://mlsanity.com/paper/2310.06177/) (2023)
- [DecoyDB: A Dataset for Graph Contrastive Learning in Protein-Ligand Binding Affinity Prediction](https://mlsanity.com/paper/2507.06366/) (2025)
- [ToxBench: A Binding Affinity Prediction Benchmark with AB-FEP-Calculated Labels for Human Estrogen Receptor Alpha](https://mlsanity.com/paper/2507.08966/) (2025)
- [Protein binding affinity prediction under multiple substitutions applying eGNNs on Residue and Atomic graphs combined with Language model information: eGRAL](https://mlsanity.com/paper/2405.02374/) (2024)
- [DualBind: A Dual-Loss Framework for Protein-Ligand Binding Affinity Prediction](https://mlsanity.com/paper/2406.07770/) (2024)
- [Energy-Based Models for Predicting Mutational Effects on Proteins](https://mlsanity.com/paper/2508.10629/) (2025)

## Abstract (arXiv)

Protein-ligand binding prediction is a fundamental problem in AI-driven drug discovery. Prior work focused on supervised learning methods using a large set of binding affinity data for small molecules, but it is hard to apply the same strategy to other drug classes like antibodies as labelled data is limited. In this paper, we explore unsupervised approaches and reformulate binding energy prediction as a generative modeling task. Specifically, we train an energy-based model on a set of unlabelled protein-ligand complexes using SE(3) denoising score matching and interpret its log-likelihood as binding affinity. Our key contribution is a new equivariant rotation prediction network called Neural Euler's Rotation Equations (NERE) for SE(3) score matching. It predicts a rotation by modeling the force and torque between protein and ligand atoms, where the force is defined as the gradient of an energy function with respect to atom coordinates. We evaluate NERE on protein-ligand and antibody-antigen binding affinity prediction benchmarks. Our model outperforms all unsupervised baselines (physics-based and statistical potentials) and matches supervised learning methods in the antibody case.