# Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Docking

arXiv: https://arxiv.org/abs/2111.07786 · HTML: https://mlsanity.com/paper/2111.07786/

## Key facts

- Cited by 82 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 82 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [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)
- [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)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data](https://mlsanity.com/paper/2002.12880/) (2020)
- [Graph Matching Networks for Learning the Similarity of Graph Structured Objects](https://mlsanity.com/paper/1904.12787/) (2019)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [LieTransformer: Equivariant self-attention for Lie Groups](https://mlsanity.com/paper/2012.10885/) (2020)
- [Iterative Refinement Graph Neural Network for Antibody Sequence-Structure Co-design](https://mlsanity.com/paper/2110.04624/) (2021)
- [Group Equivariant Stand-Alone Self-Attention For Vision](https://mlsanity.com/paper/2010.00977/) (2020)
- [Structure-aware Interactive Graph Neural Networks for the Prediction of Protein-Ligand Binding Affinity](https://mlsanity.com/paper/2107.10670/) (2021)
- [Equivariant Hamiltonian Flows](https://mlsanity.com/paper/1909.13739/) (2019)
- [AtomNet: A Deep Convolutional Neural Network for Bioactivity Prediction in Structure-based Drug Discovery](https://mlsanity.com/paper/1510.02855/) (2015)
- [End-to-End Learning on 3D Protein Structure for Interface Prediction](https://mlsanity.com/paper/1807.01297/) (2018)
- [Deep Learning of High-Order Interactions for Protein Interface Prediction](https://mlsanity.com/paper/2007.09334/) (2020)

## Built on by (most cited first, 30 of 82)

- [Riemannian Score-Based Generative Modelling](https://mlsanity.com/paper/2202.02763/) (2022)
- [EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction](https://mlsanity.com/paper/2202.05146/) (2022)
- [Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs](https://mlsanity.com/paper/2202.05441/) (2022)
- [DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design](https://mlsanity.com/paper/2403.07902/) (2024)
- [Conditional Antibody Design as 3D Equivariant Graph Translation](https://mlsanity.com/paper/2208.06073/) (2022)
- [DiffBP: Generative Diffusion of 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2211.11214/) (2022)
- [Geometrically Equivariant Graph Neural Networks: A Survey](https://mlsanity.com/paper/2202.07230/) (2022)
- [Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learning](https://mlsanity.com/paper/2206.08321/) (2022)
- [Learning Hierarchical Protein Representations via Complete 3D Graph Networks](https://mlsanity.com/paper/2207.12600/) (2022)
- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)
- [xTrimoPGLM: Unified 100B-Scale Pre-trained Transformer for Deciphering the Language of Protein](https://mlsanity.com/paper/2401.06199/) (2024)
- [End-to-End Full-Atom Antibody Design](https://mlsanity.com/paper/2302.00203/) (2023)
- [Graph Denoising Diffusion for Inverse Protein Folding](https://mlsanity.com/paper/2306.16819/) (2023)
- [Structure-based drug design with geometric deep learning](https://mlsanity.com/paper/2210.11250/) (2022)
- [Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian](https://mlsanity.com/paper/2306.04922/) (2023)
- [Aligned Diffusion Schr"odinger Bridges](https://mlsanity.com/paper/2302.11419/) (2023)
- [E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking](https://mlsanity.com/paper/2210.06069/) (2022)
- [Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3D](https://mlsanity.com/paper/2401.12046/) (2024)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [DiffDock-PP: Rigid Protein-Protein Docking with Diffusion Models](https://mlsanity.com/paper/2304.03889/) (2023)
- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
- [Fine-Tuning Graph Neural Networks via Graph Topology induced Optimal Transport](https://mlsanity.com/paper/2203.10453/) (2022)
- [Unsupervised Protein-Ligand Binding Energy Prediction via Neural Euler's Rotation Equation](https://mlsanity.com/paper/2301.10814/) (2023)
- [FABind: Fast and Accurate Protein-Ligand Binding](https://mlsanity.com/paper/2310.06763/) (2023)
- [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)
- [Antibody-Antigen Docking and Design via Hierarchical Equivariant Refinement](https://mlsanity.com/paper/2207.06616/) (2022)
- [AbODE: Ab Initio Antibody Design using Conjoined ODEs](https://mlsanity.com/paper/2306.01005/) (2023)
- [VN-EGNN: E(3)-Equivariant Graph Neural Networks with Virtual Nodes Enhance Protein Binding Site Identification](https://mlsanity.com/paper/2404.07194/) (2024)
- [Integration of Pre-trained Protein Language Models into Geometric Deep Learning Networks](https://mlsanity.com/paper/2212.03447/) (2022)

## Abstract (arXiv)

Protein complex formation is a central problem in biology, being involved in most of the cell's processes, and essential for applications, e.g. drug design or protein engineering. We tackle rigid body protein-protein docking, i.e., computationally predicting the 3D structure of a protein-protein complex from the individual unbound structures, assuming no conformational change within the proteins happens during binding. We design a novel pairwise-independent SE(3)-equivariant graph matching network to predict the rotation and translation to place one of the proteins at the right docked position relative to the second protein. We mathematically guarantee a basic principle: the predicted complex is always identical regardless of the initial locations and orientations of the two structures. Our model, named EquiDock, approximates the binding pockets and predicts the docking poses using keypoint matching and alignment, achieved through optimal transport and a differentiable Kabsch algorithm. Empirically, we achieve significant running time improvements and often outperform existing docking software despite not relying on heavy candidate sampling, structure refinement, or templates.