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Rigid Protein-Protein Docking via Equivariant Elliptic-Paraboloid Interface Prediction

Ziyang Yu, Wenbing Huang, Yang Liu

TL;DR

This paper addresses rigid protein-protein docking by predicting a pair of elliptic paraboloid interfaces for the unbound proteins and docking via interface alignment. It introduces EPIT, a pairwise $SE(3)$-equivariant GNN that yields invariant and equivariant features for global interaction modeling, followed by a four stage interface fitting pipeline that converts to standard forms and computes a relative pose. The key contributions are the elliptic paraboloid interface model with independent equivariance, the EPIT back end for robust cross protein interactions, and a training objective that enforces accurate interface fitting and non overlap during docking. The proposed ElliDock achieves the fastest inference among baselines and remains competitive with state of the art on antibody-antigen docking, demonstrating practical value for rapid docking in drug design and protein engineering.

Abstract

The study of rigid protein-protein docking plays an essential role in a variety of tasks such as drug design and protein engineering. Recently, several learning-based methods have been proposed for the task, exhibiting much faster docking speed than those computational methods. In this paper, we propose a novel learning-based method called ElliDock, which predicts an elliptic paraboloid to represent the protein-protein docking interface. To be specific, our model estimates elliptic paraboloid interfaces for the two input proteins respectively, and obtains the roto-translation transformation for docking by making two interfaces coincide. By its design, ElliDock is independently equivariant with respect to arbitrary rotations/translations of the proteins, which is an indispensable property to ensure the generalization of the docking process. Experimental evaluations show that ElliDock achieves the fastest inference time among all compared methods and is strongly competitive with current state-of-the-art learning-based models such as DiffDock-PP and Multimer particularly for antibody-antigen docking.

Rigid Protein-Protein Docking via Equivariant Elliptic-Paraboloid Interface Prediction

TL;DR

This paper addresses rigid protein-protein docking by predicting a pair of elliptic paraboloid interfaces for the unbound proteins and docking via interface alignment. It introduces EPIT, a pairwise -equivariant GNN that yields invariant and equivariant features for global interaction modeling, followed by a four stage interface fitting pipeline that converts to standard forms and computes a relative pose. The key contributions are the elliptic paraboloid interface model with independent equivariance, the EPIT back end for robust cross protein interactions, and a training objective that enforces accurate interface fitting and non overlap during docking. The proposed ElliDock achieves the fastest inference among baselines and remains competitive with state of the art on antibody-antigen docking, demonstrating practical value for rapid docking in drug design and protein engineering.

Abstract

The study of rigid protein-protein docking plays an essential role in a variety of tasks such as drug design and protein engineering. Recently, several learning-based methods have been proposed for the task, exhibiting much faster docking speed than those computational methods. In this paper, we propose a novel learning-based method called ElliDock, which predicts an elliptic paraboloid to represent the protein-protein docking interface. To be specific, our model estimates elliptic paraboloid interfaces for the two input proteins respectively, and obtains the roto-translation transformation for docking by making two interfaces coincide. By its design, ElliDock is independently equivariant with respect to arbitrary rotations/translations of the proteins, which is an indispensable property to ensure the generalization of the docking process. Experimental evaluations show that ElliDock achieves the fastest inference time among all compared methods and is strongly competitive with current state-of-the-art learning-based models such as DiffDock-PP and Multimer particularly for antibody-antigen docking.
Paper Structure (38 sections, 4 theorems, 32 equations, 8 figures, 4 tables)

This paper contains 38 sections, 4 theorems, 32 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Method
  4. Protein representation
  5. Task Formulation
  6. Equivariant polarizable interaction transformer (EPIT)
  7. Elliptic paraboloid
  8. Independent equivariance
  9. Interface prediction and docking via EPIT
  10. Predicting Standard Forms
  11. Predicting SE(3) Transformations
  12. Rotation refinement
  13. Training objective
  14. Experiments
  15. Experimental setup
  16. ...and 23 more sections

Key Result

Proposition 1

The proposed model $\mathrm{EPIT}$ is independent SE(3)-equivariant and translation-invariant, indicating that if $\vec{{\bm{V}}}_1^{(L)}, {\bm{H}}_1^{(L)}, \vec{{\bm{V}}}_2^{(L)}, {\bm{H}}_2^{(L)}=\mathrm{EPIT}(\vec{{\bm{X}}}_1, {\bm{H}}_1, {\mathcal{E}}_1, \vec{{\bm{X}}}_2, {\bm{H}}_2, {\mathcal{E

Figures (8)

  • Figure 1: EquiDock: point cloud registration vs ElliDock: interface fitting.
  • Figure 2: Docking process via interface fitting. We decompose the docking process into four steps: 1) predict elliptic paraboloid interfaces for two proteins respectively, 2) conduct general to standard transformations based on the ligand interface, 3) rotation refinement, 4) conduct standard to general transformations based on the receptor interface.
  • Figure 3: CRMSD of antibody-antigen docking on SAbDab test set.
  • Figure 4: IRMSD of antibody-antigen docking on SAbDab test set.
  • Figure 5: The comparison of DockQ between ElliDock and Alphafold-Multimer on SAbDab test set.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4