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

Abstract

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.

EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction

“…Deep learning for protein-protein docking. A related problem is protein-protein docking in which recent methods have performed direct prediction of the complex structure from the two concatenated input sequences using evolutionary information (Evans et al, 2021), or have leveraged geometric deep learning to model rigid body docking (Ganea et al, 2021a) or side-chains structures (Jindal et al, 2021).…”

“…Injecting Euclidean 3D transformations into geometric DL models has become possible using equivariant message passing layers (Cohen & Welling, 2016;Thomas et al, 2018;Fuchs et al, 2020;Satorras et al, 2021;Brandstetter et al, 2021;Batzner et al, 2021). Our method follows Ganea et al (2021a) to incorporate SE(3) pairwise equivariance into message passing neural networks for the drug binding problem. However, different from this method, we go beyond rigid docking and model ligand conformational flexibility.…”

“…Independent E(3)-equivariant transformations. Similar to (Ganea et al, 2021a), an important geometric inductive bias is to predict the same binding complex no matter how the initial molecules are positioned and oriented in space. This is especially needed for data-scarce problems such as structural drug binding.…”

“…This is especially needed for data-scarce problems such as structural drug binding. Towards this goal, we use Independent E(3)-Equivariant Graph Matching Network (IEGMN) (Ganea et al, 2021a) which combines Graph Matching Networks (Li et al, 2019) and E(3)-Equivariant Graph Neural Networks (Satorras et al, 2021). This architecture jointly transforms both features and 3D coordinates to perform intra and inter neural graph message passing.…”

“…Here, we introduce EQUIBIND, a novel geometric & graph deep learning model for structural drug binding -Figure 1. Inspired by Ganea et al (2021a), we exploit graph matching networks (GMN) (Li et al, 2019) and E(3)-equivariant graph neural networks (E(3)-GNN) (Satorras et al, 2021) to perform a direct prediction of the ligand-receptor com- plex structure without relying on heavy sampling as prior work, thus achieving significant inference time speed-ups. Moreover, since 3D structural data suffers from scarcity (e.g., only around 19K experimental complexes are publicly available in the PDBbind database), it is crucial to inject the right physical, chemical, or biological inductive biases into DL models to avoid learning these priors from insufficient amounts of data and to create trustable models.…”