E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking

Yangtian ZhangHuiyu CaiChence ShiJian Tang

article2023ICLR55 citations

Proposes E3Bind, an end-to-end equivariant neural network that iteratively predicts flexible ligand docking poses directly from protein structures, outperforming traditional physics-based tools and existing multi-stage deep learning approaches on standard benchmarks.

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Predicting how drug-like molecules bind to target proteins in the human body is a fundamental challenge in pharmaceutical research. While experimental structure determination is slow and covers only a tiny fraction of potential drug-protein pairs, computational docking methods are essential for screening vast chemical libraries. Traditional physics-based tools are slow and struggle with accuracy, whereas existing deep-learning approaches often fail because they either predict intermediate geometric distances that cannot be translated into valid 3D shapes or place molecules in a single step without allowing their shapes to adapt to the binding site. The article addresses these bottlenecks by developing and evaluating an end-to-end artificial intelligence model, named E3Bind, designed to directly and iteratively predict the precise 3D position, orientation, and flexible shape of small molecules within target proteins.

The approach introduces a specialized neural network architecture that combines a geometry-aware feature extractor with an iterative coordinate refinement module. Instead of predicting distances or placing the molecule in one shot, the model updates molecular coordinates across multiple steps, continually sensing the surrounding protein environment to resolve physical clashes and refine the fit. The model also incorporates a built-in confidence scoring mechanism to select optimal poses and flag uncertain predictions. To test the system, the authors trained and evaluated the framework on standard benchmark data comprising thousands of experimentally determined protein-ligand complexes from the PDBbind database, comparing its accuracy and speed against established physics-based software and state-of-the-art deep-learning models.

The evaluation revealed several key findings in order of importance. First, E3Bind demonstrated superior precision in flexible docking, achieving a 33% increase in high-accuracy predictions (poses within 2 angstroms of the true structure) compared to the previous leading deep-learning benchmark. Second, the system operated orders of magnitude faster than traditional physics-based tools, completing predictions in roughly two seconds on standard processors and under half a second on specialized graphics hardware, compared to minutes or hours for legacy tools. Third, iterative refinement significantly reduced physical errors; only 3.3% of test predictions produced atomic overlap clashes, compared to 21% for single-step deep-learning models. Fourth, the model showed robust binding site detection on large, challenging targets and maintained competitive performance even when tested on novel proteins that were never seen during training.

These findings suggest that end-to-end iterative modeling overcomes the major structural validity and speed trade-offs of previous docking methods. By eliminating time-consuming conformational sampling and multi-stage post-processing, the framework can substantially reduce computational costs and project timelines in virtual drug screening. Moreover, its self-confidence scoring provides drug discovery teams with a reliable filter to prioritize high-probability candidates and avoid pursuing flawed computational artifacts.

Organizations evaluating computational discovery pipelines should consider piloting iterative end-to-end models like E3Bind to accelerate early-stage screening workflows. However, decision-makers should note that the model treats the target protein as a rigid structure and exhibits lower accuracy on completely unseen proteins compared to familiar targets. Further research should focus on incorporating protein flexibility and testing the system across broader real-world biological targets before deploying it without experimental validation.

CIFAR HEC Montréal Mila – Québec Artificial Intelligence Institute Université de Montréal deep learning inference probabilistic inference E3Bind protein-ligand docking protein-ligand distance maps

arXiv: 2210.06069

Paper: E(n) Equivariant Graph Neural Networks, Victor Garcia Satorras et al. (2021). Introduces E(n)-equivariant graph neural networks with coordinate update mechanisms that provide the foundational 3D equivariant architecture adapted by E3Bind for iterative molecular coordinate refinement.
Paper: E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials, Simon Batzner et al. (2021). Establishes E(3)-equivariant directional representations for molecular systems, providing key architectural foundations for geometric feature extraction in 3D molecular environments.
Paper: Equivariant Diffusion for Molecule Generation in 3D, Emiel Hoogeboom et al. (2022). Develops equivariant continuous coordinate generation in 3D molecular spaces, demonstrating principles of symmetry-preserving coordinate updates foundational to iterative flexible docking.
Paper: ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphs, Limei Wang et al. (2022). Details complete and computationally efficient 3D message-passing frameworks for molecular graphs, informing the geometry-aware feature representation methods used to sense protein binding pockets.
Paper: SchNet: A continuous-filter convolutional neural network for modeling quantum interactions, Kristof Schütt et al. (2017). Pioneers continuous-filter convolutions over continuous 3D atomic coordinates, establishing core concepts for modeling non-grid 3D interatomic interactions.
Paper: Highly accurate protein structure prediction with AlphaFold, John Jumper et al. (2021). Demonstrates iterative refinement modules and self-confidence estimation mechanisms in 3D biological structure prediction that inspire iterative end-to-end protein-ligand pose refinement.

Paper: MolCRAFT: Structure-Based Drug Design in Continuous Parameter Space, Yanru Qu et al. (2024). Extends 3D protein-ligand modeling from docking known ligands to generative structure-based de novo drug design in continuous spatial coordinates.
Paper: Energy-Motivated Equivariant Pretraining for 3D Molecular Graphs, Rui Jiao et al. (2023). Generalizes 3D equivariant networks through energy-motivated force pretraining to enhance downstream geometric molecular tasks such as binding and conformation modeling.
Paper: SE(3)-Stochastic Flow Matching for Protein Backbone Generation, Avishek Joey Bose et al. (2024). Advances rigid SE(3) transformation modeling using continuous stochastic flow matching, representing a next-generation approach to generating flexible 3D biomolecular structures.
Paper: Protein Representation Learning by Geometric Structure Pretraining, Zuobai Zhang et al. (2023). Explores large-scale self-supervised geometric structure pretraining on 3D protein structures to further empower downstream protein-ligand binding and functional property tasks.
Paper: ProSST: Protein Language Modeling with Quantized Structure and Disentangled Attention, Mingchen Li et al. (2024). Integrates quantized 3D structural representations with language models to predict functional mutation impacts and binding pocket interactions.

Cover for E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking

Abstract

In silico prediction of the ligand binding pose to a given protein target is a crucial but challenging task in drug discovery. This work focuses on blind flexible selfdocking, where we aim to predict the positions, orientations and conformations of docked molecules. Traditional physics-based methods usually suffer from inaccurate scoring functions and high inference cost. Recently, data-driven methods based on deep learning techniques are attracting growing interest thanks to their efficiency during inference and promising performance. These methods usually either adopt a two-stage approach by first predicting the distances between proteins and ligands and then generating the final coordinates based on the predicted distances, or directly predicting the global roto-translation of ligands. In this paper, we take a different route. Inspired by the resounding success of AlphaFold2 for protein structure prediction, we propose E3Bind, an end-to-end equivariant network that iteratively updates the ligand pose. E3Bind models the protein-ligand interaction through careful consideration of the geometric constraints in docking and the local context of the binding site. Experiments on standard benchmark datasets demonstrate the superior performance of our end-to-end trainable model compared to traditional and recently-proposed deep learning methods.

Topics

deep learning inference probabilistic inference convolutional neural networks routing scheme

Keywords

E3Bind protein-ligand docking protein-ligand distance maps ligand conformation rigid docking ligand RMSD

1 Introduction
2 Related Works
3 The E3Bind Model
3.1 Preliminaries
3.2 Extracting Geometry-Consistent Information with Trioformer
3.3 Iterative Coordinate Update with Context-Aware E(3)-Equivariant Layer
3.4 Training and Inference
4 Experiments
4.1 Flexible Self Docking
4.2 Ablation Study
4.3 Case Study
5 Conclusion
References
A Experiment for blind re-docking
B Details of the Trioformer
C Details of self-confidence prediction
C.1 confidence loss
C.2 self-confidence prediction results
D Implementation Details
E Further Ablation Study Results
E.1 Ablation Study of E3Bind
E.2 Impact of Post Optimization
F Sensitivity to Initialization
G Inference Speed
H Additional trajectories and case studies
I Examining the Validity of Generated Structures
I.1 Bond Length Distribution
I.2 Steric Clash Problem

Knowls

Knowl 1 — E3Bind Architecture for End-to-End Equivariant Protein-Ligand Docking
model/method
E3Bind is an end-to-end $E(3)$ -equivariant neural network architecture for flexible blind protein-ligand docking. It directly predicts the 3D coordinates of a ligand bound to a target protein from the unbound molecular graph of the ligand and the fixed 3D structure of the protein, without relying on intermediate distance-to-coordinate optimization or post-hoc conformation sampling.

Input Representations
- Ligand Representation: The ligand is modeled as an atom-level graph $G^l = (V^l, E^l)$ with $n_l$ atoms. Initial node embeddings $\{h_i^l\}_{i=1}^{n_l} \in \mathbb{R}^{n_l \times d}$ are extracted using a Graph Isomorphism Network (GIN). Initial 3D Cartesian coordinates $\{x_i^l\}_{i=1}^{n_l} \in \mathbb{R}^{n_l \times 3}$ are obtained from an unbound conformation generated via Experimental-Torsion Knowledge Distance Geometry (ETKDG).
- Protein Representation: The protein is modeled as a residue-level $K$ -nearest neighbor graph $G^p = (V^p, E^p)$ with $n_p$ residues. Node embeddings $\{h_j^p\}_{j=1}^{n_p} \in \mathbb{R}^{n_p \times d}$ are computed with a Geometric Vector Perceptron Graph Neural Network (GVP-GNN). Residue coordinates $\{x_j^p\}_{j=1}^{n_p} \in \mathbb{R}^{n_p \times 3}$ correspond to the $C_\alpha$ atom positions and remain fixed.
- Protein-Ligand Pair Embeddings: For every protein residue $j$ and ligand atom $i$ , an initial pair embedding $z_{ij} \in \mathbb{R}^{d}$ is constructed via an Outer Product Module (OPM): $z_{ij} = \text{Linear}\left( \text{vec}\left( \text{Linear}(h_i^l) \otimes \text{Linear}(h_j^p) \right) \right)$
Pipeline
1. Trioformer Feature Extractor: An iterative geometric encoder that mixes residue, atom, and pair embeddings while injecting intra-protein and intra-ligand distance constraints into pair interactions.
2. Context-Aware $E(3)$ -Equivariant Decoder: An iterative refinement module that updates ligand coordinates and node features across $T$ iterations using Equivariant Graph Convolutional Layers (EGCL).
3. Self-Confidence Predictor: A lightweight module predicting a scalar confidence score $\hat{c} \in [0, 1]$ from the pooled final ligand representations to assess pose quality and select the best candidate across multiple binding pockets.
Knowl 2 — Trioformer Feature Extraction and Geometry-Aware Interaction Encoding
algorithm
The Trioformer is the feature extraction encoder of E3Bind. It iteratively refines protein residue embeddings $\{h_j^p\}$ , ligand atom embeddings $\{h_i^l\}$ , and cross-entity pair embeddings $\{z_{ij}\}$ across a stack of Trioformer blocks. In each block, node features are updated through multi-head cross-attention using pair representations as attention bias (MHAWithPairBias), followed by an Outer Product Module (OPM) update of pair features and geometry-aware pair attention constrained by intra-molecular distance matrices.
Input: ligand node embeddings $\{h_i^l\}_{i=1}^{n_l}$ , protein residue embeddings $\{h_j^p\}_{j=1}^{n_p}$ , pair embeddings $\{z_{ij}\}_{i=1, j=1}^{n_l, n_p}$ , intra-ligand reference distances $\{d_{ik}^*\}$ , intra-protein distances $\{d_{jk'}^*\}
Output: updated embeddings $\{h_i^l\}, \{h_j^p\}, \{z_{ij}\}
// 1. Cross-attention with pair bias on node representations
$\{h_i^l\} \leftarrow \{h_i^l\} + \text{MHAWithPairBias}(\{h_i^l\}, \{h_j^p\}, \{h_j^p\}, \{z_{ij}\})$
$\{h_j^p\} \leftarrow \{h_j^p\} + \text{MHAWithPairBias}(\{h_j^p\}, \{h_i^l\}, \{h_i^l\}, \{z_{ij}\})$
// 2. Node MLP transitions
$\{h_i^l\} \leftarrow \{h_i^l\} + \text{MLP}(\{h_i^l\})$
$\{h_j^p\} \leftarrow \{h_j^p\} + \text{MLP}(\{h_j^p\})$
// 3. Update pair embeddings via Outer Product Module (OPM)
$\{z_{ij}\} \leftarrow \{z_{ij}\} + \text{OPM}(\{h_i^l\}, \{h_j^p\})$
// 4. Geometry-aware attentive pair updates
$\{z_{ij}\} \leftarrow \{z_{ij}\} + \text{LigandConstrainedAttentivePairUpdate}(\{z_{ij}\}, \{d_{ik}^*\})$
$\{z_{ij}\} \leftarrow \{z_{ij}\} + \text{ProteinConstrainedAttentivePairUpdate}(\{z_{ij}\}, \{d_{jk'}^*\})$
// 5. Pair MLP transition
$\{z_{ij}\} \leftarrow \{z_{ij}\} + \text{MLP}(\{z_{ij}\})$
return $\{h_i^l\}, \{h_j^p\}, \{z_{ij}\}$
In MHAWithPairBias, the cross-attention weights between ligand atom $i$ and protein residue $k'$ for attention head $h$ are computed as: $a_{ik'}^{(h)} = \text{softmax}_{k'}\left( \frac{1}{\sqrt{c}} (q_i^{(h)})^\top k_{k'}^{(h)} + b_{ik'}^{(h)} \right)$ where $q_i^{(h)}$ is projected from $h_i^l$ , $k_{k'}^{(h)}$ and $v_{k'}^{(h)}$ are projected from $h_{k'}^p$ , and $b_{ik'}^{(h)}$ is a linear projection of the pair embedding $z_{ik'}$ . Node features are then updated by projecting the aggregated values $\sum_{k'=1}^{n_p} a_{ik'}^{(h)} v_{k'}^{(h)}$ across all $H$ attention heads.
Knowl 3 — Geometry-Informed Attentive Pair Updates in Trioformer
equation
In E3Bind's Trioformer, protein-ligand pair representations $z_{ij}$ are updated using triangular edge geometric constraints to ensure that cross-entity spatial relationships respect the triangle inequality with known intra-protein and intra-ligand distances.

Protein-Constrained Attentive Pair Update

For each ligand-protein pair $(i, j)$ , attention is computed over all neighboring pairs $(i, k')$ sharing the same ligand atom $i$ ( $1 \le k' \le n_p$ ): $a_{ijk'}^{(h)} = \text{softmax}_{k'}\left( \frac{1}{\sqrt{c}} (q_{ij}^{(h)})^\top k_{ik'}^{(h)} + b_{ij}^{(h)} + t_{jk'}^{(h)} \right)$ $z_{ij} \leftarrow z_{ij} + \text{Linear}\left( \text{concat}_{1 \le h \le H} \left( g_{ij}^{(h)} \odot \sum_{k'=1}^{n_p} a_{ijk'}^{(h)} v_{ik'}^{(h)} \right) \right)$ where:
- $q_{ij}^{(h)}, k_{ik'}^{(h)}, v_{ik'}^{(h)}, b_{ij}^{(h)}$ are learned linear projections of the pair embeddings $z_{ij}$ and $z_{ik'}$ for attention head $h \in \{1, \dots, H\}$ .
- $g_{ij}^{(h)} = \sigma(\text{Linear}^{(h)}(z_{ij}))$ is a per-head sigmoid gating vector.
- $t_{jk'}^{(h)} = \text{Linear}^{(h)}(d_{jk'}^*)$ is a head-specific distance bias computed from the embedded Euclidean distance $d_{jk'}^* = \|x_j^p - x_{k'}^p\|$ between residues $j$ and $k'$ in the fixed protein structure.
- $c$ is the projection feature dimension.
Ligand-Constrained Attentive Pair Update

Analogously, for a fixed protein residue $j$ , pair $(i, j)$ attends to neighboring pairs $(k, j)$ sharing the same protein residue ( $1 \le k \le n_l$ ) with an attention bias $t_{ik}^{(h)} = \text{Linear}^{(h)}(d_{ik}^*)$ derived from the intra-ligand reference distance $d_{ik}^*$ between atoms $i$ and $k$ (provided for atoms separated by $\le 2$ hops or within the same ring in the initial ETKDG unbound ligand structure).
Knowl 4 — Context-Aware E(3)-Equivariant Coordinate Refinement Layer
model/method
E3Bind refines the ligand pose iteratively over $T$ steps using an $E(3)$ -equivariant decoder. At step $t \in \{0, \dots, T-1\}$ , the decoder operates on a heterogeneous context graph consisting of ligand-protein inter-edges and ligand-ligand intra-edges, updating both node embeddings and ligand coordinates:

$\left( h^{(t+1)}, \{\Delta x_i^{(t+1)}\}_{i=1}^{n_l} \right) = \text{DecoderLayer}^{(t)}\left( h^{(t)}, \{x_i^{(t)}\}_{i=1}^{n_l}, \{x_j^p\}_{j=1}^{n_p} \right)$ $x_i^{(t+1)} = x_i^{(t)} + \Delta x_i^{(t+1)}, \quad 0 \le t < T$ where $x_j^p$ are the fixed protein $C_\alpha$ coordinates.

Equivariant Graph Convolutional Message Passing

Inter-edge messages between ligand atom $i$ and protein residue $j$ , and intra-edge messages between ligand atoms $i$ and $k$ , are computed via MLPs $\phi^m$ and $\varphi^m$ : $(m_{ij}^{(t)}, m_{ji}^{(t)}) = \phi^m\left( z_{ij}, h_i^{(t)}, h_j^{(t)}, \|x_i^{(t)} - x_j^p\| \right)$ $m_{ik}^{(t)} = \varphi^m\left( h_i^{(t)}, h_k^{(t)}, \|x_i^{(t)} - x_k^{(t)}\| \right)$

Coordinate Update

The $E(3)$ -equivariant coordinate displacement $\Delta x_i^{(t)}$ is obtained by aggregating normalized directional vectors weighted by gated MLPs $\phi^x$ and $\varphi^x$ : $\Delta x_i^{(t)} = \sum_{j=1}^{n_p} \frac{x_j^p - x_i^{(t)}}{\|x_j^p - x_i^{(t)}\|} \phi^x(m_{ij}^{(t)}) + \sum_{k=1}^{n_l} \frac{x_k^{(t)} - x_i^{(t)}}{\|x_k^{(t)} - x_i^{(t)}\|} \varphi^x(m_{ik}^{(t)})$

Node Embedding Update

$h_i^{(t+1)} = h_i^{(t)} + \sum_{j=1}^{n_p} m_{ij}^{(t)} + \sum_{k=1}^{n_l} m_{ik}^{(t)}$ $h_j^{(t+1)} = h_j^{(t)} + \sum_{i=1}^{n_l} m_{ji}^{(t)}$

Recycling Mechanism

The decoder holds parameters for 4 EGCL layers. For iterations beyond 4 (up to $T=32$ ), parameter recycling is applied by feeding the previously predicted pose back into the decoder. During training, the number of cycles is sampled from $\text{Uniform}(1, N_{\text{cycle}})$ , and gradients are backpropagated solely through the final cycle by detaching earlier pose predictions.
Knowl 5 — Self-Confidence Score Prediction and Training Loss
equation
E3Bind is trained end-to-end to directly optimize Cartesian coordinates and self-confidence estimation without distance matrix post-processing.

Training Objective

The overall training loss $\mathcal{L}$ balances coordinate deviation and self-confidence calibration: $\mathcal{L} = \mathcal{L}_{\text{coord}} + \beta \mathcal{L}_{\text{confidence}}$ where $\beta$ is a weighting hyperparameter.

Coordinate Loss

$\mathcal{L}_{\text{coord}} = \sum_{i=1}^{n_l} \|x_i - x_i^*\|^2$ where $x_i \in \mathbb{R}^3$ is the predicted coordinate of ligand atom $i$ and $x_i^* \in \mathbb{R}^3$ is the ground-truth coordinate in the bound complex.

Self-Confidence Module and Loss

The predicted confidence score $\hat{c} \in (0, 1)$ is computed from the pooled final decoder embeddings $\{h_i^{(T)}\}_{i=1}^{n_l}$ : $\hat{c} = \sigma\left( \text{MLP}\left( \sum_{i=1}^{n_l} h_i^{(T)} \right) \right)$ where $\sigma$ is the sigmoid function. The confidence loss is the mean squared error against target $c^*$ : $\mathcal{L}_{\text{confidence}} = \text{MSE}(\hat{c}, c^*)$ where $c^*$ is defined by a piece-wise linear function of the detached root-mean-square deviation (RMSD) between predicted ligand coordinates $\{x_i\}$ and ground truth $\{x_i^*\}$ : $c^* = \begin{cases} 1 - \frac{1}{2\gamma} \cdot \text{RMSD}(\{x_i\}, \{x_i^*\}), & \text{if } \text{RMSD}(\{x_i\}, \{x_i^*\}) \le \gamma \\ c_0, & \text{otherwise} \end{cases}$ where $\gamma$ is an RMSD threshold cutoff and $c_0$ is a small constant floor.
Knowl 6 — Multi-Pocket Inference and Self-Confidence-Guided Pose Selection
algorithm
To perform flexible blind self-docking on full target proteins that may have large surfaces or multiple candidate binding sites, E3Bind segments the receptor into functional blocks and uses its internal self-confidence module to select the best docked pose.
Input: Protein structure $G^p$ , unbound ligand molecular graph $G^l$ , number of refinement iterations $T = 32$
Output: Predicted docked ligand coordinates $\{x_i^*\}_{i=1}^{n_l}$
// 1. Segment protein into candidate functional blocks using P2Rank
$B \leftarrow \text{SegmentProtein}(G^p, \text{max\_blocks} = 10, \text{radius} = 20\text{ Å})$
$\text{candidates} \leftarrow [\ ]$
for each functional block $b \in B$ do
    // 2. Initialize unbound ligand pose with random rotation and translation centered at block $b$
     $\{x_i^{(0)}\}_{i=1}^{n_l} \leftarrow \text{RandomTransform}(\text{ETKDG}(G^l), \text{center} = \text{center}(b))$

    // 3. Extract protein-ligand features with Trioformer
     $\{h_i^l\}, \{h_j^p\}, \{z_{ij}\} \leftarrow \text{Trioformer}(G^l, b, \{x_i^{(0)}\})$

    // 4. Iteratively refine coordinates with context-aware E(3)-equivariant decoder
     $\{x_i^{(T)}\}, \{h_i^{(T)}\} \leftarrow \text{DecoderRecycle}(\{h_i^l\}, \{h_j^p\}, \{z_{ij}\}, \{x_i^{(0)}\}, T)$

    // 5. Predict self-confidence score
     $\hat{c}_b \leftarrow \sigma\left(\text{MLP}\left(\sum_{i=1}^{n_l} h_i^{(T)}\right)\right)$

     $\text{candidates.append}((\{x_i^{(T)}\}, \hat{c}_b))$
end for
// 6. Select pose with the highest self-confidence score
$\{x_i^*\} \leftarrow \arg\max_{\{x_i^{(T)}\}} \hat{c}_b \text{ over } (\{x_i^{(T)}\}, \hat{c}_b) \in \text{candidates}$
return $\{x_i^*\}$
Because pose selection is guided entirely by the self-confidence score $\hat{c}$ predicted from structural embeddings, E3Bind operates without requiring an auxiliary binding affinity estimation model.

Knowl 7 — Flexible Blind Self-Docking Benchmark on PDBbind v2020

data/table

Performance of E3Bind and baseline methods on the PDBbind v2020 time-split test set (363 complexes deposited after 2019, with training complexes sharing test ligands removed). Baselines include traditional scoring/sampling tools (QVina-W, GNINA, SMINA, GLIDE, Vina) and deep learning models (EquiBind, TankBind). Models suffixed with "-U" are uncorrected versions evaluated without post-optimization.

	LIGAND RMSD ()Ä						CENTROID DISTANCE ()Ä
	Percentiles $\downarrow$				% Below $\uparrow$		Percentiles $\downarrow$				% Below $\uparrow$
Method	25%	50%	75%	Mean	2Ä	5Ä	25%	50%	75%	Mean	2Ä	5Ä
QVina-W	2.5	7.7	23.7	13.6	20.9	40.2	0.9	3.7	22.9	11.9	41.0	54.6
GNINA	2.8	8.7	22.1	13.3	21.2	37.1	1.0	4.5	21.2	11.5	36.0	52.0
SMINA	3.8	8.1	17.9	12.1	13.5	33.9	1.3	3.7	16.2	9.8	38.0	55.9
GLIDE	2.6	9.3	28.1	16.2	21.8	33.6	0.8	5.6	26.9	14.4	36.1	48.7
Vina	5.7	10.7	21.4	14.7	5.5	21.2	1.9	6.2	20.1	12.1	26.5	47.1
EquiBind	3.8	6.2	10.3	8.2	5.5	39.1	1.3	2.6	7.4	5.6	40.0	67.5
TankBind	2.6	4.2	7.6	7.8	17.6	57.8	0.8	1.7	4.3	5.9	55.0	77.8
E3Bind	2.1	3.8	7.8	7.2	23.4	60.0	0.8	1.5	4.0	5.1	60.0	78.8
EquiBind-U	3.3	5.7	9.7	7.8	7.2	42.4	1.3	2.6	7.4	5.6	40.0	67.5
TankBind-U	3.9	7.7	13.6	10.5	8.0	34.7	1.3	3.0	8.2	6.6	40.5	66.4
E3Bind-U	2.0	3.8	7.7	7.2	25.6	60.6	0.8	1.5	4.0	5.1	59.0	78.8

E3Bind achieves state-of-the-art results across most metrics. In particular, the proportion of high-resolution predictions with Ligand RMSD $< 2$ Å reaches 23.4% (and 25.6% for E3Bind-U), representing a 33% relative improvement over TankBind (17.6%). E3Bind-U achieves top performance without post-optimization, confirming that the end-to-end network directly outputs physically and geometrically valid poses.

Knowl 8 — Flexible Blind Self-Docking on Unseen Target Proteins

data/table

Generalization benchmark on a test subset containing 144 protein-ligand complexes whose protein targets were entirely unseen during training, evaluating out-of-distribution transfer.

	LIGAND RMSD ()Ä						CENTROID DISTANCE ()Ä
	Percentiles $\downarrow$				% Below $\uparrow$		Percentiles $\downarrow$				% Below $\uparrow$
Method	25%	50%	75%	Mean	2Ä	5Ä	25%	50%	75%	Mean	2Ä	5Ä
QVina-W	3.4	10.3	28.1	16.9	15.3	31.9	1.3	6.5	26.8	15.2	35.4	47.9
GNINA	4.5	13.4	27.8	16.7	13.9	27.8	2.0	10.1	27.0	15.1	25.7	39.5
SMINA	4.8	10.9	26.0	15.7	9.0	25.7	1.6	6.5	25.7	13.6	29.9	41.7
GLIDE	3.4	18.0	31.4	19.6	19.6	28.7	1.1	17.6	29.1	18.1	29.4	40.6
Vina	7.9	16.6	27.1	18.7	1.4	12.0	2.4	15.7	26.2	16.1	20.4	37.3
EquiBind	5.9	9.1	14.3	11.3	0.7	18.8	2.6	6.3	12.9	8.9	16.7	43.8
TankBind	3.4	5.7	10.8	10.5	3.5	43.7	1.2	2.6	8.4	8.2	40.9	70.8
E3Bind	3.0	6.1	10.2	10.1	6.3	38.9	1.2	2.3	7.0	7.6	43.8	66.0
EquiBind-U	5.7	8.8	14.1	11.0	1.4	21.5	2.6	6.3	12.9	8.9	16.7	43.8
TankBind-U	4.0	7.9	14.9	8.3	3.5	34.0	1.4	3.3	10.9	8.3	35.4	65.2
E3Bind-U	3.1	6.0	10.6	10.1	5.6	41.0	1.2	2.3	7.8	7.7	42.4	65.3

On unseen targets, E3Bind outperforms other deep learning baselines (achieving 6.3% RMSD $< 2$ Å vs. 3.5% for TankBind and 0.7% for EquiBind). While traditional physics-based scoring methods (e.g., GLIDE at 19.6% and QVina-W at 15.3%) maintain higher fractions of $< 2$ Å poses in this out-of-distribution regime, E3Bind substantially suppresses extreme docking failures (reducing mean RMSD to 10.1 Å compared to 16.9 Å for QVina-W and 19.6 Å for GLIDE).

Knowl 9 — Ablation Study on E3Bind Architectural Components

data/table

Ablation analysis on the flexible blind self-docking task evaluating the contribution of geometry-aware constraints, Trioformer, iteration count, intra-ligand message passing, and P2Rank pocket segmentation.

	LIGAND RMSD ()Ä						CENTROID DISTANCE ()Ä
	Percentiles $\downarrow$				% Below $\uparrow$		Percentiles $\downarrow$				% Below $\uparrow$
Method	25%	50%	75%	Mean	2Ä	5Ä	25%	50%	75%	Mean	2Ä	5Ä
E3Bind	2.1	3.8	7.8	7.2	23.4	60.0	0.8	1.5	4.0	5.1	60.0	78.8
w/o Geometric Constraint	2.3	4.0	7.8	7.6	20.1	57.6	0.9	1.7	4.0	5.3	58.2	76.4
w/o Trioformer	2.8	4.5	8.1	7.9	11.7	55.2	1.2	2.0	4.5	5.6	54.2	77.4
4 Iteration	2.6	4.0	7.8	7.5	14.9	58.9	1.1	1.8	4.5	5.5	52.6	77.9
w/o Intra	2.4	4.0	7.8	7.6	17.6	56.4	0.9	1.7	4.5	5.6	55.6	78.3
w/o P2Rank	2.0	4.2	7.8	7.6	24.2	56.4	0.8	1.7	4.1	5.6	54.8	79.1

Key takeaways:

Trioformer vs. Concatenation: Replacing Trioformer with simple concatenation of protein and ligand embeddings drops RMSD $< 2$ Å from 23.4% to 11.7%.
Geometry Awareness: Removing intra-protein/ligand distance biases in pair updates reduces $< 2$ Å poses from 23.4% to 20.1%.
Iterative Refinement: Reducing decoder iterations from 32 to 4 drops $< 2$ Å poses to 14.9%.
Intra-Ligand Messages: Omitting ligand intra-edge message passing lowers $< 2$ Å poses to 17.6%.
Pocket Segmentation Independence: Segmenting proteins into 30 random blocks without P2Rank preserves a 24.2% $< 2$ Å fraction, indicating low dependence on specialized pocket pre-selectors.

Knowl 10 — Blind Rigid Re-Docking Benchmark

data/table

Blind rigid re-docking performance on the 363 PDBbind v2020 test complexes where the ground-truth bound ligand conformation is provided as prior knowledge and only global roto-translation into the pocket needs to be predicted. EquiBind-R predicts only global rigid rotation and translation without updating internal conformations.

	LIGAND RMSD ()Ä						CENTROID DISTANCE ()Ä
	Percentiles $\downarrow$				% Below $\uparrow$		Percentiles $\downarrow$				% Below $\uparrow$
Method	25%	50%	75%	Mean	2Ä	5Ä	25%	50%	75%	Mean	2Ä	5Ä
QVina-W	1.6	7.9	24.1	13.4	27.7	39.0	0.9	3.8	23.2	11.8	40.4	55.4
GNINA	1.3	6.1	22.9	12.2	32.2	46.8	0.7	2.8	22.1	10.9	43.8	58.4
SMINA	1.4	6.2	15.2	10.3	30.1	46.7	0.8	2.6	12.7	8.5	45.3	63.5
GLIDE	0.5	8.3	29.5	15.7	43.4	45.7	0.3	4.9	28.5	14.8	45.4	50.4
Vina	4.5	9.7	19.9	13.4	13.2	26.7	1.7	5.5	18.7	11.2	29.8	47.9
EquiBind-R	2.0	5.1	9.8	7.4	25.1	49.0	1.4	2.6	7.3	5.8	40.8	66.9
TankBind	1.4	3.4	7.0	7.0	37.2	63.9	0.8	1.7	4.1	5.6	55.1	78.2
E3Bind	1.2	3.3	7.2	6.7	38.3	63.9	0.6	1.3	3.8	5.1	61.4	79.0
TankBind-U	4.5	8.0	15.5	10.9	8.0	27.5	1.5	3.3	8.3	6.7	33.3	60.3
E3Bind-U	1.4	3.2	7.1	6.8	34.7	65.6	0.6	1.4	3.7	5.1	61.4	79.3

Even though E3Bind is designed for fully flexible modeling, enforcing a rigid structure through post-optimization configuration loss produces competitive RMSD (38.3% $< 2$ Å) and superior centroid localization (61.4% $< 2$ Å Centroid Distance) compared to both deep learning and classical sampling baselines.

Knowl 11 — Inference Efficiency and Structural Validity via Steric Clash Mitigation
empirical result
E3Bind provides substantial inference speedup over traditional physics-based docking software and resolves steric overlap issues common in one-shot geometric deep learning.

Inference Runtime

Average execution time per protein-ligand complex on the test set:
- Classical score-based methods (16-CPU): QVina-W: 49 s; GNINA: 247 s (146 s on GPU); SMINA: 146 s; Vina: 205 s; GLIDE (single-threaded): 1405 s.
- Deep learning methods: EquiBind-U: 0.14 s (CPU) / 0.03 s (GPU); TankBind-U: 1.2 s (CPU) / 0.87 s (GPU); E3Bind-U: 2.2 s (CPU) / 0.44 s (GPU). E3Bind-U runs 100x to 3000x faster than traditional docking baselines while including P2Rank functional block segmentation time (~0.15 s in parallel).
Steric Clash Mitigation

A steric clash is defined as any heavy-atom pair distance $< 0.4$ Å between protein and ligand.
- Occurrence Rates: EquiBind yields severe clashes on 21.0% of test complexes due to its unrefined one-shot keypoint alignment. In contrast, E3Bind exhibits clashes on only 3.3% of test complexes.
- Mechanism: The iterative refinement process dynamically senses local steric conflicts and corrects them across update cycles. Without self-confidence filtering and with only 4 iterations, 13.8% of poses contain clashes; adding confidence filtering reduces this to 6.6%, and extending refinement to 32 iterations further drops clash occurrence to 3.3%.

Coverage note — None was omitted; all core model components (Trioformer encoder, E(3)-equivariant iterative decoder, self-confidence module), training objectives, multi-pocket inference algorithms, and primary benchmark tables (flexible self-docking, unseen receptors, ablations, re-docking, and speed/clash analysis) were converted into standalone knowls.

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Citation

MLA

Zhang, Y., et al. “E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking”. arXiv, 2022, http://arxiv.org/abs/2210.06069v2.

APA

Zhang, Y., Cai, H., Shi, C., Zhong, B., & Tang, J. (2022). E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking. arXiv. http://arxiv.org/abs/2210.06069v2

Chicago

Zhang, Y., H. Cai, C. Shi, B. Zhong, and J. Tang. 2022. “E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking”. arXiv. http://arxiv.org/abs/2210.06069v2.

Harvard

Zhang, Y. et al. (2022) “E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking”, arXiv [Preprint]. Available at: http://arxiv.org/abs/2210.06069v2.

Vancouver

1. Zhang Y, Cai H, Shi C, Zhong B, Tang J (2022) E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking. arXiv

BibTeX

@article{zhang2022e3bind,
  title = {E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking},
  author = {Zhang, Yangtian and Cai, Huiyu and Shi, Chence and Zhong, Bozitao and Tang, Jian},
  year = {2022},
  journal = {arXiv},
  url = {http://arxiv.org/abs/2210.06069v2},
  eprint = {2210.06069}
}

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E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — E3Bind Architecture for End-to-End Equivariant Protein-Ligand Docking

Input Representations

Pipeline

Knowl 2 — Trioformer Feature Extraction and Geometry-Aware Interaction Encoding

Knowl 3 — Geometry-Informed Attentive Pair Updates in Trioformer

Protein-Constrained Attentive Pair Update

Ligand-Constrained Attentive Pair Update

Knowl 4 — Context-Aware E(3)-Equivariant Coordinate Refinement Layer

Equivariant Graph Convolutional Message Passing

Coordinate Update

Node Embedding Update

Recycling Mechanism

Knowl 5 — Self-Confidence Score Prediction and Training Loss

Training Objective

Coordinate Loss

Self-Confidence Module and Loss

Knowl 6 — Multi-Pocket Inference and Self-Confidence-Guided Pose Selection

Knowl 7 — Flexible Blind Self-Docking Benchmark on PDBbind v2020

Knowl 8 — Flexible Blind Self-Docking on Unseen Target Proteins

Knowl 9 — Ablation Study on E3Bind Architectural Components

Knowl 10 — Blind Rigid Re-Docking Benchmark

Knowl 11 — Inference Efficiency and Structural Validity via Steric Clash Mitigation

Inference Runtime

Steric Clash Mitigation

References

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