E3Bind: An End-to-End Equivariant Network for Protein-Ligand Docking
Authors: Yangtian Zhang
Huiyu Cai
Chence Shi
Jian Tang
Venue: ICLR 2023 poster (2023)
Keywords: protein-ligand docking
end-to-end training
iterative refinement framework
geometric deep learning

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 self-docking, 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.

Published as a conference paper at ICLR 2023
E3BIND: AN END-TO-END EQUIVARIANT NETWORK FOR PROTEIN-LIGAND DOCKING
Yangtian Zhang 12+ Huiyu Cail.2, Chence Shi Jian Tang
MMila- - Québec AI Institute. Canada Université de Montréal, Canada HHEC Montréal, Canada *CIFAR Al Research Chair {yangtian. zhang, huiyu.cal chence. shi wtweressssieeeeeeeeeeeee Yeumont ca j jian. tang@hec.ca
ABSTRACT
In silico prediction of the ligand binding pose to given protein target is a crucial but challenging task in drug discovery. This work focuses flexible blind self- docking, where we aim to predict the positions, orientations and conformations docked molecules. Traditional physics-based methods usually suffer from inac- curate scoring functions and high inference costs. Recently, data-driven methods based on deep learning techniques are attracting growing interest thanks their efficiency during inference and promising performance. These methods usually either adopt two-stage approach by first predicting the distances between pro- teins and ligands and then generating the final coordinates based on the predicted distances, or directly predicting the global roto-translation of ligands. In this pa- per, we take 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-lige -igand interaction through careful consideration of the geometric constraints in docking standard benchmark
and the local context of the binding site. Experiments datasets demonstrate the superior performance of our end-to-end trainable model compared to traditional and recently -propoodd deep learning methods.
INTRODUCTION
For nearly a century, small molecules, or organic compounds with small molecular weight, have been the major weapon of the pharmaceutical industry. They take effect by ligating (binding) their target, usually protein, to alter the molecular pathways of diseases. The structure of the protein- ligand interface holds the key to understanding the potency, mechanisms and potential side effects of small molecule drugs. Despite huge efforts made for protein- ligand complex structure determina- tion, there are by far only some 10a protein-ligand complex structures available in the protein data bank (PDB) (Berman et al. 2000), which dwarfs in front of the enormous combinatorial space of possible complexes between 10 drug-like like molecules (Hert et al. 2009 Reymond & Awale 2012) and at least 20,000 human proteins (Gaudet et al. 2017 Consortium 2019), highlighting the urgent need for in silico protein-ligamt docking methods. Furthermore, a fast and accurate docking tool capable of predicting binding poses for molecules yet be synthesized would empower mass-scale virtual screening (Lyu et al. 2019), a vital step in modern structure- based drug discovery (Ferreira) al. 2015). also provides pharmaceutical scientists with an interpretable, information-rich result.
Being a crucial task, predicting the docked pose of a ligand is also challenging one. Traditional docking methods (Halgren al., 2004 Morris et al., 1996 Trott & Olson, 2010 Coleman al. 2013)rel, on physics-inspired scoring functions and extensive conformation sampling to obtain the predicted binding pose. Some deep learning methods focus on learning more accurate scoring function (McNutt et al.] 2021: MéndezzLuuce et al., (001)), but at the cost of even lower inference speed due their adoption of the cumpling-scoring framework. Distinet from the above methods, TankBind (Lu et al.] 2022) drops the burden of conformation sampling by predicting the protein- ligand distance map, then converting the distance map to a docked pose using gradient descent. The
"qqual contribution

---

Published as a conference paper at ICLR 2023
optimization objective is the weighted sum of the protein-ligand distance error with respect to the predicted distance map and the intra-ligand distance error w.r.t. the reference intra-ligand distances. This two-stage approach might run into problems during the sestance-to-cordding
transformation, as the predicted distance map is, in many cases, not a valid Euclidean distance matrix (Liberti et al.) equivariant model that directly predicts
2014). Recently, (Stärk et al.) (2022) proposed EquiBind, the coordinates of the docked pose. EquiBind updates the ligand conformation with graph neural network, then roto-translates the ligand into the pocket using key-point alignment mechanism. It enjoys significant speedup compared to the popular docking baselines (Hassan et al. 2017 Koes al., (013) and provides good pose initializations for them, but on its own the docking performance less satisfactory. This is probably because, after the one-shot roto-translation, the ligand might fall into an unfavorable position but its conformation could not be further refined.
In this paper, we move one step forward in this important direction and propose E3Bind, the first end-to-end equivariant network that iteratively docks the ligand into the binding pocket. Inspired by AlphaFold2 (Jumper al. 2021), our model comprises a feature extractor named Trioformer and an iterative coordinate refinement module. The Trioformer encodes the protein and ligand graphs into three information-rich embeddings: the protein residue embeddings, the ligand atom embed- dings and the grotein-ligand pair embeddings, where the pair embeddings are fused with geometry awareness to enforce the implicit constraints in docking. Our coordinate refinement module de- codes the rich representations into E(3)--quivariant coordinate updates. The iterative coordinate update scheme feeds the output pose of decoder block as the initial pose of the next one, allowing the model to dynamically sense the local context and fix potential errors (see Figure 3). We fur- ther propose self-confidence predictor to select the final pose and evaluate the soundness of our predictions. E3Bind is trained end-to-end with loss directly defined on the output ligand coordi- nates, relieving the burden of conformation sampling or cestanc-tto-oordiing transformation. Our contributions can be summarized as follows:
We formulate the docking problem as an iterative refinement process where the model updates the ligand coordinates based on the current context at each iteration.
We propose an end-to-end E(3) equivariant network to generate the coordinate updates. The network comprises an expressive geometrro-wwaee encoder and an equivariant context- aware coordinate update module.
Quantitative results show that E3Bind outperforms both traditional score-based methods and recent deep learning models.
2 RELATED WORKS
Protein-ligand docking. Traditional approaches to protein-ligand docking (Morris et al. 1996. Halgren et al. 2004; [oolman et al. 2013) mainly adopt a sampling, scoring, ranking, and fine- tuning paradigm, with AutoDock Vina TTott & Olson 2010) being popular example. Each part of the docking pipeline has been extensively studied in literature to increase both accuracy and speed (Durrant & McCammon 2011 Liu et al., 2013) Hassan et al. 2017 /Zhang al.] 2020 Multiple subsequent works use deep-learning on 3D voxels (Ragoza et al.] [017]] Francoeur et al., 2020 McNutt al.] [021] Bao et al. 2021 or graphs (Méndez-Lucio et al. 2021 to improve
the scoring functions. Nevertheless, these methods are inefficient in general, often taking minutes or even more predict the docking poses of single protein-ligand pair, which hinders the accessibility of large-scale virtual screening experiments.
Recently, methods that directly model the distance geometry between protein-ligand pairs have been investigated (Masters et al.) 2022, Lu et al., 2022) Zhou et al.) 2022). They adopt a two-stage ap- proach for docking, and generate docked poses from predicted protein-ligand distance maps using post-optimization algorithms. Advanced techniques in geometric deep learning, e.g. triangle atten- tion (Jumper et al., 2021) with geometric constraints, have been leveraged to encourage the local geometrical consistency of the distance map (Lu et al. 2022). To bypass the error-prone two- stage framework, EquiBind (Stärk et al., 2022) proposes a fully differentiable equivariant model, which directly predicts coordinates of docked poses with novel attention- key-point align- ment mechanism (Ganea et al. 20216). Despite being more efficient, EquiBind fails to beat popular docking baselines on its own, stressing the importance of increasing model expressiveness.
2

---

Published as a conference paper at ICLR 2023
Iterative coordinate update
molecular Iggand-consrrineed update
mm
inter-msssage passing
atom amb.
coordinate updale
protein structure
Igand protoin
docked ligand coordinates
proten-constraned update
Intra-message passing
Trioformer
Context-Aware E(3)-Equivarianl Network
Figure 1: E3Bind model overview. E3Bind takes in molecular graph of the ligand and protein structure as input, and extracts features with the Trioformer, which include geometry-awarr pair update modules that constrain the embeddings with known intra-protein and intra-ligand distances. E3Bind then iteratively updates the ligand pose with a decoder network to produce the final pose. The context-aware network performs inter- and intra-message passing before generating an B(3)- equivariant coordinate update.
Molecular conformation generation. Deep learning has made great progress in predicting low-
energy conformations given molecular graphs (Shi al. [021] Ganea al. 2021a Xu al. 2022
Jing et al. (0022.. State-of-the-arr models are generally SE(3)-invarian or equivariant, adopting the
score-matching Vincent 2011] [Song & Ermon 2019) or diffusion (Ho al., 2020) framework.
Though protein-ligang ligand docking also aims to generate the conformation of molecule, the bound
ligand, applying standard molecular conformation generation approaches not viable because (1) there are much more atoms in the system and (2) the protein context must be carefully considered when generating the docked pose. Here we model the protein at the residue level and design our model to carefully capture the protein-ligand interactions.
Protein structure prediction. Predicting protein folds from sequences has long been a challenging task. WWan et al. (2017); [Senior et al. (2020a b) use deep learning to predict the contact map, the distance map and/or the torsion angles between protein residues, and then convert them to coordi- nates using optimization-baat forward by adopting an end-to-end approach with iterative coordinate refinement. It consists of an Evoformer extract information from Multiple Sequence Alignments (MSAs) and structural tem- plates, and a structure module to iteratively update the coordinates. Though this problem is very different from docking which models heterogeneous entities fixed protein structure and ligand molecular graph, in this paper we show that some ideas can be extended.
methods. Recently, AlphaFold2 (Jumper al. (02T) takes leap
3 THE E3BIND MODEL
E3Bind tackles the pootein-ligande docking task with an encoder for feature extraction and a decoder for coordinate update generation. Specifically, the protein and ligand graphs first encoded by standard graph encoders. Pair embeddings are constructed between every protein residue ligand atom pair. A geometry-aware Trioformer is proposed to fully mix the protein, ligand and pair em- beddings (Section (3.2). With the rich representations at hand, the iterative coordinate refinement module updates the ligand pose by a series of E(3)-qqiivarian networks generate the final docked pose (Section 3.3 The model is trained end-to-end and capable of directly generating the docked pose (Section
An overview of E3Bind is shown in Figure
3.1 PRELIMINARIES
Notation and Input Feature Construction. Following Lu et al. (2022). the ligand is treated as an atom-level molecular graph g where the edges denote chemical bonds. The ligand node features (h) calculated by a TorchDrug (Zhu et al. 2022) implementation of the graph isomor- phism network (GIN) Xu et al. 2018), where ni is the number of atoms in the ligand. Ligand coordinates are denoted as hissss bor graph gP. Each protein node j {1...., . n has 3D coordinates æ6 (which corresponds to the position of the C, atom of the residue), where np the number of residues in the protein. The
represent the protein residue-level K K-nearest neigh-
3

---

Published as a conference paper at ICLR 2023
wewtoe--eeeooootteeeiie based graph neural network (GVP-GNN) Jing et al. (2020). For each protein residue-ligand atom pair (i,j), we construct pair embedding Zij via the outer product module (OPM) which takes in protein and ligand embeddings: Zij = Linear (vee (Lincar(h)) (h)) X Linear(h?))) For notation consistency, throughout this paper we will use i, k to index ligand nodes, and j. k' for protein nodes.
protein node features { ( hesss, are calculated with
Problem Definition. Given molecular graph of the ligand compound and fixed protein structure, aim predict the binding (docked) pose of the ligand compound {ar Jisigm We focus on blind docking settings, where the binding pocket is not provided and has to be predicted by the model. In the blind re-docking setting, the docked ligand conformation is given, but its position and orientation relative to the protein are unknown. In the flexible blind self-docking setting, the docked ligand conformation needs to be inferred besides its position and orientation. The model is thus provided with an unbound ligand structure, which could be obtained by running the ETKDG algorithm (Riniker Landrum, 2015) with RDKit (Landrum et al. 2013).
Equivariance. An important inductive bias in protein ligand docking is E(3) equivariance, L.e. the input protein coordinates are transformed by some E(3) transformation g {af))ssss, = Ray + t Vj = 1... Up. the predicted ligand coordinates should also be g- g-transformed: F(g. (15))ssss,)) = g (((af))sssnn)) )s))s))), where F is the coordinate prediction model. To inject such symmetry to our model, we adopt a variant of the equivariant graph neural network (EGNN) as the building block in coordinate update steps (Satorras et al. 2021).
3.2 EXTRACTING
CONSISSEET INFORMATION WITH TRIOFORMER
The E3Bind encoder extracts information-rich ligand atom embeddings h!, protein residue embeddings h and ligand-protein pair representa- tion Zij that captures the subtle protein-ligand interactions. Note that this is a non-trivial task since implicit geometric constraints must be in- corporated in the representations. As shown in the figure on the right, the poteinn-liaadd distance du and day can not be predicted independently. They are constrained by the intra-protein distance dyk', as the protein structure is considered to be fixed during docking. In other words, by the triangle inequality, if residues j and k are close, then ligand atom can- not be both close to j and far from k.. The same thing happens when we consider the given intra-ligand distance d While using a simple con- catenation of protein and ligand embeddings as the final pair embeddings
fixed distance
ligand + protein
is common among previous methods (Méndez-Lucio et al. 202T, Masters et al. 2022). it dismisses
the above geometry constraints and might result in geometrically inconsitentt pose predictions.
Trioformer Overview. To tackle the above challenge, we propose Trioformer, an architecture that intensively updates and mixes the protein, ligand and pair embeddings. In each Trioformer block, we first update the protein and ligand node embeddings with multi-head cross-attention using the pair embeddings as attention bias. Next, we use protein and ligand embeddings to update the pair embeddings via the outer product module: žij- = Zúj + OPM hz). The pair embeddings then go through geometry-aware pair update modules described below produce geometry-consistee representations. The final block outputs are the multi-layer perceptron (MLP) transsitratt protein, ligand and pair embeddings. Details of the Trioformer are described in Section B
Geometry-Awary Pair Updates. To inject geometry awareness to the pair embeddings, we con- struet intra-ligand and intra-protein distance embeddings (dī and di respectively) and then use them to update the pair embeddings. Following (Jumper al. 2202 Lu et al.] (0022). the edge up- dates are arranged in the form of triangles comprising two ligand-protein edges and one intra-edge (intra-ligand or intra-protein edge) where the distance constraints apply.
'During docking, the bond lengths, bond angles and conformation small rings are mostly unchanged. while torsion angles of rotatable bonds might change drastically (Trott & Olson 2010 Méndez- et all 2021 Sttäkk et al. (022). In the flexible docking setting, we provide distance di of atoms i and & in the unbound ligand structure predicted by ETKDG (Riniker & Landrum 2015) to constrain the model if i, k are
2-hop neighbors members of the same ring. Distance of all other ligand atom pairs are not provided.
4

---

Published as a conference paper at ICLR 2023
For protein-constramee attentive pair updates, each pair (i.j) attends to all neighboring pairs ((ss))) with a common ligand node We compute a geometry-informee attention weight (k)
lijk' for each neighbor ki, by adding an attention bias 152"" Linear (djx²) computed from the intra-protein distance embeddings per attention head This geometry-informed atten- tion weight is a key ingredient of Trioformer that differentiates it from the AlphaFold2's Evo- former Jumper et al. (202I). We then perform a standard multi-head attention with H heads to aggregate information from neighboring pairs,
(h)
(7/0))
(8)
(N) ik' + Dij
Oik' softmaxx
(1)
gk
Ri
Zij = Zij + Linear concatisngH
93j
(1)
(1) iK!
(2)
where 9iz (A) o (Linear (M) (ziz)) is a per-head output gate, 4iz
(1)
(h) kj 1) 6/
are linear projec-
tions of the pair embedding Zij. and 1/1 a distance-based bias described above.
The ligand-come ligand-constrained attentive pair updates are designed similarly. Here, for pair (i.j), the neigh- boring pairs {(k, i those sharing the same protein node j. Multi-head attention is performed across all such neighbors with constraints from intra-ligand distances dik-
3.3 ITERATIVE COORDINATE UPDATE WITH CONTEXT-AWARE B(3)-QQUVAARANT LAYER
The coordinate update module iteratively adjusts the current ligand structure {ae] hiiisn towards the docked pose based on the extracted representations. This module is designed to satisfy the following desiderata: (1) protein context awareness: the model must have an in-depth understanding of the interaction between the ligand and its protein context in order to produce protein-ligand complex with optimized stability (i.e. lowest energy): (2) self (ligand) context awareness: the model should honor the basic geometric constraints of the ligand so that the predicted ligand conformation is phys- ically valid; (3) -quivaaareee
both the protein and the input ligand pose are transformed by an E(3) transformation, the ligand should dock into the same pocket with the same pose, with its co- ordinates transformed with the same E(3) transformation. Compared with methods that generate the final pose in one shot, iterative refinement allows the model to dynamically sense the local context and correct potential errors as the ligand gradually moves toward its final position.
We start from an unbound ligand structurg At iteration step O...., T 1, the module up- dates the protein, ligand and pair representations (summarized by ht)) and the ligand coordinates (x) histsm with context-award E(3)-equivariant layer.
(h(tt)), (A hisism) DecoderLayer (1+1)
(æjhisism,)
(3)
(++1)
x
(b) An (++1)
0SI<T,
where (æj)isisa, are the fixed protein coordinates. We now introduce "ecoderLayer in detail.
Context-Aware Message Passing. To ensure the coordinate update module captures both the pro- tein and ligand context, construct heterogeneous context graph comprising both protein and ligand nodes. In the graph, inter-edges connect protein and ligand nodes, while intra-edges connect two ligand nodes (Figure I]. We perform inter- and intra-edge message passing on the graph to
explore the current context:
11p
Fly
h
((+1)
h
(t)
m
m
ik
(t)
(5)
j=1
km
h
(1+1)
h
+
m
ja
(6)
1=1
II the rigid docking setting, this structure has the same conformation the docked ligand structure.
5

---

Published as a conference paper at ICLR 2023
Note that the three types of messages are generated using different sets of parameters.
Equivariant Coordinate Update. We use the equivariant graph convolution layer (EGCL) to pro- cess current context geometry and update ligand coordinates in E(3)=qquivariant manner. Specif- ically, we compute messages from the node (and edge) representations and distance information using MLPs 6 and Tm
(4) mij m tm
(1)
(0)
(4)
()) 2.
Zig-
2
m (t)
(1)
(0)
2
(8)
We generate equivariant coordinate updates using the following equation.
(8)
(t) (0) at
AZ
40" (m (1))
(9)
(1)
(c)
x
k
where o and fo are gated MLPs that evaluate the message importance. Ligand and protein node embeddings are updated using equations (a and respectively.
Note that decoder is also compatible with other equivariant graph layers, such the geometric vector perceptron (GVP) (Jing et al. 2020) or vector neuron (Deng et al. (202T). We choose EGCL
as it is powerful layer for molecular modeling and conformation generation (Satorras al. 2021
Huang et al. 2022 Hoogeboom et al. 2022).
Self-Confidence Prediction. At the end of our decoder, an additional self-contidence module is added to predict the model's confidence for its predicted docked pose (Jumper et al. (021). The
confidence is a value from zero to one calculated by the equation = a MMPP
Σ -i=l h (2)
3.4 TRAINING AND INFERENCE
End-to-End Training. E3Bind directly generates the predicted ligand coordinates along with confidence score. We define simple coordinate loss and train the model end-to-end: Loood = E (z; xz)²² where æ; is the predicted coordinates and æę is the ground truth. We train the self-confidence module with Leonlidence = MSE (č, c²), where MSE is the mean squared error deviation
loss and c* is the self-confidence prediction target, i.e. the (detached) (RMSD) of the predicted coordinates. Details are deferred to Section C.I Intuitively, we want our model to predict low for high-RMSD predictions. The final training Ioss is the combination of the coordinate loss and the confidence loss L = Leoord + 3 Ceodideecce where ,9 is a hyperparameter. This loss aligns with the goal of docked pose prediction and avoids the time-consuming sampling process and potentially error-prone iittance-to-cordiine
moot-mean-qquee
transformation.
Inference Process. In practice, the target protein may contain multiple binding sites, or be ex- tremely large where most parts are irrelevant for ligand binding. To solve this problem, we use P2Rank (Krivák Hoksza 2018) to segment protein to less than functional blocks (defined as 20A graph around the block center), following TankBind (Lu et al. (022). We then initialize the unbound/bound (depending on the setting) ligand structure with random rotation and translation in each block, dock the ligand, and select the predicted docked pose with the highest ceff-confidence. Note that the initial pose might clash with the protein, but these clashes are likely to be repaired dur- ing the iterative refinement process. Different from TankBind which selects the final pose through binding affinity estimation for all functional block's 's predictions, our pose selection is based on self- confidence. As result, our model only feeds on protein-ligand complex structures, leaving the potential of including more structures without paired affinity for training.
4 EXPERIMENTS
4.1 FLEXIBLE SELF DOCKING
As E3Bind is designed to model the flexibility of ligand conformation, it is natural to evaluate it in the flexible blind self-docking setting. We defer the blind re-docking results Appendix Section

---

Published as a conference paper at ICLR 2023
LIGAND RMSD
CENTROID DISTANCE
Percentiles
Below
Percentiles 4
Below
Method
25%
50%
75%
Mcan
2A
5A
25%
50%
75%
Mcan
2A
5A
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
22.1
13.3
21.2
37.1
1.0
4.5
21.2
11.5
36.0
52.0
SMINA
3.8
17.9
12.1
13.5
33.9
1.3
3.7
16.2
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
7.8
17.6
57.8
0.8
1.7
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 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
Table I: Flexible blind self-docking performance. Models with "-U" suffix do not perform post- optimization steps that further enforce intra-ligand geometry constraints.
Data. We use the PDBbind v2020 dataset (Liu et al, 2017) for training and evaluation. We fol- low the time dataset split from (Stärk et al. (022), where 363 complex structures uploaded later than 2019 serve as test examples. After removing structures sharing ligands with the test set, the remaining 16739 structures used for training and 968 structures used for validation.
Baselines. We compare E3Bind with recent deep learning (DL) models and a set of traditional score- based methods. For recent deep learning models, TankBind (Lu et al.] (2022) and EquiBind (Stärk ett al. 2022) are included. For score- methods, QVina- W (Hassan et al. 2017). GNINA (Mc-
Nutt et al. 2021). SMINA (Koes al. 2013) and GLIDE (Halgren et al. 2004) are included.
We additionally distinguish between the uncorrected and corrected versions of the recent deep learn- ing models following EquiBind. The corrected versions adopt post optimization methods (c.g. gra- dient descent in TankBind (Lu et al., 2022), fast point cloud fitting in EquiBind (Stärk et al. (022)) further enforce the intra-ligand geometry constraints when generating the predicted structure. The uncorrected versions (suffixed with -U), which do not perform post-optimization, reflect the model's 'ss own capability for pose prediction. Specifically, EquiBind-U U and E3Bind-U outputs are directly generated by the neural networks and TankBind-U outputs are optimized from the predicted distance map without the ligand configuration loss. For a fair comparison, E3Bind results are refined from the E3Bind-U predicted coordinates by the post-optimization method of TankBind.
Metrics. We evaluate the quality of the generated ligand pose by the following metrics: (1) Ligand RMSD, the root-mean-square deviation of the ligand's Cartesian coordinates, measures at the atom level how well the model captures the pootein-ligant binding mechanisms; (2) Centroid Distance, defined as the distance between the average coordinates of predicted and ground-truth ligand struc- tures, reflects the model's capacity to find the binding site. All metrics are calculated with hydrogen atoms discarded following previous work.
Performance in Flexible Self-Docking. Table 1 summarized the quantitative results in flexible blind self-docking. Our model achieves state-of-the-an on most metries. Specifically, E3Bind shows exceptional power in finding ligand poses with high resolution, where the percentage of predicted poses with RMSD < 2 A increases by 33% compared to the previous state-of-the-art DL-based model TankBind. E3Bind achieves 2. A for the 25-th percentile of the ligand RMSD, ourperform- ing all previous methods by large margin. These results verify that our model able better cap- ture the protein-ligand interactions and generate geometrically-consise among uncorrected deep learning models, E3Bind-U enjoys more significant performance improve- ment, showcasing its low dependency additional post-opiimizatio. E3Bind-U also outperforms traditional docking softwares by orders of magnitude inference speed (Section demonstrating its potential for high-throughput virtual screening.
binding pose. Notably,
Performance in Flexible Self Docking for Unseen Protein. We further evaluate our model's 's ca- pacity subset of the above test set containing 144 complexes with the protein unseen in training. As shown in T E3Bind and E3Bind-U show better generalization ability than other DL-based model. Note that this setting traditional score-based methods performs better than DL-based

---

Published as a conference paper at ICLR 2023
LIGAND RMSD
CENTROID DISTANCE
Percentiles
Below
Percentiles +
% Below f
Method
25%
50%
75%
Mean
2
5
25%
50%
75%
Mcan
2
5 A
QVina-W 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
13.4
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
14.3
11.3
18.8
2.6
6.3
12.9
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-UU
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
Table 2: Flexible blind self-docking performance on unseen receptors. Test set contains 144 com- plexes with the protein not seen in training.
models on finding high-qualine binding poses (RMSD < 2 A), highlighting the need of increasing the
generalization capability for the latter. That said, observe that E3Bind produces much fewer predictions that are far off-target (RMSD > A).
Benefit of Iterative Refinement. Figure demonstrates the benefits of iterative refinement in im- proving ligand pose prediction. As the ligand undergoes more rounds of coordinate refinement, its RMSD decreases and self-confidence score increases. Figure visualizes how E3Bind's iterative refinement process successfully identified the correct binding site after iterations and further re- fined the ligand conformation for maximal interactions with the protein. The final pose is close to the ground truth with an RMSD of 1.42 A. In contrast, Equibind, method that does not adopt the iterative refinement scheme, yields a pose with an RMSD of 4.18 Á.
Ligand AMSD (A)
Self confidence score
0.98
0.96
0.94
0-
0.93
12
1.6
28
32
12
20
24
Number of iteration
Number of iteration
Figure 2: Violin plots of the ligand RMSD (in Á, left) and the self-confidence score (right) versus the number of coordinate update iterations (top 50% examples shown).
4.2 ABLATION STUDY
series of ablation studies are done to investigate different factors influencing the performance (Section T. (1) Removing geometry constraints in the pair update modules degrades the fraction of good poses (with RMSD < 2 Å) from 23.4% to 20.1 %. (2) Replacing the Trioformer with a sim- ple concatenation of the protein and ligand embeddings hurts the performance even worse (11.7%), highlighting the strength of Trioformer in extracting geometric features for docking. (3) Decreasing the number of iterations from 32 makes the fraction of good poses drop 14.9%, reiterating the benefit of the iterative refinement process. (4) The performance degrades to 17.6% when we remove mntra-message passing in the coordinate update modules. (5) Removing P2Rank and instead
segmenting the protein into 30 random blocks for docking has little impact performance, showing that E3Bind does not rely on P2Rank much as TinkBind for binding site pre-selection.
4.3 CASE STUDY
E3Bind correctly identifies the binding site in unseen large protein. Figure 4a shows rep- resentative case of a challenging example in blind docking. For an unseen protein, EBBind (shown in magenta) correctly identifies the native binding site with low RMSD of 4.2 A, while QVna-WW
8

---

Published as a conference paper at ICLR 2023
Iteration 0
Iteration 4
Iteration 12
Iteration 32
RMSD: 12.40
RMSD: 4.01
RMSD: 2.59
RMSD: 1.42 confidence: 0.974
confidence: 0.949
confidence: 0.973
Figure 3: E3Bind coordinate refinement trajectory for ligand in PDB 6PZ4. In each figure, the ground-truth docked ligand pose shown in gray and the initialized (Iteration 0) predicted (Itera- tions 4, 12, 32) structures in magenta. RMSD and model confidence are written below the figures.
EquiBind and TankBind dock to three distinct binding sites away from the ground truth. Further ex- amination of the self-confidence score shows this pose is the only with confidence above 0.91, while poses at other binding sites all have confidence below 0.86 (Figure S2)
E3Bind strikes balance between modeling protein-ligand interaction and structure validity. Figure [4b] presents the docking result a small protein. All methods except TankBind identify the correct binding site, with E3Bind prediction aligning better the ground truth protein-ligand interaction pattern. Interestingly. TankBind produces a knotted structure that is invalid in nature. This shows that the two-stage approach might generate invalid protein-ligand distance maps that can not be transformed into plausible structures in the distance-fo-coordinate optimization stage.
cnd 42
Eodlls 58
DWweii 28
OoiraW m
(a) PDB 6N94
(b) PDB 6QLR
Figure 4: Case studies. Predicted pose from E3Bind (magenta), TankBind (orange), EquiBind (red) and QVina-W W (blue) are placed together with the target protein. RMSDs from ground truth ligand pose (grey) are shown the figure. (a) E3Bind correctly identifies the binding site from the large protein, while the other methods are off-site. (b) E3Bind outperformed the other models in predicting the binding pose accurately, while TankBind generated an invalid structure with knotted rings.
5 CONCLUSION
Fast and accurate docking methods are vital tools for small molecule drug research and discovery. This work proposes E3Bind, an end-to-ent equivariant network for pootein-ligand docking. E3Bind predicts the docked ligand pose through a feature extraction coordinate refinement pipeline. Geometry-consistent protein, ligand and pair representations are first extracted by Trioformer. Then the ligand coordinates are iteratively updated by context-aware E(3))-quivariant network. Empir- ical experiments show that E3Bind is competitive against state-of-the-art blind docking methods, especially without post-optimization of the pose. Interesting future directions include: modeling the protein backbone/side-chin dynamics to better capture the drug-target interaction and exploring better ways of feature extraction, geometry constraint incorporation and coordinate refinement.

---

Published as a conference paper at ICLR 2023
ACKNOWLEDGEMENT
We would like express sincere thanks Bozitao Zhong. He contributed lot this project. We would also like to extend our appreciation to Minkai Xu, Chang Ma, Haoxiang Yang, Minghao Xu, Zhaocheng Zhu for their helpful discussions and insightful comments. This project supported by Twitter, Intel. the Natural Sciences and Engineering Research Council (NSERC) Discovery Grant, Canada CIFAR AI Chair Program, Samsung Electronics Co., Ltd., Amazon Faculty Research Award, Tencent AI Lab Rhino-Bird Gift Fund, a NRC Collaborative R&D Project (A14D-CORE-06) as well as the IVADO Fundamental Research Project grant
REPRODUCIBILITY STATEMENT
All code for data preprocessing, training and inference will be publicly released upon acceptance. Trioformer detail can be found in Section B Detail of the confidence loss is in Section C Other
implementation details are Section D
REFERENCES
Jingxiao Bao, Xiao He, and John ZH Zhang. Deepbsp- machine learning method for accurate prediction of protein-ligand docking structures. Journal of Chemical Information and Modeling, 61(5):2231-2240, 2021.
Helen M Berman, John Westbrook, Zukang Feng, Gary Gilliland, Talapady N Bhat, Helge Weissig, Ilya N Shindyalov, and Philip E Bourne. The protein data bank. Nucleic acids research, 28(1):
235-242, 2000.
Ryan G Coleman, Michael Carchia, Teague Sterling, John J Irwin, and Brian K Shoichet. Ligand pose and orientational sampling in molecular docking. PloS one, 8(10)=77992, 2013.
UniProt Consortium. Uniprot: a worldwide hub of protein knowledge. Nucleic acids research, 47 (DI):D506-D515 2019.
Congyue Deng, Or Litany, Yueqi Duan, Adrien Poulenard, Andrea Tagliasacchi, and Leonidas J Guibas. Vector neurons: A general framework for so -3uequrrariint networks. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 12200-12209, 2021.
Jacob D Durrant and J Andrew McCammon. Nnscore 2.0: neural-network receptor-ligand scoring function. Journal of chemical information and modeling, 51(11):887-2203, 2011.
Leonardo G Ferreira, Ricardo Dos Santos, Glaucius Oliva, and Adriano D Andricopulo. Molecu- 13421, 2015.
lar docking and structure-based drug design strategies. Molecules,
Paul G Francoeur, Tomohide Masuda, Jocelyn Sunseri, Andrew Jia, Richard B lovanisci, Ian Snyder, and David R Koes. Three-dimensional convolutional neural networks and cross-docked data set for structure- based drug design. Journal of chemical information and modeling, 60(9):2200- 2020.
Octavian Ganea, Lagnajit Pattanaik, Connor Coley, Regina Barzilay, Klavs Jensen, William Green, and Tommi Jaakkola. Geomol: Torsional geometric generation of molecular 3d conformer sembles. Advances in Neural Information Processing Systems, 01113377-137666 2021a.
Octavian-Eugen Ganea, Xinyuan Huang, Charlotte Bunne, Yatao Bian, Regina Barzilay, Tommi Jaakkola, and Andreas Krause. Independent se (3)-equivariant models for end-to-end rigid protein docking. arXiv preprint
2021b.
Pascale Gaudet, Andrr Michel, Monique Zahn Zahn-Zabal, Aurore Britan, Isabelle Cusin, Marcin Domagalski, Paula D Duck, Alain Gateau, Anne Gleizes, Valérie Hinard, et al. The nextprot knowledgebase on human proteins: 2017 update. Nucleic acids research, 45(D1):D177-D188, 2017.
Thomas A Halgren, Robert B Murphy, Richard A Friesner, Hege S Beard, Leah L Frye, W Thomas Pollard, and Jay L Banks. Glide: a new approach for rapid, accurate docking and scoring. 2. en- richment factors in database screening. Journal of medicinal chemistry, 1757)1750-1175, 2004.
10

---

Published as a conference paper at ICLR 2023
Nafisa M Hassan, Amr A Alhossary, Yuguang Mu, and Chee-Keenn Kwoh. Protein Protein-ligand ligand blind docking using quickvina-w with inter-process pratio-temporc integration. Scientific reports, (1):1-13, 2017.
Jérôme Hert, John Irwin, Christian Laggner, Michael J Keiser, and Brian K Shoichet. Quantifying biogenic bias in screening libraries. Nature chemical biology, 5(7):479-483, 2009.
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in Neural Information Processing Systems, 33:6840-6851, 2020.
Emiel Hoogeboom, Vićtor Garcia Satorras, Clément Vignac, and Max Welling. Equivariant dif- fusion for molecule generation in 3d. In International Conference on Machine Learning, pp- 8867-8887. PMLR, 2022.
Wenbing Huang, Jiaqi Han, Yu Rong, Tingyang Xu, Fuchun Sun, and Junzhou Huang. Equivariant graph mechanics networks with constraints. arXiv preprint Net::2233.04422 2022.
Bowen Jing, Stephan Eismann, Patricia Suriana, Raphael JL Townshend, and Ron Dror. Learning from protein structure with geometric vector perceptrons, arXiv preprint urXiv:2009.01411 2020.
Bowen Jing, Gabriele Corso, Jeffrey Chang, Regina Barzilay, and Tommi Jaakkola. Torsional diffu- sion for molecular conformer generation. arXiv preprint arXiv:2206.01729 2022.
John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ronneberger, Kathryn Tunyasuvunakool, Russ Bates, Augustin Zidek, Anna Potapenko, et al. Highly accurate protein structure prediction with alphafold. Nature, 596(7873):583-589 2021.
David Ryan Koes, Matthew Baumgartner, and Carlos Camacho. Lessons learned in empirical scoring with smina from the csar 2011 benchmarking exercise. Journal of chemical information and modeling, 13(8):1893-19) 1904, 2013.
Radoslav Krivák and David Hoksza. P2rank: machine learning based tool for rapid and accurate prediction of ligand binding sites from protein structure. Journal of cheminformatics, 10(1):1-12, 2018.
Greg Landrum et al. Rdkit: A software suite for cheminformatics, computational chemistry, and predictive modeling. Greg Landrum, 2013.
Leo Liberti, Carlile Lavor, Nelson Maculan, and Antonio Mucherino. Euclidean distance geometry and applications. SIAM review, 56(1):3-69, 2014.
Yu Liu, Lei Zhao, Wentao Li. Dongyu Zhao, Miao Song, and Yongliang Yang. Fipsdock: new molecular docking technique driven by fully informed swarm optimization algorithm. Journal of computational chemistry, 34(1):67-75, 2013.
Zhihai Liu, Minyi Su, Li Han, Jie Liu, Qifan Yang, Yan Li, and Renxiao Wang. Forging the basis for developing piotein-ligand interaction scoring functions. Accounts of chemical research, 50 (2):302-309, 2017.
Wei Lu, Qifeng Wu, Jixian Zhang, Jiahua Rao, Chengtao Li, and Shuangjia Zheng. Tankbind: Trigonometry- neural networks for drug-protein binding structure prediction. bioRxiv, 2022.
Jiankun Lyu, Sheng Wang, Trent E Balius, Isha Singh, Anat Levit, Yurii Moroz, Matthew J O'Meara, Tao Che, Enkhjargal Algaa, Kateryna Tolmachova, et al. Ultra-large library docking for discovering new chemotypes. Nature, 566(7743):224-225 2019.
Matthew Masters, Amr H Mahmoud, Yao Wei, and Markus Alexander Lill. Deep learning model for flexible and efficient protein-ligane docking. /CLR2022 Machine Learning for Drug Discovery, 2022.
Andrew T McNutt, Paul Francoeur, Rishal Aggarwal, Tomohide Masuda, Rocco Meli, Matthew Ragoza, Jocelyn Sunseri, and David Ryan Koes. Gnina 1.0: molecular docking with deep learn- ing. Journal of cheminformatics, 13(1):1-20, 2021.

---

Published as a conference paper at ICLR 2023
Oscar Méndez-Lucio, Mazen Ahmad, Ehecatl Antonio del Rio- Rio-Chanona, and Jörg Kurt Wegner. A geometric deep learning approach to predict binding conformations of bioactive molecules. Nature Machine Intelligence, 3(12):1033-100) 2021.
Garrett M Morris, David S Goodsell, Ruth Huey, and Arthur J Olson. Distributed automated docking of flexible ligands to proteins: parallel applications of autodock 2.4. Journal of compuler-aided molecular design, 10(4):293-304, 1996.
Matthew Ragoza, Joshua Hochuli, Elisa Idrobo, Jocelyn Sunseri, and David Ryan Koes. Protein- ligand scoring with convolutional neural networks. Journal of chemical information and model- ing, 57(4))942 957, 2017.
Srinivas Ramachandran, Pradeep Kota, Feng Ding, and Nikolay V Dokholyan. Automated mini- mization of steric clashes in protein structures. Proteins: Structure, Function, and Bioinformatics, 79(1):261-270, 2011.
Jcan-Louis Reymond and Mahendra Awale. Exploring chemical space for drug discovery using the chemical universe database. ACS chemical neuroscience, 3(9):649-66)) 2012.
Sereina Riniker and Gregory A Landrum. Better informed distance geometry: using what know to improve conformation generation. Journal of chemical information and modeling, 55(12): 2562-2574, 2015.
Victor Garcia Satorras, Emiel Hoogeboom, and Max Welling. E (n) equivariant graph neural net- works. In International conference on machine learning, pp. 9-299932999999 92322.93... PMLR. 2021.
Andrew W Senior, Richard Evans, John Jumper, James Kirkpatrick, Laurent Sifre, Tim Green, Chongli Qin, Augustin Židek, Alexander WR Nelson, Alex Bridgland, et al. Improved protein structure prediction using potentials from deep learning. Nature, 577(7792):706-710, 2020a.
Andrew W Senior, Richard Evans, John Jumper, James Kirkpatrick, Laurent Sifre, Tim Green, Chongli Qin, Augustin Zidek, Alexander WR Nelson, Alex Bridgland, al. Improved protein structure prediction using potentials from deep learning. Nature, 577(7792):06--710 2020b.
Chence Shi, Shitong Luo, Minkai Xu, and Jian Tang. Learning gradient fields for molecular confor- mation generation. In International Conference on Machine Learning, Pp. 9558-9568. PMLR, 2021.
Yang Song and Stefano Ermon. Generative modeling by estimating gradients of the data distribution. Advances in Neural Information Processing Systems, 32, 2019.
Hannes Stärk, Octavian Ganea, Lagnajit Pattanaik, Regina Barzilay, and Tommi Jaakkola. Equibind: Geometric deep learning for drug binding structure prediction. In International Conference Machine Learning, pp. 20503-20521. PMLR, 2022.
Oleg Trott and Arthur Olson. Autodock vina: improving the speed and accuracy of docking with new scoring function, efficient optimization, and multithreading. Journal of computational chemistry, (1()):555 2010.
Pascal Vincent. A connection between score matching and denoising autoencoders. Neural compu- tation, 23(7):1661-11)) 2011.
Sheng Wang, Siqi Sun, Zhen Li, Renyu Zhang, and Jinbo Xu. Accurate de novo prediction of protein contact map by ultra-deep learning model. PLoS computational biology, 13(1):e 2017.
Keyulu Xu, Weihua Hu, Jure Leskovec, and Stefanie Jegelka. How powerful are graph neural networks? arXiv preprint arXiv:1810.00822 2018
Minkai Xu, Lantao Yu, Yang Song, Chence Shi, Stefano Ermon, and Jian Tang. Geodiff: geo- metric diffusion model for molecular conformation generation. arXiv preprint arXiv:2203.02922, 2022.
Wenyi Zhang, Eric W Bell, Minghao Yin, and Yang Zhang. Edock: blind protein-ligand docking by replica-exchange monte carlo simulation. Journal of cheminformatics, 12(1):1-17, 2020.
12

---

Published as a conference paper at ICLR 2023
Gengmo Zhou, Zhifeng Gao, Qiankun Ding, Hang Zheng, Hongteng Xu, Zhewei Wei, Linfeng Zhang, and Guolin Ke. Uni-mol: A universal 3d molecular representation learning framework. ChemRxiv, 2022. doi: 1226644/chemmxxi-2222---ii
v3.
Zhaocheng Zhu, Chence Shi, Zuobai Zhang, Shengchao Liu, Minghao Xu, Xinyu Yuan, Yangtian Zhang, Junkun Chen, Huiyu Cai, Jiarui Lu, et al. Torchdrug: A powerful and flexible machine learning platform for drug discovery. arXiv preprint arXiv:2202.08220, 2022.
13

---

Published as a conference paper at ICLR 2023
A EXPERIMENT FOR BLIND RE-DOCKING
The setting of blind re-docking allows the model to take the ground-truth conformation as prior knowledge. Note that this is less realistic setting, since in many real-world applications the bound ligand conformation is not known in advance. Compared to the flexible blind self-docking, the model is given the full ligand conformation the higidbody motion for the molecule to dock into the binding site. Although the nature of rigid docking is somewhat contradictory the E3Bind model as it allows the full flexibility of the ligand structure, we are still able to enforce rigid structure through TankBind-style gradient descent post- optimization (Lu et al. 2022) using the ground truth conformation configuration loss.
geometric constraints, and only needs to predict
LIGAND RMSD
CENTROID DISTANCE
Percentiles
% Below
Percentiles |
% Below
Method
25%
50%
75%
Mean
2 À
5
25%
50%
75%
Mean
2
5 A
QVina-W W
1.6
7.9
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
19.9
13.4
26.7
1.7
5.5
18.7
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
Table S1: Blind re-docking performance. EquiBind-R is variant of EquiBind that does not update the ligand conformation with IEGMN and only predicts a translation and rotation.
Results of blind rigid docking are shown in Table SI Although the setting of rigid docking is not very suitable for our E3Bind model, we achieve SOTA most metrics, especially centroid distance.
B DETAILS OF THE TRIOFORMER
The Trioformer comprises stack of Trioformer blocks detailed Algorithm 1 AlphaFold2's Evoformer with baked-in geometry awareness. In each block, the ligand embeddings {h.} } are updated with a multi-head cross attention module, with the transformed pair embeddings bias (MHAWithPairBian
It is a variant of
softmaxx
(
(R)
+
+
(10)
up
h h! Linear concati
sk UK
(11)
The protein embeddings { are updated likewise. The node-level embeddings then go through a two-layer MLP transition modules and reach the block output state. On another track, the pair embeddings {ziz} are first updated with the node-level embeddings via the outer product module. Then, geometry-aware attentive pair update modules (detailed Section 3.2p injects implicit geo- metric constraints into the pair embeddings. Finally, the pair embeddings go through MI.P transition modules and become the remaining part of block outputs.
C DETAILS OF SELF-CONHIDENCE PREDICTION
C.I CONFIDENCE LOSS
We train the self confidennee module with a confidence prediction loss Leonfidences which is the mean squared error (MSE) between the predicted self-confidence and its target value e ot is dependent
14

---

Published as a conference paper at ICLR 2023
Algorithm 1: Trioformer Block
Input: ligand embeddings { protein embeddings { pair embeddings {zig),
intra-ligand distances {dua); ) intra-protein distances {dga>}
/* Cross attent ion updates ligand and protein with pair +/
[h.] + [h] + MHAAitthPairBais(((((( (hh)) (K)) (h5), (zy));
[h]] + [ + MHAWithPairDBass(( ((h)): [h.) (.a)))
/* Node level transitions +/
[h.] + MLP(()))
[h]) +
/8 OPM updates pair embeddings with ligand and protein x/
(z +
(h)]):
/8 Geometry aware pair update modules +/
(1)) + [zn]]
((z)) {dx}, ) {dj })
8ig t [zi
PaocaaCCossniiickttttteeehaaahhd (f Eigh, {dae). {dzx 1):
/* Pair transition +/
{z1g} < {zig} + MLP((=;))):
return (h.) (h.)) {zi}}
on the root-mean- square deviation (RMSD) of the coordinate prediction: linearly increases with the RMSD of the predicted pose when the latter is small, and is set to small value co once RMSD reaches 7:
RMSD ((a!)), [ar]),(()')) (ar'))
if RMSD (fa!)) (at")) Sr (12)
1
([x!))
27
otherwise.
3.0-
14
Pearson: 0.641
12
Spearman: -0. 0.783
Density
2.0-
Upand Rorso
10-
1.5
Successful Case
Falled Case
0.5-
0.0
0.70
0.95
0.60
0.90 0.95 1.60
0.4
0.6
0.8
1.0
Confidence Score
Self Confidence Score
Figure S1: Behavior of the self-confidence model. (Left) Jointplot showing the relationship between the predicted confidence score and ligand RMSD Å) for test examples. (Right) E3Bind self- confidence module can distinguish successfully-docked (RMSD 5A) poses from failed ones.
C.2 SELF-CONFIDENCE PREDICTION RESULTS
We plot the relationship between the predicted confidence score and the ligand RMSD for test ex- amples on the left plot of Figure SI Most data points have high confidence scores and low ligand RMSDs. We further calculate the correlation metrics between the negative RMSD and the pre- dicted confidence score. The results give Pearson correlation coefficient of 0.641 and a Spearman correlation coefficient of 0.783, indicating decent pose-selection capability our self-confidence prediction module.
We next investigate the behavior the self-confidence score for success and failure cases (Figure right). The distribution plot shows that the distributions for these two cases have high divergence.
15

---

Published as a conference paper at ICLR 2023
For successful docking examples (RMSD 5A), the average confidence score is 0.91, while for failure cases, the average confidence score is 0.61.
0.743
0.916
0.798
Figure S2: Case study on E3Bind's self-confidence module: PDB 6N94. The ligand pose (in ma- genta) closest to the ground truth (in grey) has the highest confidence score of 0.916. The confidence scores of the two wrongly predicted ligand poses (in magenta, half-transparent) are both below 0.8.
D IMPLEMENTATION DETAILS
The dimensions of protein, ligand and pair embeddings are set to 128. Layer normalization and dropout applied in each block. For the implementation of EGCL, ordinate differences instead of the original coordinate differences. Specifically, all coordinates are divided by 5 before fed into EGCL and the final coordinates function is used in the EGCL layers and LeakyReLU is used in the Trioformer blocks. All models including variants in ablation study are trained with Adam optimizer with learning rate 0.0001 for 300 epochs. The model with the best valid score (measured by the fraction of predicted pose with RMSD 2A) evaluated on the test set. We use the TankBind (Lu et al. 2022) pipeline for data preprocessing, protein segmentation and featurization. The only modification is that we remove all complexes in the training set sharing ligands with the test set to reduce information leak test time.
the normalized co-
multiplied by 5. SiLU activation
For the context-aware decoder, instead of using set of parameters for each EGCL layer, adopt the recycling technique of AlphaFold2 (Jumper et al. 2021). Specifically, E3Bind's decoder contains 4 EGCL layers (i.e. holds parameters for 4 coordinate update iterations). For iterations longer than 4, we recycle the decoder parameters by feeding the previously predicted pose to the decoder as the initial pose. During training, randomly select the number of cycles from Uniform(1. Noycle), ) and only backpropagate through the last cycle (by detaching the gradient of initial pose) to reduce the computational cost. Nyelee is 32 in our experiments.
16

---

Published as a conference paper at ICLR 2023
E FURTHER ABLATION STUDY RESULTS
E.1
ABLATION STUDY OF E3BIND
LIGAND RMSD
CENTROID DISTANCE
Percentiles +
% Below
Percentiles
% Below 1
Method
25%
50%
75%
Mean
2
S
25%
50%
75%
Mean
2
5
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 Aware
2.3
4,0
7.8
7.6
20.1
57.6
0.9
4.0
5.3
58.2
76.4
Trioformer
2.8
4.5
8.1
55.2
1.2
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
P2Rank
24.2
5.6
54.8
79.1
Table S2: Ablation Study of E3Bind. For discussions, see Section 4.2
E.2 IMPACT OF POST OPTIMIZATION
To investigate the impact on time cost and performance of different post-optimization methods, we plug each model into each post-optimization method and log the performance in Table [S3 In practice, fast point cloud fitting is faster but yields worse results. This justifies the choice of gradient descent the post-optimization method for E3Bind. Note that for the two benchmarked post- optimization methods, our model consistently outperforms EquiBind and Tank
LIgAND RMSD
CENTROID DISTANCE
Percentiles
% Below 1
Percentiles
S Below
Post Optimization
Method
25%
50%
75%
Mean
2
5
25%
50%
75%
Mean
2
5
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
Fast Point Cloud Fitting (0.01
Tank
5.8
8.4
E3Bind
2.3
4.1
7.8
7.4
19.3
$7.8
0.8
1.5
4.0
5.1
$9.0
78.8
Gradient Descent (0.44 s)
EquiBind
3.5
5.8
10.2
8.0
4.4
42.7
1.3
2.7
7.0
5.5
40.8
68.6
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
Table S3: Performance and run time a 16-CPU machine of deep-learning models paired with post-optimization methods on the flexible blind self-docking task. Fast point cloud fitting (Stärk) al. 2022) changes torsion angles of the initial pose to best match the generated pose by perform- ing maximum likelihood estimates of von Mises distributions. Gradient descent (Lu al., 2222) minimizes the weighted sum of the protein- protein-ligand distance error w.r.t. the predicted distance map and the intra-ligand distance error w.r.t. the reference distances.
17

---

Published as a conference paper at ICLR 2023
F SENSITIVITY TO INITIALIZATION
E3Bind model's iterative refinement start from some initial structure at the functional block. The initial structure is generated by RDKit and placed in the functional block with random rotation and translation. Here we investigate the influence of initialization for the model's final performance. We generate 30 pose predictions for each ppotein-ligand complex with different translation and ro- tation. As shown in Figure [S3] 80% of the test set examples have their standard deviation of ligand RMSD within 0.196 Å and standard deviation of centroid distance within 0. 0818 The result indi- cates E3Bind's s low sensitivity to ligand pose initialization and the strong robustness of its iterative refinement process.
120
120
Numbbe of Preditions
100
Percentile: 80%
Number of Predictions
100
Percentile: 80%
80
80
60-
40
0
0.0
0.8
1.0
0.0
0.8
0.8
Slandard deviation prediction's ligand RMSD (A)
Standard deviation prediction's centroid distance (A)
Figure S3: Experiment result sensitivity for different initialization
G INFERENCE SPEED
The inference speed of different methods is shown in Table $4 Here we report the average time cost seconds for single prediction. shown in Section G can arbitrarily compose deep learning methods and post-optimization methods. Therefore, here we compare the inference speed of their uncorrected versions. For TankBind and E3Bind, P2Rank segmentation time (~ 0.15 parallel) is included. For TankBind, the time for also included. As shown in Table S44, the inference speed of E3Bind exceeds traditional methods by a large margin.
optimization (~ 0.44 s in parallel) is
Avg. Sec. 16-CPU
Avg. Sec. GPU
Method
QVINA-W
49
GNINA
247
146
SMINA
146
GLIDE
1405*
VINA
205
EquiBind-U
0.14
0.03
TankBind-U
1.2
0.87
E3Bind-U
2.2
0.44
Table S4: Inference Speed. Numbers for score-based methods are taken from the EquiBind pa- per (Stärk et al., 2022). "The GLIDE only uses single thread since the multi-threaded version requires separate license.
18

---

Published as a conference paper at ICLR 2023
H
ADDITIONAL TRAJECTORIES AND CASE STUDIES
Iteration
Iteration 4
Iteration 12
Iteration 32
RMSD: 7.31
RMSD: 3.76
RMSD: 2.26
RMSD: 1.38 confidence: 0.980
confidence: 0.961
confidence: 0.980
Figure S4: E3Bind coordinate refinement trajectory for ligand in PDB 6UWP. In each figure, The ground-truth docked ligand pose shown in gray and predicted structures shown in magenta. RMSD and model confidence are written below the figures. E3Bind achieves an RMSD of 1.38 Á after 32 iterations.
PDB 6N4E
PDB 6HHT
PDB 6K1S
Figure S5: Additional case studies. (a, b) Predicted pose from E3Bind (magenta), TankBind (or- ange), EquiBind (red) and QVina-W (blue) are placed together with the target protein. RMSD from ground truth ligand pose (grey) are shown on the figure.
(a) E3Bind correctly identifies the bind- ing site from the large protein, while EquiBind and QVina-W are off-site. The predicted structure of E3Bind has low RMSD of 2.37 Å. (b) In this relatively small protein, E3Bind produces lig- and pose with the lowest RMSD. (c) An example a potential binding pocket predicted with high self self-confidence by E3Bind. The predicted ligand pose is shown in magenta and protein (including backbone cartoons and sidechain sticks) are shown in green. Contact between the predicted pose and ths protein are highlighted in yellow.
19

---

Published as a conference paper at ICLR 2023
1 EXAMINING THE VALIDITY OF GENERATED STRUCTURES
1.1 BOND LENGTH DISTRIBUTION
Here we examine the validity of our generated structures by comparing the bond length distribution plots between the predicted and ground truth structures. We can see from Figure S6 that E3Bind outputs have very similar bond distributions compared the ground truth.
C SINGLE
CSNNGLE O
SINGLE
AROMATIC
DOUBLE
Density
10-
Ground Truth
E3Bind Prediction
3 Length
2 Bond Length
3 Length
Bond Length
Bond Length
Figure S6: Distribution of bond lengths in E3Bind (orange) and ground truth (green)
ligand structures, grouped by bond types.
I.2 STERIC CLASH PROBLEM
Steric clash is a common problem in docking, where two non-bonding atoms show an unnatural overlap in the predicted structure. While traditional docking methods avoid generating steric clashes by incorporating a repulsion term the scoring function, deep learning models have yet to solve this issue.
In our experiments, we find that E3Bind produces very few steric clashes (3.3% the test set con- tain at least steric clash), while EquiBind (Stärk et al. 2022) are more likely to produce severe steric clashes (21 % of the test set have clashes) as shown in S7b This is mainly because EquiBind docks the ligand into protein by key-poin matching in shot manner, which prohibits further ligand conformational changes to fit in the protein pocket. On the other hand, E3Bind iteratively refines the ligand's 's position, orientation and conformation, which means could correct its previous errors, resulting in much fewer steric clash problems.
also observed that our self-confidence prediction module plays an important role in selecting structures with fewer steric clashes, Without the confidence module, E3Bind with only 4 iterations has 13.8% % change of generating pose with steric clashes. When we apply the confidence mod- ule for filtering, the fraction drops to 6.6%. Subsequent iterations of E3Bind further decrease the fraction 3.3%.
(a) PDB 6QLR
(b) PDB 6SEN
Figure S7: Illustration of two types of steric clashes. (a) Tank predicted pose containing a knotted structure, which is physically impossible. The error is due to an unrealizable distance map predicted by TankBind. (b) EquiBind predicted pose (in magenta) with its protein context. The protein atoms within 1.5 Á of the ligand (i.e. having severe clashes with the ligand) are highlighted with a lime sphere. Stick models of the corresponding residues are shown in gray. The protein cartoon is shown in dark green.
A steric clash is defined by pair of heavy atoms with distance of less than 0.4 Á following (Ramachan- dran 201T).
20


Reviews:
[{"review_id": "rmazTe_AFoQ", "reviewer": "Reviewer_ofea", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes an end-to-end encoder-decoder approach for ligand-protein binding (blind docking) where the ligand can conform while the protein structure is assumed fixed. In the encoder part, the individual atomic representation of ligand and residue-based representation of ligand is learnt through graph networks which in turn leads to an embedding for pairs of atoms and residues and are all update within a transformer. The decoder iteratively processes the embeddings to output Euclidean coordinates for the ligand atoms where it respects the SE(3) equivariance of rotation and translations of the ligand and protein.", "summary_of_the_review": "The empirical results are relatively strong, the work has the minimal required novelty in the general design as well as the attention mechanism. On the other hand, a conclusive message on the performance can benefit from the above-mentioned additional experiments. I lean towards accepting the paper.", "strength_and_weaknesses": "strengths:\n+ The encoder-decoder architecture for ligand-protein binding can be considered novel although comprised of modules that have been proposed in the literature before, save for the following point.\n+ The distance-based attention mechanism to update the pair embeddings seems to somewhat respect the 3D Euclidean geometry of the individual protein and the individual ligand in an interaction.\n+ The general setup has taken many inspirations from recent works on protein structure modeling and protein binding including alphafold.\n+ From (although limited) ablation studies it seems at least some of the additions are generally successful in improving the docking performance.\n+ The results show clear improvements over recent baselines on protein-ligand binding.\n\npossible improvements:\n- The proposed method is comprised of many learnable components. It would be informative to compare the capacity of the model in some form with prior similar works, at least the more recent ones EquiBind and TankBind. Then, it would be important to empirically verify that it is not the increased capacity that explains the improved performance.\n\n- An important ablation study seems to be missing for the distance-based attention mechanism in updating the pair embeddings which seems to be the main technical novelty of the work apart from the general constellation of the approach.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "p63q_9jgyJ", "reviewer": "Reviewer_5skX", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This work tackles the problem of protein-ligand binding structure prediction. The authors propose an E(3) equivariant network to iteratively update the poses. Alphafold-inspired feature encoders are introduced to capture the information of proteins and ligands, respectively. The whole architecture is trained in an end2end fashion. The model could achieve state-of-the-art performance in both binding position prediction and binding affinity prediction tasks.\n", "summary_of_the_review": "Generally, I think it's a good paper. But the clarity of novelty should be improved and some of the results should be further explained. Also, no code has been released. I vote for a borderline acceptance.", "strength_and_weaknesses": "Strengths:\n1. The proposed method addresses the two-stage optimization problem of previous work by performing coordinate iteration through a context-aware equivariant module, enabling end-to-end training.\n2. The paper is overall well-written and easy to follow.\n3. The proposed method shows superior empirical performance over existing baselines.\n\nWeaknesses and questions: \n\n1. The technical contributions should be further clarified. The architecture of this model is similar to the combination of Alphafold and TankBind. Although it solves the separated coordinate optimization problem of TankBind, the additional modules are mainly borrowed from Alphafold. The authors should elaborate more on their own contributions.\n2. It seems that pair embedding z_ij does not change during the iterative coordinate update. Is this on purpose or a compromise made because of computation cost?\n3. The authors could comment on why the performance on unseen protein is still worse than GLIDE as measured by RMSD <2Å. Does this indicate that the model has poor generalization ability? Also, the performance gain over TankBind is not significant.\n4. There is a recent work DiffDock that can also iteratively generate poses. The authors may need to consider differentiation from DiffDock (https://arxiv.org/abs/2210.01776) or state the superiority of the proposed method.\n5. Binding affinity prediction is a key subtask for protein-ligand interaction prediction. Could this work perform affinity prediction and how?\n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "OReat0GZx9S", "reviewer": "Reviewer_eHD3", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper describes a new method for molecular docking that uses equivariant neural networks. The positions of ligand atoms are refined in each step, and the per-atom translation is computed by DecoderLayer that uses equivariant graph convolution layers. The protein and ligand are encoded with graph neural networks and protein-ligand interactions are modeled by Trioformer, a transformer updating atom pair information based on triplets of atoms from both the protein and ligand. The model can be trained in the end-to-end manner. The presented results are competitive compared to the recent neural docking algorithms and the classical ones.", "summary_of_the_review": "Based on the above comments, I am leaning towards the acceptance of this paper if all the issues are addressed by the authors.\n", "strength_and_weaknesses": "Strengths:\n- The selection of graph neural networks for encoding the ligands and binding pockets is reasonable.\n- Trioformer is proposed to tackle the problem of preserving the geometry constraints when modeling atom pair embeddings.\n- I really like the self-confidence estimator that is trained along with the docking objective. Figure 2 clearly shows the benefits of this predictor.\n- The case study shows the usefulness of the proposed method in a real-life scenario.\n- An ablation study was conducted, where different components of the architecture were removed.\n- A quantitative evaluation of the improvement over multiple refinement steps is presented, as well as a qualitative refinement trajectory in the supplementary materials.\n\nWeaknesses:\n- Is Trioformer a new architecture that is introduced in this paper? This should be emphasized more, and the differences between Trioformer and former architectures (Evoformer, triangle attention) should be accentuated in my opinion.\n- In the problem definition paragraph, the naming of blind docking problems seems a little confusing to me. Is “re-docking” and “self-docking” used synonymously? If so, maybe the names “rigid blind self-docking” and “flexible blind self-docking” would be better in this context?\n- The model does not have any formal constraints on the validity of the generated 3D structure. Atoms can move freely, and, although the shown structures look realistic, there is no guarantee that the resulting compounds are not knotted or do not include very long bonds. Can you provide a plot showing a distribution of bond lengths? Another interesting plot would be depiction of the number of invalid structures (steric clashes) as the number of refinement steps increases.\n- The code was not included in the submission, so it is difficult to assess the reproducibility of the experiments.\n\nQuestions:\n- How can you output rigid structures in the rigid docking experiment? According to the footnote on page 5, you start with the same conformation as the docked ligand structure, but do you change this conformation via per-atom position updates?\n- Only to confirm, is gradient detached from the RMSD term when training the self-confidence predictor? How do you select beta to achieve the best tradeoff between the docking performance and top pose selection?\n- In the experimental results, what corrections are applied to each model? Is the set of post-processing methods the same across different methods?\n\nMinor points:\n- Typos, e.g. \n“we achieves SOTA in most metrics” -> “we achieve SOTA in most metrics”\n“Figure ??” -> “Figure 5”\n“prediction’s” -> “predictions”\n“uncorrcted” -> “uncorrected”\n- Some references should be fixed, e.g. referencing Section B in Section 3.2 (it should be indicated that the appendix is referenced), referencing “E” in Section 4.2, and referencing Figures 5 and 7 that are not included in the main text body.\n- Section G of the Appendix should be referenced in Section 4.1, where there is a statement about superior inference speed - currently this feels like an unsupported claim.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "1q0AMHIii9y", "reviewer": "Reviewer_GTTE", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "In the proposed work, the authors present E3bind, an fully-equivariant and differentiable approach for protein-ligand docking. Similar works have recently become available in the literature, the claimed advantage of the presented one being that it iteratively docks the ligand into a (possibly unknown) protein binding pocket.\n\nMost of the questions/issues for the authors are presented in the review summary section.", "summary_of_the_review": "Overall, while this is very solid work and deserves to be published, I believe it needs further work, as many of the parts feel rushed. I would have also enjoyed if the authors had provided code to back up the claims supported in the study and for overall reproducibility, as this is a field that is very rapidly advancing in the last couple of years. \n\n* In the introduction, the authors make a comparison to other methods that only output a \"scalar\" score. It should be noted that this is also the case for classical docking algorithms, whose scoring function also outputs a scalar for a specific pose. The amount of information provided is somewhat similar - I believe the comparison is not well defined here.\n* The claim on the introduction that the performance of Equibind is not strong enough needs further motivation, so as to claim that rapid generation of binding poses remains an unsolved problem.\n* On the Related Works section, there is a claim about Equibind failinf to beat popular docking baselines without finetuning which needs to be further justified/motivated.\n* Overall, figure captions on the manuscript could be heavily improved upon (within reasonable constraints of the page limit) as they are not descriptive at all.\n* In general, I think the reader would have benefited from further details about the Trioformer architecture, as it is mentioned without it being properly presented. Is this naming convention used in previous works?\n* In Section 3.1, the authors mention that they use only the carbon alpha atoms to represent the protein in the model. Was this choice made for computational efficiency issues, or did the authors compared against  a full-atom representation?\n* Why are the message passing networks of the protein (GVP-GNN) and ligand (GIN) chosen differently? There does not seem to be any motivation for this choice.\n* In section 3.3, the authors claim that the iterative refinement method allows the ligand to sense the local environment compared to the one-shot approaches, but no motivation behind this intuition is provided.\n* On the self-confidence prediction idea. The plot on Appendix Section C.2 seems to indicate that these scores are not very well aligned with ligand RMSD, as they tend to concentrate on the right-hand side of the distribution (most of them over 0.9). Could the authors consider providing an appropriate scaling as well as checking the pearson correlation between the score and rmsd?\n* In Section 3.4, is the loss only computed on predicted vs. experimental ligand coordinates?\n* In Section 3.4 (inference process), the authors mention that they use a binding site algorithm to first segment the protein into functional blocks. Are the other methods also making use of this step? Could this potentially bias the improvements shown in the results? How computationally expensive is this segmentation step - is it taken into account when computing the numbers provided in Appendix Section G? The authors also mention in this section that their model does not require binding affinity for training but this is usually never the case for docking tasks, so I do not understand why this is explicitly mentioned.\n* How is the ligand initialization done? The authors claim that it is randomly initialized in each segmented block before docking. Does this result in possible clashes with the protein target?\n* In terms of the performance on flexible self docking scenarios, it should be noted that that many standard docking pipelines (and not only GLIDE, as mentioned in the paper) actually outperform the DL-based alternatives.\n* On the \"benefit of iterative refinement\" section. How does the self-confidence score behave under non-successfully docked examples?\n\nOther notes:\n* Page 2: \n* Page 2: \"it's\" -> \"its\"\n* In the Geometry-aware pair updates section, why is the word \"neighboring\" under quotes?\n* Equations are missing commas and periods when appropriate.\n* Equation 10, the loss is missing equation number.\n* Is the \\sigma in the self-confidence prediction section a sigmoid function? \n", "strength_and_weaknesses": "Strengths:\n\n* Noticeable improvement over well-established benchmark\n\nWeaknesses:\n* Motivation for the architecture somewhat lacking\n* Incremental work\n* Manuscript feels rushed and reads clunkily at times\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster