TANKBind: Trigonometry-Aware Neural NetworKs for Drug-Protein Binding Structure Prediction
Authors: Wei Lu
Qifeng Wu
Jixian Zhang
Jiahua Rao
Chengtao Li
Shuangjia Zheng
Venue: NeurIPS 2022 Accept (2022)
Keywords: drug-protein interaction
protein-ligand docking
molecular docking
drug discovery
proteins
molecules
geometry deep learning
trigonometry
deep learning
neural networks

Abstract: Illuminating interactions between proteins and small drug molecules is a long-standing challenge in the field of drug discovery. Despite the importance of understanding these interactions, most previous works are limited by hand-designed scoring functions and insufficient conformation sampling. The recently-proposed graph neural network-based methods provides alternatives to predict protein-ligand complex conformation in a one-shot manner. However, these methods neglect the geometric constraints of the complex structure and weaken the role of local functional regions. As a result, they might produce unreasonable conformations for challenging targets and generalize poorly to novel proteins. In this paper, we propose Trigonometry-Aware Neural networKs for binding structure prediction, TANKBind, that builds trigonometry constraint as a vigorous inductive bias into the model and explicitly attends to all possible binding sites for each protein by segmenting the whole protein into functional blocks. We construct novel contrastive losses with local region negative sampling to jointly optimize the binding interaction and affinity. Extensive experiments show substantial performance gains in comparison to state-of-the-art physics-based and deep learning-based methods on commonly-used benchmark datasets for both binding structure and affinity predictions with variant settings.

TANKBind: Trigonometry-Aware Neural NetworKs for Drug-Protein Binding Structure Prediction
Wei Lu Galixir Technologies
Qifeng Wui Fudan University
Jixian Zhang Galixir Technologies
Jiahua Rao Sun Yat-sen University
Chengtao Li Galixir Technologies
Shuangjia Zheng" Galixir Technologics Sun Yat-sen University
Abstract
Illuminating interactions between proteins and small drug molecules is long- standing challenge in the field of drug discovery. Despite the importance of un- derstanding these interactions, most previous works are limited by hand-designed proposed graph neural network- -ased methods provides alternatives predict protein-ligand complex conformation in a one-shot manner. However, these methods neglect the geometric constraints of the complex structure and weaken the role of local functional regions. As result, they might produce unreasonable conformations for challenging targets and generalize poorly novel proteins. this paper, we propose Trigonometry-Awarr Neural networKs for binding structure prediction, TANKBind, that builds trigonometry constraint as a vigorous inductive bias into the model and explicitly attends to all possible binding sites for each protein by segmenting the whole protein into functional blocks. We construct novel con- trastive losses with local region negative sampling to jointly optimize the binding interaction and affinity. Extensive experiments show substantial performance gains in comparison state-of-the-art physics-based and deep learning-basee methods on commonly- benchmark datasets for both binding structure and affinity predictions with variant settings.
scoring functions and insufficient conformation sampling. The recently-proposed
Introduction
Proteins are the workhorses of human bodies. They have wide range of interaction partners, small molecules, other proteins, and DNA/RNA, for example. this paper, we focus on drug-like small molecules as the interaction partners for proteins. The words ligands, drugs, small molecules and compounds are used interchangeably throughout the paper. Small molecules activate or inhibit activities of target proteins through mostly non-covalent interactions. In 2021, FDA approved 60 new drugs, among which 36 were small molecules Kinch et al. (002). Understanding the mechanism- of-actions and off-target effects of drug molecules typically requires analyzing the structures of the related protein-ligan ligand complexes Boopathi et al. (2021), Xie et al. [2011), but solving the complex an extremely challenging task. Despite tremendous effort spent on this topic over the last 50 years, only about 19, 99,000 protein-ligand complex structures have been solved experimentally using X-ray, Cryo-EM or NMR Liu al. [2015]. On the other hand, the estimated chemical space of drug is 1060 and estimated number of unique proteins in human body is
structure experimentally
Cryo-
"Correspondance (wei.lu, thunngjia.zheng] @ @galixir.com
'These authors contribute equally to this work. Qifeng Wu and Jiahua Rao work interns at Galixir.
36th Conference on Neural Information Processing Systems (NcurIPS 2022).

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at least 20, 000, making the number of possible -iggand complex far exceeding the number of experimentally solved structures Reymond al. (2010), Ponomarenko et al. [2016].
On the computational side, molecular docking is a commonly-used method for predicting the protein- ligand complex structures the corresponding binding affinities Trott and Olson [2ieO],
FFrisnner et al.) (2004), Ackloo et al. [2022). Gentile et al. (2022). Generally, the docking process involves three main stages: (I) locating favorable binding sites given protein target; (2) sampling the ligand conformation as well as its position and orientation within these sites; (3) scoring and ranking the conformations of the complex using thysies-inspirg empirical energy functions to refine the structures and assess -rogaid binding affinity. Due to its good interpretability and usability, docking has been integrated in drug development process for long time and a number of successful cases have been reported Anderson (2003). However, most open-source docking packages use atom- Andersod/nndrron
level pairwise scoring functions, limiting the capacity to model the many-body effects. Moreover, they need to sample large range of possible ligand poses and protein side-chain conformations,
which leads to relatively high computational cost Trott and Olson 2010). Jain 2006].
To overcome these challenges, we propose a two-stage deep learning framework to neuralize the molecular docking process and predict the binding structures with better accuracy and lower com- putational cost. In the first stage, we segment the whole protein into functional blocks and predict their interactions with the ligand, creating an mootein-ligand interaction energy landscape using a novel iigonometry-awwrr architecture. The trigonometry module has enough model capacity to capture many-body effects. In the second stage, we prioritize the crystallized binding structures by constrastively ensuring weaker binding affinity for non-native interactions. In particular, our model improves the drug-protein binding structure predictions with a combination of (i) novel trigonometry-avee architecture that jointly infuses trigonometry constraints and excluded-volume effects as inductive biases, (ii) a new divide-anddconquer strategy that constructs the protein-ligand local functional binding pairs in a contrastive manner. By doing so, we create a funnel-shape energy landscape for the inter-molecular interaction, removing the need of extensive sampling Jumper et al.
102T ain 2006 Chen et al. [2200a] Onuchic et al. [997].
Our novel method well-motivated by leveraging prior knowledge from physics and biology. Physically, the inter-molecular trigonometry module, inspired by the intra-molecular Evoformer module used in AlphaFold2 Jumper et al. (02TT) ensures that our energy landscape disfavors configurations of protein-ligand complexes that are prohibited by laws of nature, for instance, no two atoms could overlap and the distances between atoms have to satisfy triangle inequality theorem in euclidean geometry. More details on these constraints is shown in section 3.3 Biologically, the functional regions of proteins tend to be more conserved and closely associated with binding De Juan et al. [2013). Glaser et al. 22003. allowing the model to learn critical information and generalize better to unseen proteins.
We evaluate our algorithm against several state-of-the-ar deep learning and physics-basee docking methods on task of binding structure prediction under multiple settings. Compared with baselines, our model increase the fraction of predictions with ligand root-mean-squee -quare deviation (RMSD) less than 5Á by 16% in re-docking setting, 22% in self-docking setting, and 42% in the more difficult new- protein setting. Our model is also capable of predicting binding affinities, achieving better correlations with experimentally-meet measured values than sequence- sequence-based, structure- based and even complex based methods. We also show that TankBind has the potential to discover novel mechanism- of-actions of drug molecules by identifying unseen protein binding sites.
2 Related Work
Geometric Deep Learning for drug discovery. There has been a surge of interest in integrating
geometric priors for representation learning in the domain of drug discovery Jumper et al. [202T]
Baek et al. [2021] Jing et al. [202T]. Ganea et al. (202T). Jin et al. [2021] Ingraaha et al. (001
AlQuraishi 2019]. Schütt et al. [217]] Somnath et al. [2021]. Recent researches have incorporated
geometric information and symmetry properties of the input signals to improve the spatial perception
of the learned representations. These works have been shown great potential
various applications like protein structure modeling Jumper et al. (021)) Baek et al. [2021], Jing et al. [2021] Ganea et al.
[202T], J, molecular low-energy generation prediction Shi et al. [2021]. 11, Xu et al. [022], Mendez-LLucio
et al. 2021), property/fiuncton prediction Schütt et al. 2017]] Somnath al. [021] and molecule
2

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Block Mapa
Seg mental on
X
hr
Interation Wap Precistion
Protein
Functiona Blocka
Cormande
Priotizattn
Interaciion Mutrix x
Bincting Afrity Precictio
3D Intialization
Tagaro Message Updating
Ligend Distance Map
Drug Ligand
Conformer
Figure 1: Overview of TankBind Model. The whole protein is divided into blocks of radius 20A, each block is going through the TankBind model along with the drug compound. Both protein blocks and drug compound are modeled as graphs. The block-compound interaction matrix evolved multiple times with additional input based on the distance maps of the protein block and the compound through trigonometry module. Based on the updated interaction embedding, the model predicts the binding affinity of the compound to the blocks and the block-ligand distance maps. A constrastive loss function is used to ensure the native block binds stronger the compound than decoys.
design Jin et al. 2021] Ingraham al. 2019 Among which, AlphaFold 2 achieved outstanding performance in protein structure prediction Jumper et al. (202T], representing the state-of-the-we geometry-awan method. Our work is inspired from this groundbreaking work, adapting it from the intra-molecular structure prediction to the field of predicting the inter-molecular binding structure and binding affinity.
Drug-protein Interaction (DPI) prediction. The goal of DPI prediction is to illustrate the binding structure binding affinity between protein and ligand. Apart from docking- -baed approaches Trott
and Olson 2010). Friesner al. (2004), prior machine learning-based works either use complex free
models to predict the binding affinity directly from protein-ligane pairs Wang and Dokholyan [2021]
Li al. 2020 Tsubaki et al. 2019], Gao et al. [2018) Karimi et al. [2019] Zheng al. [220 or
make predictions through complex structure that has been previously obtained by experimental or docking approaches Jiménez et al. [2018), Lim al. [2019). Morrone al. [2020). The former ones are less interpretable while the latter requires data involved in vast experimental costs and labour. approach by directly predicting the key points on both the protein and the compound, and aligning their key points through the ingeniously designed optimal transport loss. However, this method may generate compound structures clashing with the protein structures and currently lacks the capability to predict the binding affinity, limiting its in drug discovery. In contrast, our approach has trigonometry module imposing geometry constraints and state-of-the-art binding affinity prediction capability.
More recently, EquiBind (Stärk al. [002 takes
3 TankBind Model
3.1 Overview of Bank model
The general protocol of our model is shown figure The encoding of protein and compound
described in section 3.2 The rationale and implementation of trigonometry module is detailed in section 33.3 The design of loss functions for training is described in section 33.4 The generation of atom coordinates from predicted inter-molecular distance map is introduced in section 3.5
3.2 Structural encoders of protein and drug
Our model input is the separate structures of protein and drug compound, both encoded graphs. Indices i, & always operate on the residue dimension, j, always on the compound dimension. the number of protein nodes and is the number of compound nodes.

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Protein. The protein is represented as a proximity 3D graph following Jing et al. (020). We denote the protein graph as G (V",E") ).), where each node of V corresponds to an amino acid, and has feature hg with both scalar and vector features. Each node also has position x E R equal to the Cartesian coordinate of C..- An edge t exists if by. is among the 30 nearest neighbors of of. Each edge *xx E Ed also encodes both the scalar and the vector features. We then apply the geometric vector perceptrons (GVP) et al. [2000] 2021] to embed the protein and arrive at feature h" E Rax* after graph propagation, where is the number of nodes and is the embedding size.
To implicitly model side-chain flexibility, we choose a residue-level representation ignoring the finer details of protein structure, separating our method from other methods that use all-atoms or surface vertexes representation Jiang et al. [20TT] Gainza et al. (022)) Also, as shown by Jumper al.) 2021 2018), residue-level embedding is enough to infer the side-chain conformation.
Motivated by protein co-evolution De Juan et al. 2013) and divide-and-conquer theory, the protein graph, G further divided into subgraphs G Each subgraph G includes all the vf, and ei inside
the functional block. The subgraph is denoted as GP' = ((b", < ||x x..l s 20A, ||x - x,ol S 20A), where X, is the center of the functional block predicted by widely-used ligand-agnostic method, P2rank (published 2018|Krivák and Hoksza (018). Justification for the size of radius and use of P2rank is described in appendix G
Drug compound. The drug compound is represented as a graph using TorchDrug toolkit Zhu et al. 2022 The compound graph denoted as G = (V", Ed) where each node Dj V corresponds to
heavy atom (non-hydrogen atom), and has feature hg and each edge Ei has feature h (((²), We use Graph Isomorphism Network (GIN) Xu al.) [2018) to embed the compound and arrive feature h E R after graph propagation, where m is the number of heavy atoms and s is the embedding
(d)
size.
3.3 Details of trigonometry module
The compound feature, h" and the protein block feature, h", are used to form the initial interaction embedding (0)) E _axxxx zi h² @ hy. The interaction em- bedding will be further updated with pair distance map of protein nodes, D = ||x - x and pair distance map of compound nodes, DiN = |x] ||
The rationale for including both the pair distance map of the protein nodes and the pair distance map of the com- pound nodes in updating the protein-compoume interaction embedding is explained with two simplified examples. As shown in the upper part of figure 2, if protein node A is in close proximity with compound node B, then com- pound node C will not be in contact with node A due to the large distance constraint between node B and C. Distance constraint between compound nodes B and D could also force node D to be in close contact with protein node A.
dyj
Rier
eyp
K
Rationale for including trigonometry module. Upper: Protein node in square, compound nodes in cir- cles. Lower: Trigonometry module en- sures that the interaction between protein node and compound node j depends on all protein and compound nodes k; k'.
Figure 2:
To build this observation trigonometry constraints into our model, we design the following module to update the interaction embedding, in layer E, (i,
T
(8) 2
(8)
( a
Put
where Pia = +(D),) is the linear embedding of encoded pair distance between protein nodes. p E Raxxxs n is the number of nodes in protein block, s the embedding size. Cja- = ((D),)) ) the
linear embedding of encoded pair distance between compound nodes. c E Rmxmxx m the number (e) the same gated linear transformations of Zig but with non- of compound nodes. t,y and (())
(C)

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shared parameters, E. = Linear(2,) 2i ) jog(z))
(0)
(0) 10 E Ruxmxx g((,)) sigmoid((inear(e (2:) )
)),
Φ is a layernorm function followed by a linear transformation.
Another type of physical constraint need to be take into consideration is the Excluded-volume (Van Der Waals) and saturation effect. As shown in the upper figure if protein node forms a strong interaction, hydrogen bonding for example, with compound node B, then node D is unlikely to form the same type of interaction with node A because node A has limited number of hydrogen donors or acceptors. To account for these effects, we designed self-attention module to modulate the interaction between a protein node and all compound nodes by taking the whole interaction between this protein node and all compound nodes into consideration.
(()) Zij
(concatt
(E) (0) A ih
g0((()))) (x(())
go
(2)
w
(A) rkk
softmax; (q.
(9)
(E) dk'
(3)
(f)h
(2)a
h2)h
linear transformation of Zij h is number of attention heads. Function g" is the standard g with reshaping the embedding into heads at the end, a linear transformation.
where 9ij kj
Vij
Lastly, a non-linear transition module is added to transit the interaction embedding to the next layer through multilayer perceptron, Zij (f+1) MLP(Z!))) The whole trigonometry module is composed of three consecutive parts, the trigonometry update, the self-attention modulation, and the non-linear transition module. Layernorm is applied on every input zi and 25% dropout is applied to the trigonometry update and self attentotnn modulation during training. The final outputs, drug-proteis binding affinity, à Σi= Σø= Linear(z!,)) (z( and inter- distance map, D g(2ig (1) Linear(z); (!2)), are predicted directly based on the last layer embedding (I.) where L is the number of module stacks.
3.4 Design of binding interaction and affinity loss functions
Many previous works model the interaction between compound and protein by only preserving the interaction region, residues that far away are ignored Townshend et al. [2020), Méndez-Lucio et al. [02TT] On the positive side, the computation and memory demand for characterize the interaction between protein and the drug compound is greatly reduced by focusing regional interaction. But the fact of not binding to alternative binding sites is also a valuable information. By the nature of crystallization, if protein- protein-compound complex could be successfully crystallized, other possible binding sites on this protein definitely bind less strongly than the native binding site to the compound, therefore, those other binding sites could be used as high-valued decoys. Based on this observation, we designed a max-margin constrastive affinity loss, equation [4] following the idea of Hadsell et al. (2006). Such that the compound's predicted affinity, to the decoys is less than the experimentally measured affinity, a, by margin value, e.
Lattiity (āc, a) = (C) - a)² + (())) max(0, âç (a )))
(4)
where àc is the predicted affinity to block Ç. and indicator function [CC = 1 when block Ç encloses the native ligand, and 1 (C) 0 otherwise. We, therefore, take full use of information stored in the whole protein instead of only the native binding region. We also include a mean squared erorr
(MSE) loss for native interaction distance map, Ldistance = 1()) 1 Σ 1= (D
m (Dered Dzy)²
The overall training objective of TankBind is: L Latlinity + Laistance-
3.5 Generation of drug coordinates based on predicted inter-molecular distance map.
The Cartesian coordinates, (x)). of the heavy atoms of drug compound could be deduced ana- lytically based on the predicted inter-molecular distance matrix, Derred the coordinates of protein nodes, (x(") ). and the pair distance matrix of compound nodes, Di Masters al. [2022] Hoffmann and Noë [2019] But since predicted distance matrix contains noise, we take a numerical approach Masters et al. 2022 soldos et al. [007]. By minimizing the total loss, Legnerrtion which consists of two parts, the interaction loss and the compound configuration loss, could derive the coordinates
5

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Table 1: Blind self-docking. All models take pair of ligand structure (generated by RDKit) and protein structure as imput, trying to predict the atom coordinates of the ligand after binding. blind docking, the protein binding site is assumed unknown. Test set is composed of 363 protein-ligand structure crystallized after 2019 curated by PDBbind database. Details about model runtime and the number of model parameters are in appendix
Ligand RMSD
Centroid Distance
Percentiles |
% Below Threshold
Percentiles +
% Below Threshold
Methods
25%
50%
75%
Mean
2
5A
25%
50%
75%
Mcan
2
5
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(c.)
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-U
3.3
9.7
7.2
42.4
1.3
7.4
67.5
EQUIBIND
3.8
6.2
10.3
5.5
39.1
1.3
7.4
40.0
67.5
TANKBind-R
2.8
5.2
11.2
9.4
16.0
47.9
1.0
2.3
7.7
7.3
44.9
69.4
TANKBind-C
2.4
4.5
8.4
8.2
19.6
54.8
0.9
1.9
5.4
6.3
53.2
73.3
TANKBind-P
2.6
4.5
8.1
8.5
16.3
54.0
0.9
1.9
5.2
6.4
53.2
74.4
TANKBind
2.4
7.7
19.3
61.7
0.9
4.2
5.5
56.5
77.4
of the docked drug coordinates, {89).
generration
Linteraction
Leontiguration
= ΣΣ(1g - Dpred 1) +
Σ
(1D jK
Djell)
(5)
- -x=11, 1|,5 1 &
(6)
where is the number of protein nodes, and m is number of compound nodes, and {xx) are the Carte- sian coordinates of protein nodes. All inter- mite--ool distances are clamped have an upper bound of 10Å focus the direct interaction. In self-docking setting, when the compound configuration is known, we add a local atomic structures (LAS) mask to the configuration loss to allow for compound flexibility while enforcing basic geometric constraint, Lecaliguration Σj Σx 1 (())) -5 where 1 (j, K) = 1 when compound atom j and & are connected by connected by bond, or 2-hop away, or the same ring structure, and (j, K') otherwise Stärk al. [002). Trott and Olson (2010). For every test protein-ligand pair, TankBind predicts the binding affinity of the ligand to all segmented functional blocks and chooses the one with strongest affinity to generate the binding
structures.
4 Evaluation
4.1 Protein-ligand binding structure prediction
Dataset. We used publicly available PDBbind v2020 dataset Liu et al. 2015 which has the
structures of 19443 protein-ligand complexes along with their experimentally measured binding affinity. PDBbind is database curated based the Protein Data Bank (PDB) Burley al. [2021]. followed the same time split as defined in EquiBind paper Stärk et al. 2022 in which the training and validation data are the protein-ligand complex structures deposited before 2019 and the test set the structures deposited after 2019. After removing a few structures that unable to process using RDKit from the training set, had 1 17787 structures for training, 968 for validation and 363 for testingLandrum et al. [2013). We also reduced the possibility encountering equally valid binding sites by removing chains that have no atom within 10Å from any atom of the ligand following the protocol described in Stärk et al. 2022]
Baselines. We compared TankBind with the most widely-used docking method AutoDock Ving Trottrott and Olson 2010 and the recent proposed geometry-based DL method EquiBind Stärk et al. 2022 also included four popular docking methods QVina-W W, GINAMMeNtt et al. 2021]. SMINA Koes
al. 2013 and GLIDEFriesner al. (2004) as listed in Stärk et al. [022

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Table 2: Blind self-docking for unseen receptors. All models evaluated on 142 crystallized protein- compound structures where the proteins have not been observed in training set.
Ligand RMSD
Centroid Distance
Percentiles +
% Below Threshold
Percentiles +
% Below Threshold
Methods
25%
50%
75%
Mean
2
5A
25%
50%
75%
Mean
2
5A
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
13.7
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-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
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 R
3.6
6.9
17.0
12.6
5.6
35.2
1.3
3.6
15.7
10.3
35.2
58.5
TANKBind-C
3.4
9.8
9.2
43.0
1.1
8.1
7.9
65.5
TiNKBind-P
3.3
10.9
11.2
5.6
45.1
1.3
2.3
7.9
9.1
66.9
TANKBind
2.9
4.7
8.8
9.1
4.9
55.6
1.3
2.3
4.8
7.0
45.1
75.4
Evaluation metrics. We follow prior work Stärk et al. 2022 and use ligand root-mean-see square deviation (RMSD) of atomic positions and centroid distance to compare predicted binding structures with ground-truths The Ligand RMSD calculates the normalized Frobenius norm of the two corresponding matrices ligand coordinates. The centroid distance is defined as the the distance between the averaged 3D coordinates of the predicted and ground-truth bound ligand atoms, indicating the model capability of identifying correct binding region. Hydrogens are not involved in the calculation.
Performance in blind flexible self-docking We start with real-world blind self-docking experi- ment, which the ligand conformation is not fixed, and the result re-docking experiment, in which the native ligand conformation is given, is reported in Appendix A. As shown in the table Tink achieves state-of of the-art performance, outperforming geometry DL-based model EquiBind. This advantage is particularly evident in the top 25% and top 50% ligand RMSD, which allows method to predict 22% more qualified (below Threshold 5Å) binding poses than EquiBind. This results also consistent in the metrics of centroid distance, demonstrating that our method also has clear advantage in the identification of binding region. Even though GLIDE (commercial) and Autodock Vina are established docking software with more than a decade continuous development, our model remarkably frequently outperforms them. At the same time, than them, and on the same level as EquiBind (Appendix C). In addition, we explore the possible of TankBind-R, where randomly segment the protein, Bind-P, where summation over protein nodes in equation 1 and TindCC, where we only sum over compound nodes. The performance reduction the these variants supports view that trigonometry message passing between proteins and ligand and segmentation choice are critical to the prediction of binding structures.
orders of magnitude faster
only doing the
Performance in self-docking unseen protein We next focus on the new protein setting, in which the tested proteins have not been observed in the training set. ( that Tankbind leads to larger improvements over EquiBind and docking methods with regard ligand-RMSI RMMdDDDMDDDDD and centriod distance. This is in line with expectation that TankBind has better generalization ability due the thysical-inspired trigonometry module and explicit consideration of conservative functional blocks. In this setting, as shown in Figure and table [ for fractions smaller than 2A, 5Á and 15A, the performance between EquiBind and other docking method are comparable, while TankBind is always
better by large margin, further confirming the effectiveness our method and indicating that the proposed strategy has practical values for the virtual screening of new proteins.

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Poattes of Postictere with lover RMSDD
Fradicon Polleil mith Jowest Dosenne
0.7
0.7
0.5
TANKiied
TANKBRGGC
0.2
TASKBNO
0.2
VANILl
TANEDia
0.1
IQUESEND
Ligrod Angarors
Angsoorn
Figure 3: Estimator of the Cumulative Distribution Function (ECDF) plot for ligand RMSD (left) and Centroid Distance (right) from result evaluated on new receptors subset. The axis of the figure stops at 15Á because comparison for larger RMSD is less meaningful when the predicted location of the ligand is away from the true binding site, RMSD of 15Á is not better than RMSD 50Å.
Methods
RMSEJ Pearson" Spearman MAE
Methods
Ligand Centroid, Below2A1 Below5At
TransCPI
1.741
0.576
0.540
1.404
w/o P2Rank
9.37
7.30
44.90
69.42
MONN
1.438
0.624
0.589
1.143
w/o Trig
8.73
6.44
44.08
74.93
PIGNet
2.640
0.511
0.489
2.110
TAPE
8,81
6.89
50.69
73.00
IGN
1.433
0.698
0.641
1.169
GAT
8.27
6.23
56.47
78.51
HOLOPROT
1.546
0.602
0.571
1.208
TankBind-P
8.47
6.44
53.17
74.38
STAMPDPI
1.658
0.545
0.411
1.325
TankBind-C
8.20
6.27
53.17
73.28
TANKBind
1.346
0.726
0.703
1.070
Origin
7.43
5.51
56.47
77.41
Table 3: Binding affinity prediction. TankBind achieves SOTA on four metrics.
Table 4: Ablation results. We listed four main metrics here, a complete table is in appendix B
4.2 Protein-ligand binding affinity prediction
TankBind is also capable of predicting protein-ligand binding affinity because of the constrastive affinity loss function. Since segmented the whole protein into protein blocks, the predicted binding affinity of ligand to the whole protein is equal to the binding affinity to the one protein block that predicted bind strongest with the ligand. To demonstrate the ability, compared TankBind with the state-of-ft of the-art binding affinity prediction models.
Dataset. We split the dataset into training, test and validation splits based the same time split described earlier. The experimentally measured affinity data in PDBbind dataset has three different names, depending the exact experiment setups, 50% inhibiting concentration (IC50), inhibition constant (K2), and dissociation constant (Kp) p). all converted to the unit of molar concentration. Similar previous methods Sommath al. [2021] Townshend et al. (2020). we predict negative fog-transformed binding affinity.
Baselines and evaluation metries. We compare Tank against state-of-the-art sequence- based methods, Transformer Chen et al. 2020b] and MONN Li et al. [2020]. two complex- based methods, IGN Jiang et al. (2021] and PIGN et Moon et al. [2022] both requiring prior knowledge of the inter- molecular structure to predict affinity, and two structure-
methods, HOLOPTOT Somnath et al. [021] and STAMPDPI Wang et al. [2022). For evaluating various methods, we use four metrics root mean squared error (RMSE), Pearson correlation coefficient, Spearman correlation coefficient and mean absolute error (MAE). We also include the mean and standard deviation across 3 experimental runs in appendix

---

Centroid Distance (A)
Centroid Distance (A)
TankBind: 0.85
TankBind: 0.77
EquiBind: 12.31
EquiBind 16.14
VINA: 27.36
(a) PDB 8K18
VINA: 14.89
(b) POB 6ORG
Figure 4: (a) An example of TankBind identifying an unseen binding site. The protein shown in white, co-crystallized compounds of three PDBs in the training set is shown in purple. The ligand of 6KIS shown in green. TankBind is able to find this correct pose for the compound, shown in red, while the other two, Vina in orange, and Equibind in cyan, place the compound away from the true binding site. (b) For PDB 6QRG, both protein and compound have been seen in the training set. But TankBind still find the correct pose. Crystallized ligand colored in green, TankBind prediction in red, EquiBind cyan and Vina result in organ.
Result As shown in Table 3 our model obtains the best performance in PDBbind test set, con- sistently outperforms SOTA binding affinity prediction methods. Note that even without the prior interaction information, TankBind also achieves better result than complex-based methods (PIGNET and IGN), proving that the predicted binding structural information provided considerable gain the affinity prediction task.
4.3 Ablation study
We conducted ablation studies to investigate factors that influence the performance of proposed TankBind framework. shown Table the original version of TankBind with the trigonometry message passing between protein and ligand shows the best performance among all architectures. Replacing the P2rank with randomly split blocks performed the worst, which verifies our hypothesis that functional block segmentation can improve generalization. Simple architecture substitutions for protein (TAPE) Rao et al. [2019] and molecular representation (GAT) Veličkovid et al. 2017 decrease slightly the model performance. Replacing the intra tntra-trigonometty module with the uni-modal variants (TankBind and TankBind-C) both caused noticeable decreases in performances.
4.4 Case studies
TankBind correctly identifies unseen binding site for drug compound. As represen- tative case, in PDB 6K1S, a seen protein binds a new drug compound at site that has not been observed before. This protein has three co-crystallized complex structures in the training set, PDB 4X60, 4X61, 4X63. As shown the left of figure our method, shown in red, aligns well with the true ligand, shown in green, despite method has before. While other two methods, EquiBind in cyan, Vina in orange identify an incorrect site for this compound. Packages Kalign, Biopython, and Smith-Waterman library used systematically
any compound locates at this site
analyze the results Lassmann 2020). Cock et al. 2009 Li et al. 2020 Zhao et al. (013 (see Appendix H)
Tank finds the correct pose when both compound and protein are unseen. We picked two representative examples with both compound and protein are unseen, one, PDB 6QRG, the right of figure 4 and another, PDB 6KQI, in appendix B Both PDB 6QRG and PDB 6KQI have max protein

---

similarity below 0.8 (6QRG 0.78, 6KQI 0.57), and max compound similarity below 0.4 (6QRG 0.36, 6KQI 0.27).
5
Conclusion
In this work, we propose novel binding structure and affinity prediction model, TankBind, that builds trigonometry constraints into the model and explicitly attends all possible binding sites by segmenting the whole protein into functional blocks. We observe significant improvements binding structure prediction over existing deep learning methods: a 22% increase in the fraction of prediction below 5Å ligand RMSD, and a 42% increase when the proteins have not been observed in the training set. Moreover, we demonstrate that the model is able to predict affinity and outperform SOTA methods on PDBbind. This work opens a new direction for modelling the moter-molecular interaction between protein and drug molecule. Numerous directions for further exploration include incorporating a ligand conformer generation module, enhancing the dataset with Alphafold-prediceee structure and public available SAR data, integrating the segmentation of functional block in an end-to-end manner, and combining the model with protein backbone dynamics modeling to handle larger scale conformation changes induced by troteprotein interactions.
task of
Acknowledgments and Disclosure of Funding
We thank Prof. Yuedong Yang. Dr.Leilei Shi, Dr. Jiahui Tong for their helpful discussions; Penglei Wang for his support in binding affinity experiments; Meihui Song for her support in figure drawing. We thank the Guangzhou National Supercomputer Center for providing computational source. Z acknowledges support from the National Key R&D Program of China (2020YFB2004003) and National Natural Science Foundation China (21773313 and 61772566).
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14


Reviews:
[{"review_id": "UPeVGptF6fh", "reviewer": "Reviewer_YkVW", "summary": "This paper proposes a Trigonometry-Aware Neural Network (TankBind) for drug-protein binding site prediction. In the proposed method,  the protein is first segmented into several functional blocks by an out-of-shelf model. Then, a trigonometry module inspired by Evoformer of AlphaFold2 is applied to update the pairwise embedding between protein and ligand. The contrastive loss with local region negative sampling is applied to jointly optimize the binding position and affinity. The model could achieve state-of-the-art performance in both binding position prediction and binding affinity prediction tasks.", "questions": "- Is the ligand conformer fixed after the 3D initialization?\n- How is the margin value epsilon determined in Equation 4? \n- In the binding affinity prediction experiment, is the same loss function (Eq. 4) applied? Is the binding site given as known information? If so, there is no need to apply the contrastive loss.\n- In the docking experiments, are methods listed in Table 2 all deterministic? If not, have you run these methods multiple times to make results more reliable?", "limitations": "The authors discuss several future work directions in the conclusion section. There is not negative social impact.", "rating": 7, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 4, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- The proposed method is novel, especially combining different designs together: breaking proteins into functional blocks, applying trigonometry module to update distance maps, performing affinity and binding poses joint training with contrastive losses.\n- The paper is well-written and easy to follow.\n- The proposed method shows superior empirical performance over existing baselines.\n\nGenerally, I think it's a very good paper and didn't see any major weakness. Only some minor questions left,  see details in Questions.", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ""}, "extra_text": {}}, {"review_id": "HC9z9Xs4CZj", "reviewer": "Reviewer_DdyQ", "summary": "Based on Geometric Vector Perceptron (GVP) for protein modelling and  Graph Isomorphism Network (GIN) for drug processing, the paper proposes a method for drug-protein binding structure prediction.  The main idea is to build a trigonometry constraint and explicitly attend to all possible binding sites for each protein by segmenting the whole protein into functional blocks. ", "questions": "1. Although I recognize that the paper is mostly technically sound, such as using the sum of local protein and protein information to reflect the interaction, I feel some details are not well motivated. Specifically, according to Eq. (1) and Eq. (2), the method employs many gates, whose motivation is not very clear. Moreover, it could be better to visualize the gates to show some insights. \n\n\n2. The framework includes a  self-attention module to modulate the interaction between a protein node and all compound nodes by taking the whole interaction between this protein node and all compound nodes into consideration.  As a  self-attention module, it could be better to visualize the self-attention map via a few examples to verify the motivation. \n\n\n3.  Trigonometry is the main contribution or novelty and is similar to or inspired by the Evoformer module used in AlphaFold2. The difference should be highlighted.  ", "limitations": "NA.", "rating": 5, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "1. The paper is well written. Readers can learn a lot about drug-protein interaction from the paper.\n\n2. The method is mostly technically sound.  \n\n3. Comprehensive experiments show the effectiveness of the proposed method. ", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ["I don’t know"]}, "extra_text": {}}, {"review_id": "B1IkRpfUwdS", "reviewer": "Reviewer_DuMw", "summary": "In this manuscript, the authors propose Trigonometry-Aware Neural networKs for binding structure prediction, TANKBind, that builds trigonometry constraint as a vigorous inductive bias into  the model and explicitly attends to all possible binding sites for each protein by  segmenting the whole protein into functional blocks.  The algorithm is trained by minimizing a novel contrastive loss with local region negative sampling. The model is able to predict both the binding poses and binding affinity between protein targets and small molecules.", "questions": "Questions:\n1. What is the overlap between the training data of P2rank and Tankbind? It is necessary to check whether there is information leak for training and test datasets.\n2. I did not find the definition of ‘blind’ \n3. It might take biologists decades to verify a new drug target. A more practical experiment is to show the generalizability to the new compounds instead of new protein targets.\n4. It seems that the predicted protien-ligand complex is not feasible even using the trigonometry update function. That is why the authors need to use Eq 5 and 6. Please add discussion that why this component is still necessary when trigonometry update function is applied.", "limitations": "No obvious limitations and potential negative societal impact", "rating": 5, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths: So far as I know, this is the first algorithm which adopts the geometric consistency to the binding of proteins and small molecules. Another contribution is the loss function which treats the non-binding sites on the same protein as the negative training data. \n\nWeakness: First, I want to emphasize that geometric consistency (trigonometry) is first proposed by AlphaFold2. The embedding z_ij for a pair of amino acids i,j is updated by another two embeddings z_ik and z_kj to satisfy the triangle constraints. Tankbind changes the transformer of AlphaFold2 to another gating function. In theory, it is easy to modify the StructureModule of AlphaFold2 to also fit this task. For me, this decreases the novelty of this work. Second, my major concern is that it is not clear what is the impact of P2rank which predicts the functional site of proteins. VINA-based methods and EquiBind both identify the binding sites by themselves. If AUTODOCK predicts a wrong binding site, it will yield a super low score. However, what if the authors first run the P2rank to predict the binding sites and then feed the predicted binding sites to AUTODOCK and EquiBind? The ablation study also shows that P2rank is the most important component and removing the P2rank will decrease the performance. \n", "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"ethics_review_area": ["I don’t know"]}, "extra_text": {}}]

Author rebuttal:

Decision: Accept