A 3D Generative Model for Structure-Based Drug Design
Authors: Shitong Luo
Jiaqi Guan
Jianzhu Ma
Jian Peng
Venue: NeurIPS 2021 Poster (2021)
Keywords: molecule generation
3d generative models
drug design

Abstract: We study a fundamental problem in structure-based drug design --- generating molecules that bind to specific protein binding sites. While we have witnessed the great success of deep generative models in drug design, the existing methods are mostly string-based or graph-based. They are limited by the lack of spatial information and thus unable to be applied to structure-based design tasks. Particularly, such models have no or little knowledge of how molecules interact with their target proteins exactly in 3D space. In this paper, we propose a 3D generative model that generates molecules given a designated 3D protein binding site. Specifically, given a binding site as the 3D context, our model estimates the probability density of atom's occurrences in 3D space --- positions that are more likely to have atoms will be assigned higher probability. To generate 3D molecules, we propose an auto-regressive sampling scheme --- atoms are sampled sequentially from the learned distribution until there is no room for new atoms. Combined with this sampling scheme, our model can generate valid and diverse molecules, which could be applicable to various structure-based molecular design tasks such as molecule sampling and linker design. Experimental results demonstrate that molecules sampled from our model exhibit high binding affinity to specific targets and good drug properties such as drug-likeness even if the model is not explicitly optimized for them.

A 3D Generative Model for
Structure-Based Drug Design
Shitong Luo HeliXon Research luost@helixoo com 1uost26@gmail.c com
Jiaqi Guan
University of Illinois Urbana- Urbana-Champaa Champaign jiaqi0illinois edu
Jianzhu Ma Peking University majiinni majianzhu@pku. edu.
Jian Peng
University of Illinois Urbana- Champaann
jianpeng@ill iinngiiiliiiii....i edu
Abstract
We study fundamental problem in structure-based drug design generating molecules that bind to specific protein binding sites. While we have witnessed the great success of deep generative models in drug design, the existing methods are mostly string- shing- or graph-based. They are limited by the lack of spatial information and thus unable to be applied to sruuctue--bsee design tasks. Partic- ularly, such models have no or little knowledge of how molecules interact with their target proteins exactly in 3D space. In this paper, propose 3D generative model that generates molecules given a designated 3D protein binding site. Specifi- cally, given binding site the 3D context, our model estimates the probability density of atom's 's occurrences in 3D space - positions that are more likely to have atoms will be assigned higher probability. To generate 3D molecules, propose an auto-regressive sampling scheme - atoms are sampled sequentially from the learned distribution until there is room for new atoms. Combined with this sampling scheme, our model can generate valid and diverse molecules, which could be applicable to various structure-basee molecular design tasks such as molecule sampling and linker design. Experimental results demonstrate that molecules sampled from our model exhibit high binding affinity specific targets and good drug properties such as drug- drug-likeness even the model is not explicitly optimized for them.
Introduction
Designing molecules that bind to specific protein binding site, also known structure-based drug design, is one the most challenging tasks in drug discovery (2). Searching for suitable molecule candidates in silico usually involves massive computational efforts because of the enormous space of synthetically feasible chemicals [22] and conformational degree of freedom of both compound and protein structures 11I.
In recent years, we have witnessed the success machine learning approaches to problems in drug design, especially molecule generation. Most of these approaches use deep generative models to propose drug candidates by learning the underlying distribution of desirable molecules. However, most of such methods are generally EMILES/string-birt based [10] 17] graph-based [9] [3] 14). They are limited by the lack of spatial information and unable to perceive how molecules interact with proteins in 3D space. Hence, these methods not applicable generating molecules that fit to specific protein structure which is also known as the drug target. Another line of work studies
35th Conference on Neural Information Processing Systems (NcurIPS 2021).

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30 15]. Most of them 8 28 29 can only handle very small organic molecules, not sufficient to generate drug-scale molecules which usually contain dozens of heavy atoms. 20 proposes to generate voxelized molecular images and use post-processing algorithm to reconstruct molecular structures. Though this method could produce drugescale molecules for specific protein pockets, the quality of the sampling is heavily limited by voxelization. Therefore, generating high-quality drug molecules for specific 3D protein binding sites remains challenging.
generating molecules directly in 3D space 28 29 20
In this work, we propose a 3D generative model to approach this task. Specifically, we aim at modeling the distribution of atom occurrence in the 3D space of the binding site. Formally, given binding site C as input, we model the distribution p(e, r r(C), where r R is an arbitrary 3D coordinate and is atom type. To realize this distribution, we design a neural network architecture which takes as input a query 3D coordinate r, conditional on the 3D) context C, and outputs the probability of r being occupied by an atom of particular chemical element. In order to ensure the distribution is equivariant to C's rotation and translation, we utilize rotationally invariant graph neural networks to perceive the context of each query coordinate.
Despite having a neural network to model the distribution of atom occurrence p(e, rlC), how to generate valid and diverse molecules still remains technically challenging, mainly for the following two reasons: First, simply drawing i.i.d. samples from the distribution p(e, rC) does not yield valid molecules because atoms within a molecule are not independent of each other. Second, desirable sampling algorithm should capture the multi-modality of the feasible chemical space, i.e, should be able to generate diverse set of desired molecules given a specific binding context. To tackle the challenge, we propose an auto-regressive sampling algorithm. In specific, we start with a context consisting of only protein atoms. Then, we iteratively sample one atom from the distribution at each step and add it to the context to be used in the next step, until there is no room for new atoms. Compared to other recent methods (20] 233, our auto-regressive algorithm is simpler and more advantageous. It does not rely on post-processing algorithms to infer atom placements from density. More importantly, it is capable of multi-modal sampling by the nature of nuto-regressive, avoiding additional latent variables via VAEs [16] or GANs which would bring about extra architectural complexity and training difficulty.
We conduct extensive experiments to evaluate our approach. Quantitative and qualitative results show that: (1) our method is able to generate diverse drug-like molecules that have high binding affinity to specific targets based on 3D structures of protein binding sites; (2) our method is able to generate molecules with fairly high drug-likeness score (QED) 4 and synthetic accessibility score (SA) [6] even if the model is not specifically optimized for them; (3) in addition to molecule generation, the proposed method is also applicable to other relevant tasks such as linker design.
2 Related Work
SMILES-Based and Graph-Based Molecule Generation Deep generative models have been prevalent in molecule design. The overall idea is to use deep generative models to propose molecule candidates by learning the underlying distribution of desirable molecules. Existing works can be roughly divided into two classes- - string- baaed and graph-based. String-based methods represent molecules as linear strings, e.g. SMILES strings (34), making a wide range of language modeling tools readily applicable. For example, 10 26 utilize recurrent neural networks to learn a language model of SMILES strings. However, string- baand representations fail to capture molecular similarities, making it a sub-optimal representation for molecules [3]. In contrast, graph representations are more natural, and graph-based approaches have drawn great attention. The majority of graph-based models generate molecules in an auto-regressive fashion, i.e., adding atoms or fragments sequentially, which could be implemented based upon VAES [3]. normalizing flows (27]. reinforcement learning (35 14) etc. Despite the progress made in string-based and graph-based approaches, they are limited by the lack of spatial information and thus unable be directly applied to structure- based drug design tasks (2). Specifically, as ID/2D-base based methods, they are unable to perceive how molecules interact with their target proteins exactly in 3D space.
Molecule Generation in 3D Space There has been another line of methods that generate molecules directly in 3D space. [8] proposes an rugo-segrese model which takes partially generated molecule as input and outputs the next atom's 's chemical element and the distances to previous atoms and places
2

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the atoms in the 3D space according to the distance constraints. 128 29 approach this task via reinforcement learning by generating 3D molecules in a sequential way. Different from the previous [8), they mainly rely on a reward function derived from the potential energy function of atomic systems. These works could generate realistic 3D molecules. However, they can only handle small organic molecules, not sufficient to generate drug-scale molecules which usually contain dozens of heavy atoms.
propose a non-autoregressive approach to 3D molecular generation which is able to generate drug-scale molecules. It represents molecules as 3D images by voxelizing molecules onto 3D meshgrids. In this way, the molecular generation problem is transformed into an image generation problem, making it possible leverage sophisticated image generation techniques. In specific, employs convolutional neural network-based VAEs [16] or GANs (9] to generate such molecular images. also attempts to fuse the binding site structures into the generative network, enabling the model to generate molecules for designated binding targets. In order to reconstruct the molecular structures from images, leverages a post-proest prot-proesssing algorithm to search for atom placements that best fit the image. In comparison to previous methods which can only generate small 3D molecules, this method can generate drug-scale 3D molecules. However, the quality of its generated molecules is not satisfying because of the following major limitations. First, it is hardly scalable to large binding pockets, as the number of voxels grows cubically to the size of the binding site. Second, the resolution of the 3D molecular images is another bottleneck that significantly limits the precision due to the same scalability issue. Last, conventional CNNs are not cntation-equvarri which is crucial for modeling molecular systems (25].
20 23
3 Method
Our goal is to generate a set of atoms that is able to form a valid drug-like molecule fitting to a specific binding site. To this end, first present a 3D generative model in Se.tion[3.] that predicts the probability of atom occurrence in 3D space of the binding site, Second, we present in Section 33.2 the auto-regressive sampling algorithm for generating valid and multi-modal molecules from the model. Finally, in Section 3.3. we derive the training objective, by which the model learns to predict where should be placed and atoms and what type of atom should be placed.
3.1 3D Generative Model Design
A binding site can be defined as set of atoms C {a,, r:)
;= where N₂ is the number of atoms in the binding site, a; is the i-th atom's 's attributes such as chemical element, belonging amino acid, etc., and r; is its 3D coordinate. To generate atoms in the binding site, consider modeling the probability of atom occurring at some position r in the site. Formally, this is to model the density p(e/r, C), where element. Intuitively, this density can be interpreted as a classifier that takes as input a 3D coordinate conditional on C and predicts the probability of being occupied by an atom of type e.
R33 is arbitrary 3D coordinate, and 3 (H. C, ..... } is the chemical
To model p(e|r: r C), we devise model consisting of two parts: Context Encoder learns the repre- sentation of each atom in the context C' via graph neural networks. Spatial Classifier takes input query position r, then aggregates the representation of contextual atoms nearby it, and finally predicts p(e|r, C). The implementation of these two parts is detailed as follows.
Context Encoder The purpose of the context encoder to extract information-rice representations for each atom in C. We assume a desirable representation should satisfy two properties: (1) context- awareness: the representation of an atom should not only encode the property of the atom itself, but also encode its context. (2) rotational and translational invariance: since the physical and biological properties of the system do not change according to rigid transforms, the representations that reflect these properties should be invariant rigid transforms well. To this end, we employ rotationally and translationally invariant graph neural networks 25 as the backbone of the context encoder, described as follows.
First of all, since there is generally no natural topology in C, we construct a n-nnaorst-neiihhor graph based on inter-atomic distances, denoted as G (C. A), where A is the adjacency matrix. We also denote the K--N neighborhood of atom i as Nr(r;) (r) for convenience. The context encoder will take G as input and output structure-awes aware node embeddings.
3

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S Gurikrall de deli
& Ui (itima)) efunno
Gu ((R.na)
Binding Siu (Pocket)) Generated Alom
Deredly of Carbsn
Damily of Oryggns
Derelyy Nitroges
Figure I: An illustration of the sampling process. Atoms sampled sequentially. The probability density changes as we place new atoms. The sampling process naturally diverges, leading to different samples.
The first layer of the encoder is a linear layer. maps atomic attributes {a,} to initial embeddings { Then, these embeddings along with the graph structure A are fed into L message passing layers. Specifically, the formula of message passing takes the form:
n ((+1)
Wi
E
wiw(d;)) o Wih
(EN((r.)
where wr-)) is weight network and dij denotes the distance between atom and atom j. The formula
is similar to continuous filter convolution [25] Note that, the weight of message from j to depends
(2) only on day, ensuring its invariance to rotation and translation. Finally, we obtain { } set of embeddings for each atom in C.
Spatial Classifier
The spatial classifier takes as input a query position r E R and predicts the type of atom occupying v. In order to make successful predictions, the model should be able to perceive the context around r. Therefore, the first step of this part aggregate atom embeddings from the context encoder:
Σ Wo (|r Ty W (T)
v
jEM
where (r) is the k-nearest neighborhood of Note that weight different embedding using the weight network Wagar() (-) according to distances because it is necessary to distinguish the contribution of different atoms in the context. Finally, in order to predict p(e|r, C), the aggregated feature is then passed to a classical multi-layer perceptron classifier:
c = MLP(v),
(3)
where is the non-normalized probability of chemical elements. The estimated probability of position r being occupied by atom of type is:
exp(c(e)
p(err,)) = I EeEs exp (cle'))
(4)
where & is the set of possible chemical elements. Unlike typical classifiers that apply softmax to c, make of the extra degree of freedom by adding to the denominator, that the probability of "nothing" can be expressed as:
pNNothing/r.C)- I+ E+Eeen exp(cle(1)
(5)
3.2 Sampling
Sampling molecule amounts to generating set of atoms {(es, N However, formulating an effective sampling algorithm non-trivial because of the following three challenges. First, we have to define the joint distribution of and i.c. p(e, r(C), from which we can jointly sample atom's

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chemical element and its position. Second, notice that simply drawing i..d. samples from p(e, r/C) doesn't t make sense because atoms are clearly not independent of each other. Thus, the sampling algorithm should be able to attend to the dependencies between atoms. Third, the sampling algorithm should produce multi-modal samples. This is important because in reality there usually more than one molecule that can bind to a specific target.
In the following, we first define the joint distribution p(e, rIC). Then, we present an auto-regressive sampling algorithm to tackle the second and the third challenges.
Joint Distribution
We define the joint distribution of coordinate and atom type e using Eq 4
ple, r(C) = exp (cle)
(6)
Z
where Z is an unknown normalizing constant and e is function of r and C as defined in Eq Though p(e, r) is non-normalized distribution, drawing samples from it would be efficient because the dimension of is only 3. Viable sampling methods include Markov chain Monte Carlo (MCMC) or discretization.
Auto-Regressio Sampling We sample a molecule by progressively sampling one atom at each step. In specific, at step t, the context C, contains not only protein atoms but also atoms sampled beforehand. Sampled atoms in C, are treated equally as protein atoms in the model, but they have different attributes in order to differentiate themselves from protein atoms. Then, the (t + 1)-th atom will be sampled from p(e, r Ce) and will be added to C,, leading to the context for next step C(+1- The sampling process is illustrated in Figure !
Formally, we have:
(ce+1, Te41) ~ r(c,) C++1 C. U ((e+11
To determine when the auto-regressive sampling should stop, we employ an auxiliary network. The network takes as input the embedding of previously sampled atoms, and classifies them into two categories: frontier and non-frontier. If all the existing atoms are non-frontier, which means there is no room for more atoms, the sampling will be terminated. Finally, we use OpenBabel 21 20 to obtain bonds of generated structures.
In summary, the proposed auto-regressive algorithm succeeds to settle the aforementioned two challenges. First, the model is aware of other atoms when placing new atoms, thus being able to consider the dependencies between them. Second, auto-regressive sampling is a stochastic process. Its sampling path naturally diverges, leading diverse samples.
3.3 Training
As we adopt auto-regressive sampling strategies, we propose a cloze-filling training scheme at training time, a random portion of the target molecule is masked, and the network learns to predict the masked part from the observable part and the binding site. This emulates the sampling process where the model can only observe partial molecules. The training loss consists of three terms described below.
First, to make sure the model is able to predict positions that actually have atoms (positive positions). we include a binary cross entropy loss contrast positive positions against negative positions:
LBCE = EErep [log (1 p(Nothinggr. C))] EEr-p_ [log Mlog((Nohinggi (ea.iiingn..).... C)].
(8)
Here, P+ is a positive sampler that yields coordinates of masked atoms. p- is negative sampler that yields random coordinates in the ambient space. p- empirically defined as Gaussian mixture model containing CI components centered at each atom in C. The standard deviation of each component is set to 2 in order cover to the ambient space. Intuitively, the first term in Eq g increases the likelihood of atom placement for positions that should get an atom. The second term decreases the likelihood for other positions.
Second, our model should be able predict the chemical element of atoms. Hence, further include a standard categorical cross entropy loss:
LCAT -((, [logp(e/r,C).
(9)
5

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(b)
Enbokingg
9
Frontier Net.
Chocifer
(a)
Positive
Sampling
Binding Site and Mesked ligand
Shanod
Training Loss
Canzal Brooda
(d)
c CN
Nogative Sampling
Sportel
Figure 2: (a) A portion of the molecule is masked. (b) Positive coordinates are drawn from the masked atoms' positions and negative coordinates drawn from the ambient space. (c) Both positive and negative coordinates are fed into the model. The model predicts the probability of atom occurrence
the coordinates. (d) Training losses are computed based on the discrepancy between predicted probabilities and ground truth.
Third, as introduced in Section 3.2, the sampling algorithm requires frontier network to tell whether the sampling should be terminated. This leads to the last term a standard binary cross entropy loss for training the frontier network:
LF
Σ logo(F(h.)) iEFCC
Σ iEFC
log(1 (F(hh)))
(10)
where F the set of frontier atoms in C, a the sigmoid function, and F()) (-) is the frontier network that takes atom embedding During training, an atom is regarded as a frontier if and only if (1) the atom is a part of the target molecule, and (2) at least one of its bonded atom is masked.
input and predicts the logit probability of the atom being frontier.
Finally, by summing up LACE, LCAT, and Lp. we obtain the full training loss LBCE + LCAT + Lr. The full training process is illustrated in Figure
4 Experiments
We evaluate the proposed method on two relevant structure-based drug design tasks: (1) Molecule Design is to generate molecules for given binding sites (Section 4.1p, and (2) Linker Prediction to generate substructures to link two given fragments in the binding site. (Section 4.2). Below, describe common setups shared across tasks. Detailed task-specific setups are provided in each subsection.
Data We use the CrossDocked dataset 7 following [20] The dataset originally contains 22.5 million docked protein-ligand pairs at different levels quality. We filter out data points whose binding pose RMSD greater than 1Å, leading to a refined subset consisting of 184,057 data points. We mmseqs2 [31] to cluster data 30% sequence identity, and randomly draw 100,000 protein-ligant pairs for training and 100 proteins from remaining clusters for testing.
We trained a universal model for all the tasks. The number of message passing layers context encoder L. is 6, and the hidden dimension is 256. We train the model using the Adam optimizer at learning rate 0.0001. Other details about model architectures and training parameters are provided the supplementary material and the open source repository: https::/ h//githubb com/ luost26/3D- Sttpp//e--Genrriie----eS-
Model

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Metric
liGAN
Ours
Ref
IIGAN Reference
Vina Score (kcal/mol, !)
Avg.
-6.144
-6.344
-7.158
Med.
-6.100
-6.200
-6.950
Avg.
0.371
0.525
0.484
QED (1)
Med.
0.369
0.519
0.469
Avg.
0.591
0.657
0.733
SA (t)
Med.
0.570
0.650
0.745
Ours
High Affinity (%, f)
Avg.
23.77
29.09
Med.
11.00
18,50
-10 -12
00 02 04 a5 on 10 on a1 04 Ds on 10
Diversity (1)
Avg.
0.655
0.720
QED
Med.
0.676
0.736
Table Mean and median values of the four met- rics generation quality. (1) indicates higher is better. (4) indicates lower better.
Figure 3: Distributions of Vina, QED, and SA scores all the generated molecules.
4.1 Molecule Design
this task, we generate molecules specific binding sites with our model and baselines. The input to models are binding sites extracted from the proteins in the testing set. We sample 100 unique molecules for each target.
Baselines We compare approach with the state-of-the-arr baseline liGAN (20). liGAN is based on conventional 3D convolutional neural networks. generates voxelized molecular images and relies on a post-processing algorithm to reconstruct the molecule from the generated image.
Metrics We evaluate the quality of generated molecules from three main aspects: (1) Binding Affinity measures how well the generated molecules fit the binding site. We use Vina 33 1 to compute the binding affinity (Vina Score). Before feeding the molecules to Vina, we employ the universal force fields (UFF) [24] to refine the generated structures following (20). (2) Drug Likeness reflects how much a molecule is like a drug. We use QED score 4 as the metric for drug-likeness. (3) Synthesizability assesses the ease of synthesis of generated molecules. We use normalized SA
score 6 35 to measure molecules' synthesizability.
In order to evaluate the generation quality and diversity for each binding site, we define two additional metrics: (1) Percentage of Samples with High Affinity, which measures the percentage of binding site's generated molecules whose binding affinity is higher than equal to the reference ligand. (2) Diversity [1,, which measures the diversity of generated molecules for a binding site. It calculated by averaging pairwise Tanimoto similarities 3 32] over Morgan fingerprints among the generated molecules of a target.
Results We first calculate Vina Score, QED, and SA for each of the generated molecules. Figure the mean and median values of them
presents the histogram of these three metrics and Table over all generated molecules. For each binding site, we further calculate Percentage of Samples with High Affinity and Diversity. We report their mean and median values in the bottom half Table [ From the quantitative results, we find that in general, that have higher binding affinity to specific targets. Besides, the generated molecules from our model also exhibit other desirable properties including fairly high drug-likeness and synthesizability. When compared to the CNN baseline liGAN 20),, our method achieves clearly better performance on all metrics, especially on the drug-liken likeness score QED, which indicates that model produces more realistic drug-like molecules.
model is able to discover diverse molecules
To better understand the results, we select two binding sites in the testing set and visualize their top affinity samples for closer inspection. The top row Figure is the first example (PDB ID:2hej). The average QED and SA scores of the generated molecules for this target are 0.483 and 0.663

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Ours (2hc))
Reference (2hc))
Win: -7.3 QED: Vina:-7.1
Vinz -6.8 QED:
Vina:
Vins: -66
Vina--6..
QED: 0.46
Ours (4rlu)
Reference (4rlu)
Ving: -9.4
Vina:-9.3
Vina:-9.1
Vina:-911
Vina -9.0
-9. QED: 0.87
Vina:-8.4
QED: 0.80
S/c 0.93
QED:0.93
5A:066
QED: 0,90
S/: 0.63
QED:0.3
Sh:066
QED: 0.88
S/: 0.93
SA: 0.75
QED:0.58 SA:088
Figure 4: Generated molecules with top binding affinity and the reference molecule for two represen- tative binding sites. Lower Vina score indicates higher binding affinity.
respectively, around the median of these two scores. 8% of the generated molecules have higher binding affinity than the reference molecule, below the median 18.5%. The second example (PDB ID:4rlu) is shown in the bottom row. The average QED and SA scores are 0.728 and 0.785, and 18% of sampled molecules achieve higher binding affinity. From these two examples in Figure 4 we can that the generated molecules have overall structures similar to the reference molecule and they share some common important substructures, which indicates that the generated molecules fit into the binding site well as the reference one. Besides, the top affinity molecules generally achieve QED and SA score comparable to or even higher than the reference molecule, which reflects that the top affinity molecules not only fit well into the binding site but also exhibit desirable quality. In conclusion, the above two representative cases evidence the model's 's ability to generate drug-like and high binding affinity molecules for designated targets.
4.2 Linker Prediction
Linker prediction is to build molecule that incorpo- rates two given disconnected fragments in the con- text of binding site [12] Our model is capable of linker design without any task-specific adaptation or
Table 2: Performance of linker prediction.
Metrie
DeLinner
Ours
Avg.
0.612
0.701
re-training. In specific, given binding site and some fragments as input, we compose the initial context Co containing both the binding site and the fragments. Then, we run the auto-regressive sampling algorithm sequentially add atoms until the molecule is complete. (kcal/mol, +))
Similarity (1)
Med.
0.600
0.722
Recovered (%, f)
40.00
48.33
Vina Score
Avg.
-8.512
-8,603
Med.
-8.576
-8,575
we construct fragments of molecules the testing set by enumerating possible double-cuts of acyelic single bonds. The pre-processing results in 120 data points in total. Each of them consists of two disconnected molecule fragments.
Data Preparation Following 12
Baselines
We compare our model with DeLinker 12 Despite that DeLinke incorporates some information, it is still a graph-based generative model. contrast, our method operates fully in 3D space and thus is able to fully utilize the 3D context.

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Fragments
Predicted
Reference
Simllrity:
Simiarity:
Similarity:
Simliarity:
Similaity:
Similrrity:
Similarity:
compute the the generated Similarity, 0.48
Similarity; 0.41
Similarity:
Figure 5: Two example of linker prediction. Atoms highlighted in red are predicted linkers.
Metries We assess the generated molecules from fragments with four main metries: (1) Similarity: We use Tanimoto Similarity 332 3
over Morgan fingerprints [14] measure the similarity between the molecular graphs of generated molecule and the reference molecule. (2) Percentage of Recovered Molecules: We say a test molecule recovered the model is able generate molecule that perfectly matches it (Similarity 1.0). We calculate the percentage of test molecules that are recovered by the model. (3) Binding Affinity: We use Vina 33 molecules' binding affinity to the target.
Results For each data point, we use our model and DeLinker generate 100 molecules. We first calculate the average similarity for each data point and report their overall mean and median values. Then, we calculate the percentage test molecules that are successfully recovered by the model. Finally, we use Vina to evaluate the generated molecules' binding affinity. These results are summarized Table 2 As shown the table, when measured by Vina score, our proposed method
method's performance is on par with the graph-based baseline DeLinker. However, clearly outperforms DeLinker on Similarity and Percentage of Recovery, suggesting that our method is able to link fragments in more realistic way. In addition, present two examples along with generated molecules at different similarities in Figure The example demonstrates the model's ability to generate suitable linkers.
5 Conclusions and Discussions
In this paper, we propose a new approach to structure-based drug design. In specific, we design 3D generative model that estimates the probability density of atom's occurrences in 3D space and formulate an auto-regressive sampling algorithm. Combined with the sampling algorithm, the model able generate drug-like molecules for specific binding sites. By conducting extensive experiments, we demonstrate our model's ss effectiveness in designing molecules for specific targets. Though our proposed method achieves reasonable performance in structure- based molecule design, there is no guarantee that the model always generates valid molecules successfully. To build more robust and useful model, we can consider incorporating graph representations building 3D molecules future work, such that we can leverage on sophisticated techniques for generating valid molecular graphs such valency check 335 and property optimization [4

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11


Reviews:
[{"review_id": "vu4qqTQFgpz", "reviewer": "Reviewer_GUvn", "summary": "The paper proposed a deep generative model to design novel molecules in 3D space that bind to specific targets. Concretely, given the binding site as context, the generative model estimates the probability density of atoms’ occurrences in 3D space. Then after learning the distribution of atoms, they design an auto-regressive sampling scheme to generate atoms sequentially. Experimental results verifies the effectiveness of the proposed generative model in designing 3D molecules for specific proteins in binding pockets. ", "questions": "", "limitations": "", "rating": 7, "confidence": 3, "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": "The paper designs a deep generative model to form a valid drug-like molecule fitting to a\nspecific binding site. The generation procedure is split into two parts: (i) it predicts\nthe probability density of atom occurrence in 3D space of the binding site, where the binding target is used as context and roto-translation invariance neural network is used; (ii) it leverages auto-regressive sampling algorithm for generating valid and multi-modal molecules from the learned atoms’ density. 3D molecule design is an important and popular topic in recent years and is highly valuable. \n\nHowever, there are some issues in experiments. \n\nFirst, the docking score (in terms of Vina) of the generated molecules is relatively poor. In Figure 4 and 5, none of the docking scores is better than -10. Also, in Table 1, the average vina score is -6.3, which does not indicate high affinity. \n\nSecond, during empirical studies, some important baseline methods are missing, e.g., [Masuda et al, Generating 3d molecular structures conditional on a receptor binding site with deep generative models] and [Ragoza et al. Learning a continuous representation of 3d molecular structures with deep generative models]. \n\n\n==================\n\nI have read authors' responses and other reviews, and do not change my score. \n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "NA", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "3"}, "extra_text": {}}, {"review_id": "USIMrIfBnrR", "reviewer": "Reviewer_RaVz", "summary": "This paper introduces a novel generative method for molecular design that uses 3D spatial information and the binding pocket embedding to generate molecules with high binding affinity towards a selected target protein. The method allows for multimodal sampling of valid and diverse molecules. In the experiments, the model is evaluated in two scenarios. The first scenario is a structure-based de novo drug design, and the second one is linker prediction. In both cases, the proposed model manages to generate reasonable compounds that fit into the binding pocket. Additionally, the generated compounds exhibit high drug-likeness and synthetic accessibility.", "questions": "", "limitations": "", "rating": 7, "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": "The method presented in the paper is very original. The model can perceive 3D relation between generated ligand and target protein. There are not many generative models that are designed to create molecules that directly fit the 3D space of the binding pocket. The proposed model is certainly unique in the category of structure-based generative models Another method in this category is the shape-based model by Skalic et al. [1], which is missing in the references. This method generates compounds based on the predicted 3D shape that fits the binding pocket. However, also this method uses the SMILES representation instead of working directly on 3D atoms.\n\nThe presented experimental results are convincing. The authors present qualitative results in Table 1 which could be improved by adding more models to the comparison (e.g. [1]) and adding error bars based on multiple runs of the models. The qualitative results in Figures 4 and 5 clearly show that the proposed method can generate reasonable compounds. What seems a little bit suspicious is that in Figure 4 the generated compounds look very similar to the reference compound. It may suggest data leakage, e.g. compounds that are very similar to the reference one (e.g. the same analog series) are included in the training set. A scaffold split would prevent this from happening. To make these experiments more convincing, the whole protein families that are present in the testing set should be also discarded from the training set.\n\nThe paper is clearly written, and there are only minor issues that generate confusion. In Equation 1, the notation $W^\\ell(d_{ij})$ may suggest that $W^\\ell$ is a function, and in the text it is said that “weight of message from $j$ to $i$ depends only on $d_{ij}$”. On the other hand, this function is not defined, but instead it is said that $W$ is a learnable matrix. Equations 11 and 12 in the supplemental material are much more precise and do not seem equivalent to what is presented in the paper. The architecture of the frontier network $F$ is not described at all.\n\nThe proposed method supports multi-modal sampling of valid compounds thanks to a simple (not using a latent space) autoregressive method. The experiments show that the proposed generative model creates compounds that are drug-like and synthetically accessible without directly optimizing for these values. Additionally, a linker prediction task is performed and the results are compared with a popular model for this task, DeLinker. Having considered all that, the method presented in the paper is of high value to the field of computer-aided drug discovery.\n\nOther comments:\n- Why is ‘Nothing’ not a separate class in the probability vector $c$, but instead it always artificially gets value 0 by the means of Equation 5? Does the loss in Equation 8 not converge otherwise?\n- In Figure 5, the PDB ID is missing.\n- In Figure 5, the atoms with a red overlay are hardly readable.\n- In Figure 3, it is not clear what the vertical dashed lines signify.\n\nBased on all the above, I am leaning toward the acceptance of this paper.\n\n[1] Skalic, Miha, et al. \"Shape-based generative modeling for de novo drug design.\" Journal of chemical information and modeling 59.3 (2019): 1205-1214.", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "The authors could elaborate more on the limitations of the method, e.g. what the success rate of sampling molecules is or what is the time complexity of the method considering the sampling methods used. The negative societal impact is not described. The presented method is a general method for designing active compounds, so potential societal impacts may include improving drug discovery pipelines but also acceleration of the design of harmful compounds, e.g. toxic psychoactive substances.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4"}, "extra_text": {}}, {"review_id": "Iwv104YE0KF", "reviewer": "Reviewer_kPk1", "summary": "This paper addresses the task of 3D molecular generation within a 3D protein binding pocket. An autoregressive model is used to predict probability distributions of atom occupancies, which are iteratively sampled to construct a full molecular structure inside the binding site. ", "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": "The approach is presented clearly and is remarkably simple. The sampling approach provides a natural way to decode the continuous distribution into a discrete molecular structure. The sampling procedure for training of observing masked molecular structures and training the joint distribution through sampling both positive and negative spatial coordinates is procedurally simple (in a good way, in my opinion). The primary criticism of this work would be that it does not provide any significant machine learning advance and lacks quantitative comparisons to plausible alternative approaches, instead focusing exclusively on a comparison to ref [21]. However, I do think this is an interesting task from a domain perspective. \n\nContextualization\n\n1.\tWhat are the aspects of the approaches in refs. 8, 30, and 31 that render them unable to handle larger molecules? This does not seem to be a fundamental limitation of the method but perhaps a limitation of the evaluations in those original papers.\n\n2.\tThe statement that 1D/2D methods are unable to be applied to structure-based design tasks seems to be an oversimplification. String-based and graph-based methods have been applied to the optimization of docking scores as a structure-based oracle function (e.g., https://pubs.acs.org/doi/10.1021/acs.jcim.0c00833)  While not conditioning generation on a 3D structure explicitly, this may be considered an application to SBDD.\n\n3.\tThere is a family of methods designed for atom-by-atom or fragment-by-fragment ligand generation within a fixed protein pocket (e.g., AutoGrow4). Is it feasible to do any performance comparisons to these non-ML methods? The problem formulation is different, as they use Vina Scores as intermediate signals during generation, but it is realistic to have access to a docking oracle function. The procedure is similar enough to this work that a comparison is warranted.\n\n\nExperiments\n\n4.\tThe performance of the model (i.e., Vina Scores) is not reported when the force field refinement is omitted. This paper does not state whether the force field refinement operates on the ligands alone or the ligands and the binding site together, but the reference implies the latter. Ref 21 also states that Vina was used for reoptimization (including of the pose), whereas this work implies that only the Vina scoring function was used. In the evaluation workflow, were structures taken as their 3D conformations or re-optimized? Insufficient details are provided with respect to this evaluation and the dataset used, although the authors do state that code/data will be made available upon publication.\n\n5.\tIn the experiments, evaluation of activity focuses on the average and median values. However, the goal would arguably be to minimize the docking scores. It appears as though the model does not have the ability to learn how to generate the “most favorable” ligand by considering docking scores during training, but merely generate a representative ligand. Most generated molecules have binding affinity scores that are worse than the reference ligand.  \n\n6.\tIt seems surprising that in the top row of Figure 4, so many of the generated compounds have the same heterocyclic motif as the reference compound, not to mention the terminal phosphate group. Did this scaffold appear in the training set for a very similar protein? Or did the model truly rediscover it from scratch? \n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Extensions are discussed; social impact is not.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "3"}, "extra_text": {}}, {"review_id": "88ppB6K2eP0", "reviewer": "Reviewer_jsjN", "summary": "This paper tackles the problem of generating molecules that bind to a specific protein. To make use of the spatial information to target the proteins exactly in 3D space, the paper proposes an autoregressive model where the atoms are sampled sequentially from a learned distribution that estimates the probability of atoms' occurrence in 3D space. In fact,   the paper models the probability of a position in 3D space being occupied by a certain type of atom given as input the 3D coordinate and the binding site.  the model encodes the context which is the binding site and concatenates it with the input query position r  and finally predicts the type atom that could occur at the position r. ", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "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": "The paper is well motivated and clearly written. They tackle the problem of structure-based drug design which is a very interesting and crucial step for using ml models for drug design.  The experiment results show clear improvement over the baselines. \n\nThere are few concerns\n1. They only include one single baseline but I am sure there are many works that exist in this line and should be taken into consideration. For instance the work [30] and [31].\n\n2.  In table 1, it is shown that the proposed model has a better score of not only Vina but also SA score and QED score. I can understand the model could lead to a better Vina score as the model is tailored to solve this specific problem but it is not clear what factor of the model leads to a better SA score and QED score when compared to the baseline. ", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Limitation: the experiment did not include enough baselines that tackle similar problems. ", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4 hours"}, "extra_text": {}}]

Author rebuttal:

Meta-review: The AC and reviewers all agree that this is an interesting submission. 

We strongly urge the authors to incorporate their clarifying comments into the manuscript. In addition, as mentioned by several reviewers, it is important that the authors be clear about the relative value of Vina score. As noted by kPk1, coming up with a new metric that is more appropriate would be a valuable direction for future study.

Reviewer RaVz made some very pertinent point on Tanimoto similarity, SA scores...etc. It would be very exciting to see these comments addressed either in the present manuscript or in future work.
Decision: Accept (Poster)