GraphVF: Controllable Protein-Specific 3D Molecule Generation with Variational Flow
Authors: Fang Sun
Zhihao Zhan
Hongyu Guo
Ming Zhang
Jian Tang
Venue: Submitted to ICLR 2023 (2023)
Keywords: Controllable Molecular Generation
Pocket-based Drug Design
Variational Flow

Abstract: Designing molecules that bind to specific target proteins is a fundamental task in drug discovery. Recent generative models leveraging geometrical constraints imposed by proteins and molecules  have shown great potential in generating protein-specific 3D molecules.  Nevertheless, these existing methods fail to generate 3D molecules with 2D skeletal curtailments, which encode pharmacophoric patterns essential to drug potency. To cope with this challenge, we propose GraphVF, which seamlessly integrates geometrical and skeletal restraints into a variational flow framework, where the former is captured through a flow transformation and the latter is encoded by an amortized factorized Gaussian. We empirically verify that our method achieves state-of-the-art performance on protein-specific 3D molecule generation in terms of binding affinity and some other drug properties. In particular, it represents the first controllable geometry-aware, protein-specific molecule generation method, which enables creating 3D molecules with specified chemical sub-structures or drug properties.


Under review as a conference paper at ICLR 2023
GRAPHVF: CONTROLLABLE PROTEIN-SPECIFIC 3D MOLECULE GENERATION WITH VARIATIONAL FLOW
Anonymous authors
Paper under double-blind review
ABSTRACT
Designing molecules that bind to specific target proteins is fundamental task in drug discovery. Recent generative models leveraging geometrical constraints imposed by proteins and molecules have shown great potential in generating protein-specific 3D molecules. Nevertheless, these methods fail to generate 3D molecules with 2D skeletal curtailments, which encode pharmacophorie patterns essential to drug potency and synthesizability. To cope with this challenge, we propose GraphVF, which integrates geometrical and skeletal restraints into vari- ational flow framework, where the former is captured through a normalizing flow transformation and the latter is encoded by an amortized factorized Gaussian. We empirically verify that our method achieves state-of-the-art performance on protein-specific 3D molecule generation in terms of binding affinity and some other drug properties. In particular, it represents the first controllable geometry- aware, protein- -ppeiispecciiic molecule generation method, which enables creating bind- ing 3D molecules with specified chemical sub-structures or drug properties.
INTRODUCTION
The de novo design of synthetically feasible drug-like molecules that bind to specific protein pockets a crucial yet very challenging task in drug discovery. To cope with such challenge, there has been a recent surge of interest in leveraging deep generative models to effectively searching the chemical space for molecules with desired properties. These machine learning models typically encode the chemical structures of molecules into a low-dimensional space, which then can be optimized and sampled to generate potential 2D or 3D molecule candidates (lin al., 2018 Shi et al. 2020 Zhu
et al. 2022 Hoogeboom et al. [002]. Along this research line, a more promising direction has also been explored recently: generating 3D molecules that bind to given proteins.
Such binding 3D molecule generation is fundamentally important because binding in fact mainly facilitates the functionalities of drugs. Fortunately, leveraging autoregressive models to generate drug molccules (i.e., ligands) directly based the 3D geometry of the binding pocket has shown promising potential (Luo et al.] [021] Peng et al.) 2022 Liu et al.] (022). These methods explic- itly capture the fine-grained atomic interactions in the 3D space, and produce ligand poses that can directly fit into the given binding pocket. Nevertheless, two critical issues remains unsolved for these existing geometric approaches: 1) effeectve encoding and sufficient preservation of pharma- cophoric structural patterns in the ligand candidates, and 2) controllable ligand generation that aims specified drug properties or sub-structures. The former prevents generating ligands that seem ge- ometrically plausible, yet structurally invalid or pharmacophorrcally impotent; the later dominates the synthesibility and the practical usefulness of the drugs. We further elaborate them next.
In practice. it is extremely valuable to keep track of the pharmacophoric patterns in the existing ligands, which indeed determines a ligand's bio-chemical activities and binding affinity to large extent (Wermuth et al. 1998). Consider, for example, the molecules of serotonin (a benign neu- rostransmiter) and N.N- A.N-Dimttylltyptaminne (DMT, a famous hallucinogen). As can be seen in Figure 5g from Appendix E. serotonin and DMT share large common bulk of their structures, which both possess an indole and an ethylamine group, but differ enormously in their neural activi- ties. In fact, the extra Methyl groups in DMT's NHMc, are pharmacophoric, inducing attractive charge interaction with Asp-231 (Gomez-Jeria & Gobles-Navare 2015).. This pharmacophoric fea- ture gives rise DMT's binding affinity with the 5-HT22 2A binding site and produces hallucination.

---

Under review as a conference paper at ICLR 2023
Table 1: Comparison among representative molecular generative methods.
Moleculer Encoding
Controlled Generation
Name
Generative Model
Atom
Bond 3D Coord.
Ligand Strue.
Receptor Conf.
Generic Prop.
EDM
Diffusion VAE VAE
DMCG
JT-VAE
GraphAF
Autoregressive Flow
GraphBP
Autoregressive Flow
/
Pocket2Mol
Spatial Autoregression
GraphVF
Variational Flow
Such observations suggest that effectively enforcing pharmacophoric patterns in ligands is critical for binding.
Equally important, controlling molecular properties like solubility, polarizability and heat capacity instrumental to drug quality. This is to make sure that the synthesized drug molecules have good exposure, egg. efficacy in clinical trials (Egan 2010). It is worth noting that, although recent diffusion models like EDM (Hoogeboom et al. 2022) have been popular for their capability to perform controlled generation on these properties, performing such control while being pertinent given pocket structure for binding remains under-explored by previous works.
(ADME) in vivo, and thus, sufficient
To address the aforementioned two issues, we propose GraphVF, a protein- molecule gen- eration framework that integrates both geometrical and skeletal constraints, aiming at controlling over the structure and property of the generated ligands. To attain this goal, we leverage flow-based architecture that combines amortized variational inference (Zhang et al., 2018) and autoregressive normalizing- flow generation. tion tree (Jin et al. 2018), and fine-grained geometrical context of the protein receptor is encoded via a valence-aware E(3)-NNN, These two constraints are integrated into a variational flow architecture, where the former enforces the variational distribution globally, while the latter administers the flow transformations autoregressively.
specific, global structure of the drug ligand organized as a junc-
We show empirically that, GraphVF generates drug molecules with high binding affinity to the ceptor proteins, with or without the aid of reference ligands, outperforming state-of-the-art methods in terms of binding affinity and some other drug properties. More importantly, Graph exposes a clean-cut interface for imposing customized constraints, which is extremely useful practice for controlling the sub-structure and bio-chemical property of generated drug ligands. To specify what our proposed model can actually do, we compare Graph VF with several representative models for molecule generation in Table
Our main contributions are summarized as follows.
We devise a novel variational flow-based framework to seamlessly integrate geometrical and skeletal restraints to improve protein-specific 3D molecule generation.
We show the first method that enables generating 3D molecules with specified chemical sub-structures or bio-chemical properties.
We empirically demonstrate our method's superior performance to state-of-the-art ap- proaches on generating binding 3D molecules.
2 RELATED WORK
Non-Protein Specific Molecule Generation Different generative techniques have been applied to the task of molecular generation, including Variational Autoencoders (VAEs) (Kingma & Welling
2013). Diffusson Models (Sohl-Dickstein et al. 2013), Normalizing Flows (NFs) (Dinh et 2016) and Autoregressive Models (Van Oord et al.] (016)). The line of work usually context-iree, aiming to produce high-quality molecules from scratch, or to render reasonable 3D conformations of given molecules. For example, JT-VAE (Jin et al./ 2018) generates molecular graphs with the guidance of tree-structured scaffold over chemical substructures. GraphAF (Shi et al. (020)) uses flow-based model to generate atoms and bonds in an autoregressive manner. DMCG (Zhu et al. 2022) and EDM (Hooeeooom al. 2022) leverage equivariant diffusion or iterative sampling and de-noising to generate 3D conformations from 2D structures. Unlike these methods, our approach aims at generating molecules that bind to given 3D protein pockets.
2

---

Under review as a conference paper at ICLR 2023
3D Molecule Generation for Target Protein Binding With the wide availability of large-scale datasets (Francoeur et al. 2020 Li et al. 2021) for target protein binding, recent works have been able to generate drug ligands directly based on the 3D geometry of the binding pockets. For exam- ple, Pocket2Mol (Peng et al. 2022) leverages a apatial-autoregressii model; it directly models the p.d.f. for atom occurrence the 3D space as Gaussian mixture (GMM), and then iteratively places the atoms from the learned distribution until there is no room for new atoms, GraphBP (Liu et al.) 2022), an autoregressive model, retains good model capacity via normalizing flow; variables are ran- domly sampled from compact latent space, before they are projected into the chemical space by an arbitrarily complex flow transformation. Despise their promising potential, these methods ignore the topological organization of the drug ligand itself, as well as the structural patterns and pharma- cophoric features embodied in it. As a result, existing methods tend to generate ligands that seem geometrically plausible, yet structurally invalid or pharmacophorically impotent. Our approach here aims to address this problem. Also, our method enables controllable molecule generation, facilitat- ing generating drug ligand candidates with specified chemical sub-structures or drug properties.
3
PRELIMINARIES
Our proposed method leverages an autoregressive flow strategy to generate binding molecules.
3.1 AUTOREGRESSIVE FL.Ww MODELS
Given a prior distribution Pz. a flow model (Dinh et al.) 2014; Rezende & Mohamed] 2015 Weng 2018) is defined as an invertible parameterized function fa z E R² - X E R2,, where & represents the parameters of f, and D is the dimension for z and x. This maps the latent variable pz to the data variable x, and the log-likelihood of x is calculated as
log (x) = log (J + log det 0. (x)
8x
Autoregressive flow model (Papamakarios et al. 2017) formulates a flow model with an autoregres- sive computation to enable easy Jacobian determinant computation. Let be the i-th component of x and x, conditions on X The inverse function fø" is then defined as follows:
az (x @ z, + 14((x1..-1); i i= 1...D,
where @ denotes element-wise wise multiplication, a.(()) E and (xx(-) E TR are non-linear functions of X1.. Doing so, we can effectively calculate the follows:
05 (x)
X;
14i
Z;
det
Oi
Õx
0i
3.2 PROBLEM FORMULATION AND NOTATIONS
Given a specific protein receptor, our task is to generate ligand molecule that binds effectively to it. Here, proteins and ligands are represented as graphs in the 3D geometric space. Node features include atom type and position while edge feature involves bond type b. For training, given pairs of protein P and ligand R. in their binding poses. For generation, we are given protein targets P to generate drug ligands that bind tightly to them. Consider given protein-ligand pair with M and N atoms respectively. We denote the protein as P = (V.E), where V {(ā,, f.) ) and E = (bا and the ligand as R = (V, E'), where V = ((a,, r.) and E = {beg 1if=1 With slight abuse of notation, the 2D topology of the ligand structure also referred as R.
IN
THE PROPOSED METHOD
In this section, we first introduce how we encode both the ligand scaffold (Section and the protein-ligant geometry information these two pieces of knowledge used generate a binding molecule autoregressively. Finally, in Section 4.4] we detail how we cope with three challenges arising in Section 4.3 through a variational flow model.
This is followed by Section 4.3 which presents how
3

---

Under review as a conference paper at ICLR 2023
4.1
LIGAND SCAFFOLDS ENCODING
HaC
HaC
CHg
CH3
P.
Parsing
Pooling
Fncoding
Σn
Ligand Molecule R
Occluded Sub-structures
Tree Strueture
Embedding
Figure Ligand molecule (e.g. DMT) is first parsed into compilation of canonical sub- structures, then pooled into junction tree structure, and finally encoded into sp (HRR Ex)
Inspired by (Tin al. 2018), we extract the coarse-graiee graiind structural patterns the ligand scaffold in fragment-driven approach. The whole procedure is illustrated in Figure [ and the detail is discussed next.
First, the ligand molecule R is parsed into compilation of occluded canonical sub-structures, cording to a set of pre-defined vocabulary (more details are in Appendix A.T.. Next, the result- ing graph structure is pooled into a junction tree structure. Structural patterns are well exposed in the junction tree, where each node represents a sub-structure. Finally, the structral encoding (PR = (HRR ΣR) is derived from the tree structure via Gated Recurrent Unit (GRU) (Chung al. 2014) adapted for tree message passing. In particular, μRR and Σn are equally-sized dense vectors, which parameterize the amortized variational distribution be discussed in Sections 4.3 and 4.4 Note that FR is merely the shorthand symbol for the concatenation of μR and Σx. It should also be emphasized that GRU encoder and PR are not fixed: they are trained an end-2-end manner alongside the whole model to avoid deviations from the training objective. Refer to Appendix A.2 for implementation details about the GRU architecture.
4.2 GROMETRY GRAPH ENCODING
Equivariant graph neural networks like SchNet (Schutt et al. 2017) and EGNN (Satorras et al., 2021] have become a routine component in this receptor-based based line of work, which are essential for encoding molecular features with roto- too-trranslationl equivariance. Atoms around the binding pocket are organized into KNN/radius graph, based on their euclidean distance in the 3D space. This distance-based approach is appropriate for modeling non-covalent interactions like hydrogen bonds and hydrophobic interactions, but remains inadequate for modeling covalent bonds. Bond lenghs are known be characteristic, e.g. C=N 1.16 A. C-C 1.34 Á (Lide 2012). Explicitly incorporating bond types during message passing is thus beneficial for better perception atomic interactions and more reasonable delineation of molecular structures.
To achieve this goal, we devise Echnet, an -quiivaata graph neural network specially tailored for bond type message passing in the 3D geometric setting, which is formulated follows:
(0) Emb(a:)
h
(4)
m. concat [Erbf( - ryll), Emb(b,)) Σ
(5)
h (1) h (1-1)
h (1-1) @ (10 (m):) 1 1,.,..,
(6)
KEN
where & is the feed-forward neural network, Erb((-) is radial basis function (Liu al. 2022
Emb(-) the embedding layer, concat(-) is the concatenation of two vectors, and + is the feed-
forward neural network. L the number of convolution layers, h stands for the encoding of atom i the tth convolution layer, and m, is message passed from atom i j.

---

Under review as a conference paper at ICLR 2023
Construct redius greph For Echnet encoding
Select focal atom Spherical Coordinate System (SCS)
Add atom, semple its atom type and bond with existing atoms
Sample position (d, d) of new atom w.r.t. focal atomn
proSein
ligand
protein atonn
ligand atom
focal atom
newly generated atom
chemical bond
graph odge
pending chemical bond
b, d, sampled features
Figure 2: Generation procedure of GraphVF. Atoms are added autoregressively, whose types, bonds and positions are sampled from prior distribution ((4pp Σp) and predicted via normalizing flow.
4.3 BINDING LIGAND GENERATION
We formalize the procedure of new ligand generation as a Markovian sampling process, where atoms and bonds are autoregressively added according to the intermediary state the binding site. The generation process at step
4 is illustrated in Figure 2 In particular, we provide a prior distribution N (ppp Σp) to control certain desired traits of the generated ligand. The implication and derivation of N Ep) will be discussed in Section 4.4 When not specified, the prior is set to (O, I) by default. We now elucidate the generation process at step i.
Firstly, we construct radius graph G. based on protein graph P and ligand sub-graph R1s-1;
G (P R1
where the radius operator T(-) adds edges (of bond order 0) to neighboring atoms within radius т. In particular, generation step when no ligand atoms have yet been generated, G3 is simply 7(P). Echnet outputs the encoding of each atom in both protein and ligand:
CI:M C1:N-1 Echnet(g,)
Secondly, we select focal atom fo with the focal classifier. Except in the first step, fa is only selected from the drug ligand. Based on f. and two of its nearest neighbors, we construct spherical coordinate system (SCS), transforming Cartesian coordinates into polar coordinates (d. 0, o).
Finally, we add new atom the drug ligand via sequential generation of its atom type a,, bindings with existing atoms b1.i-1. 1. and position r; = (d;, 8, d;), in order to better capture the underlying dependencies (Liu et al. (0022). The prior random variables are sampled from A (Mtp Σp), including (node) (hond)
2 21 and z poss The priors are then consecutively projected to the 3D geometric space
via flow transformation Fe:
(node)
li- 1
(bond)
(pos)
Fi (node)
2
115i-1,1 z
Z
(bond) (pos),
te..-11)
(9)
Specifically, the flow transformation F; is parameterized as follows:
1 (node)
(uode)
Node-MLP(e,.)
(10)
(node)
(node)
(node)
+ (node)
ai
c z
(11)
(bond)
(bond)
Bond-MP BiaddMMPP(E MIIP(MPPP-----
x (node))
(12)
1,1
1ii-1,i
(bond)
(bond)
1:1-1,1 + (bond)
(bond)
(13)
M1#--1,1
p
(pos)
(pns)
Position-Mii -Mittion-MPP(ee....
x;
(node) (hond)
11:1 1,2
(14)
(pos)
o (pos)
z
(pos)
+ 1
(pos)
(15)
where O denotes element wise multiplication, and x; (node)
(bond)
poss) the vectorized repre-
x 1 x
sentation of atom type, bond type and position, and o,, a are parameters for flow transformation. The sequential dependency between a, b. d is embodied in Equations 12 and 14 where new atom/bond
5

---

Under review as a conference paper at ICLR 2023
types that have just been generated are immediately used to parameterize and j of the next flow transformation.
Thus, have rendered all the sampled features d, 014--1,6 d, 8,, Ø; from step i, and successfully generate the new atom and its associated bonds. We go on with this iteration, until the focal classifier reports that atom is eligible for fi. and the generation procedure is called to end. Algorithm from Appendix[Bo B explainn the generation algorithm in more detail.
4.4 VARIATIONAL FLOW TRAINING
Though self-contained, the generation procedure in Section 4.3 puts forward three critical technical challenges nonetheless:
1) Integration of both binding pocket geometry and ligand structural patterns;
2) Generation molecules with high binding affinity, even without reference ligands;
3) Controllable generation interface for customized bio-chemical constraints.
We propose variational flow, dedicated training framework, to solve the above challenges. As is illustrated in Figure [ the term is coined according to the two key components in the framework: the amortized variational distribution N ([RR, ER) ), and the invertible flow function F,,. We proceed to discuss the different components of this training framework.
Training:
Flow Backward
M~NNus NN Ex)
(HR, Eg) PR READDRT
F (x))
KL Divergence
Generation:
Flow Forward
2;
N(O,I) I)
F. + GRAPH-READOUT
(8:)
Figure 3: Comparison of a single training/generation step the variational flow framework
Encode 2D structure: The primary difference between training and generation is that, the complete structure of the reference ligand is only available during training. Therefore, for each druug-liande pair, the junction tree encoder (Section 4. encode the reference ligand's structral pattern as PR = (UR Σx) on the fly, which parameterizes the variational distribution N W(HR. Σx)
Encode 3D geometry: As is suggested in Figure this procedure is basically the inverse to the generation step (equation 9):
2
(ndde)
1
(hond)
(pos)
=F-1
x
(node) (bond) (pes)
x Lii-1,83
e1:N-1)
(16)
To be specific, z; is derived as follows in the training phase:
(node)
(uode)
(node)
1 (nddc)
2
(17)
(bond)
(bond)
(boud)
1
x 1:i- Z 1: 1,3
11i
(boud)
(18)
σ 11-11,1
z
(pos)
x
(pos)
(pos)
(pos)
(19)
a
where o; and μ4 are derived in the way as Equations 10
12 and
14
Optimization: At the core of the variational flow methodology our belief that molecular data are intrinsically multi-modal and representations of different modality should be rendered back into the same molecular entity. That is to say, whether the input data is 2D structure or 3D geometry, a well-trained model would project them to the same distribution in the chemical space. That is why in

---

Under review as a conference paper at ICLR 2023
Figure would expect the generated molecular distribution X; overlap with the ground-truth distribution X₁, even without the guidance of 2D structure R. We formalize this intuition into a
bi-level optimization task for training step
maximize
Px; px; (xi)
(20)
subject to PRI (Xilx.))) <
(21)
since Fi are invertible functions (i N...N), the LHS of Inequality 21 can be transformed into:
f (x.((x,
(22)
(R.((F(2))
(23)
(211(2
(24)
DNI(WNUR, [R)(
(25)
where b stands for a particular protein-ligand pair. This is an interesting result, which shows that across the N training steps of the same protein-ligand pair, we need only control the KL divergence
between N (HR, Σx) and A(0, I). Note that N (peR. Ex) is contingent on structure R: they are the same across different protein-ligand pairs.
As for Equation 20, it corresponds to the flow loss term described in Equation I can be elaborated as:
For step in pair
4 (uode) = log( (groodd(N((,, (node) 1RR, ER.)) - loo( Prod
))
(26)
(odey)
C (boud) 1:1-1, log (og(Pro((V(21.-1) MR.: ER))) (Prod(
(boud)
(27)
(bond)
1,i
c(Pes) Jog(Prod(N((])) (noo) URR ER))) (Po(Prod(
(28)
pos
flow = c. + ((bond) (poos)
(29)
Therefore, the bilevel optimization task adopts a 3-regularized loss form. Note that N N(RR, ΣR) is involved both loss terms:
N
1
Chotal
Blo + 3C
(30)
We use mini-batch training, and optimize the batch loss =b=1 C Chotal with Adam (Kigmma & Ba 2014). We use 3-annealing for adequate training of both 2D and 3D encoders, and to trade-off be- tween binding affinity and controllability of the generated molecules. Algorithm frrom Appendix B explains the training algorithm in more detail.
Controllable generation: During generation, the variational prior provides flexible interface for controlling certain properties of the generated molccules, without the need to even re-train the model. This can be achieved by taking collection of molecules with a certain desirable property p. denotes as {Ra Tag. where I is the index set. The latent distribution for the desired property is defined as N(pp: Ep), which can be naturally parameterized as:
(mps Ep)
T [MRR, ER.).
(31)
where (HR.. ER.) (a E I) can be obtained from the tree encoder. Intuitively, (H2, Ep) contains inductive bias for the desired property p. and ligands that are sampled from this distribution should be more likely to possess property
EXPERIMENTS
5.1 3D MOLECULAR GENERATION CONDITIONED ON PROTEIN POCKET
Dataset. We the benchmarking CrossDocked dataset (Francoeur al. 2020). which contains 22.5 million protein-ligant pairs, to evaluate the generation performance of Graph VF. For fair com- parison, follow Pocker2Mol (Peng et al. 2022 prepare and split the data.
7

---

Under review as a conference paper at ICLR 2023
Method
HA
SAT
QEDi
LogP
Diversityt
Time!
GraphBP
0.134
0.585
0.515
2.610
0.835
20
Pocket2Mol
0.272
0.765
0.563
1.586
0.688
2504
Graph (w/o 2D encoder)
0.263*
0.542
0.310
3.567
0.807
68
GraphVF (ours)
0.311
0.570
0.406
0.141
0.930
32
Table 2: Performance of different methods on 3D molecular generation based on protein pockets. Higher values indicate better results. Best results are in bold. Result with is dealt with special valency constraints. Valency constraints are detailed in Appendix C.
Setup. Following GraphBP (Liu al. 2022 and Mocket2Mol, we randomly sample 100 molecules
for every protein pocket in the generation stage. The quality of generated molecules is evaluated
by 6 widely adopted metrics. (1) High Affinity (HA), which estimates the percentage of generated
molecules that have higher CNNAfinity calculated by the Gnina program (McNutt et al.) [021] I; (2)
Synthetic Accessibility (SA), which represents the easiness of drug synthesis;
(3) Quantitative
Estimation of ity (Bickerton al. p (4) LopP denotes the octanol- partition coefficient, and good drug
(QED), a measure of drug-likeness based on the concept of desirabil-
candidates always have a LogP between -0.4 and 5.6 (Ghose et al. 1998) (5) Diversity is calculated
as 1 average Tanimoto similarities of generated molecules for every protein pockets, following Pocket2Mol; (6) Time estimates the time(s) spent generating 100 molecules for pocket. We choose GraphBP and Pocket2Mol as our baselines, which reprent the state-of-art models for binding molecule generation. For GraphBP and GraphVF, we trained them on the dataset for 40 epochs with the same byperparameters. For Pocket2Mol (Peng et al. (022), we obtain the pre-trained model from their authors, and then compute the scores using Gnina.
Results. The comparison results are presented in Table [ We can see that our GraphVF outper- forms the two state-of-the baselines in terms of both binding affinity (HA) and Diversity. As shown by the generation time, GraphVFis much more efficient than Pocket2Mol in 2 orders of magnitude. We have also attained comparable performance on certain properties like QED, LogP and SA, even without the explicit guidance from the variational prior. We also conduct experiment on the ablational 'w/o 2D encoder' variant Table 5 Without the information provided by the 2D encoder, the HA value for the abalational variant drops drastically from 31.1% to 26.3%. This shows that VF learns better with the 2D encoder, and significantly benefits from the varia- tional flow architecture. We also provide visualizations of selected generated ligands in Figure from Appendix
5.2 SUB- SUB-STRUCTURE ANALYSIS
Setup. As it is pointed out in Pocket2Mol Peng et al. (022)) that conventional metrics could not reflect the geometry of sampled molecules, we conduct additional sub-structure analysis following Pocket2Mol. For the distribution of bond angles and dihedral angles, we evaluate Graph VF by KL divergence on the same benchmarks as Pocket2Mol. We perform extra experiments the distribution of bond length.
Results. The results are presented in Appendix D In comparision to GraphBP and Pocket2Mol, Vr yields the best results on dihedral angles, which indicates it is more capable at modeling complex dependencies. At the same time, it achieves compatible results on bond length and bond angles.
5.3 CONTROLLABLE GENERATION FOR SPECIFIED CHEMICAL SUB- SESSSTRUTTURSS
Our pretrained framework could be used to encourage the desired sub-structures to be generated without losing diversity. We carry out case studies on generation molecules containing the follow- ing motifs: oxhydryl, peptide bond, 6-member carbon ring, and 5-member ring containing element S. For each motif, we calculate (Jp.. Σp) among 500 randomly sampled reference ligand molecules that contain the motif as sub-structure. Finally, that contain the desired sub-structures on the test set, which is compared with the results of directly sampling from prior distribution N(0 T).
calculate the rate of the generated molecules
8

---

Under review as a conference paper at ICLR 2023
With the prior distributions collected from molecules that contain certain desired sub-structures, our model is more likely to generate ligand molecules with those sub-structures.
The experimental results are summarized in Table B
Table 3: Controllable Generation for Specified Chemical Sub-structures.
Rate of desired sub-structure( %)
w/ latent
w/o latent
oxhydryl
51.7
42.8
peptide bond
6.4
1.5
6-member carbon ring
14.5
0.3
5-member ring containing element S
29.7
0.4
5.4 CONTROLLABLE MOLECULAR GENERATION FOR SPECIFIED DRUG PROPERTIES
Our framework can also be explicitly controlled to generate drug-like molecules with desired prop- erties. To support this claim, we perform studies under two classical pharmaceutic settings:
1) Antibiotic Discovery (Stokes et al. 2020) This task aims to identify molecules that inhibit the growth of coli, a bacterium canonically used for testing antibiotic activity.
2) SARS Inhibition (Tokars & Mesecar (022). This task is identify molecules that inhibit the 3CL protease of SARS-CoV, the pathogen to respiratory pandemic during the 2000s.
For antibiotic discovery (likewise for SARS Inhibition), the inhibition scores all the reference ligands in the CrossDocked test set evaluated via pretrained ensemble model (Yang et al. 2019). We select the top 5% among them with the highest inhibition scores to calculate (Mpr Ep)
Results for the two studies presented in Table 4 which clearly shows that the latent P is effective terms of manipulating desired properties of the generated molecules.
Table 4: Controllable Generation for Antibiotic Discovery and SARS Inhibition.
Avg. Inhibition %)
w/ latent p
w/o latent
Antibiotic SARS
3.26
1.03
28.3
11.5
CONCLUDING REMARKS
We proposed GraphVF, a novel variational flow-based framework for controllable binding 3D molecule generation. We empirically demonstrated that, through effectively integrating 2D struc- ture semantics and 3D pocket geometry, GraphVF obtained superior performance to the state-of- the-art strategies for pocket-based 3D molecule generation. We also experimentally showed that, GraphVF can effectively generate binding molecules with desired ligand sub-structures and bio- chemical properties.
Our work here demonstrates that domain constraints can be effectively leveraged by deep generative models to improve the qualities of molecule design and fulfill the needs for controllable molecule generation. Our studies here shed light on the potential of generating binding ligands with sophisti- cated domain knowledge and finer-grained control over a variety of bio-chemical properties.

---

Under review as a conference paper at ICLR 2023
REFERENCES
G. R. Bickerton, G. V. Paolini, J. Besnard, S. Muresan, and A. L. Hopkins, Quantifying the chemical beauty of drugs, Nature chemistry, 4(2):90-92, 2012.
Junyoung Chung, Caglar Gulcehre, KyungHyun Cho, and Yoshua Bengio. Empirical evaluation of gated recurrent neural networks sequence modeling. arXiv preprint arXiv:1412.3355, 2014.
Laurent Dinh, David Krueger, and Yoshua Bengio. Nice: Non-linear independent components esti-
mation. arXiv preprint arXiv:1410.8510 2014.
Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio. Density estimation using real nvp. arXiv preprint 1605v 08803, 2016.
William J Egan. Predicting adme properties in drug discovery. Drug Design: Structure-and Ligand- Based Approaches, pp. 165-177 2010.
Paul G Francocur, Tomohide Masuda, Jocelyn Sunseri, Andrew Jia, Richard B lovanisci, Ian Snyder, and David R Koes. dinee-dimensional convolutional neural networks and cross-docked data set for structure- based drug design. Journal of chemical information and modeling, 60(9))4200- 4215, 2020.
A. K. Ghose, V. N. Viswanadhan, and J. J. Wendoloski. knowledge-basede approach in designing combinatorial or medicinal chemistry libraries for drug discovery. 1. qualitative and quantitative characterization known drug databases. Journal of Combinatorial Chemistry, 1998.
Juan S Gomez-Jeria and Andres Robles-Navarro. A note on the docking of some hallucinogens to the 5-ht2a receptor. Journal of Computational Methods in Molecular Design, 5(1):45-57, 2015.
Emiel Hoogeboom, Victor Garcia Satorras, Clement Vignac, and Max Welling. Equivariant dif- fusion for molecule generation in 3d. In International Conference Machine Learning, pp. 8867-8887, PMLR, 2022.
Wengong Jin, Regina Barzilay, and Tommi Jaakkola. Junction tree variational autoencoder for molecular graph generation. In International conference on machine learning, pp. 2323-2332. PMLR, 2018.
Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6966 6.800, 2014.
Diederik P. Kingma and Max Welling, Auto-encoding variational bayes. In 2nd International Conference on Learning Representations, 2013.
Yibo Li, Jianfeng Pei, and Luhua Lai. Structure- de novo drug design using 3d deep generative models. Chemical science, ((41):13664-13777 2021.
David Lide. Characteristic bond lengths in free molecules. CRC Handbook of Chemistry and Physics. CRC Press/Taylor and Francis,, 2012.
Meng Liu, Youzhi Luo, Kanji Uchino, Koji Maruhashi, and Shuiwang Ji. Generating 3d molecules for target protein binding. arXiv preprint arXiv:2204.0944 094400 2022.
Shitong Luo, Jiaqi Guan, Jianzhu Ma, and Jian Peng. A 3d generative model for structure-based drug design. Advances in Neural Information Processing Systems, 34:6229 6239, 2021.
A. T. McNutt, P. Francocur, R. Aggarwal, T. Masuda, R. Meli, M. Ragoza, J. Sunseri, and D. R. Koes. Gnina 1.0: Molecular docking with deep learning. Journal of cheminformatics, 2021.
George Papamakarios, Theo Pavlakou, and lain Murray. Masked autoregressive flow for density es- timation. In Proceedings of the 31st International Conference on Neural Information Processing Systems, pp. 2335-23320 2344, 2017.
Xingang Peng. Shitong Luo, Jiaqi Guan, Qi Xie, Jian Peng, and Jianzhu Ma. Pocket2mol: Efficient molecular sampling based on 3d protein pockets. arXiv preprint arXiv:2205.07249) 2022.
10

---

Under review as a conference paper at ICLR 2023
Danilo Rezende and Shakir Mohamed. Variational inference with normalizing flows. In Interna- tional Conference on Machine Learning, pp. 1530-1538, 2015.
Victor Garcia Satorras, Emiel Hoogeboom, and Max Welling, E (n) equivariant graph neural net- works. In International conference on machine learning, pp. 9323-9332. PMLR, 2021.
K. T. Schutt, P.-. Kindermans, E. Sauceda, S. Chmiela, A. Tkatchenko, and K.-R. Muller. Schnet: A continuous-filter convolutional neural network for modeling quantum interactions. arXiv preprint arXiv: /706. 170..08666..666. 2017.
Chence Shi, Minkai Xu, Zhaocheng Zhu, Weinan Zhang, Ming Zhang, and Jian Tang. Graphaf: flow-based autoregressive model for molecular graph generation. arXiv preprint arXiv:2001.09382, 2020.
Jascha Sohl-Dickstein, Eric Weiss, Niru Maheswaranathan, and Surya Ganguli. Deep unsupervised learning using nonequilibrium thermodynamics. In International Conference on Machine Learn- ing. pp. 2256-2265, PMLR, 2015.
Jonathan M Stokes, Kevin Yang, Kyle Swanson, Wengong Jin, Andres Cubillos-Ruiz, Nina M Donghia, Craig MacNair, Shawn French, Lindsey Carfrae, Zohar Bloom-Ackermann, et al. A deep learning approach to antibiotic discovery. Cell, 180(4))688-702, 2020.
Valerie Tokars and Andrew Mesecar. Qfret-based primary biochemical high throughput screening assay to identify inhibitors of the sars coronavirus 3c-like protease (3clpro), 2021.
Aaron Van Oord, Nal Kalchbrenner, and Koray Kavukcuoglu. Pixel recurrent neural networks. In International Conference on Machine Learning, pp. 1747-1756, 2016.
Lilian Weng. Flow-based deep generative models. lilianweng. github. io/lil-log, 2018.
C. G. Wermuth, C. R. Ganellin, P. Lindberg, and L. A. Mitscher. Glossary of terms used in medicinal chemistry (iupac recommendations 1998). Pure and Applied Chemistry, 70(5): 1229 199870051 1143, 1998. doi: 19981111//111999990001 129. URL
pac199870051123
Kevin Yang. Kyle Swanson, Wengong Jin, Connor Coley, Philipp Eiden, Hua Gao, Angel Guzman- Perez, Timothy Hopper, Brian Kelley, Miriam Mathea, et al. Analyzing learned molecular repre- sentations for property prediction. Journal of chemical information and modeling, 59(8)33300 3388, 2019.
Cheng Zhang, Judith Butepage, Hedvig Kjellstrom, and Stephan Mandt. Advances in variational inference. IEEE transactions on pattern analysis and machine intelligence, 41( 2018.
Jinhua Zhu, Yingee Xia, Chang Liu, Lijun Wu, Shufang Xie, Tong Wang, Yusong Wang, Wengang Zhou, Tao Qin, Houqiang Li, et al. Direct molecular conformation generation. arXiv preprint arXiv:2202.013566 2022.

---

Under review as a conference paper at ICLR 2023
Appendix
A DISCUSSIONS ON LIGAND SCAFFOLDS ENCODING
A.1 PARSING AND POOLING
There are types of canonical sub-structures, as are exemplified by the DMT molecule Figure
1) Rings, e.g. the blue, green nodes;
2) Non-ring covalent atom pairs, e.g. the red, yellow and purple nodes;
3) Pivot atoms that are connected to 3 or more items, e.g. the gray node.
The rules for identifying sub-structures is self-contained, yielding a relative sparse and stable set of vocabulary. A total of 427 canonical sub-structures are identified from the 100,000 reference ligands in the CrossDocked dataset.
Once the ligand molecule is parsed into compilation of sub-structures, the molecular graph can be pooled into junction tree in straight-forwart manner, where each sub-structure corresponds to tree node, and any two intersecting sub-structures yield edge between their corresponding nodes.
A.2 TREE GRU ENCODER
We adopt the same junction tree encoder architecture as Jin et al. (011)) Namely, the tree message passing scheme arbitrarily selects a leaf node as the root, and pass messages from child nodes to parent nodes iteratively in bottom-up approach. We denote the message from node to j as m.j. which is updated via GRU adapted for tree propagation:
myj- = GRU(x; (mi))ENN()))
(32)
To be more specific, the GRU architecture is formulated as follows:
Sij Σ maa-
(33)
Zij (W + U + b²).
(34)
Tki oWW',, U'mai + b").
(35)
m tanh Wx; +U Σ Fke ① m.))
(36)
KEN(M
my
2:j) Sig + Zij maj-
(37)
where x; is one-hot vector, indicating the type of canonical sub-structure of node i. The latent representation of each node h; can derived by aggregating all the inwards messages from its child nodes:
h = W +
Σ U'm
(38)
REN()
Finally, the structural encoding of the whole molecule is obtained by feeding hro through MLP. The resulting vector ΩR is split into two equally-sized dense vector (JuR, ER), which parameterize the mean and variance of an amortized diagonal Gaussian distribution A (HR ER):
(pR. ER) PR MLP(broa
(39)
It should be emphasized that all the parameters that appear in this section are trainable. Our earlier attempts with a pretrained version of GRU would result in a serious degradation the quality of generated molecules. Thus, end-2-end training of these parameters is ideal for achieving better model performance.
12

---

Under review as a conference paper at ICLR 2023
B ALGORITHMS FOR TRAINING AND GENERATION
The pseudo codes of training and generation algorithms are in Algorithms and
Algorithm Training algorithm GraphVF
Input: 7 learning rate, B batch size, maximum epoch number, Variational annealing hyperparam- eters Smins Smax, use Prod(-) as the product of elements across dimensions of tensor
Initial: Parameters 0 of Graph (Echnet, Junction Tree Encoder, and Node//Edge/PositionMM\P
1: for = 1, T do
2: 3 Smin + (Smax Bmin) sin? (m1
f-annealing acc. to epoch number
3: for b = 1,... B
4:
Sample a receptor-ligant pair from dataset, with receptor size and ligand size
5:
Protein receptor P = (V, F), where V = {(ā;, )=)) and E. {he J
12==1
6:
Drug ligand R = (V; F.,, where V {(as, r;) r:)] and F. = =(b;) [bbs)
7:
Re-order R with ring-first graph traversal
8:
(KR. Rx) = JT-Ennoder((R), where prior Z N N(RR, ER)
2D Global
9:
for i 1, .... .N do
3D Autoregressive
10:
Construct sub-graph 9 == T(P U R15-1)
11:
Construct SCS upon focal atom fi
12:
êI:M, ēI. = Echnet
b Encode 3D conformation
13:
(node)
+ u, (1, 1)d
Atom type dequantization
(node)
(oode) = Node-MLP(er.)
14:
(uode)
x (node) (node)
15:
nondy
16:
1:1-1.1
(bond)
b1:1-1,t +
4(0,1) 1) 1)xd
Bond type dequantization
(bond)
(hond) = -oond-ML((e.:: (node))
17:
11
0 11-1,
(boud)
(boud)
(bond)
1:1-1,2
X1:i-1,1
1i-i-1,1
115-1.
19:
(pos)
RBF (ri)
Spherize atom position to fa
14 (pos)
(pos)
Position MLP fo x
(node) (bond)
x11-1.3
21:
[os]
(pos)
(pos)
[pco]
22:
C (node)
log (rodd [N (node)
RR. ER])) log((Pod)
Gooday
(band) log( Prod (N (band)
23:
1á-13
MRR ER))) log( Prod
[ond)
1:1-1.t
24:
c (pos)
log(Prod([(zz) (pos)
URR ΣR))) logoProd
[pos)
25:
flow c (uode) + (boudd) c (pos)
cib
> Step-wise loss term for normalizing flow
26:
end for
CkL DRL(N ER),)
Global loss for variational distribution Z
28:
C N (EN filow) + BC
29:
end for
ADAM(E Ciotal: 0,1)
Parameter update
31:
end for
13

---

Under review as a conference paper at ICLR 2023
Algorithm 2 Generation algorithm of GraphVF
Input: T number of protein receptors, B number of drug ligands generate for each receptor, N maximum number of atoms in the generated ligand. Optional parameters (14p Ep) as the cue to certain desired property p. (0, I) by default.
Initial: Trained GraphVF model (Echnet, Junction Tree Encoder, and Note/Edge/Positioo-MLL.
1: for t I,, do
2: Sample a protein receptor from dataset, with receptor size M
LigGen, 3: Protein receptor P = (V, E), where V = {(ās, (e) and = (big (b1))
4:
5:
for = B do
6:
Drug ligand representation R == E), initialized as empty for i 1..... do
7:
8:
Construct sub-graph G (P U R15-1)
9:
ft = FocalClassifier((..
10:
if none eligible for fi then
D. Signal for generatioin complete
11:
break inner loop
12:
end if
13:
01:M; C1:N-1 = Echnet((;)
b Encode 3D conformation
14:
Sample
2;
(node)
(H Ep)
15:
(node)
(node)
Node-MLP((,,)
(node)
(node)
(nade) u1
(uode)
Atom type generation
17:
Sample
2 1,8-1,00
(hond)
N Ep)
(bond)
(hond)
Mond-MLP(e1ss-1 (node)
18:
11--11.5 1.a: 11-1,
19:
1,1-1,1
(bond)
1:i-1,i
(bond)
21--1,
(bond) + M1=-1.
(bond)
> Bond type generation
20:
Sample
(pos)
(ppp Σp)
(pos)
o; (pos)
= Position- Ciattion-MP((e,,,, (node) (bond)
21:
14;
x11
x (pos)
(pos)
(pos)
+ ue (pos)
22:
=
z;
> Atom position generation
23:
Derive (a;, r:) from (xx
((oodd)) x x(noa)); b1.5-1.8 from x
1
(bond)
24:
Vappend (1 ((r r;))); E.append( (fbra1,1))))
Autoregressive ligand generation
25:
end for
27: end for
end for
29:
return [igGen, LigGen,,... LigGeny)
C IMPLEMENTATION DETAILS
Network Architecture. We stack 6 layers of the Echnet and 20 layers of the tree GRU. We use 6 variational flow layers for generation.
Training Details. We train Graph VF for 40 epochs on the full training split by batch size 4. We use Adam optimizer while setting learning rate as lc-4 and weight decay as le-6, For the 3-annealing which is applied to the whole training process, we pick the minimum 3 as le-4 and maximum B as 0.015.
Generation Details. We sample 100 molecules for each pocket in the test set. Molecules that have less than 15 atoms are excluded and re-samlled, while molecules that have more than atoms are truncated the 50-th atom. Additionally, to help Graph generate ligand molecules with good geometric properties, we limit the sample space by three validity constraints during generation:
1. A bond exists between the newly generated atom and the focal atom;
2. At most other atom could be connected to the newly generated atom with bond.
14

---

Under review as a conference paper at ICLR 2023
3.
The newly generated atom could only have bonds with atoms that is predicted positive by the focal classifier.
Empirically, these constraints can help. We apply all validity constraints by default for all experi- ments. Specially, found that without constraint Graph VF could produce better results HA. So we removed that constraint only for that case.
D RESULTS ON STRUCTURAL ANALYSIS
(
(b)
(0)
Figure 4: Visualization of bond distributions. (a) CC Bond Length; (b) COC Bond Angle; (c) CCCC
Dihedral Angle.
Sub-Structure
GraphBP
Pocket2Mol
Graph (w/o 2D encoder)
Graph VF
CC
0.27
2.18
1.05
0.22
C=O
0.83
3.78
0.73
0.67
CN
0.70
1.78
1.27
0.77
CCC
1.31
1.02
1.07
1.25
CCO
0.61
1.38
0.52
0.51
NCC
1.00
1.05
0.62
0.83
CCCC
2.15
2.10
2.03
2.00
CCCO
2.37
2.27
2.17
2.17
CC=CC
2.20
2.85
2.70
2.04
Table 5: The KL divergence of the distance (upper part), bond angles (middle part) and dihedral angles (lower part) with the test set. Lowercase letters denotes atoms in aromatic rings. Best results in bold.
15

---

Under review as a conference paper at ICLR 2023
E VISUALIZATION OF PROTEIN-LIGANC INTERACTIONS
PHE339
HgC
NHz
N
CH2
HO
RHE234
SER159
ASP231
VAL
Serotonin
N.N-Dimetyytttypaanine (DMT)
(a)
Figure 5: (a) Comparison between Serotonin and DMT structure; (b) Binding pose of DMT with 2-HT2A, pay special attention the interaction between NHMe₂ and Asp-231.
OCPE-YEAST.W--6-- 1olp-A/tjmm-lyy
GRINI -1P---1-----------0 NNteAAidyy-rr
EMBR D-BUMAN--D---666 A27i-A-
UMBR E-RUUAANN D9--7--00 7
PIIA PTA--NRAANN----0000
Referuece Mokcala
322
4.99
3.36
3.55
4.65
Genorated Medecales
528
5.9
Figure 6: Examples of generated molecules with higher binding affinity (Gnina score than the reference molecules. Protein names and residue/ligand IDs are listed on top.
16


Reviews:
[{"review_id": "ux1BgR2QFx", "reviewer": "Reviewer_6f2G", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes GraphVF, a novel method for generating 3D ligand molecules that can bind to specific target proteins. GraphVF adopts junction tree based scaffold encoding and SE(3)-invariant geometry encoding during training, and a variational flow framework to sequentially generate ligands atom-by-atom. GraphVF achieves good performance in ligand generation and drug property targeted generation tasks.", "summary_of_the_review": "Though this paper presents an interesting method for controllable ligand generation and achieves good experimental performance, it has major issues concerning the motivation of using scaffold encoding, flow modeling, and bond generation. Hence, I vote for rejection and encourage authors to solve the critical issues in the revision.", "strength_and_weaknesses": "Strengths:\n\n(+) This is the work that first considers generating molecules with good drug properties in ligand generation, which is very meaningful and useful for practical applications.\n\n(+) The effectiveness of the proposed GraphVF method is demonstrated by good performance in various experiments.\n\nWeaknesses:\n\n(-) (major) The paper does not clearly motivate and explain the novelty contribution of GraphVF. The design of the generation process in GraphVF (use flow models to atom-by-atom generate ligands, generate 3D positions by distances, angles, and torsion angles) largely follows the existing method GraphBP [1]. To me, the only novelty contribution is to additionally encode ligand scaffolds with junction-tree based encoders. However, it is not clear why this scaffold encoding is used and important, since the ligand generation process does not include any junction-tree generation. It is strongly recommended to add detailed discussion to clarify the difference between GraphVF and GraphBP, and the importance of using scaffold encoding.\n\n(-) (major) It is not clear why a variational-inference-style flow model is used. As described in section 4.3 and figure 3, during training, the flow models output latent variables subjected to the Gaussian distribution $\\mathcal{N}(\\mu_R,\\Sigma_R)$, but in loss function (equation 14-16) the latent distribution is optimized to be close to the standard Gaussian distribution, and the generation process with flow models also sample from the standard Gaussian distribution. Then what is the advantage of this method over directly modeling the outputted latent variables as the standard Gaussian distribution during training? Is it specially designed for controlled generation targeted at good drug properties? It is better to provide more detailed explanation or clarification.\n\n(-) (major) At each generation step of GraphVF, the bonds between the new atom and previously generated atoms are generated. However, prior 3D molecule generation methods (e.g., EDM [2] and GraphBP) do not explicitly generate bonds, but infer bonds from the generated 3D conformations, and they evaluate the bond valency validity. Hence, why GraphVF does not follow this setting? Do the generated bonds match those inferred from 3D conformations? And if possible, could authors report the bond valency validity in experiments?\n\n(-) (minor) Tables and figures in the paper do not follow some frequently used style habits in academic papers. It is better to make Figure 1, 2, 3 at the top of the page like Figure 4, make caption of Table 2 before the table, and use three-line (with \\toprule and \\bottomrule at the beginning and end of the table) for Table 2, 3, 4.\n\n(-) (minor) The description about EDM in the first paragraph of section 2 is incorrect. EDM generates 3D molecular conformations from scratch, not from 2D structures.\n\n(-) (minor) In section 3.2, use $b_i^{lig}\\in\\mathbb{Z}^{i-1}$ instead of $|b_i^{lig}|=i-1$ to represent an integer vector.\n\n[1] Liu, Meng, et al. \"Generating 3D Molecules for Target Protein Binding.\" International Conference on Machine Learning. PMLR, 2022.\n\n[2] Hoogeboom, Emiel, et al. \"Equivariant diffusion for molecule generation in 3d.\" International Conference on Machine Learning. PMLR, 2022.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "VKvZr6QNg6", "reviewer": "Reviewer_uWFf", "summary": "", "questions": "", "limitations": "", "rating": 3, "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": "", "summary_of_the_paper": "A generative model generates molecules conditioned on a protein pocket, and optionally also conditioned on a reference molecule or some desired substructures. Atom types, bonds, and atom positions are generated one at a time using an autoregressive flow model.", "summary_of_the_review": "There is a good idea here, but the description of the implementation is hard to understand, and the evaluation is superficial.", "strength_and_weaknesses": "The key novelty here seems to be the idea of conditioning the generation of new ligands on the coarse-grained structure of a reference ligand, or on presence of some desired substructures, by sampling the latent z from a distribution that depends on the reference ligand or on the desired substructures. This is a good idea, but the implementation is not clearly explained, and the evaluation is somewhat lacking.\n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "1: The contributions are neither significant nor novel."}, "extra_text": {}}, {"review_id": "9tbdRCEpIL7", "reviewer": "Reviewer_Ruu5", "summary": "", "questions": "", "limitations": "", "rating": 1, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes to use generation flow to generate molecules with the control of 3D structure and 2D constraints and claims to outperform other methods.", "summary_of_the_review": "Overall, the idae is interesting for molecule generation. However, it's clearly unfinished work and should have more comprehensive experiments to support the claim. With just one evaluation metric, the results can be questioned by the readers as cherry-picked. ", "strength_and_weaknesses": "## Major comments\n\n1. In general, the idea is simple and easy to implement. It is a combination of JT-VAE, SchNet, Chemprop, and variational flow without much novelty.\n2. There are many evaluation metrics to show, e.g. QED, SA, LogP, but only high affinity is shown in Table 2. The claim is not convincing.\n3. In evaluation, the number of potential similar or duplicate molecules is not investigated. Also, the reported Pocket2Mol result is much lower than that in the original paper, which should be explained.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "1: The main claims of the paper are incorrect or not at all supported by theory or empirical results.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "4Od7Ow9PJE", "reviewer": "Reviewer_Mkbw", "summary": "", "questions": "", "limitations": "", "rating": 3, "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": "", "summary_of_the_paper": "A controllable 3D molecule generation framework named GraohVF is proposed, in particular, the proposed GraohVF is based on variational flow and integrates geometrical and skeletal restraints for protein target generation. \n", "summary_of_the_review": "Overall, this paper is hard to follow due to poor organization. Although the motivation for incorporating geometrical and skeletal restraints for controllable generation is novel and interesting, the proposed method is not technically sound. This paper should be highly polished to highlight the technique contributions and the connection of different components. \n\n", "strength_and_weaknesses": "Strength：\n\n(1) Incorporating geometrical and skeletal restraints for controllable generation is novel and interesting.\n\n(2) The experiment results demonstrate the proposed method achieves superior performance than the state-of-the-art methods. \n\nWeaknesses:\n\n(1) The writing of the paper is obscure. There are many notations used without explanation. The technique part of this paper is very confusing. Some equations about network structure can be put into the appendix. \n\n(2) The technique contribution of this method is not clear. It seems the core component of the method is same as existing methods, but the difference is not highlighted.\n\n(3) It seems that contributions 1 & 2 are the same to me. More elaborations about this are needed if I am wrong. \n\n(4) What do graph clustering and tree encoding refer to? The construction of the mean and variance $\\mu_{\\mathcal{R}}, \\Sigma_{\\mathcal{R}}$ for target proteins is very important for the whole method but is less discussed. \n\n(5) From Eq.14, Eq.15, and Eq.16, it seems the mean and variance $\\mu_{\\mathcal{R}}, \\Sigma_{\\mathcal{R}}$ about target proteins are fixed while optimizing the variational flow. If this is the case, the novelty of this paper would be straightforward. \n\n(6) It seems the whole method is highly correlated to GraphBP, thus the technique difference of these two methods should be discussed. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject