Functional-Group-Based Diffusion for Pocket-Specific Molecule Generation and Elaboration
Authors: Haitao Lin
Yufei Huang
Odin Zhang
Yunfan Liu
Lirong Wu
Siyuan Li
Zhiyuan Chen
Stan Z. Li
Venue: NeurIPS 2023 poster (2023)
Keywords: sturcture-based drug design; molecule generation; diffusion model

Abstract: In recent years, AI-assisted drug design methods have been proposed to generate molecules given the pockets' structures of target proteins. Most of them are  {\em atom-level-based} methods, which consider atoms as basic components and generate atom positions and types. In this way, however, it is hard to generate realistic fragments with complicated structures. To solve this, we propose \textsc{D3FG}, a {\em functional-group-based} diffusion model for pocket-specific molecule generation and elaboration. \textsc{D3FG} decomposes molecules into two categories of components: functional groups defined as rigid bodies and linkers as mass points. And the two kinds of components can together form complicated fragments that enhance ligand-protein interactions.
 To be specific, in the diffusion process, \textsc{D3FG} diffuses the data distribution of the positions, orientations, and types of the components into a prior distribution; In the generative process, the noise is gradually removed from the three variables by denoisers parameterized with designed equivariant graph neural networks.  In the experiments, our method can generate molecules with more realistic 3D structures, competitive affinities toward the protein targets, and better drug properties. Besides, \textsc{D3FG} as a solution to a new task of molecule elaboration, could generate molecules with high affinities based on existing ligands and the hotspots of target proteins.

Functiona--GroupBaseed Diffusion for Pocket-Specific Molecule Generation and Elaboration
Haitao Lin Westlake University
Yufei Huang Westlake University huangyufe ei @westlake edu. cn
Linhaitao@westlake edu. cn
Odin Zhang Zhejiang University
Lirong Wu
Westlake University
haotianzhangēzju. edu. cn
wulirong@westlake edu. cn
Siyuan Li
Zhiyuan Chen
Westlake University lisiyuanvvestlake wew.ttlaeeeeeuuu...... cn
Deep Potential
chenzhiyuanddp.cmm tech
Stan Z. Li
Westlake University
stan. 1i@westlawe edu. cn
Abstract
In recent years, Al-assisted drug design methods have been proposed to generate molecules given the pockets' structures of target proteins. Most of them are atom- level-based methods, which consider atoms basic components and generate atom positions and types. this way, however, it is hard to generate realistic fragments with complicated structures. To solve this, propose D3FG, f.functional-gree -roup-- based diffusion model for pocket-specific molecule generation and elaboration. D3FG decomposes molecules into two categories of components: functional groups defined as rigid bodies and linkers as mass points. And the two kinds components together form complicated fragments that enhance ligand-proteds interactions. To be specific, in the diffusion process, D3FG diffuses the data distribution of the positions, orientations, and types of the components into a prior distribution; In the generative process, the noise is gradually removed from the three variables by denoisers parameterized with designed equivariant graph neural networks. In the experiments, our method can generate molecules with more realistic 3D structures, competitive affinities toward the protein targets, and better drug properties. Besides, D3FG as solution to new task of molecule elaboration, could generate molecules with high affinities based on existing ligands and the hotspots of target proteins.
Introduction
The established notion in drug-target identification is that similar structures perform similar func- tions. This principle allows classical computer-aided drug design (CADD) to abstract protein-ligand interactions as pharmacophores, aligning similar functional groups and extracting pharmaceutical
"Corrsponiing Author.
37th Conference on Neural Information Processing Systems (NcurIPS 2023).

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information from these structures. Fitting suitable functional groups into the pharmacophores can enhance ligand proteen interactions, thus improving drug efficiency 2
Artificial intelligence has already achieved outstanding success in protein design 138 and thus led to new round of attention in drug design focused on Al-assisted drug design (AIDD). A number of methods of Al-assisted drug design on pocket-specific molecule generation are emerging [9H55) thanks developments in deep generative models [16-21] and graph neural networks (GNNs) 1222311 These methods usually focus on atom-level generation, which first generates atom types and positions and then assembles atoms into molecules that can bind to the protein pockets. Although significant progress has been made, they are still weak in two aspects. For one thing, it is hard for them to generate realistic functional groups that contribute pharmacological effects the target as classical CADD methods are able to. It is shown that generating benzene rings is uncommon compared with the reference molecules, not to mention some large functional groups with complex structure constraints such as purine, indole, etc (Table. [ in Sec. 5.2). For another, trade-offs between efficiency and sufficiency of protein context place them in a dilemma. For example, TA TIFGETDIFF [3] employs sufficient protein context, which disassembles the amino acids into atoms, but leads to inefficiency due to a large node number (412. 14 on average) in GNN's message passing. DIFFSBD [4] simplifies the representation of protein context, by only using C. 's positions and residue types, resulting in a reduction of GNNs' node number (68.10 on average) but the insufficiency of context information.
To address the above issues, we establish Lunctional-groupy grou---oouuuuddedd diffusion model (D3FG), including the following contributions: 1. Method Novelty. We denote the molecules' functional groups and proteins' amino acids as the same level's fragments, in which the intra-relative positions of atoms are fixed like rigid bodies, and represent single atoms as linkers. The positions and orientation of local structures and the atom type variables are generated gradually through denoising processes. The fragment-linker designation leads the binding systems to heterogeneous graphs, and thereby, two schemes are proposed as solutions, which achieve competitive performance in terms of molecule structures, binding affinity, and drug properties, and sufficiency in encoding protein context by employing more features. 2. Dataset Establishment. Though the CrossDocked2020 [2] has been a widely-used dataset for evaluation methods' performance on the task, the analysis of the molecules' functional groups of it is missing. We deeply explore the details of the inter-relative positions and types of functional groups of the molecules and establish extendable database of common functional groups. 3. New task. Besides molecule generation, we propose molecule elaboration as another task that our model can fulfill. Fragment hotspot maps (FHM) 33 3 used to preprocess paired proleie- in CrossDocked2022 for the task. As a result, our model generates molecules with high binding affinity based on the reference.
2 Problem Statement
For binding system composed of protein-molecule pair (also called protein-ligand pair) as C, which contains Naa amino acids of proteins and Nig functional groups and Na single atoms of molecules, we represent the index set of the molecule's s single atoms as Iat, functional groups as Itg- and the protein's 's amino acids as Tas, where [Zgl = Nig. [Iae| = Nat and [Zaal = Naa. Note that a molecule can be disassembled into functional groups and single atoms other than functional groups, which we also call linkers. For protein, the amino acids can be represented by its type, C. atom coordinate, and the orientation, denoted as 8; E (1...., 20}, n; E RR3 O, E SO(3), where E Ian- For molecule, assuming there are Mfg and Mat possible types in total functional groups and linker atoms respectively, the functional groups can be represented as the three elements if the inter-relative positions are fixed, as 5j. 3jj and O,, where 8; E [21,... 21 + Mfg is the type, 2; E R is the predefined center atom's 's coordinate, and O, E SO(() can also be obtained in the same way as amino acids (See Sec. and Appendix. D) for j Ingi And its linkers can be represented 8k, 2& and Og, with s E [22 + Mig...., 22 + Mig + +Mau) k E Iat and O = diag 1, 1, 1} =
Therefore, C {(s, xi, O,)) Nm. N Noa can be split into two sets as C = P U M, where P = [(*,, x; 0.) : E Ian) and M a(, O,) j E Irg U For protein-specific molecule generation, our goal is to establish a probabilistic model to learn the distribution of molecules conditioned on the target proteins, i.e. p(M[P). In the following, we omit E Ima and j E Lgg Lat by default unless specified.
2

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3 Related Work
3D molecule generation. Previous methods on molecule generation fucus on ID-smiles-string In recent years, more works concentrate on 3D molecule
[35-38] or 2D-molecule-graph [3-45] 4
generation, thanks to fast development in equivariant graph neural networks [44 and generative models [16-21]. Molecular conformation generation aims to generate 3D structures of molecules with stability, given 2D molecule graph structure, [47/5T]. Further, De novo molecular generation attempts to generate both 2D chemical formulas and 3D structures from scratch [52
Fragment-based drug design. Previously, works on fragment- based molecule generation are proposed. For example, JT- [55] generates tree-structured scaffold over chemical substructures and combines them into a 2D-molecule. PS-VAE [56] can automatically discover frequent principal subgraphs from the dataset, and assemble generated subgraphs as the final output molecule in
2D. Further, DEEPFRAG (57] predicts fragments conditioned on parents and the pockets, SQUID [58] generates molecules fragment level conditioned on molecule's 's shapes. FLAG [59] auto- regressively generates fragments as motifs based on the protein structures in 3D.
Structure-based drug design. Success in 3D molecule generation and an increasing amount of available structural data of protein and molecules raises scientific interests in structure-based -based drug
design (SBDD), which aims to generate both 2D molecule graphs and 3D structures conditioned on
target protein structure as contextual constraints. For example, LIGAN [60] and 3DSBDD [12] are grid-based models which predict whether the grid points are occupied by specific atoms. By harnessing 3D equivariant graph neural networks, POCKET2MoL [9] and GRAPHBP [10] generate atoms auto-regressively and model the probability of the next atom's ' type as discrete categorical attribute and position continuous geometry. FLAG[59] is also fragment- based, but still generates motifs in an auto-regressive way. Recently, utilizing the diffusion denoising probability models 66 53 64] series of SBDD methods generate ligands conditioned on the target pockets at full
atom levels 13 13
4 Method
D3FG firstly decomposes molecules into two categories of components: functional groups and linkers, and them use the diffision generative model to learn the type and geometry distributions of the components. In this section, we describe the D3FG by four parts: (i) the diffusion model as the generative framework, in which the three variables generated; (ii) the denoiser parameterized by graph neural networks, satisfying certain symmetries so that the generative model is SE-(3) invariant; (iii) the sampling process in which the molecules are generated by the trained models; (iv) the further problems resulted from heterogenous graph with two solutions.
4.1 Diffusion Models
Diffusion models construct two Markov processes learn the data distributions. The first called the forward diffusion process adds noises gradually until the noisy data's distribution reaches the prior distribution; The other called the generative denoising process, gradually removes the noise from the data sampled from the prior distribution until they are recovered to the desired data distribution. Assume there are T steps in both processes, and we denote M {(s}. x²j. } as the t-th
noisy state in the forward process, with MT ~ Prior(M""). and M .M, where the transition distribution is denoted as q(1-:); In the generative process, sample goes from T to 0, in which the transition distribution is denoted as p(-1-). Here we define the forward and generative processes of s). z³. and O
Absorbing diffusion for functional group and linker types. Let s as the one-hot encoding of the type of a single functional group or linker. The forward process followed by D3PM (65] randomly transits of into the absorbing state K (K- 23 Mi + Mar) with
{( (0 4-1 = Multinomial (s/-1Q))
(1)
(( (s))11))
Multinomial (sQ
3

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Division Mergence
Joint Scheme
Initial Distribution
bilusion
o....
0_ Unifomm
Two-stage
Oflusion
4 x
of M(
(.,
of M(u.)
Abcaroting Type
(.)
0 Uniform
Commrationn
Figure 1: An illustration of the workflows of D3FG of the two schemes.
where Q' Q²Q² ... Q' and [Q'Imn probabilities, with
a($)
=1ss]=
m) denotes diffusion transition
m
[Q')
1
3
m = n # K
(2)
type
type
if m # K K
Ptype monotonically increases from 0 to I, means that when t = T. all the type variables are absorbed into the K-th category. In the generative process. it first samples Nat linkers and Nis functional groups whose types are all in the absorbing states, selects (1 - 0 Stype) x 100% of them respectively, and transforms their types from the absorbing states the predicted ones by
p(s 1 IM', P) = Multinomial (F(M',
where F is the type denoiser parameterized with neural network, and :() predicts the probabil- ity of the types for the j-th selected functional groups linkers. With the effectiveness of BERT-style training [66], the denoiser directly predicts p(s M' P), leading to a training objective as
Laype
EMt Σ Loggp(s3IMM.
Gaussian diffusion for center atom positions. By defining the center atom in functional group as shown in Appendix. D and itself as the center in a linker, the Cartesian coordinate of center nodes æy represents its position. The forward transition distributions followed by DDPM [6]] read
u(attar = =N
-N(2; (ar)
Bpos arj :ppo!
(5)
a<</|=)) = N (2iiy /apos 2)), (1 apca)
in which ot.s increases from 0 to 1, means that the noise levels are increasing and the data's 's coordinate
signals fade out during the forward diffusion. with apos 1 Bt afpce = ap a aposs and
finally x (). Note that Eq. (5) is equivalent to the Markov process of æ / aappe x/
T pos Ej. where E, ~ (0 r). Rather than predicting the mean value of the reverse transition distribution in the generative process, the position denoiser G approximates the added noise E, with the reparameterization trick as
p(z MM' P) = Nx, (M'" (), P). I)
1
gt
(6)
(M'
x
G(M ,M][
Vapos
á pos

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The training objective is thus established in acore-based way, as
EIGGM P)L c
Lpss Ex
SO(3) diffusion for functional group orientations. By regarding the functional groups as rigid bodies, orientations together with the center atoms' positions determine all atoms' positions. Here we represent the orientation geometry as elements in SO(3). Following [67], we use isotropic Gaussian distribution on SO(3) [68] to formulate the process, i.e. IG s- Mor: oori), ) in which Mori and ozi are viewed as mean orientation and variance, in analogy with Gaussian distribution. The transition distribution for orientation matrices O2 reads
q (0)109) =03) (O) O1), (1-) dor)),
(8)
aari orl+ O is the geodesic flow from I to O by the amount o as Aori 09) exp (a'n log (D)),, where exp(-) and log(-) exponential and logarithm map the SO(3) man- ifold. As ori + 0, Aori ( 09) - I. { the predefined noise level schedule ranging from 0 to 1 as t increases, anii = fhr and d = o lani...ag ...a..i-
In the generative process, an orientation denoiser H is used to predict the mean orientation in the isotropic Gaussian distribution, which reads
PO = I9
(H
(9)
We use the same loss function in [69 to minimize the expected discrepancy measured by the inner product between the data orientation matrices and the predicted ones, which reads
[IIT0O PMDDO 1
T. = EM:
(10)
4.2 Parametrization of Denoisers with Neural Networks
Amino acid context encoding. order to decrease the computational complexity, we denote the protein context at amino-acid levels. Besides the amino acid types, C. atom coordinate and the orientation, each atom's coordinates in the local system and three torsion angles including angles around 'N-C," bond, 'C.-C" bond and 'C-N' bond, are also used as intra-amino-ach features, which are concatenated and embedded by an MLP to create the intra-amino-acio embedding vector e; For inter-amino-ace features, the pair of amino acid types, sequential relationships (if the two amino acids are adjacent the protein sequence), pairwise distances between C2 and inter-residue dihedrals are all embedded inter-amino-ee amino-acii acid embedding vector 21,, with i, Iaa. Note that these embedding vectors are all translational and rotational invariant (Appendix. C
Denoisers with equivariance. In the setting of generative models, the learned distribution p(M[P) should be equivariant to translation and rotation, such that ((T,(MM)TT,,P)) 9 SE(3), where Tg is the corresponding oto-translltional transformations, and T (M) means each atom in the molecule is rotated and translated by Tg. In the setting of diffusion models, the following proposition indicates the translational and rotational equivariance of each denoisers.
P(M(P (P) for any
Proposition 1. Let p(x")) TT) p(OT), and p(s"") be SE(3)-invariant distribution, and the transition distributions p(æ= -1 [M P) be SE(3)-equivariant, p(O'-1 MM P) be T(3)-invariant and SO(3)- cquivariant, and pss |MM be SEv3)-invariant, then the density p(MlP) modeled by the reverse Markov Chains in the generative process of diffusion models is -Equivqquvariaat..
According to the Proposition 1, while the denoisers for functional group and linker types are roto- translational invariant, the denoiser for positions should be roto- translational equivariant, and it for orientations should be translational invariant and rotational equivariant. Therefore, we employ our denoiser's s network structures with IPA 3 by harnessing the expressivity of TRANSFORMER [70] and loto-translational equivariance of LOCS 77 Denote the binding system as a graph, in which the nodes composed of amino acids, functional groups, and linkers, and the edges established with
5

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Algorithm Joint Generation for Molecules using D3FG
Input: Zero-centered protein {8:; Ri, OiJigTua and graph denoiser F, G, H, and node number sampler Olig Dat-
Sample Nig ~ &lg Nat ~ Pat. leading to the index set Igg and Tss.
Sample initial states of functional groups, {s} 33 Djizeuuu where s) = K, x] ~ (0, I).
O Uniformso(3) for j E Itg else Oz I. for t in T - 1.T
1-1 -2..... do
Sample {s} 2 O JEITL IIa as Eq.
3 (6
and (9) and update M
end for
Output: M = {69. ag.. 0 JET
K-nearest neighbor. Let (h, E Taa U Igg Uas) } be the node embedding which is SE(3)-inariiant, (e, : E Taa U.2 UTaae] } and [z., : i,j E Iaa Uig U be the previously defined intra- and inter- amino acid embedding, with e; = 0 and z1,5 0 if Ian or j $ Ian The attention mechanism in IPA updates the embedding of node as
i1= E exp JEN(S) ESENO) exp
+ =.)) + 2,,)
(11)
where e h; + e;, h is the updated node embedding. Wg W W. are learnable parameters, and (i) is neighborhood of node i obtained by the edges. Because h; es and ži, are all SE(3)- invariant, h' ulso invariant. Three heads parameterized with MLP are stacked after several layers of Transformers update the node embedding, denoted by MLPx(-), (L) and ML.P (.) is used
for updating 8/-1, (x111 and 0 The LOCS updates the parameters in Eq.
(6 and (9 by
F (M', P) [s] = MLP (hl)
(M', P) [5] = MLP c (h²))
(12)
H (M',P) [i] exp (MLPH(h))))
The output of G means predicting the coordinate deviations in the local coordinate systems and then projecting it into the global one; In H, MLP,, y first predicts a vector in Lie group so(3) and the exponential map SO(3) converts into rotation matrix. The updating process ensures the equivariance and the invariance of the transition distributions in Proposition 1, which is proved in 7 and [69] However, since O for any E Iac. the equivariance of G' on linkers will not be preserved, so we instead use EGNN 44 to get the output of G' (Appendix.
4.3 Sampling Process
In sampling, we first use two prior distributions as the empirical distributions dat and dity drawn from the training set to sample the linker Nat and functional group number Nig. As p(x") p p(O")
and p(s²) should be SEE())invariant, p(s") 1 ((K)((²)) p(x") Ni=" |0, I) and p(0 Uniformsora)) (OT) satisfy the conditions, where 1-))) is the indicator function and Uniformsora) (.) the uniform distribution on SO(3). And the iteratively generative process of p(s P).
p(a' P) and p(O' P) are given in Eq. (3) (6) and 9 The detailed sampling algorithm is given in Algorithm.
4.4 Heterogeneous graph: Joint or Two-stage?
Amino acids and functional groups are both fragments composed of atoms in proteins and molecules, regarded as rigid bodies, while the linkers are single atoms, regarded as mass points. Therefore, in of different kinds, thus leading
the binding graph, nodes of different levels and connections the graph to be heterogeneous. For this reason, we propose two generative schemes: joint generation scheme and two-stage generation scheme as shown in Figure. [
In joint scheme, we regard amino acids, functional groups, and linkers at the same level, and use one single neural network to predict the three variables and update them. In detail, this scheme directly

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models p(M = p(f3;, I, Os OsIvez,, UZ. P),, where the parameterized transition distribution is - 0f P). Note that O I for any t if E Iat-
In two-stage scheme, we regard amino acids and functional groups at the fragment level, and linkers at the atom level, and use two different neural networks to parameterize the transition distribution. the first stage, the functional groups are generated, and then single atoms as linkers will be generated to connect the generated functional groups as full molecule. The two-stage generative scheme is similar to CADD, which first determines the pharmacophores towards the target protein, fits functional groups with high activity into them, and then searches for the possible molecules with these functional groups. In specific, the generative process reads p(M(P) = p( ((85,, Ty jezz. St, Li, Oz) P)p( (si, Z;; Orhiez
IP). The transition distribution of the first stage pl (8/ ((6--1, _,/1, he |6], att Oi P) is parameterized by one neural network; In the second stage, the generated {st, 21, OrJien, is used as context, so that the other neural network models a hez.. af1s, aiheIA (sr, 2i Oz)iezyy
5
Experiments
5.1 Data Processing.
In the experiments, on generating molecules at the atom level, differing from our functional functional--roup-buee grooup-bbseeddd generation, so our first target is divide the molecules into functional groups and linkers. We use EFGs [72) to segment molecules. We select the 25 functional groups that appear most frequently with stable structures, which are partly shown in Figure. For some functional groups, chirality exists in their structures, and we treat them as two functional groups. As a result, we finally build up dataset as a corpus including 27 functional groups (two of the 25 have chirality) for Crossdocked2020, with their intra-structures fixed as rigid bodies, and assure that most molecules can be decomposed into the substructures in our corpus datasets. Details are given in Appendix. [D] For linkers, we choose {B, C. N, O, F, P, CI, Br, I} as representative heavy atoms. After the processing, we obtain Mg = 27 and Mat = 10 in our experiments. Besides, by the fragment-linker designation of a binding graph, the node number is reduced to 53.62 average in GNN's message- passssgg.....ng.....
CrossDocked2020 (2) for evaluation. In the prevailing works, they focus
5.2 Pocket-Specific Molecule Generation
Dataset. The datasets for training and evaluation are split according to POCKET2MOL 9 and TARGETDIFF 13. 22.5 million docked protein binding complexes with low RMSD ( < 1Å) and sequence identity less than 30% are selected, leading 100,000 pairs of pocket-ligand complexes, with 100 novel complexes as references for evaluation.
Setup. For performance comparison, our methods are compared with basclines including LIGAN 60
3DSBDD [12). GRAPHBP [10). POCKET2MoL [54], DIFFSBDD [14] and TARGETDUFF
LIGAN as 3D CNN-based method generates atoms on regular grids, with VAE 773 as its generative model. 3DSBDD, GRAPHBP and POCKET2MOL are all GNN-based, generating atoms in an auto regressieee way. DIFFSBDD and TIRGETDIFF are two diffusion- methods that generate molecules at the full atom level, with equivariant GNNs the denoisers. The two schemes of generation lead to two variants of our method, written as (3Fn())int) and (SaGeSt In some parts, we choose POCKET2MOL. the representative autoregressive methods, and DIFFSBDD and TARGETDIFF as the benchmarks employing diffusion models, because these three baselines are the
13
clocecel
NC-6
C-CO
<leence)
clncc2ndoM):221
MH2
HO
Figure 2: Five of twenty-five functional groups with stable structures that occur most frequently in Crossdocked2020 and are used in D3FG.
7

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Table 1: 'Ratio' of the top ten functional groups with the highest frequency in Crossdocked2020..
'Ref.' is calculated in the training set. MAE is obtained between rows of 'Ref.' and different methods
'Ratio' and ISD is calculated by 'Freq'. which is in detail given in Appendix. F 'Ratio" in bold means
is the closest to 'Ref., and MAE/JSD bold means is the lowest.
Functional Group
Ref.
PoCKET2MoL
TARGETDIFE
DIFFBBD
D3FG (Joint)
D3FG (Stage)
cloceecl
0.712
0.583
0.293
0.131
0.548
0.608
NC=0
0.266
0.089
0,149
0.010
0.120
0.159
O=CO
0.216
0.200
0.320
0,025
0.226
0.127
cleenee1
0.082
0.086
0.052
0,001
0,040
0.078
el 2n
0.061
0.001
0.000
0.000
0.002
0.030
NS(=O)=O
0.055
0.000
0.000
0.001
0.001
0.001
O=P(OXOjO
0.040
0,004
0.000
0.011
0.015
OCO
0.034
0.001
0.067
0.075
elenenel
0.032
0.010
0.015
0.000
0.003
0.013
clen[nH]el
0.029
0.013
0.002
0.000
0.004
0.006
MAF (L)
0.030
0.045
0.071
0.024
0.020
JSD(L)
0.248
0.301
0.553
0.223
0.201
Table 2:
Jensen-Shannon divergence between the distributions of bond distance for reference vs.
generated molecules. The smaller, the better. Value in bold is the lowest.
Bond
LiGAN
3DSBDD
PocKeT2MoL. TARGETDuFF
DirSBDD
D3FG (Joint)
D3FG (Stage)
C-C 0.599
0.424
0.416
0.346
0.385
0.339
0.281
C=C
0.665
0,545
0.516
0.503
0.565
0.485
0.469
C-N
0.631
0.424
0.401
0,299
0.421
0.307
0.313
C=N
0,742
0.671
0.628
0,547
0.569
0.530
0,523
C-O
0.656
0.547
0.445
0.408
0.413
0.412
0,406
C=0
0,662
0.638
0,532
0.467
0.541
0.490
0.488
cic 0,494
0,410
0.398
0.264
0.339
0.327
0.302
c:
0.634
0.443
0.457
0.228
0.260
0.246
0.237
latest works that show good empirical performance. We sample 100 valid molecules for each pocket for the baselines and D3FG, leading to 10,000 pairs complexes. After the molecules are generated by the model, Dpenbabel [74] is used to construct chemical bonds between atoms, and Universal Force Field (UFF) minimization [75] is used for refinement. The following evaluations are based on the samples. Figure. givess example of generated molecules by different methods.
Structure analysis. We first analyze the functional groups of generated molecules by different methods. We show the 'Ratio' and 'Freq' of the included functional groups partly, where 'Ratio' means how many specified functional groups in each molecule average, and 'Freq' means the statistical frequency of occurrence of the specified functional group in the generated molecules. Mean absolute error (MAB) overall metrics is calculated according reference 'Ratio' and generated "Ratio"; Jensen-Shannon divergence (JSD) is calculated according to reference 'Freq' and generated "Freq"- The smaller MAE and JSD are, the better performance the method achieves. Table. [ shows the metrics of different methods' generated molecules, demonstrating D3FG's superiority in generating molecules with realistic drug structures since distributions of the functional groups in generated molecules are more similar to the real drug molecules'. Secondly, we analyze the atom type, bond distance, bond angle, dihedral and atom type distribution. JSDs calculated between the distributions of bond distance for reference vs. generated molecules. "-' "=',":" represents single, double, and aromatic bonds, respectively. Besides, we report MAE on reference 'Ratio' vs. generated 'Ratio' and JSD on reference 'Freq' vs. generated 'Freq" based on atom type distribution. Table. and Figure. gives details atom type analysis. For other geometries, please refer to Appendix. found that (SFagSt) outperforms D3FG(Joi in generating more realistic molecules, and has competitive performance with TARGETDIFF.
Binding affinity. We secondly make comparison Binding Affinity. Following 3DSBDD and LIGAN, we employed two evaluation metrics including Vina docking score [76] and Gnina docking score [77]. Vina docking 78 as a classical docking tool, gives a lower score as Vina energy the docking tool,
binding affinity of the molecule is better, while Gnina docking as deep-learning-basee gives it higher score. Affiiiiy measures the percentage of generated molecules that have better predicted binding affinity than the corresponding reference molecules. Table. shows that our D3FG

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PederpMall
Toperti
Method
MAE(L)
JSD(4)
Danoge D3fGtsmmel
POCKET2MOL
0.573
0.098
0231 C.1 sills
TARGET
0.059
Frequency
DIFSBEDD
0.627
0.054
D3FG(Jeint)
0.528
0.075
D3FG(Saage)
Table MAE and JSD of dif- ferent methods' atom type num- ber and distribution vs. the ref- erence. Values in bold are the lowest.
Atom Type
Figure 3: Atom type distribution and metrics.
Table 4: Evaluation Binding affinity and other chemical drug properties for baselines and variants of D3FG. & means the smaller the value, the better the performance, and means the opposite. Values in bold are the top-2 best metrics.
Vina
Vina Afffinity (1)
Gnina Score (f)
Gnina (tfliity((t)
Score (1)
QED (t)
SA (t)
LogP
Lipinski (1)
Ref. (Test)
-7.06
5,37
0.471
0.725
0.818
4.247
LIGAN
-6.17
21.24%
4,29
21.68% %
0.382
0.584
-0.138
4,046
GRAPHIB
-6.36
27.41%
4.52
26.54%
0.437
0,502
3.024
4.448
3DSBDD
-6.12
20.73%
4.48
19.22%
0.426
0.625
0.266
4.735
POCKET2MOL
-6.92
45.86%
5.34
40.68%
0.543
0.746
1.584
4,904
TARGET
-7.11
49.52%
5,41
42.40%
0.474
0.581
1.402
4.487
DIrSBDD
-6.37
31.32%
4.63
27.96%
0.494
0.343
-0.157
4,895
D3FG (Join))
-6.89
37.32%
5.30
33.45%
0.507
0.832
2.796
4,943
D3FG (Stage)
-6.96
45.88%
5,43
43,36%
0,501
0.840
2.821
4.965
D3FG (EHot)
-7.19
51.78%
5.51
56.53%
0.482
0.731
0.814
4,330
D3FG (ECold)
-7.02
44.03%
5.16
32.69%
0.476
0.707
0.820
4.228
of the two-stage scheme achieves competitive affinity scores, comparable to TARGETDIFF and much better than D3FG of the joint scheme.
Drug property. Moreover, chemical properties evaluated with RdKit (79,, including QED 80 (quantitative estimation of drug-likenn (rug-likeness). SA [81] (synthetic accessibility score), LogP 82 (the octanol-water partition coefficient, which should be between -0.4 and 5.6 for good drug candidates), and Lipinski [83 84) (number of rules the drug follow the Lipinski's rule of five). QED, SA, and Lipinski are three metrics with preferences for atom numbers, demonstrated in DIFFBP Table. demonstrates that two variants of D3FG achieve overall best performance in these metrics.
Ref.
(b) D3FG (Stage)
(c) D3FG (Joint)
(d) DIFESBDD
(e) TARGETDIFF
(1) POKECT2MOL
Figure 4: Generated molecules by different methods on pocket 3o96 @o96_A_rec. The diffusion-based methods generated molecules more similar to the reference, appearing to be 'vertical'.

---

5.3 Pocket-Specific Molecule Elaboration
Introduction. Molecule elaboration as sub-task of molecule optimization, aims to elaborate fragment of existing molecules amenable to chemical modification for improving binding affinity. To fulfill we here first select functional group in a ligand that contributes to binding affinity and remove it to obtain the editable fragments. Then, we attempt to use D3FG to generate the new type of functional groups with its structures, for modifying the fragments and thus building up new molecule with higher binding affinity to the target protein.
Dataset. The selection of a functional group for replacement the first problem. Pharmacophoric information is extracted by calculating the fragment hotspot map (FHM) 33 34 of the target protein. In specific, FHM describes regions of the binding pocket that are likely to make a positive contribution to binding affinity. Then, by placing the molecules into the pockets, we can thus obtain each functional group's ss hotspot scores, according to the binding complexes. The higher hotspot score functional group reaches, the more contributions it makes to the binding affinity. Functional groups' hotspot scores of each ligand are calculated based on 100,000 pairs of pocket-ligand complexes in Crossdocked2020, and the selection of functional groups be based on their scores. Finally, established our new datasets for molecule elaboration based on FHM.
Binding affinity and drug property. We here consider two schemes for molecule elaboration, the first is to remove the functional groups with the highest scores, and elaborate the remaining fragments by replacing them with the functional group generated by D3FG. We write this D3FG(EHot). The second (FFG(E,,, on the other hand, replaces the functional groups of the lowest scores). We report the D3FG's elaborated molecules by the two schemes in Table. It shows that D3FG(EHot) tends to generate more molecules with higher affinity, while molecules elaborated by D3FG(ECold) show tiny differences in binding affinity from the raw references. Besides, on other chemical properties, the elaborated molecules are very close to the raw references, since the differences lie only in single functional group, and the major molecular skeletons are almost identical.
6 Conclusion and Future Work
In this paper, functional-group-baan diffusion model called D3FG is proposed to generate molecules in with protein structures as its context. Joint and two-stage generation schemes lead to two variants of D3FG. The molecules generated by the two-stage generation scheme show more realistic structures, competitive binding performance, and better drug properties. Besides, in molecule elaboration, D3FG can also generate molecules with good binding affinity. However, limitation still exists. First, the functional group datasets are still small, which will be enlarged the future. Second, the binding affinities of generated molecules still remain to be improved, since other diffusion models even show better binding performance.
Acknowledgements
This work was supported by National Key R&D Program of China (No. 20222D0115100, National Natural Science Foundation of China Project (No. A214277,, and Project (No. WU2022A009) from the Center of Synthetic Biology and Integrated Bioengineering of Westlake University.
10

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15

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Note that A Proof of Proposition 1.
First, we here denote all atom's positions in the molecules as XM E R.x.x3 and in the protein as XM E X and linker and functional group type as SM ( one functional group may contain several atoms so that Naa Nig < Na.
SE(3) group roto-translation group in R&, can be divided into two groups: SO(3) the rotation group and T(3) as the translation group. For a E R and g = + with g E SE(3), r E SO(3), o E T(3), Tg (z) T (x) = T, (x)
Lemma A1. If the The equivariance and invariance the distribution in the reverse diffusion process are listed as
= (X S/ Xp, Sp) p (T M [T,, TXp)) -
p -
= ( X M Sh. Xp, Sp)
(13)
p (S M [T (X)) S (xp), ( X S X Sp)
Then (X M: S/ Xp. Sp) is SE(3) invariant. Proof. Since T gg(M) = {S, (x(M)) we can write the joint generative process as
p P(T SM (Xp)),
= =f (T S Sp)
T-1
Il t=0
(T Sh. T (X), dMo.T-1
p
/ / SMI Xp, Sp)
II (T
S IT, Sh. TX(P), dMMO:-1
T
= / p (X SMi Xp, Sp)
(T, (M, (S IT, P)) a.
= =ʃ p (X Shi Xp. Xp. Sp)
T-1
II
IM
P MMM P) aMO.--1
M
t=
= =f p (X S/ Xp, Sp)
II
(X
1-1 M
- Mr S. Xp, Sp) dMo-T-1
1=0
=p M.. SM Xp. Sp)
(14)
Then, let's consider single atom's position. We here denote each atom's 's anjs
IMM a'c + o
(15)
where & is the defined center atom's position in the functional group, øt is the relative position of the atom in the local coordinate system centering at o O is the rotation matrices of the local coordinate system with respect to the global system. Moreover, because the functional group is regarded as rigid bodies, 2/. = æR is constant. To be specific, if œ refers to linker's position, 0% O.
Proposition A2. If each atom's relative positions in the local coordinate systems are fixed, and p( |MM IIM', P) is -quiivaauv and p(O - 'MM', P) is squiivaana and T(3) i(3)-invariant, such that p "I) (M')P) (M'', P)) p p "IMM, P)) and p (T, (IT P))
p (0% ( where r 80(3), E T(3),r + = g E SE(3), then p( |M* MM,P) P) SO(3) -quivvaquiaa
Proof. According to the convolution formula in probability theory, if u + u, then
/ plu, w u)du = / p(w- v)d
p(w)= =
(16)
16

---

By using the Eq. 16 we can write every single atom's 's position density function as
p p (M'
=P (06 I
/ (xto a''i'' - MM', P) dx
(17)
/ (a6 M'' (a al IM' PM da
Since and
p (T (T, (M', P)) = ( MM' M P).
(18)
p PTT IT (M P)) = p (0 IMM P).
(19)
We can obtain that
(T 1-1 TT P))
= (Tn (M (M')
1 p (T. (M, P1)
(20)
1 p p (0 P)
DR
=p (2 M P)
-p (a<h
MM P)
Therefore, according Eq. T8
20), and
(T (T P)) / p (T
p
(T a6 "|T (MM',
(M', P)) day
/ p (Tgae (T ()) P (T, (T
(M ,P)) dal
(21)
/ pl IM' P) p (2 IM's dat
=p (M
Proof of Proposition The sufficiency of SE(3)-invariance of p(s IM', AMMP7 M) and p(s") is given in
Lemma A.1, and the sufficiency of SE(3)-cquivariance of p(x'-I|M P), and -Qu)eeqqivaaiiane and in3)-invariance of p(O'=I[M' P) is given Proposition A.2. Besides, easy to obtain that if p(O²)) and p(æ"") is SE(3)-ivvariat distribution, then p( will be invariant.
B Model Comparisons.
With Pocket2Mol and GraphBP. Pocket2Mol and GraphBP are all auto-regressive models, which violate the physical rules from the perspective of energy [5), while the diffusion models which consider the global interactions are a solution to the problem. Besides, to decide which atom will be added a bond with the next atom, Pocket2Mol needs classifier to predict the focal atom, so that the training and the prediction are not end-to-end. Finally, D3FG is functional-grow or fragment- based method, while these two models generate molecules at the atom level.
With DifISBDD and TifgetDiff. These two methods are diffusion-basee which considers the global interactions between atoms. the atom type generation, DiffSBDD uses continuous latent spaces generation, while Targetdiff diffuses the atom types in a uniform distribution. These two models all generate molecules at the atom level, while D3FG generates at the fragment level, and besides the types and positions, the orientations of the functional groups are generated.
17

---

With FLAG. is still an auto-regressive model and does not support end-to-end generation since the focal atom needs be predicted. Besides, we defined our functional groups as rigid bodies with stable intra-structures, while the motifs in FLAAG are 2D smiles, with the structures generated by RDKIT. The 3D structures of functional groups are obtained by the training set in D3FG, thus avoiding the problem of distribution shift of FLAG since the training/test motif substructures may not match the RDKIT's generation.
With DrepFrag. It a model for fragment- basedd lead optimization, in which the protein and the parent is used as condition and the fragment type is predicted by the model. In this way. it is more like an elaboration task defined in D3FG. Here we point out several advantages of D3FGGEHot/Cold) over Deepfrag. First, Deepfrag, just predicts the fragment type, without 3D structures, so that the problem of equivariance is not included, but D3FG generates 3D positions of the molecules. Second, although the type is the (E(3)-invariant variable, the model uses CNNs as the model backbone rather than EGNN, so the invariance can also not be preserved. Instead, D3FG assures physical symmetries by using EGNN. Finally, D3FG is generative model with stochasticity, while Deepfrag only gives the probability the fragment types, as a discriminative model.
C Method Details
Amino acid context encoding. Several geometric or type features are embedded to encode amino acids. For the geometric features including torsion angles/dihedrals, and pairwise distances, they are all aro-ttranslational invariant, since the geometric features are all scalars obtained from relative coordinates. Besides, the local coordinates of atoms in a single amino acid are also invariant because is always fixed in the local frame established by C... C and N. For the type features including amino acid types, sequential relationships, and pair of amino acid types, the translational and rotational operation is unrelated to them. Thus, the encoded amino acid contexts are roto-translational invariant, leading to the invariance of all the follow-up embeddings.
Equivariant neural network for linkers. For the -rootraanlatiinal equivariance of positions for single atoms, since O = I. Eq. 12 will be written as G (M', P) [j] = MLP (h',) unable to satisfy the equivariance. In this way, we revised it for single atoms by using the EGNN 44 stacked in the final layer for updating the positions, which reads
G (MM' Lil +
1 C.
Σ iET
(x,-
(22)
where we choose Cj = ||0,||22 +
D Data Preprocessing
Local frame establishment. In 3D Euclidian space, for rigid body including more than mass points that are not co-linear, a local frame can be established. We first choose a center node (center point) A as the origin, and a second node B, leading to AB as the direction of x-axis. Then, third node C' is selected. By Schmidt orthogonalization of AC with respect to AB, the direction of y-axis can be computed. And finally, the direction of z-axis is obtained by the cross gross-product of the unit vectors in the direction and y direction. By this means, the local frame is established by the three nodes, and the other nodes' local coordinates can be determined the local frame. Because the local frame requires least three points establish, the functional groups including only 2 atoms are divided into two linkers.
Functional group datasets. We give detailed information on the included functional groups, including 2D graph, 3D structure, time of occurrence in the CrossDocked2020, and the center node (node A). node B, and node C of the functional group in Table. [T]
Note that in beneze, the symmetric structures lead the frame nodes to be any three consecutive points on the hexagon. Besides, for the functional groups of 'NS(=0)=O' and 'O=CNO', two stable conformations exist, so we in practice regard them four diffferent types.
18

---

Table Frequency of the top ten functional groups that occur most frequently in Crossdocked2020.
Functional Group
Ref.
Pocket2Mol
TargetDiff
DiftSBDD
D3FG(Joint)
D3FG(Stage)
clcccecl
0.392
0.491
0.277
0,007
0.372
0.409
NC=0
0.147
0.075
0.142
0,201
0.082
0.107
O=CO
0.119
0.169
0.303
0,579
0.154
0.085
eleeneel
0.045
0.072
0.049
0.018
0.027
0.052
0.034
0.001
0.000
0.000
0.001
0.020
NS(=0)=0
0.030
0.000
0.000
0.008
0.001
0.001
O=P(O)(O)0
0.022
0.003
0.193
0.000
0.007
0.010
OCO
0.019
0,024
0.091
0,016
0,045
0.050
elenenel
0.017
0.008
0.138
0,000
0.002
0.009
elen[nH]el
0.016
0.011
0.001
0.000
0.003
0.004
JSD
0.248
0.301
0.553
0.223
0.201
Table 6: Ratio of the atoms.
Atom
Ref.
Pocket2Mol
TargetDiff
DifiSBDD
D3FG(Joint)
D3FG(Stage)
C
15.866
14.956
17.744
13.526
17.766
15,999
N
2.765
1.956
2.192
2,236
2.157
1.943
O
4.006
2.538
4.389
3.071
3.732
3.353
F 0.309
0.084
0.239
0.160
0.193
0.170
P 0.263
0.024
0.119
0.034
0,969
0,088
S 0.266
0.038
0.104
0.149
0.169
0.153
CI
0.152
0,016
0.064
0.006
0.145
0.122
MAE
0.573
0.471
0.627
0.528
0.294
E
Experiment Details
Platform. We use single NVIDIA A 1100(8 (090019))))))) GPU for a trial. The codes are implemented in Python 3.9 mainly with Pytorch 1.12, and run on Ubuntu Linux.
Model Details. In the diffusion of orientation and position, we employ a cosine variance schedule at, which reads
ā cos ( ++5(((++))) 5)) cos? (5s(((
(23)
where 0.01. In the diffuusion atom type, B, is set as 3, = 4. For the denoiser, the layer number is set as 6, and the embedding size is set as 256. The model is trained with Adam optimizer in 5000 epochs.
Functional group and Atom type analysis. We give detailed analysis of functional groups and atom types, in Table. and
Bond Angle and Dihedral analysis. Besides bond distance, detailed analysis of bond angle and dihedral shown in Table. S and molecules, and demonstrates that D3FG generates more realistic drug molecules in comparison with other baselines.
gives the JSD between the reference and the generated
19

---

Table 7: Frequency of the atoms.
Atom
Ref.
Pocket2Mol
TirgetDiff
DiftSBDD
D3FG(Joint)
D3FG(Stage)
C
0.672
0.762
0.714
0.702
0.741
0.733
N
0.117
0.100
0,088
0.116
0.124
0.089
O
0.170
0.129
0.176
0.159
0.175
0.154
F 0.013
0.004
0.009
0.008
0.009
0.008
P
0.011
0.001
0,005
0.002
0.002
0.004
0.011
0.002
0,004
0.007
0.001
0.007
CI
0.006
0.001
0.002
0.003
0.001
0.006
JSD
0.098
0.059
0.054
0.075
0.056
Table 8: JSD on bond angle distributions.
Angle
Pocket2Mol
TargetDiff
DiftSBDD
D3FGGStage)
D3FG(Joint)
C-C-C
0.269
0.272
0.304
0.255
0.258
C-C-N
0.254
0.267
0.313
0.256
0.255
C-N-C
0,286
0.241
0.319
0.269
0.277
C-C-O
0.317
0.295
0.345
0.293
0,295
C-O-C
0,308
0.311
0.372
0.310
0.314
C-N-N
0.294
0.276
0.301
0.270
0.281
N-C-O
0,300
0.295
0.326
0.282
0,291
N-C-N
0.304
0.288
0.342
0.282
0.292
Table JSD on dihedral distributions.
Dihedral
Pocket2Mol
TargetDiff
DiffSBDD
D3FG(Stagg)
D3FG(Joint)
C-C-C-C
0.151
0.149
0.158
0.141
0.138
C-C-C-N
0.176
0.165
0.224
0.169
0.175
C-C-C-0
0.183
0.159
0.206
0.156
0.164
C-C-0-C
0.180
0.174
0.231
0.167
0.149
C-C-N-C
0.165
0.142
0.223
0.136
0.146
C-C-N-O
0.277
0.270
0.285
0.264
0.293
C-N-C-O
0.453
0,430
0.398
0,358
0.335
N-C-C-0
0.315
0.253
0.303
0.244
0.272
C-N-C-N
0.340
0.317
0.328
0,254
0.263
20

---

Table 10: The included functional groups in D3FG. 'T' is the occurrence times of the functional group in the datasets (100,000 ligands).
Smiles
2D graph 3D structures
B C
CH4 CHi5
clccceel
Cato
0
131148
CH2-2 CH1l
NC=O
0 2
49023
O=CO
1
0
2
39863
CH14 CH:5
clccneel
3
2
4
15115
Nº
C9.0
CH22 CHr1
CInce2nc[nH]c2n1
3
6
11369
s
0:3
NS(=0)=0
0
2
10121
2N:0
0.2
HO.4
O=P(O)(O))
00:2
1
7451
0.0
0H:3
OCO
OH:0
0 2
6405
CHZ11
CH:5
clenencl
5965
CH:0
M2 CH11
CH:1
clen[nH]el
3
5404
CH:0
CH14
21

---

Smiles
2D graph
3D structures A
C
T
OH:3
O=P(O)O
0
center(2.3) 5271
0:0
OH:
clccc2cccc22c
3
2
4
4742
CH22 CHil
clecsel
3
2
4
4334
N=CN
H2N-2
MHd
4315
H2N22
M22
NC(N)=O
4167
O=<lcc(nH]j(==O)(nt]]
7
4145
clcc2ncccc22
3
2
4
3519
clesen
2
3
3466
CH
G12 Mea
clccc2[nH]enc2el
3462
bid
clc[nH]enl
NHHa
2964
CH N4
O=[N+][O-]
1
0
2
2702
22

---

Smiles
2D graph
3D structures
C
T
O=CNO
10 2 2477
H1:3
NH2:C
NC(=0)0
1 0 2
2438
O=S=0
0 2
2375
0.0
clcoc2[nH]ecccel
2
2301
45
23

---

60.0%
-6.4
Vina
affinity
55.0%
6.6
50.0%
Size
15
20
25
-68
-45.0%
QED
0.489
0.484
0.502
0.496
0.501
SA
0.821
0.814
0.836
0.843
0.840
-7.0
-00.0
LogP
2.774
2.795
2.802
2.759
2.821
-72-
35.00
Lipinski
4.910
4.983
4.937
4.931
4.965
-.4
Table 11: Metrics of chemical properties with the
change of repository sizes
10
15 Repository
Figure 5: Affinity metrics with the change of repos- itory sizes.
24


Reviews:
[{"review_id": "ujW5JqzbWc", "reviewer": "Reviewer_6wRC", "summary": "The paper presents a novel method for generating 3D molecules that bind to specific protein pockets based on a functional-group-based diffusion model (D3FG). The model decomposes molecules into functional groups and linkers and generates their types, positions, and orientations gradually through a denoising process. The model uses equivariant graph neural networks to parameterize the denoisers and ensure the roto-translational invariance of the molecule distribution. The paper also introduces a new task of molecule elaboration, which aims to modify existing molecules based on the fragment hotspot maps of the protein pockets. The paper evaluates the model on the CrossDocked2020 dataset and shows that it can generate molecules with realistic structures, competitive binding affinity, and good drug properties. The paper also demonstrates that the model can perform molecule elaboration and generate molecules with higher affinity than the reference molecules. The paper claims that D3FG is a novel and effective method for structure-based drug design that leverages the pharmacological information of functional groups.", "questions": "- How did the authors select the 25 functional groups used for their method? How did they ensure these functional groups cover a diverse and representative range of pharmacological properties and structures? How sensitive is their method to the choice of functional groups?\n- How did the authors evaluate the quality and diversity of the generated molecules? Did they use any metrics or criteria to measure the novelty, validity, and diversity of the generated molecules? How did they compare their method with prior methods regarding these metrics or criteria?\n- How did the authors handle the cases where the generated molecules violate chemical or physical constraints, such as bond angles, bond lengths, steric clashes, or chirality? How did they ensure that the generated molecules were chemically feasible and stable?\n- How did the authors handle the cases where the target protein pockets have multiple binding sites or modes? How did they ensure that their method can generate molecules that can bind to different sites or modes of the same protein pocket?\n- How scalable is their method to larger, more complex protein pockets and molecules? What are the computational and memory requirements of their method? How does their method compare with prior methods regarding efficiency and scalability?", "limitations": "The authors have not adequately addressed the limitations and potential negative societal impact of their work. The authors only briefly mention some limitations of their method in the conclusion section, but they do not provide a detailed discussion of how these limitations affect their results and how they can be overcome in future work. The authors also do not discuss any potential negative societal impact of their work, such as the ethical, legal, or environmental implications of generating novel molecules that can bind to specific protein pockets.", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The paper proposes a functional-group-based diffusion model for pocket-specific molecule generation and elaboration called D3FG. The method decomposes molecules into two categories of components: functional groups defined as rigid bodies and linkers as mass points. The two kinds of components can form complicated fragments that enhance ligand-protein interactions. In the experiments, the authors claim the method can generate molecules with more realistic 3D structures, competitive affinities toward the protein targets, and better drug properties. The paper is original in its approach to generating molecules given the pockets’ structures of target proteins and its use of functional groups as basic components instead of atoms. The paper is clear in its description of the method and its results. \n\nThe paper is well-written and clearly describes the proposed method, its implementation details, and its evaluation results. The authors provide sufficient background information on related work and explain how their method differs from prior methods. The authors also provide detailed explanations of the model's components, such as the functional group decomposition, equivariant graph neural networks, and molecule elaboration. The authors use appropriate visualizations to illustrate their method's outputs and compare them with reference molecules. \n\nThe paper's originality lies in its novel approach to generating 3D molecules that can bind to specific protein pockets by leveraging functional groups' pharmacological information. The authors show their method can generate molecules with realistic structures, competitive binding affinity, and good drug properties. The paper's significance lies in its potential to improve structure-based drug design by enabling the generation of novel molecules that can bind to specific protein pockets with high affinity.", "weaknesses": "The paper's main weakness is that it does not provide a detailed comparison with prior methods for generating 3D molecules that can bind to specific protein pockets. The authors briefly mention some related work, but they do not provide a comprehensive comparison of their method with prior methods in terms of performance, efficiency, and scalability. The authors also do not provide a detailed analysis of the limitations of their method, such as the types of molecules it may not be able to generate or the types of protein pockets that it may not be able to bind to. \n\nAnother weakness of the paper is that it does not provide a detailed analysis of the interpretability and explainability of its method. The authors briefly mention some visualizations and explanations of their method's outputs. Still, they do not provide a systematic analysis of how their method's components contribute to its performance and how they can be interpreted in terms of pharmacological properties. \n\nTo improve the paper, the authors could perform a more comprehensive comparison with prior methods for generating 3D molecules that can bind to specific protein pockets, including both quantitative and qualitative analyses. The authors could also perform a more detailed analysis of the limitations of their method and how they can be addressed in future work. Finally, the authors could perform a more systematic analysis of the interpretability and explainability of their method, including sensitivity analyses, feature importance analyses, and pharmacophore analyses.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "\nWe thank you a lot for your constructive advice and answer your questions one by one, as below.\n\nResponse to Q1: \nWe use EFGS[1] to decompose the molecules, and analysis the stability of the substructures, so that manually established a repository of functional groups that most molecules can be decomposed in. As you can see in Table 8 in the Appendix, the `c1ccc2[nH]ccc2c1’ functional group is the 25th ones, only 2.3% of molecules have the substructures, so we assure the 25 functional groups are enough to consist of a repository and cover most generation tasks in Crossdocked. In detail, we test the sensitivity of performance affected by repository size in CQ2 in General response. We hope it can remove your doubts.\n\nResponse to Q2:\nIn D3FG, we did not compare these metrics except 'Validity' since we follow the protocol of experiments [2,3], which are different from tasks of molecule generation[4]. Here we conduct experiments on D3FG, and give these metrics on DiffSBDD and D3FG.\n'Validity' is calculated as the ratio of generated 3D molecules that are chemically valid; 'Novelty' is defined in [5], where $C$ is the training set; 'Diversity' is the average pairwise Tanimoto distances. Table. 1 gives details.\n\nTable.1. molecule metrics of three diffusion methods.\n|            | Validity | Novelty | Diversity |\n|------------|----------|---------|------------|\n| DiffSBDD   | 95.61%   | 99.98%  | 0.704      |\n| TargetDiff | 95.73%   | 97.42%  | 0.718      |\n| D3FG       | 96.64%   | 96.81%  | 0.684      |\n\nThe difference is minor, and these three models all perform well in these three metrics. The novelty and diversity of D3FG are relatively low because the substructures are fixed and the same as training and test data, so in Tanimoto distance calculation, some fingerprints are likely to be the same.\n\n\nResponse to Q3: We follow DiffSBDD's post-process, by using Openbable to connect the atoms as molecules, and select the largest fragments when there are disconnected atoms. In this way, two metrics are relevant: connectivity and validity. The validity has been reported, and the connectivity is 87.16% of D3FG v.s. 79.52% of DiffSBDD reported in [6].\n\nResponse to Q4: The Crossdocked datasets is a paired pocket-ligand datasets, so usually, previous methods (3DSBDD, Pocket2Mol, DiffSBDD, TargetDiff) all focus on 'one-to-one' task, and it cannot be generalized to 'one-to-many' or 'many-to-one' tasks. The molecules are generated by D3FG conditioned on a certain pocket structures, so when it is 'many-to-one' tasks, D3FG will use many pockets contextual information as inputs, and generate the corresponding number of molecules. We cannot ensure that the generated molecules can bind to a set of pockets if we do not know their structures and other information.\n\nResponse to Q5: \nWe here report the average generation time and memory usage of different diffusion methods on test set per 100 samples, and training time and memory per epoch. The batch size is set as 16 in training.\n\n|            | Time(Gen) | Memory(Gen) | Time(Train) | Memory(Trian) |\n|------------|-----------|-------------|-------------|---------------|\n| DiffSBDD   | 5'48\"     | 4396MB      | 7'36\"       | 31154Mb       |\n| TargetDiff | 15'52\"    | 8944MB      | 34'43\"      | 44138MB       |\n| D3FG       | 4'44\"     | 4558MB      | 15'15\"      | 31432MB       |\n\nIt shows that TargetDiff is the most computationally comprehensive because the nodes in GNNs in TargetDiff are atoms (412.14 on average),  and DiffSBDD and D3FG are of no significant differences since the nodes in GNNs are amino acids in protein and atom/functional groups in DiffSBDD(68.10 nodes on average) and D3FG(53.62 nodes on average). Besides, on scalability, D3FG and DiffSBDD can handle most protein pockets, since the number of animo acids in a single pocket hardly exceeds 100. \n\n[1] Extended Functional Groups (EFG): An Efficient Set for Chemical Characterization and Structure-Activity Relationship Studies of Chemical Compounds. 2015\n\n[2] Pocket2Mol: Efficient Molecular Sampling Based on 3D Protein Pockets. 2022\n\n[3] 3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction. 2022\n\n[4] E(n) Equivariant Normalizing Flows. 2021\n\n[5] Graphvae: Towards generation of small graphs using variational autoencoders. 2018\n\n[6] Structure-based Drug Design with Equivariant Diffusion Models. 2022\n"}, {"review_id": "dxJG2hINbf", "reviewer": "Reviewer_i3fG", "summary": "This paper proposes to generate 3D molecules using functional groups and linker atoms in a diffusion model. Using functional groups as building blocks help the model to generate realistic local structures. In the proposed diffusion model, the atom/functional group type, coordinates and orientation are predicted.  In addition, the authors experimented with two strategies, joint and two-stage, to generate heterogenous graph, which contains functional groups and linker atoms. The performance indicates the proposed method achieves SOTA performance in structure-based drug design task. \n\nThis paper also proposed a new molecular elaboration task and curated a dataset for this task. ", "questions": "1. How many percentage of the generated molecules are complete (all the generated atoms are connected into one molecule)?\n2. In molecular elaboration task, is the remaining fragments included in D3FG as a condition for elaboration? If not, can the proposed model guarantee that the newly generate fragment is suitable to be connected with the remaining fragments?\n3.  Why does the two-stage approach consistently outperform the joint training one? Is there any explanation? ", "limitations": "N/A", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper implement functional groups in diffusion-based structure-based drug design model for the first time. \n2. The performance indicates using functional groups as building blocks can improve QED and SA, which have been a challenge for previous diffusion models. \n3. This paper proposes a new task, molecule elaboration, for structure-based drug design and provides a dataset for it. ", "weaknesses": "The paper proposed a new molecule elaboration task, and some existing baselines (e.g. Pocket2Mol[1], 3DSBDD[2], TargetDiff[3] and DiffSBDD[4]) and can be easily adapted for this task. Currently, there is no performance comparison for molecule elaboration task, and it is recommended for the authors to evaluate their model with existing baselines which can be used for this task. \n\n\n[1] Peng, Xingang, et al. \"Pocket2mol: Efficient molecular sampling based on 3d protein pockets.\" ICML 2022.\n\n[2]Luo, Shitong, et al. \"A 3D generative model for structure-based drug design.\" NeurIPS 2021.\n\n[3] Guan, Jiaqi, et al. \"3d equivariant diffusion for target-aware molecule generation and affinity prediction.\" ICLR 2023. \n\n[4]Schneuing, Arne, et al. \"Structure-based drug design with equivariant diffusion models.\" arXiv preprint arXiv:2210.13695 (2022).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "\nWe sincerely thank you a lot for your appreciation of the work, and the advice with deep insights. Here is the response to your concerns.\n\nResponse to comparison to baselines for molecule elaboration: \nAs the model for molecule elaboration task in 3D is scarce, we here use STRIFE [1] (auto-regressively-vae) as a reasonable alternative since the STRIFE also extracts the pharmacophoric information with hotspots map. However, the model only elaborates molecules in 2D, so we firstly use the re-trained models to generate 2D molecules conditioned on protein’s structural information and the large fragments without the hottest/coldest functional groups, then use MMFF in RDKit to obtain the conformation, so that the docking score can be calculated.  The metrics on metrics are presented below:\n\n|             | Vina Score | Vina Delta Aff | Gnina Score | Gnina Delta Aff | QED   | SA    | LogP  | Lipinski |\n|-------------|------------|----------------|-------------|-----------------|-------|-------|-------|----------|\n| STRIFE(Hot)  | -7.01      | 42.86%         | 5.13        | 33.35%          | 0.483 | 0.722 | 0.811 | 4.220    |\n| STRIFE(Cold) | -6.96      | 40.20%         | 5.14        | 34.49%          | 0.479 | 0.724 | 0.809 | 4.225    |\n| D3FG(EHot)  | -7.19      | 51.78%         | 5.51        | 56.53%          | 0.482 | 0.731 | 0.814 | 4.330    |\n| D3FG(ECold) | -7.02      | 44.03%         | 5.16        | 32.69%          | 0.476 | 0.707 | 0.820 | 4.228    |\n\n\n\nIt shows that in the four chemical properties, the differences are very small. However, in the docking score evaluation, the differences are significant. One of the suspectable reasons is that STRIFE elaborates the molecule auto-regressively at the atom level, and thus the generated fragments in the binding sites are usually small and cannot form complete functional groups with pharmacodynamic function because the problem of early-stopping and unrealistic substructures in the auto-regressive method [2]. And thus, since the D3FG generates larger fragments in the binding sites, interactions are more likely to occur [2, 3].  \n\n\nResponse to Q1. \nStatistically, in D3FG(stage) 87.16% molecules are generated with all bonds connected, so the restricted validity is 87.16%. In practice, when there are disconnected bonds, we will select the largest fragments as the molecules as DiffSBDD does, and preserve it if the size is larger than 80% of the generated ones. In this way, the non-strict validity is 96.64%. However, in D3FG(joint), the two metrics are only 71.42% and 92.37%.  We add the metrics in the Appendix. \n\nResponse to Q2.\nIn the elaboration task, both the pocket and the remaining fragments are all used as contextual information. The model is re-trained on this task, and it only generates one functional group with its type, position and orientation.\n\nResponse to Q3.\nWe think that in the binding system, the functional groups are considered as the fragment level, and the linkers are at the atom level. In section 4.4, we give a brief description of these two levels of nodes. To be specific, in the two-stage scheme, the first diffusion model will locate the pharmacophoric sites and fill the appropriate functional groups into it, and then, the second diffusion model with the other GNN as its denoiser will use the linkers to link them, which is conditioned on pocket and functional groups' structure. Since functional groups are rigid bodies that occupy a certain space, the second model learns that the linkers should not intersect into the generated fragments, so the validity is better, and the generated molecules are more realistic than the ones generated by joint scheme, in which the linkers and functional groups are all regarded at the same level, and denoised by a single GNN.\n\n[1] Incorporating Target-Specific Pharmacophoric Information into Deep Generative Models for Fragment Elaboration. J Chem Inf Model. 2022 May \n\n[2] Diffbp: Generative diffusion of 3d molecules for target protein binding, 2022\n\n[3] 3d equivariant diffusion for target-aware molecule generation and affinity prediction. In International Conference on Learning Representations, 2023"}, {"review_id": "v3fmZQfCid", "reviewer": "Reviewer_sFPS", "summary": "This paper proposes a so-called functional-group-based diffusion generative model, namely D3FG, to generate molecules with realistic substructures conditioned on the protein binding sites. D3FG represents the protein-ligand docking system as a fragment-based system. The molecule fragments are molecule substructures and the protein fragments are amino acids. Thus, the original protein-ligand docking system is reduced to a coarsen graph with molecule substructures and amino acids as nodes. The molecule substructures are connected with heavy atoms as linkers. Thus, the denoising and diffusion processes are defined with molecule substructure translation probabilities. Although this idea is interesting, the reviewer is concerned about the paper presentation, literature reviewer, and marginal performance improvement.", "questions": "The Questions are listed in the Weaknesses Section above.", "limitations": "N/A", "rating": 3, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "Representing the protein-molecule docking system as the coarsened graph reduces the computation expenses of the diffusion generative models. Recently, this scheme has drawn much attention and there are some related work has already shown the efficiency of this scheme. Moreover, molecule elaboration is also related to ligand optimization, which aim to optimize the ligand efficiency by modifying it structure.", "weaknesses": "1. Limited Novelty and Insufficient literature review. This paper represents the fragment-based method for ligand generation and claims no prior work employs the fragment-based generation scheme. However, there are already some methods that employ fragment-based generation. For example, Deepfrag [1], FLAG [2], and SQUID [3] are all fragment-based generative methods for target-aware molecule design. It is necessary to discuss the difference and highlight the contributions. \n\n2. The paper presentation needs to be improved. For example, what is the intuition of the definition of absorbing state in Line 105? What is the connection between the BERT-style objective and the denoising objective in Eq.4? What are the different levels of nodes in Section 4?\n\n3. Definition of \"functional group\". The functional group often refers to the molecule substructures that contribute most to the chemical properties. However, as shown in Section 5.1, the functional group in this paper refers to the most frequent substructures. Mining the most frequent substructures for molecule generation is not new and has been employed in [2,4].\n\n4. Marginal empirical improvement. Moreover, there is only marginal empirical improvement over the baseline methods as shown in Table 4.\n\n5. Unfair comparison. Since the proposed method already employs the most frequent substructures for model training, it is unfair to choose the \"'Ratio’ of the top ten functional groups with the highest frequency\" as an evaluation metric in Table 1.\n\n\n[1]. Deepfrag: a deep convolutional neural network for fragment-based lead optimization. Chemical Science.\n\n[2]. Molecule generation for target protein binding with structural motif. ICLR 2023.\n\n[3]. Equivariant shape-conditioned generation of 3d molecules for ligand-based drug design. ICLR 2023.\n\n[4]. Molecule Generation by Principal Subgraph Mining and Assembling. NeurIPS 2022.\n\n", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "\nWe thank you a lot for your constructive advice and answer your questions one by one, as below.\n\nResponse to Q1:\nWe add the three methods to the related work as discussed in CQ3 in General Response. In detail, the novelty of D3FG and its differences are listed below:\n\n- We did not compare FLAG[2] in method and experiment because the code is open to the public with a bug fixed on May 10, 2023. When we cannot have insights through the source code, details are hard to be provided. Here we give comparisons with FLAG. (i)It is an auto-regressive model, violating the physical rules from the perspective of energy[5], while the diffusion models which consider the global interactions are solutions. (ii)It needs a classifier to decide which atom will be added a bond with the next motif, so the training and the prediction are not end-to-end. In contrast, D3FG generates molecules with a diffusion model as long as the number of nodes is given. (iii) Finally, functional groups are rigid bodies in D3FG, while the motifs in FLAG are 2D smiles (https://github.com/zaixizhang/FLAG/blob/main/utils/vocab.txt), with the structures generated by RDKIT(Line. 188, 189 in motif_sample.py in the same link). The 3D structures of functional groups are obtained by the training set in D3FG, thus avoiding the problem of distribution shift of FLAG since the training/test motif substructures may not match the RDKIT’s generation, which has been discussed in [6]. Besides, since the pre-trained model of FLAG is not provided, we cannot give a detailed experimental comparison.\n\n- For Deepfrag[1], it is a model for fragment-based lead optimization, in which the protein and the parent is used as condition and the fragment type is predicted by the model. So it is more like an elaboration task defined in D3FG. Here are several advantages of D3FG(EHot/Cold) over Deepfrag. (i)Deepfrag just predicts the fragment type, without 3D structures, so that the problems of symmetry are not included, but D3FG generates 3D positions of the molecules. (ii)Although the type is SE(3)-invariant, the model uses CNNs as the backbone rather than EGNN, so the invariance cannot be preserved. Instead, D3FG assures physical symmetries by using EGNN. (iii)D3FG is a generative model with stochasticity, while Deepfrag only gives the probability of the fragment types, as a discriminative model.\n \n- For SQUID[3], it is a shape-conditioned molecule generation, in which the shape is defined as a point cloud as the outline of the molecule’s 3D structure, while our task is pocket-specific molecule generation, where the shape of the pocket may not be similar as the outline of molecules. In the experiments, we cannot find a similar task to SBDD in SQUID. Therefore, the only common idea of D3FG and SQUID lies in `Fragment-based’. To tell the novelty of ours, SQUID is still an auto-regressive model, similar to Pocket2Mol, with the focal atom prediction modules, different from our end-to-end diffusion model. And we use SO(3) diffusion to generate the orientation of fragments.\n\nResponse to Q2:\nThe absorbing state and BERT-style training objective is given in the reference[8] (D3PM) in the new version, we are sorry that we miss the reference. The nodes diffused into an absorbing state can be regarded as masked linker/functional groups, so optimizing a cross-entropy defined in Eq.(4) is like pre-training BERT.  As discussed in Sec.4.4, functional groups are regarded as rigid bodies, which occupy a certain volume of space, while linkers are mass points, so the nodes are of different levels: Nodes of functional groups are higher-level nodes consisting of atoms as lower-level nodes.\n\nResponse to Q3:\nWe use EFGS[7] to decompose the molecules, in which the substructures are defined as ‘a group of atoms that has similar chemical properties whenever it occurs in different compounds’, rather than the general defined motifs with substructures that vary with the datasets. We did not aim to ’MINE’ the frequent substructures. Instead, we try to establish a repository of functional groups that most molecules can be decomposed in, and use the repository to generate or elaborate the new molecules. We suppose that the manual establishment of such a repository with both 2D and stable 3D structures is one of our contributions.\n\nResponse to Q4:\nWe admit that improvements are not significant in the binding scores compared with TargetDiff, which is one of D3FG’s limitation, but other chemical properties show advantages. Besides, we argue that D3FG generates more realistic molecules with complex substructures from Table.1 and Table.2 and 3 in the General Response.\n\nResponse to Q5:\nFirst, it is our motivation of generating complex functional groups as substructures in molecules (Line 32, 33), so it is natural to compare the generated complex substructures of different methods to show that D3FG fixes the problem. Secondly, even if the complex substructures are generated, they may not be assembled as a valid molecules, because they occupy a large space, and lead to linker-fragment intersection. Therefore, the problem is not trivial, and D3FG(Stage) is a good solution, by regarding the graph as heterogenous and using two-stage generation scheme.\n\n[1] Deepfrag: a deep convolutional neural network for fragment-based lead optimization. Chemical Science.\n\n[2] Molecule generation for target protein binding with structural motif. ICLR 2023.\n\n[3] Equivariant shape-conditioned generation of 3d molecules for ligand-based drug design. ICLR 2023.\n\n[4] Molecule Generation by Principal Subgraph Mining and Assembling. NeurIPS 2022.\n\n[5] Diffbp: Generative diffusion of 3d molecules for target protein binding, 2022\n\n[6] Torsional Diffusion for Molecular Conformer Generation, 2022\n\n[7] Extended Functional Groups (EFG): An Efficient Set for Chemical Characterization and Structure-Activity Relationship Studies of Chemical Compounds. 2015 \n\n[8] Structured denoising diffusion models in discrete state-spaces, 2023"}, {"review_id": "VpC1eEzWgu", "reviewer": "Reviewer_Y6qT", "summary": "Pocket-specific molecule generation has received considerable attention in recent years, and the authors propose a functional-group-based diffusion model to address this task. The model considers the generation of complete molecules as the assembly of functional groups (fragments) and atoms that connect these functional groups. They employ a diffusion-based generative scheme to determine the coordinates, orientation, and types of these fragments. The experiments demonstrate the satisfactory generation performance of the model and its potential applications in molecule elaboration.", "questions": "1. In the Introduction, it is mentioned that protein amino acids are represented as functional groups and linking atoms (Line 42). However, in the Method section, the amino acid space I_aa is preserved (Line 60). Why is the amino acid space still necessary if any node can be considered either a functional group or atom?\n2. The functional groups are treated as rigid fragments, and their orientations are predicted. But what if the functional groups have internal rotatable bonds and cannot be regarded as rigid (e.g., O=CNO)?  Additionally, how is the symmetry of functional groups considered when defining orientation? For example, a benzene ring can have multiple orientations resulting in the same arrangement of the six atoms. Which orientation is chosen during training?\n3. In the experiments, why did you use EFGs to segment molecules instead of BRICS composition, as done in many previous fragment-based works? Why did you choose 25 functional groups? How does this choice cover the total number of atoms in a molecule, i.e., the ratio of atoms in functional groups to the total number of atoms for a molecule? Did you consider other sizes for the set of functional groups?\n4. Does the node number include the protein in Line 220?\n5. For the molecule elaboration experiment, did you retrain the model specifically for this task, or did you use the same model as in the molecule generation experiment?\n6. In Line 288, what does the word \"them\" refer to? It seems ambiguous.\n7. Why does D3FG(EHot) generate molecules with higher affinities? In my opinion, since functional groups with high binding contributions were removed, it is likely that the generated functional groups have weaker binding, resulting in new molecules with weaker affinities. On the other hand, in the D3FG(ECold) experiments, a functional group with higher binding contribution is more likely to be generated, replacing the weaker functional group and leading to higher affinities. Why do the experimental results not align with this explanation?", "limitations": "The authors have addressed the limitations.", "rating": 7, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "1. The paper is well-written, and the narrative is clear and concise.\n2. The authors address many important details, including the determination of functional groups, handling chirality, and generating heterogeneous graphs.\n3. Overall, while the idea of decomposing molecules is not novel, the authors provide a robust model and conduct experiments to validate its superiority.", "weaknesses": "1. In the Method section, it would be beneficial to provide an overview of the entire method before delving into the specifics of each part.\n2. The aromatic elements C:C and C:N in Table 2 could be written in lowercase to maintain consistency with convention.\n3. It would be beneficial to include more visualizations (2D/3D) of generated molecules.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We sincerely thank you a lot for your appreciation of the work, and the advice with deep insights. Here is the response to your concerns.\n\n\nResponse to Q1. The amino acid index set is preserved because, in the diffusion process, only the linkers and functional groups are added with noise, so the index sets of the three types of nodes are defined for differentiating them. Besides, in description of the amino acid embedding, the index set is also used.\n\nResponse to Q2. By using EFGs to decompose the molecules, we find that the functional groups with high frequency usually have stable structures. In detail, we randomly choose one functional group's structures which are split from one molecule, and match all the other functional groups with the same smiles but from other molecules in 3D. We define the substructures are stable if the RMSD is less equal than 0.005A. When there are RMSE larger than the threshold, we pick all of them and repeat the process. In this way, we find the functional groups are stable in 3D, since most of them only have one stable structure, and only two have multiple structures. The orientation is defined as a global vector that is the z-axis in the local frame. For example, in a benzene ring, the six atoms are coplanar, so no matter how the local frame is built, the z-axis is the normal vector to that face, and this normal vector serves as a representation of the rotational orientation.\n\nResponse to Q3. Our D3FG method is adaptable and can be applied to various fragment databases. Although technically the selection of EFGs and BRICS can be interchangeable, the EFGs method aligns better with our objectives. Unlike BRICS, which deconstructs molecules into synthesizable building blocks, the EFGs method provides a viable approach to obtaining a series of chemical fragments. Reports have shown that the number of fragments derived from BRICS increases linearly with the size of the molecular library[1]. Conversely, the fragments from EFGs are manually curated, thus providing a robust representation of molecular diversity. These fragments effectively cover drug-like chemical space and have demonstrated efficacy in distinguishing between inhibitors and non-inhibitors[2]. Therefore, we opted to use EFGs in this work, and shifting to the BRICS setting is straightforward and can be done according to the user's preference. Besides, in choosing the functional groups, we aim to establish a repository of functional groups that most molecules can be decomposed in. As you can see in Table 8 in the appendix, the `c1ccc2[nH]ccc2c1’ functional groups are the 25th ones, only 2.3% of molecules have the substructures, so we assure the 25 functional groups are enough to consist of a repository and cover most generation tasks in Crossdocked. In detail, we test the sensitivity of performance affected by repository size in CQ2 in General response. We hope it can remove your doubts.\n\nResponse to Q4. Yes, it includes, since D3FG and DiffSBDD represent protein pockets at amino acid levels, the node numbers are much lower than TargetDiff.\n\nResponse to Q5. The model is retrained, since the contextual information changes. In molecule generation, the condition is the protein structure, and in the elaboration task, it is the protein and the remaining molecule's fragments.\n\nResponse to Q6.  'Them' refers to the 'removed functional groups with the highest scores'. we are sorry that the confusion made by our presentation, and will change the description in the next version.\n\nResponse to Q7. As the pharmacophoric sites are usually fixed in a pocket, and the functional groups with high hotmap scores usually lie in the sites. By replacing it with other fragments with different local structures and orientations, the likelihood of enhanced interactions with proteins is higher. However, when removing the functional groups with low scores, the generated functional groups usually lies in the 'cold' sites as a result of energy constraints within the molecule, so optimizing this part of fragments often contributes very little to the binding affinity.\n\n[1] HierS: hierarchical scaffold clustering using topological chemical graphs. Journal of medicinal chemistry\n\n[2] Fingerprint-based in silico models for the prediction of P-glycoprotein substrates and inhibitors\n"}, {"review_id": "XWpFi44vJA", "reviewer": "Reviewer_6gZx", "summary": "In this paper, a functional-group-based diffusion model called D3FG is proposed to generate molecules in 3D for target protein binding. Two generation schemes including joint and two-stage generation schemes are formulated. ", "questions": "1. It seems that the reported scores in Table. 4 are different from the original papers of baselines. Could the authors explain that?", "limitations": "Yes, the authors have adequately discussed the limitations.", "rating": 4, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 1, "strengths": "1. The paper is well-written and easy to follow.\n2. It is the first functional-group-based diffusion model for structure-based drug design.", "weaknesses": "1.  The performance improvement over previous methods is limited. For example, in table.2, TargetDiff achieves the lowest JS divergence on most bond distances. In Table. 4, TargetDiff achieves the best performance on the vina score. In Figure. 3 the D3FG does not show an advantage over other baselines with respect to atom type distribution.\n2. The evaluations are not comprehensive. For example, besides divergence between bond distances, bond angles and dihedral angles should be evaluated. The influence of the size of the functional group set is not explored. \n3. The technical contribution is limited. The application of diffusion models for drug design is not new. It seems the required techniques are proposed in previous works including TargetDiff [7], DiffSBDD [8], and DiffAB [52]. \n4. Some related works are not discussed. For example, some previous methods also leverage functional groups or motifs for molecule design: JT-VAE [1], PS-VAE [2], and FLAG [3].\n\n[1] Jin et al., Junction tree variational autoencoder for molecular graph generation, ICML 2018\n[2] Kong et al., Molecule generation by principal subgraph mining and assembling, NeurIPS 2022\n[3] Zhang et al., Molecule generation for target protein binding with structural motifs, ICLR 2023", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "\nThanks for your advice, and we add more experimental details in the Appendix E according to your advice as shown in CQ2 in General Response. Here is the response to your doubts.\n\nResponse to W1: On one hand, the improvements in docking scores are not significant, according to Table.4, but the other chemical properties of generated molecules are overall the best. On the other hand, D3FG can generate more realistic drug-like molecules, with complex substructures (Table. 1 in paper). On atom type distribution, it achieves the lowest MAE. Besides, on the other geometries like bond length, bond angle, and dihedral distribution, it shows the overall best performance, according to the Table.2 in the paper and Table.2 and 3 in the CQ2 in General response.\n\nResponse to W2: We hope CQ2 in General Response can remove your doubts and change your opinion.\n\nResponse to W3: We have discussed the technical contributions of D3FG over TargetDiff and DiffSBDD in the paper, and concluded them as three points. (i) Functional-group-based method, so that more complex substructures with pharmacodynamic function can be generated. (ii) SO(3) Diffusion, to generate the orientation of functional groups regarded as rigid bodies. (iii) Fragment-linker designation, with two solutions whose  effectiveness is validated through experiments.  The of two-stage schemes, which is similar to classical CADD, perform better. Our contributions over DiffAB can be concluded as: (i) Establish a repository consisting of a functional group with stable substructures, rather than amino acids which have been completely defined so that positions, orientations, and types can be generated through diffusion models. (ii) Consider single atoms as linkers, symmetries of which IPA cannot handle, and use EGNN as another head to generate positions. (iii) Employ Bert-style diffusion (D3PM) rather than uniform diffusion on categorical variables. \n\nResponse to W4: We add these methods into related works as shown in CQ3, and hope it helps to enhance the integrity of the article and changes your opinion. the code is open to the public with a bug fixed on May 10, 2023. When we cannot have insights through the source code, details are hard to be provided.  Besides,here we give comparisons with FLAG. (i)It is an auto-regressive model, violating the physical rules from the perspective of energy[5], while the diffusion models which consider the global interactions are solutions. (ii)It needs a classifier to decide which atom will be added a bond with the next motif, so the training and the prediction are not end-to-end. In contrast, D3FG generates molecules with a diffusion model as long as the number of nodes is given. (iii) Finally, functional groups are rigid bodies in D3FG, while the motifs in FLAG are 2D smiles (https://github.com/zaixizhang/FLAG/blob/main/utils/vocab.txt), with the structures generated by RDKIT(Line. 188, 189 in motif_sample.py in the same link). The 3D structures of functional groups are obtained by the training set in D3FG, thus avoiding the problem of distribution shift of FLAG since the training/test motif substructures may not match the RDKIT’s generation, which has been discussed in [6]. Besides, since the pre-trained model of FLAG is not provided, we cannot give a detailed experimental comparison.\n\nResponse to Q1:  All the metrics are reported based on our reproduction of the methods, but there are unavoidable differences from the original papers. We think there are two main reasons:\n- (i) Different platform. We take Pocket2Mol as examples. As you can see, the original test platform is 'NVIDIA V100 GPUs with Python 3.8 and Pytorch 1.9.0 a', while in our experiments, it is ' NVIDIA A100(81920MiB) GPU with Python 3.9 and Pytorch 1.12.'. The CUDA version, pytorch version and many environmental variables affect the test results. However, once the protocol is unified on the same one, we can ensure the rigor of experiments.\n- (ii) Stochasiticity. All these methods are generative models, so that randomness is unavoidable.\n\nOverall, the differences are acceptable. The vina docking score of Pocket2Mol is reported as -7.288 originally and -7.05 in DiffSBDD, and in our experiments, it is -6.92, of minor and acceptable deviation."}]

Author rebuttal:
**General Response**:

Here we conclude several common concerns of the reviewers, and respond to them as below:

CQ1: Sensitive Analysis (How the size of functional group repository affects the generative performance?)

We conduct experiments about the effects of the size of the repository on performance. Here, we choose top-5, top-10,... , top-20, top-25 functional groups in Table.8 in the paper as the smaller repository, and give Vina docking scores, Vina Delta affinity, and other four chemical properties in these situations. In the implementation, we add $-1e8$ to the logits corresponding to the removed 20, 15, 10, ... functional group types, to force the model to generate the remaining ones. Table.1 ( or Figure. 5 and Table. 11 ) in the newly updated supplementary material gives details, which will be added in the new version. 

Table 1.  Effects of number of functional groups on performance
| repository size | 5      | 10     | 15     | 20     | 25     |
|-----------------|--------|--------|--------|--------|--------|
| Vina score      | -6.59  | -6.7   | -6.99  | -7.06  | -7.04  |
| Vina delta affinity  | 32.14% | 39.39% | 45.42% | 47.33% | 46.58% |
| qed             | 0.489  | 0.484  | 0.502  | 0.496  | 0.501  |
| sa              | 0.821  | 0.814  | 0.836  | 0.843  | 0.84   |
| logp            | 2.774  | 2.795  | 2.802  | 2.759  | 2.821  |
| Lipinski        | 4.91   | 4.983  | 4.937  | 4.931  | 4.965  |

It shows that in docking score, when the removed functional groups are small, the performance deterioration is minor, but significant when only 5 or 10 functional groups remains. One of the explanations is that the least common 5 to 15 functional groups just appear very rarely in the training set. For example, 'O = P(O)O', although it is the 15th most common functional group, occurs only 4167/100000 = 4.167%. Therefore, its exclusion will not have a particularly large impact on the overall performance. In contrast, when 'NS(=O)=O', which has a frequency of up to 10%, is excluded, its generation can only rely on the diffusion of linker atoms, which drastically reduces the frequency of occurrence and affects the overall performance. Besides, in QED, SA, and other scores, the differences are not significant.


CQ2: Detailed analysis of geometries like bond angle and dihedral. 

We add some experimental results on JSD of bond angle and dihedral of the molecules generated by different methods v.s. references, as below. Table 2 and 3 demonstrate that D3FG generates more realistic drug molecules in comparison with other baselines.

Table 2. JSD of bond angle distributions.
| Angle   | Pocket2Mol | TargetDiff | DiffSBDD | D3FG(Stage) | D3FG(Joint) |
|---------|------------|------------|----------|-------------|-------------|
| C-C-C   | 0.269      | 0.272      | 0.304    | 0.255       | 0.253       |
| C-C-N   | 0.254      | 0.267      | 0.313    | 0.256       | 0.255       |
| C-N-C   | 0.286      | 0.241      | 0.319    | 0.269       | 0.277       |
| C-C-O   | 0.317      | 0.295      | 0.345    | 0.293       | 0.295       |
| C-O-C   | 0.308      | 0.311      | 0.372    | 0.310       | 0.304       |
| C-N-N   | 0.294      | 0.276      | 0.301    | 0.270       | 0.281       |
| N-C-O   | 0.300      | 0.295      | 0.326    | 0.282       | 0.291       |
| N-C-N   | 0.304      | 0.288      | 0.342    | 0.282       | 0.292       |


Table 3. JSD of dihedral distributions.
| Dihedral | Pocket2Mol | TargetDiff | DiffSBDD | D3FG(Stage) | D3FG(Joint) |
|----------|------------|------------|----------|-------------|-------------|
| C-C-C-C  | 0.151      | 0.149      | 0.158    | 0.141       | 0.138       |
| C-C-C-N  | 0.176      | 0.165      | 0.224    | 0.169       | 0.175       |
| C-C-C-O  | 0.183      | 0.159      | 0.206    | 0.156       | 0.164       |
| C-C-O-C  | 0.180      | 0.174      | 0.231    | 0.167       | 0.149       |
| C-C-N-C  | 0.165      | 0.142      | 0.223    | 0.136       | 0.146       |
| C-C-N-O  | 0.277      | 0.270      | 0.285    | 0.264       | 0.293       |
| C-N-C-O  | 0.453      | 0.430      | 0.398    | 0.358       | 0.335       |
| N-C-C-O  | 0.315      | 0.253      | 0.303    | 0.244       | 0.272       |
| C-N-C-N  | 0.340      | 0.317      | 0.328    | 0.254       | 0.263       |

CQ3: More related works on fragment-based molecule generation.

We add a paragraph to the related work in the new version, as below.

**Fragment-based drug design**. Previously, works on fragment-based molecule generation are proposed. For example, JT-VAE[44] generates a tree-structured scaffold over chemical substructures and combines them into a 2D-molecule. PS-VAE[45] can automatically discover frequent principal subgraphs from the dataset, and assemble generated subgraphs as the final output molecule in 2D. Further, DeepFrag [46] predicts fragments conditioned on parents and the pockets, SQUID[47] generates molecules in a fragment level conditioned on molecule’s shapes. FLAG[48] auto-regressively generates fragments as motifs based on the protein structures in 3D.

[44] Wengong Jin, Regina Barzilay, and Tommi Jaakkola. Junction tree variational autoencoder for molecular graph generation, 2019

[45]Xiangzhe Kong, Wenbing Huang, Zhixing Tan, and Yang Liu. Molecule generation by principal subgraph mining and assembling, 2022.

[46]Harrison Green, David R. Koesb, and Jacob D. Durrant. Deepfrag: a deep convolutional neural network for fragment-based lead optimization. Chemical Science, 2021

[47] Keir Adams and Connor W. Coley. Equivariant shape-conditioned generation of 3d molecules for ligand-based drug design. In The Eleventh International Conference on Learning Representations, 2023.

[48]ZAIXI ZHANG, Shuxin Zheng, Yaosen Min, and Qi Liu. Molecule generation for target protein binding with structural motifs. In International Conference on Learning Representations, 2023


Meta-review: The paper presents a novel method for generating 3D molecules that bind to specific protein pockets based on a functional-group-based diffusion model (D3FG). The method is novel, the results are strong on QED and SA, and the new dataset would be beneficial for the community. Reviewers have major concerns about comparison with prior 3D fragment based approaches. Additional results provided in response are convincing. I would encourage authors to add these to the paper. Overall, I would support the paper to be included in the conference.
Decision: Accept (poster)