DecompOpt: Controllable and Decomposed Diffusion Models for Structure-based Molecular Optimization
Authors: Xiangxin Zhou
Xiwei Cheng
Yuwei Yang
Yu Bao
Liang Wang
Quanquan Gu
Venue: ICLR 2024 poster (2024)
Keywords: Structure-based drug design
molecule optimization
diffusion models
3D molecule generation
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: Recently, 3D generative models have shown promising performances in structure-based drug design by learning to generate ligands given target binding sites. However, only modeling the target-ligand distribution can hardly fulfill one of the main goals in drug discovery -- designing novel ligands with desired properties, e.g., high binding affinity, easily synthesizable, etc. This challenge becomes particularly pronounced when the target-ligand pairs used for training do not align with these desired properties. Moreover, most existing methods aim at solving de novo design task, while many generative scenarios requiring flexible controllability, such as R-group optimization and scaffold hopping, have received little attention. In this work, we propose DecompOpt, a structure-based molecular optimization method based on a controllable and decomposed diffusion model. DecompOpt presents a new generation paradigm which combines optimization with conditional diffusion models to achieve desired properties while adhering to the molecular grammar. Additionally, DecompOpt offers a unified framework covering both de novo design and controllable generation. To achieve so, ligands are decomposed into substructures which allows fine-grained control and local optimization. Experiments show that DecompOpt can efficiently generate molecules with improved properties than strong de novo baselines, and demonstrate great potential in controllable generation tasks.

Published as a conference paper at ICLR 2024
CONTROLLABLE AND DECOMPOSED DIFFUSION MOD- ELS FOR STRUCTURE-BASE MOLECULAR OPTIMIZA- TION
Xiangxin Zhou 1,2,3 Xiwei Cheng" Yuwei Yang² Yu Bao Liang Wang Quanquan Gu
1 School of Artificial Intelligence, University of Chinese Academy of Sciences
Center for Research on Intelligent Perception and Computing (CRIPAC),
State Key Laboratory of Multimodal Artificial Intelligence Systems (MAIS),
Institute of Automation, Chinese Academy of Sciences (CASIA)
SByteDance Research
HHahcooglu Data Science Institute, University of Californa San Diego
ABSTRACT
Recently, 3D generative models have shown promising performances in structure- based drug design by learning to generate ligands given target binding sites. How- ever, only modeling the target-ligand distribution can hardly fulfill one of the main goals in drug discovery - designing novel ligands with desired properties, e.g., high binding affinity, easily synthesizable, etc. This challenge becomes particularly pronounced when the target-ligand pairs used for training do not align with these desired properties. Moreover, most existing methods aim at solving de novo design task, while many generative scenarios requiring flexible controllability, such as R-group optimization and scaffold hopping, have received little attention. In this work, we propose DECOMPOPT, a structure-bass molecular optimization method based a controllable and decomposed diffusion model. DECOMPÔPT presents a new generation paradigm which combines optimization with conditional diffusion models to achieve desired properties while adhering the molecular grammar. Ad- ditionally, DECOMPOPT offers unified framework covering both de novo design and controllable generation. To achieve so, ligands are decomposed into substrue- tures which allows fine- ane-grained control and local optimization. Experiments show that DECOMPOPT can efficiently generate molecules with improved properties than strong de novo baselines, and demonstrate great potential in controllable generation tasks.
INTRODUCTION
Structure-based drug design (SBDD) (Anderson 2003) is an approach that involves designing drug molecules based the 3D structure of a target. The goal of SBDD is to generate ligands with desired properties which can bind tightly to the target bind- ing site. Recently, several works have cast SBDD into conditional 31D molecular generation task and achieved remarkable success thanks to the powerful deep generative models. In these models, the target binding site serves as the condition and the condi- tional distribution of ligands learnt in driven manner using various generative models. Peng et al. (2022) and Zhang et al. (2022) proposed to generate molecules given pockets in auto-regressive fasion using atoms or fragments as building blocks respec-
density
-17.5 -15.0 -12.5 -00.0 -7.5
-5.0
-2.5
0.0
Figure 1: Vina Scores distribution of protein- ligand pairs in CrossDocked2020 dataset. - 8.188 kcal/mol, marked by the red vertical line, commonly used value representing moderate binding affinity.
"Equal Contribution. Work was done during Xiangxin's 's and Xiwei's internship at ByteDance. 1 "ooresponndig Author: Quanquan Gu (quanquan, gu bytedance.com).

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tively. Guan et al. (2023a) Schneuing al. (2022) Lin al. (2022 diffusion models to generate ligands by modeling atom types and positions.
Generative models are powerful approaches for extracting the underlying molecular grammar (e.g.. the reasonable atomic valence, stable molecular conformation, etc.). However, they cannot generate molecules with desired properties if the training data do not align with these properties as well. Indeed, unsatisfying data quality is a common challenges in drug discovery (Vamathevan et al. 2019). As Figure[] shows. the ligands in CrossDocked2020 (Francoeur et al., 2020), a widely used training dataset for SBDD models, have moderate binding affinities measured by molecular docking scores. Solely maximizing the likelihood of training data can mislead SBDD models and cause inefficiency in generating potential drug candidates. To overcome this limitation, molecular optimization (Xiel et al.) 2021 Fu et al. 2022) offers a direct path for searching molecules with desired properties in the broad chemical space. However, its application to 3D molecule generation remains unexplored.
On the other hand, current SBDD models are mostly limited to De novo design (Hartenfeller & Schneider 201T), which focuses on generating ligands from scratch, the main task that most efforts have been devoted to. However, controllable molecular generation scenarios, such R-group design (Takeuchi et al.] 2021) (also known as biosteric replacement) and scaffold hopping (Böhm et al.) 2004), are equally, if not more, important. Unlike de novo design, controllable generation tasks start from an existing compound, and only modify a local substructure to improve the synthetic accessibility. potency and drug-likeness properties or to move into novel chemical space for patenting (Langdon et al. 2010). Controllable generation aims to utilize prior knowledge, such as a known active compound, in the design process to increase the chance of finding promising candidates. Some initial efforts have been made to address controllable molecular generation problem. For example, Igashov al. (2022); Imrie et al. (2020) 202T); Huang al. (2022) propose use generative models to design linkers between the given fragments. However, these methods are designed for a specific controllable generation task and cannot be generalized.
To overcome the aforementioned challenges and limitations in existing SBDD approaches, we propose DECOMPOPT, a controllable and decomposed diffusion model for structure- based molecular optimization. DECOMPÔPT combines diffusion models with optimization algorithm to harness the advantages of both approaches. Diffusion models are used to extract molecular grammar in a data-driven fashion, while optimization algorithm used to effectively optimize the desired properties. Furthermore, DECOMPOPT offers unified generation framework for both de novo design and controllable generation through ligands decomposition. Notably, a ligand that binds to a target binding site can be naturally decomposed into several substructures, i.e., arms and scaffold, where arms locally interact with corresponding subpockets and scaffold links all arms to form a complete molecule. Such decomposition motivates to design conditional diffusion models in the decomposed drug space which ensures flexible and fine-grained control over each substructure. We highlight our main contributions follows:
We propose new molecular generation paradigm, which combines diffusion models with iterative optimization learn molecular grammar and optimize desired properties simultaneously.
We design a unified generation framework for de novo design and controllable generation via a controllable and decomposed diffusion model.
For de novo design, our method can generate ligands with an average Vina Dock score of -8.98 and Success Rate of 52.5%, achieving a new SOTA on the CrossDocked2020 benchmark.
For controllable generation, our method shows promising results in various practical tasks of SBDD, including R-group design and scaffold hopping.
2 RELATED WORK
Molecule Generation Deep generative models have shown promising results in molecule genera- tion. In the last decade, researchers have explored various representations and models for molecule generation. Molecules can be represented in ID (e.g.. SMILES (Weininger) 1988). SELFIES (Krenn) al. 2020 2D (i.e., molecular graph (Bonchev) 1991), ). and 3D. Among them, 3D representations attract recent attention since they capture the complete information of molecules, and have better potential to generate and optimize molecules with regard to 3D properties, such bioactivity for
given target (Baillif et al. 2023).
SBDD represents an important application for 3D molecule generation. Ragoza et al. (2022) generate 3ID molecules in atomic density grids using variational autoencoder (Kingma & Welling 2013).
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Luo et al. (2021): Liu et al. (2022); Peng al. (2022) propose generated atoms (and bonds)
rutooregressively in 3D space. while Zhang et al. (2022) use fragment as building blocks instead.
Guan et al. (2023a); Lin et al. (2022); y Schneuing et al. (2222) introduce -quiiaaaana diffusion
models for SBDD. More recent works have incorporated domain knowledge into 3D generative
models, such as the correspondence between local fragments and subpockets. [Guan al. (2023a)
suggest to break ligands into substructures and model them using decomposed priors in a diffusion framework, leading remarkably improved binding affinities of the generated molecules, Zhang & -eoooypp-aggeeteee 3D molecule generation scheme to establish the relation between subpockets and their corresponding fragments. Existing methods based on deep generative models are powerful at distribution learning. However, when the training examples do not have the desired properties, these models can hardly generate out-of-distribution samples with these properties.
Liu (2023) propose a subpocket
Molecule Optimization Optimization-based algorithms are another popular approach to design drug molecules. Methods within this category rely on predefined computable objectives to guide the optimization. Various optimization methods have been proposed for 2D drug design. JTVAE (Jin et al., 2018) uses Bayesian optimization the latent space to indirectly optimize molecules. Reinforcement learning is used to manipulate SMILES strings (Olivecrona et al., 2017) and 2D molecular graphs (Zhou et al. 2019; Jin et al. 2020). MARS (Xie et al.) (021)) leverages adaptive Markov chain Monte Carlo sampling to accelerate the exploration of chemical space. RetMol develops a retrieval-based generation scheme for iteratively improving molecular properties. Genetic algorithm is also popular choice. GA+D (Nigam et al. (020) uses deep learning enhanced genetic algorithm to design SELFIES strings. Graph-GA (Jensen 2019) conducts genetic algorithm on molecular graph representation. GEGL (Ahn et al. 2020) adopts genetic algorithm to generate high quality samples for imitation learning by deep neural networks. AutoGrow 4 (Spiegel & Durrant 2020) and RGA (Fu al., 2022) are genetic algorithms for SBDD which incorporate target structures in molecular optimization. Both of them use molecular docking score as an objective to optimize the
fitness between target structure and the generated ligands. In addition, RGA uses neural models to stablize genetic algorithm and includes target structures as a condition in its modeling. To our best knowledge, there are limited efforts on generating 3D molecules using molecular optimization.
Although optimization algorithms offers direct approach achieve desired properties, they require computable and accurate objectives to guide the exploration. However, not all desired properties for drug design can be easily formulated as objectives, such as molecular validity. Considering the benefits of both generative models and optimization algorithm, it is reasonable to combine them to achieve further enhanced results.
Controllable Generation De novo design aims to generate molecules from scratch, and the above- mentioned methods mainly focus on this task. Besides it, another line of research focuses on controllable molecule generation, which requires generating or optimizing partial molecules. R-group design is a task to decorate a fixed scaffold with fragments to enhance the desired properties. [Langevin] al. (2020) and Maziarz al. (2022); Imrie et al. (022]) propose to constrain the scaffold region using SMILES- based and 2D graph-based models. However, similar attempts have been rarely observed in 3D molecule generation. Scaffold hopping, on the other hand, requires the replacement of the scaffold to explore novel chemical space while maintaining the favorable decorative substructures. Imrie et al. (2020) 202T) propose autoregressive models to design 2D linker conditioning on geometric features of the input fragments and pharmacophores. [Huang et al. (2022); ; [gashov et al. (2022) extend the application to the 3D space using variational autoencoders and diffusion models. However, existing 3D controllable generation methods specifically designed for single task. There lacks
an unified framework to cover all possible conditional generation tasks, as well as de novo design.
3 METHOD
In this section, we will present our method, named DECOMPOPT, illustrated in Figure 2 In Section [.I] we show how to design a controllable and decomposed diffusion model that can generate ligand molecules conditioning on both protein subpockets and reference arms. In Section 3.2 show how to efficiently optimize the properties of the generated ligand molecules in the decomposed drug space by improving the arm conditions.
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Controllable and Decomposed Diffusion Model
999
t=
Reverse Process Forward Process
Reverse Process
HR
F Forward Process
Sampling & Decompese
Arm conditions
Get Reference Arms
Figure 2: Illustration of DECOMPÔPT. In each iteration of optimization: (1) For each subpocket, reference arm is sampled from the ordered arm list. (2) The controllable and decomposed diffusion model generated ligand molecules based on arm (and subpocket) conditions. (3) The generated ligand molecules are collected and further decomposed into scaffolds and arms. (4) Poor arms in the ordered arm lists are replaced with the new arms that show better properties.
3.1
CONTROLLABLE AND DECOMPOSED DIFFUSION MODELS
ligand molecule that binds to a specific protein pocket can be naturally decomposed into several components (i.e., arms and scaffold). The arms of ligand molecule locally interact with subpockets of the target protein. Notably, they are the main contributors to binding affinity. The scaffold links all the arms form a complete molecule. Inspired by this, Guan et al. (2023b) introduced decomposed priors to diffusion models for SBDD. The decomposed priors not only induce better variational lower bound as the training objective but also provides possibilities to achieve controllability in molecular generation. Specifically, the decomposed priors allow for relatively independent modeling of each arm. To combine generative models with optimization, flexible and controllable generation framework is need. Thus we propose controllable and decomposed diffusion model that allows for fine-grained control over the arms of the generated ligands. Considering the different functionalities of the arms and scaffold, we only control the arms that play important roles in interaction with pockets, and leave room for the generative model on the scaffold to achieve the trade-off between controllability and diversity.
Provided with target binding site that can be represented as P = ((x, "E")) we aim to generate a ligand molecule that can be represented M (a;M u.M. bytt) (aje)........................... No and NM are the number atoms in the protein pocket and ligand molecule, respectively. Here E R3 ligand molecule M can be decomposed into a scaffold and several arms (EE..E where M SUA, AK.. We denote the subpocket that is within 10Å of the atoms of the k-th arm Av as Px. The controllable and decomposed diffusion model is expected to generate a ligand molecule M given protein pocket P and several reference arms {Aa ). which can be formulated as modeling the conditional distribution (MMPP {A+)). And the arms of the generated ligand molecules are expected to be similar to the corresponding reference arms.
Rd b R denote the atom position, atom type, and bond type, respectively. A
Generally, there are two critical modules in our model: a condition encoder and diffusion-basee decoder. We employ an -Euuiaaqqi neural network (Satorras al., (202), named EGNN, to encode reference arm As and its surrounding subpocket Pk. We introduce subpockets here to include information of intermolecular interaction and relative positions. Specifically, we build e-nearest-ncighbor (knn) geometric graph on the complex of the reference arm and its surrounding subpocket and apply the EGNN to learn its representation as follows: [Ag, Px] = Enc(Aç, Pk), where A E IR Ax|xD, Pt E R Pe P D. [.] denotes concatenation along the first dimension. Each row of A (resp. P&) corresponds to condition feature of an atom in the reference arm Aş (resp. the subpocket Px). a = Agg([A,, P&]) e RR" is the global SE(3)-invariant condition feature aggregated from the atom-wise condition features.
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The diffusion model first perturbs samples by iteratively injecting random noises which are indepen- dent of the arm conditions. This leads to the forward process as follows:
(MarIMo. P,(As)) a(Murl P) = II M(MiMM-.,)))
(I)
t=1
where Mo PMM {A+}) and (M,) is sequence of perturbed ligands. We will introduced the aforementioned condition features into the reverse (generative) process the diffusion model as:
T II
Po Mr. P, (AA))
((Ac))
(2)
To model MMMMM-IM,,,,.AA
for the imput (i.e., the ligand molecule being generated at time step !) of the diffusion-based decoder, we denote the SE(3)-invariant feature of its each arm atom of1 and each scaffold atom as wzM. For each arm atom that belongs to its k-th arm, we incorporate the aforementioned arm condition as oz = MLP((17 axl). For each scaffold atom, we do not introduce any condition (i.e., 0f == MLP(o.)) and leave enough room for let
the generative model to generate diverse scaffolds. For each atom of the protein pocket, v."" MLP([U," Age Age (MLP((,) ")... MLP(o;")D)) where v," is the atom condition feature that corresponds to specific row of Ps if this atom belongs to the k-th subpocket and is set to be otherwise. For the SEuu)-equivariant feature (i.e., the coordinate 3D space) of each atom, we do not introduce any conditions. Nevertheless, the geometric information is embedded in the SE(3)-invariant features thanks the particular design of EGNN. After the input feature is augmented by the condition, the rest of the diffusion-basse decoder mainly follows DecompDiff (Guan et al. 2023b), including the decomposed prior distribution, model architecture, training loss, etc.
To shed lights the insights behind the ded- icated model design, we will discuss more about our special considerations as follows. The encoded conditions follow the principle of decomposition.
Algorithm Optimization Process
Input:
A specific protein pocket P with detected subpockets {P*})==,.....k a reference ligand M, pre-trained decomposed and controllable diffusion model denoted as Enc(-) and DifiDee(-)
notable that differ- ent reference arms that locally interact with different subpockets are encoded and play roles in parallel, which allows us to control the generation more flexibly. For example, control the different arms of the gen- erated ligand molecules separately. Another concern about diversity. We do not explic- itly introduce any regularization like VAE (Kingma Welling 2013) over the represen- lation space of conditions in consideration of the unsmooth nature of chemical space. Nevertheless, the source of randomness is two-fold: the sampling procedure of the dif- fusion model and the degree of freedom of scaffold. Notably, the scaffold and arms will impact each other in the generative process and the randomness of scaffolds will also flow into arms. Expectedly, the arm of the generated ligand molecule will be similar to its corresponding reference arm but not ex- actly the same, which is the workhorse of our framework. This characteristic reflects both the abilities of exploration and exploitation, which is critical to the optimization process that will be introduced in the following.
Output: OAL(Px)
Intialize all ordered arm lists for arms.
{ + Decompose (M, M,P? P. (Px})
for + to do
# is the evaluated score.
Ask)As) < DockEval(AAs, Pk))
OAL( +- (()),A))
end for
# Start iterative optimization. for < to N do
The inner loop is just for better illustration
and is paralled as a batch in practice.
for
B do Sample } from OAL(Ps)
M + DiffDec(P, (Enc(A) Pb)))
{AAt ) + Decompose( M. P, (Px))
for 1 to K do
(sk; Ar.) < DockEval(Ai, Pi)
Append (Sk, As) ) to OAL(
Sort OAL(Ps) by sk
Keep top-M elements in OAL(Pk)
end for
end for
end for
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3.2 OPTIMIZATION IN THE DECOMPOSED DRUG SPACE
Thanks to the controllability and decomposition of the model introduced above, we can optimize the ligand molecules in the decomposed drug space. We will introduce the optimization process of DECOMPOPT as follows.
Due to the characteristics of decomposition, different arms that locally interact with different sub- pockets can be evaluated seperately. Thus we can define a score for each arm, which can be single objective or a value that scalarizes multiple objectives by weighted sum. The following optimization process is oriented towards a given protein pocket. For each subpocket of the given protein pocket, we build an ordered list with a certain max size to store potential arms sorted by their scores. We can initialize the ordered arm lists (OAL) by decomposing reference ligands or ligand molecules gener- ated by generative models. In each iteration of optimization, we use the controllable and decomposed diffusion models to generate a batch of ligand molecules conditioned from the ordered arm lists and further decompose them to get new arm candidates. The new arms are first refined by re-docking and then evaluated by oracles. Here we introduce an optional re-docking procedure to assign each arm with a higher-quality pose so that better interaction information can be injected into arm conditions. Then the new arms are inserted into the corresponding ordered lists and the arms with bad scores will be remove to keep predefined max size. As the process goes on, more and more arms that can well interact with the subpockets will be discovered.
reference arms sampled
The optimization process based DECOMPOPT is summarized as Algorithm [
This optimization process shares similar ideas with well-recognized evolutionary algorithms. Arms in each ordered arm list evolve towards desired properties. The controllable generation can be viewed as one kind of mutation. But, differently, generative mutation is more efficient than the widely-used mutation defined by rule-based perturbation.
4 EXPERIMENTS
4.1
EXPERIMENTAL SETUP
Dataset We utilized the CrossDocked2020 dataset (Francocur et al. (020)) to train and evaluate model. Additionally, we adopted the same filtering and splitting strategies as the previous work (Luo)
et al. 2021 Peng al. 2022, Guan et al., 2023a). The strategy focuses retaining high-quality complexes (RMSD < IA) and diverse proteins (sequence identity < 30%), leading to 100, 000 protein-binding complexes for training and 100 novel protein for testing.
Implementation Details For iterative optimization, we select arms with desired properties as conditions. We initialize the list of arms with 20 molecules generated by DecompDiff our experiment. To better align with the practical requirements of pharmaceutical practice, where the goal is to generate molecules with high drug likeness, synthesis feasibility, binding affinity, and other pertinent properties, we introduced multi-objective optimization score effectively balance these different objectives. In each iteration, we evaluate QED, SA, Vina Min (which will be introduced in detail later) of decomposed arms from generated molecules, then calculate Z-score(x.) = (I; mean( (X),, I₁ E X (also known as the standard score (Zill 2020)) of each property, where X denotes the of evaluated values of specific property. The Z-scores of each property are aggregated with same weights as criteria for selecting the top-M arms as next iteration conditions. In our experiment, we conduct 30 rounds of optimization and sample 20 molecules in each round. For top-M arm selection, we set M=3. For each protein pocket, if the average properties of sampled ligand molecules are no longer improved, the optimization process will be early stopped.
Baselines There are two types of baselines from the perspective of generation and optimization, respectively. Generation Perspective: We compare our model with various representative generative baselines: liGAN (Ragoza al. 2022), is 3D CNN-based conditional VAE model which generate ligand molecules in atomic density grids. AR (Luo et al. (201)). Pocket2Mol (Peng et al.) (202)) and GraphBP (Liu et al. 2022) are GNN-based methods that generate 3D molecules atom by atom in an autoregressive manner. TargetDiff (Guan et al.) 2023a) is diffusion- -based method which generates atom coordinates and atom types in a non-autoregressive way, and the prior distribution a standard Gaussian and bonds are generated with OpenBabel (O Boyle et al.) 2011)) DecompDiff (Guan et al.) 2023b) is a diffusion- atoms and bonds of 3D ligand molecules in end-to-end manner. Decompdiff has three optional decomposed priors: reference priors, pocket priors, and optimal priors. Our method also follows this setting. Optimization Perspective: We choose the most related work, RGA (Fu et al. 2022). which
method with decomposed priors and validity guidance which generates

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Table 1: Summary of different properties of reference molecules and molecules generated by our model and other generation (Gen.) and optimization (Opt.) baselines. (t) (4) denotes larger / smaller number is better. Top 2 results are highlighted with bold text and underlined text, respectively.
Methods
Scure (4)
(1)
Duck
High Affinity
QED
Diversity
Success
Avg.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Rate
Reference
-6.36
-646
.6.71
-6.99
-7.45
-7.26
0.48
0.47
0.73
0.74
25.0%
LIGAN
-6.33
-6.20
21.1%
11.15
0.39
0.39
0.39
0.57
0.66
0.67
3,9%
GraphBP
-4.80
-470
14.2%
6.7%
0.4
0.45
0.49
0.48
0.79
0.78
0.1%
Gen.
AR
-5.55
-5.64
+6.18
-5.88
-6.75
-6.6
37.9%
31.0%
0.51
0.50
0.63
0.63
0.70
0.70
7.1%
Pocket2Mol
-5.14
-4.70
-6.12
-5.82
-7.15
-..9
18.4%
51.0%
0.56
0.57
0.74
0.75
0.69
0.71
24.1%
TargeDDiff
-5.47
66.30
-6.64
-6.83
-7.80
-7.91
58.1%
59.11
0.48
0.48
0.58
0.58
0.72
0.71
10.5%
DecompDidt
-5.67
-6.04
-7.04
-7.09
.8.39
-8.43
64.4%
71,0%%
0.45
0.43
0.61
0.50
0.68
0.68
24.5%
Opt.
RGA
-8.01
-8.17
64.1%
89.3%
0.57
0.57
0.71
0.73
0.41
0.41
16.2%
Gen.
TargetDiff w/ Oge.
-7887
-7,48
-7.82
-7.48
-8.30
-8.15
71.5%
95.9%
0.66
0.68
0.68
0.67
0.31
0.30
25.8%
Ope.
DECOMPOPT
-5.87
-6.81
-7.35
-7.72
-8,98
-9.01
73.5%
93.3%
0.48
0.45
0.65
0.65
0.60
0.61
52.5%
is a reinforced genetic algorithm with policy networks and also focus structure-based molecular optimization, as the baseline. Besides, we also introduced the controllability into TargetDiff by whole molecule conditions rather than arm conditions. We name this baseline as TargetDiff' w/ Opt..
Metires We evaluate the generated molecules from target binding affinity and molecular prop- erties. We employ AutoDock Vina (Eberhardt et al., 2021) to estimate the target binding affinity, following the same setup as al. (2021]: Ragoza et al. (2022). We collect all generated molecules across 100 test proteins and report the mean and median of affinity-related metries (Vina Score, Vina Min, Vina Dock, and Hlgh Affinity) and property-relatet metrics (drug-likeness QED (Bickerton) et al. 2012), synthesizability SA (Ertl & Schuffenhauer 2009), and diversity). Vina Score directly estimates the binding affinity based on the generated 3D molecules, Vina Min conducts a local structure minimization before estimation, Vina Dock involves a re-docking process and reflects the best possible binding affinity, and High Affinity measures the percentage of how many generated molecules binds better than the reference molecule per test protein. Following Yang et al. (202T): Long et al. (022);: Guan et al. (2023b): Yang et al. (2024), we further report the percentage of molecules which pass certain criteria (QED > 0.25, SA > 0.59, Vina Dock < 18.18) as Success Rate for comprehensive evaluation, considering that practical drug design also requires the generated molecules to be drug-like, synthesizable, and maintain high binding affinity simultaneously (Jin et al.) 2020: Xie et al. (021). Additionally, we also evaluate the generated molecules from the perspective of molecular conformation. Please refer to Appendix for more results.
4.2 MAIN RESULTT
We evaluate the effectiveness of our model in terms of binding affinity and molecular properties. As shown in Table [ DECOMPOPT outperforms baselines by a large margin in affinity-related metrics and Success Rate, a comprehensive metric. Specifically, DECOMPOPT surpasses the strong baseline DecompDiff in all metrics, except diversity. All these gains clearly indicate that the optimization works expected and our method better aligns with the goal of drug discovery compared with the generative baselines.
Notably, RGA, which also focuses on structure-based molecular optimization, achieves promising Sucess Rate. And our method performs even better. More importantly, molecular optimization methods like RGA inevitably encounter the pitfalls of low diversity and inefficiency. Because these optimization methods usually start with reference ligand and iteratively make small changes it to gradually improve the property. They are easy to be trapped in local solutions. However, DECOmPPPt inherites advantages of both optimization and generation, achieving high Success Rate and considerable diversity at the same time. See Appendix C for additional results.
4.3 ABLATION STUDIES
Single-Objective Optimization To further validate the effectiveness of DECOMPÔPT, we test our method on the setting of single-objective optimization with reference priors. Specifically, we use QED, SA, and Vina Min as the objective and analyze the results of three experiments, respectively. As shown in Table each experiment effectively improves the corresponding property.
Benefits of Decomposed Optimization The decomposed drug space allows for optimizing each arm of a ligand molecule separately. In method, arms of each subpockets are evaluated and
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Table 2: Summary of results of single-objeetive optimization. The improvements of DECOMPÔPT over the baseline are highlighted in green.
Table 3: Comparison of optimiza- tion strategies using molecule-level and arm-level conditions.
DecompDiff
DECOMPOPT
Vina Min (
Property
Method
Avg.
Med.
Avg.
Med.
Avg.
Med.
QED (t)
0.48
0.48
0.52 (+8.3%)
0.53 (+10.4%)
DecompDilf
-6.01
-5.98
SA (f)
0.67
0.66
0.74 (+100.%%)
0.74 (+12.19)
Molecule-Ievel Opt.
-6.62
-6.66
Vina Min (U)
-6.01
-5.98
-6.72 (+11.8%)
-6.72 (+12.4%)
Arm-level Opt.
-6.72
-6.72
selected independently (namely, arm-level optimization). We also tried evaluating the property of the whole ligand molecules, choosing those with desired property, and decomposing them to serve as the arm conditions in the next optimization iteration (namely, molecule-Ievel optimization). We compare these two optimization under the setting of reference prior. As shown in Table arm-wise optimization performs better than molecule wise optimization, which demonstrates benefits brought by decomposition in terms of optimization efficiency.
4.4 CONTROLLABILITY
Various molecular optimization scenarios, including R-group design and scaffold hopping, play crucial role in real-world drug discovery. They enhance binding affinity, potency, and other relevant molecular properties with greater precision. Our controllable and decomposed diffusion model seamlessly integrates with these scenarios by incorporating expert knowledge through decomposed arm conditions, better aligned with the demands and objectives of the pharmaceutical industry.
Table 4: Scaffold hopping results of Decompdiff and DECOMPOPT on CrossDocked2020 test set.
Valid (t)
Unique (t)
Novel (t)
Complete Rate (1)
Scaffold Similarity (1)
Methods
DecompDiff-Impainiing
0.95
0.48
0.85
89.2%
0.40
DECOMPOPT +Inpainting
0.96
0.46
0.88
93.0%
0.35
R-group Design R-group optimization is widely used technique to optimize molecules' sub- stituents for improving biological activity. Our model is well-suited for this task by employing finer-level arm conditions to guide the optimization. To achieve the optimization goal, decompose the compound into a scaffold and multiple arms. Subsequently, we choose a specific arm for opti- mization to enhance its binding affinity. The optimization process involves conditional inpainting (Lugmayr et al. (022) inspired by Schneuing et al. (2022).
We diffuse the remaining part of the compound while predicting the selected arm, which is conditioned on the reference optimize. From the molecules generated through this process, we can select substituents with higher Vina Min Score to serve as the condition for the next iteration. Results of R-group optimization on protein 3DAF and 4FIM are presented in Figure 3 More results on protein 4G3D can be found in Appendix D After 30 rounds of optimization, our generated molecules achieve vina minimize score more than kcal/mol better than the reference. Moreover, we compare DECOMPOPT with Decompdiff for R-group optimization on Vina minimize, Tanimoto similarity, and Complete rate with detailed result in Appendix D Tanimoto similarity is calculated using rdkit GetMorgann i nigerpp rprrrii and T i mi larits ty functions. Complete rate measures the proportion of completed molecules in generated result. As Table [4] shows, the decomposed conditional arms bring greater controllability over the shape, positioning, and properties of the generated substituents compared to diffusion inpainting.
at each step. We initialize the list of arms by the arms defined as r-group to
Fragment growing is a another technique for R-group design. Unlike R-group optimization, fragment growing aims to design new substituents instead of optimization existing ones. By designing novel arms priors and predicting the number of atoms through chemistry software or expert guidance, DECOMPPPT can naturally facilitate incremental growth and optimization of newly generated arms, leading to improved biological activity. A case study on the application of fragment growing can be found in Appendix D
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Scaffold Hopping In contrast R-group design, scaffold hopping involves the generation of scaf- folds to connect pivotal groups, which play critical role in inter- action with proteins. We apply our decomposed conditional diffusion model to scaffold hopping by in- painting scaffold fixed arms and incorporating pivotal arms as struc- tural conditions. We generate 20 molecules for each target our test set. Following Huang et al. (2022), measure the Validity Uniqueness, and Novelty of gener- ated molecules. Additionally, we compute the Complete Rate, which measures the proportion of success- fully constructed molecules with all atoms connected. To better under- stand the influence of conditional arms on scaffold generation, we es- timate Scaffold Similarity between generated scaffold and reference scaffold following Polykovskiy al. (2020). A detailed description scaffold hopping evaluation met- rics can be found Appendix [D] The supplementary information pro- vided indicates the inclusion of arm conditions can influence scaffold generation through message pass- ing, leading to more consistent scaffold when compared to diffu- sion inpainting without arm condi- tions. As Table shows, our model achieves higher validity and com- plete rate. Higher novelty and lower scaffold similarity indicate that our model is better at maintaining diver- sity and exploring novel molecules while controlling pivotal groups. Figure 4 we show results of seaf- fold hopping on IRIH and SAEH.
Reference Ligands
DecompOpt for R-group Optimization
3DAF
Vina Mini 9.27
Vina Mini -10.19
Vina Mini -10.42
4F1M
XAL
Vina Min: -5.78
Mina Min: -6.84
Vina Min: -6.95
Figure 3: Visualization of reference binding molecules (left column). molecules generated by DECOMPOPT (middle and right column) with 30 rounds of optimization on protein 3DAF (top row) and 4F1M (bottom row). Optimized R-group are highlighted in red.
Reference Ligands
DecompOpt for Scaffold Hopping
1R1H
SAEH
More visualization results can be found in Appendix
Figure 4: Examples of scaffold hopping accomplished by DE- СОMРOPT. For each row, the left image shows the reference ligand, the middle and right images are two examples gener- ated by DECOMPOPT. Reference and generated scaffolds are highlighted in green.
5 CONCLUSIONS
In this work, we proposed con- trollable and decomposed diffusion model for structure-based molecu- lar optimization and opened a new paradigm that combines generation and optimization for structure-based drug design. Our method shows promising performance on both de novo design and controllable generation, indicating its great potential in drug discovery. We would like to point out that in current controllable diffusion models, we did not explore the best way for oulti-objective optimization. We plan to investigate it in future work.

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A IMPLEMENTATION DETAILS
In this section, we will provide more implementation details of our methods. Though some contents, such as the equivvaran layer and the loss function, can be referred to Guan et al. (2023b), we still include them here to make our paper more self-containing.
A.1 FEATURIZATION
We follow the decomposition algorithm proposed by Guan et al. (2023b) to decompose ligand molecules into arms and scaffold. We define the part of proteins that lies within 10Å of any atom of an arm as its corresponding subpocket.
Following Deco (Guan et al., 2023b), we represent each protein atom with the following features: one-hot element indicator (H, C, N, O, S. Se), one-hot amino acid type indicator (20 dimension), one-dim flag indicating whether the atom is a backbone atom, and one-hot arm/scaffold region indicator. If the distance between the protein atom and any arm center is within 10A, the protein atom will be labeled as belonging to an arm region and otherwise a scaffold region. The ligand atom is represented with following features: one-hot element indicator (C, N, O, F, P, S, CI) and one-hot arm/scaffold indicator. Different from DecompDiff, the atom features are enhanced by concatenating an SE(3)-invariant feature of arms and their corresponding subpockets encoded by the condition encoder after the orignal features.
Two graphs are constructed for message passing in the protein-ligand complex: a k-nearest neighbors graph 9K upon ligand atoms and protein atoms (we choose h 32 in all experiments) and fully-connected graph Gr. upon ligand atoms. The edge features are the outer products of distance embedding and edge type. The distance embedding is obtained by expanding distance with radial basis functions (RBF) located at 20 centers between OÅ and 10Å. The edge type is a 4-dim one-hot vector indicating the edge is between ligand atoms, protein atoms, higand-protein atoms protein- ligand atoms. In the ligand graph, the ligand bond is represented with a one-hot bond type vector (non-bond, single, double, triple, aromatic), an additional feature indicating whether or not two ligand atoms are from the same arm/scaffold.
A.2 MODEL. DETAILS
The controllable and decomposed diffusion model consist of two parts: a condition encoder and a diffusion-based decoder. The building block is an SE(3)-equivariant layer that is composed of three layers: atom update layer, bond update layer, and position update layer.
We denote the protein pocket as P = {(x?" v {(x,, v; (t..)..
! and the ligand molecule as M where is the atom position, is the atom type, and bij the chemical bond type between the atom i and the atom j. For brevity, we omit the superscript P or M in the following. We use h, to denote the the SE(()-invariant hidden state of i-th atom, x; to denote the i-th atom's 's coordinate, which is SE(3) SE(3)-equivariant, and e:j to denote the hidden state of the edge between the i-th atom and the j-th atom. They can be obtained as we described in the previous subsection. And use t denote the time embedding that in Ho et al. (2020).
Atom Update Layer We denote the atom update layer as d, == (Qa1 Pa2i daIi das). We first use the atom update layer dai model protein- protein-ligand interation as follows:
Abg
Σ
Φai hj, |x; xyyl.ci,, ti
(E
where Nx (i) is the set of neighbors of the i-th atom in the protein-ligand complex graph Gx- We then further use the atom update layer da2 and d.a to model the interaction inside the ligand as follows:
mij da2(11x; - xyl1,
(4)
AbL <
Σ
Soz hj, mza
(5)
(eN
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where (1) represents the set of neighbors of the i-th atom in the ligand graph Gz. Finally, update the hidden state of atoms by the atom update layer Øot as follows:
h - h, + (Abk, + Ahz,s)
(6)
Bond Update Layer follows:
We update the hidden states of the edges by the bond update layer @b as
eij
Σ
do, hy, has maj, mja, ().
(EN6)
Position Update Layer {dpl. pp2] follows:
The atom positions are updated by the position update layer op =
AXK.
E (x, x1) (hi, hy, ||x; - -xyll
(8)
jENw(()
E (x) x1)0 hy ||x - Xyl1, mja (),
(9)
(ENL(0
X, f X4 (Axk, + AXL,) mol.
(10)
where mot is the indicator of ligand atoms since we assume the protein atoms are fixed as the context.
In practice, the condition encoder consists of two (B(3))-quvvaria layers and the diffusion based decoder consists of six SE(3) eqqiivarai layers. In each -qquivraaa layer, following Guan et al.) (2023b), we apply graph attention to aggregate the message of each node/edge. The key/value/query embedding obtained through 2-layer MLP with LayerNorm and ReLU activation. Stacking these three layers block, our model consists of 6 blocks with hi hidden_dim 128 and n_heads 1 6. Additionally, the diffusion-base decoder also have two prediction heads (which are simply 2-layer MLPs and following Softmax function) that maps the learned hidden states of atoms and edges the predicted atom type and bond type.
A.3 TRAINING DETAILS
Condition
Diffusion-based
Condition Feature
Position
Predict
Feature
Feature
Feature
Molecule
Squie-eqiivariant Layer
SE(3)-oquivariant Layer
Atom
Bond Feature
Poxition Feature
Atom Feature
Bond Feature
Position Feature
Reconstruction
Feature
Loss
Add Noise
Arm & Subpocket 1
Molecule at time & Pocket
Figure 5: Illustration of training. For this case, there actually three pairs of arms and subpockets input to the condition encoders separately. For brevity, we only plot one as an example.
Given pair of protein and ligand molecule, first decompose the molecule to get the arms. We add noise to the ligand molecules in the training set to get the perturbed molecules as the forward process of diffusion models (equation I The forward process is a Markov chain with fixed variance schedule
(3. (8:))=1....7 (Ho et al. 2020 We denote 0a
Br and ar II Osg- More specifically, the
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noises time are injected as follows:
(xx//x0) Nxxx vārxo (1 1 T) q vo) = C(velãeVo + (1- 0+)/ Ka), ((b, (bo C + +(1 -ā,)///////))))) Ki),
(11)
(12)
(13)
where Ka and K₁, are the number of atom classes and bond classes respectively.
Then the arms and subpockets are input to the condition encoder. The output of condition encoder and the perturbed ligand are further input to the diffusion- -baeed decoder. Then the reconstruction loss L at time is defined follows:
Ka c(vy, vol& log c(Vi, vo)& c(vi, volk
1.
(14)
k=1
K
bu)k c(b,, bol log c(br, bo)
L,
(15)
k=1
L = ||xo - xol1? L. [ + 7oL (t) + 7
(16)
(17)
where (x,, vt, by). (Xo. Vr. by), and (Xu. vo. bo) represents atom positions, atom types, and bond
types of the perturbed molecule at time I, ground truth molecule, and the predicted molecule respectively, c(vi, vo) c² / Ku of and c* (V,, vo) [arv, + (1 az) Ka] [ā-- + (1
ā at-1)/Kal c(b,, bo) = / k= e and (b,, bu) = [a,b, + (1- (1-a)) / o [ā.- + (1
(/)). Note that the condition encoder and the ciffusion-basee decoder are jointly trained.
In practice, we set the loss weights % = 100 and n = 100. Follwing the setting of Guan et al.
(2023b), we set the number of diffusion steps as 1000. For this diffusion noise schedule, we choose to use sigmoid/ |3 schedule with 31 = 7 and 3r = 2 for atom coordinates, and a cosine B schedule suggested in Nichol & Dhariwal (2021) with s = 0.01 for atom types and bond types.
We use Adam Kingma & Ba (2014) with O. ,999 to train the model. And we set ca 6 and clip-gradieeeeeecooooo ent wwwddiiinnttnnnmmaeeeeeeeee _norm=8. 8. Dur- ing the training phase, we add a small Gaussian noise with a standard deviation of 0.1 to protein atom coordinates as data augmentation. We also schedule to decay the learning rate exponentially with factor of 0.6 and a minimum learning rate of 1e-6. The learning rate is decayed if there is no improvement for the validation loss in 10 consecutive evaluations. The evaluation is performed for every 1000 training steps. We trained our model on one NVIDIA GeForce GTX A100 GPU, and could converge within 237k steps.
winiinggaaaaa. 0005, betas= (0. 95,
A.4 SAMPLING DETAILS
To sample molecules using the pre-trained controllable and decomposed diffusion model, assume that there are available arms as conditions, we can first sample noisy molecule from the prior distribution and derive molecule by iteratively denoising following the reverse process (equation ()) More specifically, the denoising step at time & corresponds to sampling molecules from the following distributions:
q(x,- X4, 20) = (x ū. Ro), 3,1), 9(v,-1 Vr, vo) = C(vi--lii vo)),
(18)
(19)
q( b [b,, bo) = (br bo)).
(20)
where jūr (X:, xn) = v 18 19,
l-a; 80 + (1 Xx, Br = 1- Br, ē(V,, vo) = -
k=l क and
T-a,
ēt (V,,, vo) = Jo,V; + (1 0z)/ K2] ④ [ā-1 vo + (1 10--0, oz-1)/ I)/K), o(b, bo) = ō" Σ
k= 22 and C f bu (1-00-1)/be /K] Here (St,, vo. b)) is the molecule output by the diffusion-bran based decoder, whose input is the noisy molecule at time t and the condition feature. The sampling step is illustrated as Figure During sampling, we also apply validity guidance
(b,,, bb) (a,b; (1 (1-11000 a.) (1-aa)/Ki)
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Condition Encoder
Difusion-based Decoder
Position
Predict
Feature
Feature
Feature
Feature
Position Updute Layer
Molecule
at time
Bond Update Layer
SE(D)-quivvrriat Layer
SF(a)-equlvarian
X6
Sample
Atom Update Layer
Atom Feature
Bond Feature
Position Feature
Atom Feature
Bond Feature
Position Feature
Molecule at time t-1
Arm & Subpocket
Molecule time & Pocket
Figure 6: Illustration of the sampling.
proposed by Guan et al. (003b), which encourages the model to generate molecules with valid structures.
A.5 OPTIMIZATION DETAILS
Controllable and Decomposed Diffusion Model
Denoise by Diffusion-bar based Decoder Reverse Process
Denoise
t=
Diffusion-biee -hado- Decoder Reverse Process wone # Forward Process Add
Add Noise
Encode Arm conditions by Condition Encoder
Decompose
Get Arms
Figure 7: Illustration of molecular optimization (revised based on Figure 2 It is highlighted where we apply the condition encoder and the diffusion-basee decoder.
To generate molecules with desired properties, posed diffusion models for structure-based molecular optimization without any fine-tuning. The optimization procedure is summarized Algorithm and illustrated Figure In practice, since reference ligands are not available, we can initialize the arm lists with 20 ligands generated by DecompDiff, and this is the actual setting in our experiment. We have provided the optimization procedure in detail that can be found in Section 3.2 and Section
apply the pre-trained controllable and decom-
B EVALUATION OF MOLECULAR CONFORMATION
To evaluate generated molecules from the perspective molecular conformation, we compute the Sansen-Shannor divergences (JSD) in atom distance distributions between the reference molecules and the generated molecules (see Figure
We also compute different bond distance and bond angle distributions the generated molecules and compare them against the corresponding reference empirical distributions in Tables ann
To further measure the quality of generated conformation, we optimize the generated structures with Merck Molecular Force Field (MMFF) (Halgren 1996) and calculate the energy difference between
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Pocket2Nol (J50:8.24)
Targetbiff (JSD:8.09)
DecompDiff (J5D:0.05)
DecompOpt (J50:0.04)
12
Distance of all atom pairs (A)
Figure 8: Comparing the distribution for distances of all-atom for reference molecules in the test. set and model-generated molecules. Jensen-Shannol divergence (JSD) between two distributions is reported.
Table 5: Jensen-S Censen-Shannon divergence between bond distance distributions of the reference molecules and generated molecules, and lower values indicate better performances. "_", "=", and "." represent single, double, and aromatic bonds, respectively. We highlight the best two results with bold text and underlined text, respectively.
Bond
liGAN
GraphBP
AR
Pocket2 Mol
Target Diff
Decomp Diff'
Ours
C-C
0.601
0.368
0.609
0.496
0.369
0.359
0.362
C=C
0.665
0.530
0.620
0.561
0.505
0.537
0.504
C-N
0.634
0,456
0.474
0.416
0.363
0.344
0.328
C=N
0.749
0.693
0.635
0.629
0.550
0.584
0.566
C-O 0.656
0.467
0.492
0.454
0.421
0.376
0.373
C=0 0.661
0.471
0.558
0.516
0.461
0.374
0.329
C:C 0.497
0.407
0.451
0,416
0.263
0.251
0.196
C.N 0.638
0.689
0.552
0.487
0.235
0.269
0.219
pre- and pos- MMFT-optimized coordinates for different rigid fragments that do not contain any rotatable bonds. As Table 7 and Figure 9 show, DECOMPÔPT achieves low energy differences and outperforms baselines in most cases. We also calculate the energy difference before and after force field optimization for the whole molecules. As Table and Figure I0 show, notably, DECOMPOPT outperforms all diffusion-basee methods by large margin and achieve comparable performance with the best baseline. These results show that the conformation of ligands generated by DECOMPOPT is high-quality and stable.
Table Median energy difference for rigid fragment of different fragment size (3/4/5/6/7/8 atoms) before and after the firce-field optimization.
Median Energy Difference (L)
Methods
3
4
5
7
8
LiGAN
86.32
165.15 15
105.96
185.70
243.79
332.81
AR
25.79
73.06
23.89
30.42
56.47
76.50
Pocket2Mol
10.43
33.93
34.47
27.86
33.90
42.97
TargetDiff
7.31
30.57
18.01
11.98
28.92
50.42
DecompDiff
6.01
29.20
10.78
4.33
12.74
30.68
DECOMPOPT
6.00
16.59
9.89
2.61
13.29
31.49
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Table 6: Sansen-Shannon divergence between bond angle distributions of the reference molecules and the generated molecules, and lower values indicate better performances. We highlight the best two results with bold text and underlined text, respectively.
Pocket2 Mol
Target Diff
Decomp Diff
Angle
liGAN
GraphBP
AR
Ours
CCC
0.598
0.424
0.340
0.323
0.328
0.314
0.280
CCO
0.637
0.354
0.442
0.401
0.385
0.324
0.331
CNC
0.604
0.469
0.419
0.237
0.367
0.297
0.280
OPO
0.512
0.684
0.367
0.274
0.303
0.217
0.198
NCC
0.621
0.372
0.392
0.351
0.354
0.294
0.266
CC=0
0.636
0.377
0.476
0.353
0.356
0.259
0.257
COC
0.606
0.482
0.459
0.317
0.389
0.339
0.338
Median Energy Difference (kcal/mol)
Pocket2Mol
TargetDiff
DecompDiff
DecompOpt
150
100
50
4
Fragment Size
Figure 9: Median energy difference for molecules with different number of rotatable bonds before and after the force-field optimization.
Table 8: Median energy difference for molecules with different number of rotatable bonds (1/2/3/4/5/6/7 rotatable bonds) before and after the force-field optimization.
Median Energy Difference (L)
Methods
3
6
LiGAN
810.45
981.53
1145.96
1783.95
1960.24
2547.32
2735.75
AR
176.67
222.74
244.51
268.01
332.89
388.70
441.90
Pocket2Mol
105.64
125.19
168.84
199.33
204.82
226.73
263.96
TargetDifff
225,48
253.72
303.60
344.12
360.74
420.47
434.30
DecompDiff
279.44
264.16
268.23
265.57
262.69
279.73
289.07
DECOMPOPT
63.33
169.17
215.19
248.35
202.81
237.38
238.32
C ADDITIONAL RESULTS
C.I FULL EVALUATION RESULTS
We provide box plots of evaluation metrics shown in Figure 11
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Median Energy Difference (kcal/mol)
AR
Packet2Mol
TargetDiff
DecompDiff
1250
DecompOpt
1000
750
500
Number of rotatable bonds
Figure 10: Median energy difference for molecules with different number of rotatable bonds before and after the force-field optimization.
5A(t)
Vina
Vina Min
Vina Dook
00
CVAE
AR
Packet2Mol
TargetDiff
DecompDitt
DecompOpt
RGA
Figure 11: The boxplots of QED, SA, Vina Score, Vina Minimize, and Vina Dock of ligands generated by DECOMPOPT and baseline models.
Following Guan et al. (2033b), model also has variants of priors. Table 9 shows the results of multiple variants our models. The setting of Ref Prior, Pocket Prior, and Opt Prior strictly follows DecompDiff (Guan al. 2023b). Ref Best means using the best checkpoint instead of the last checkpoint for each target pocket during optimization with reference priors for evaluation. For Pocket/Opt Best, it is similar. Best of Best means using the best checkpoint across all checkpoints with Ref Prior and Pocket Prior during optimization for each target pocket.
Table 9: Summary of different properties of reference molecules and molecules generated by our model and other generation (Gen.) and optimization (Opt.) baselines. (t) (4) denotes larger smaller number is better.
Visa Scoce (})
Vina (})
Dock
High Affinity Avg.
SA (t)
Diversity (t)
Suceess
Avg.
Med.
Avg.
Mod.
Ave
Mod.
Med.
Avg.
Med.
Avg.
Med.
Avg
Med.
Rate
Referance
6.36
-6.46
-6.71
.649
.7.45
-7.26
0.48
0.47
0.73
0.74
25.0%
DECOMFOPT (Ref Priot)
-568
-5.88
-6.53
6.49
-7.49
-7.66
59.2%
65.0%
0.56
0.58
0.73
0.73
0.64
0.56
35.4%
DEcosFOFT (Ref Best)
-575
-5.97
-6.88
4.70
-7.63
74.3%
0.56
0.59
0.73
0.65
0.67
Decomrdrr (Pocket Prior)
-5.27
-6.38
-7.07
-7.45
-3.55
-3.72
71.4%
93.8%
0.40
0.36
0.63
0.63
0.60
0.61
29 29.2%
DECOMPÖPT (Pocket
-533
DECOMPOET (Opt Pricc)
-5.73
-6.64
-7.29
-7.53
-8.78
9.72
70.3%
59.9%
0.46
0.44
0.65
0.65
0.61
0.51
38.1%
DECOMPOPT (Opt Best)
-587
-7.35
-7.73
-9.01
73.5%
0.45
0.60
0.61
DECOMPÖPT (Best of Best)
6:22
-6,96
-7.50
-7.4
3.98
-8.95
76.2%
100%
0.51
0.51
0.67
0.67
0.61
0.63
50.6%
C.2 TRADE-OFF BETWEEN SUCCESS RATE AND DIVERSITY
In addition to overall performance, we also show the trade-off between Success Rate and diversity of RGA, TifgetDiff w/ Opt., and DECOMPÔPT for each target protein pocket in Figure 12 DECOMPÔPT
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shows general superiority to the other two baselines in most cases considering both Success Rate and diversity.
100%
80%
60%
DecompOpt
TargetDiff
40%
20%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Diversity
Figure 12: Trade-off of Success Rate and diversity. Each point with coordinate (x, y) represents pocket with Success Rate x and diversity y. The closer to the top right, the better.
C.3 EVALUATION OF THE ABILITY TO DESIGN NOVEL LIGANDS
We additionally test the Novelty and Similarity of generated ligands compared with the reference ligand. Novelty is defined as the ratio of generated ligands that different from the reference ligands of the corresponding pockets in the test set. Similarity is defined as the Tanimoto Similarity between the generated ligands and the corresponding reference ligands. The results show that the generated ligands are not similar to reference ligands in the test set. Besides, we also test Uniqueness and Diversity of generated ligands. Uniqueness is the percentage of unique molecules among all the generated molecules. Diversity is the same as that in Section 4.1 The results are reported in Table TO These results show that DECOMPOPT can design novel ligands, which is an important ability for drug discovery.
Table 10: Evaluation of the ability to design novel ligands.
Methods
Novelty
Similarity
Uniqueness
Diversity
LiGAN
100%
0.22
87.82%
0.66
AR
100%
0.24
100%
0.70
Pocket2Mol
100%
0.26
100%
0.69
TirgetDiff
100%
0.30
99.63%
0.72
DecompDiff
100%
0.34
99.99%
0.68
RGA 100%
0.37
96.82%
0.41
DECOMPOPT
100%
0.36
100%
0.60
C.4 EFFECTS OF SUBPOCKETS.
To study the influence of subpockets in controlling the optimization, we further conducted an ablation study using only arms without subpockets as conditions. As TI while DECOMPOPT, when solely with arms conditions, is capable of optimizing all metrics, its efficiency in this scenario not as well as DECOMPOPT that utilizes both arms and pockets as conditions. Recall that we use SE(3)-invaraint features of arms (and subpockets) as conditions. Without subpockets, this feature would be agnostic to the molecular interaction and spatial relation between the arms and subpockets. Such information is important
of the properties (e.g., Vina scores). The SEE3)-invaraint
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features from pairs of subpockets and arms contain the aforementioned information and are better aligned with the protein-ligand ligand complex being generated.
Table I1: Comparison of DECOMPOPT optimization results with only arms and arm-pocket com-
plexes conditions. (t) / (L) denotes larger smaller number is better.
Methods
Score (4)
())
(ec
High Affinity
QED (f)
SA
Divenity (f)
Med.
Med.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Med.
Rate
Decompliit
-7044
-7.99
.3.39
64.4%
0.68
DecOMBOPT (arms-only)
-5.52
4.26
7,005
-7.26
..65
-8.4
66.6%
86.1%
0:46
0.43
0.63
0.63
0.63
0.63
45,7%
DECOMPOPT
-5.87
-.81
-7.3
-.72
-3.98
-9.01
73.5%
93.3%
0.48
0.45
0.65
0.63
0.60
0.61
52.5%
C.5 INFLUENCE OF THE QUALITY OF INITIAL LIGANDS ON PERFORMANCE
To study the influence of the quality of initial ligands on performance of structure-based molecular optimization, we have conducted an ablation study focusing on Vina Min score optimization, using ligands with high and low Vina Min scores as initializations for the arm lists. Due limited resources, we chose to conduct this study on the protein 2V3R, which is randomly chosen from our test set. We generated 100 ligands using DecompDiff and selected 20 ligands with the highest and lowest Vina Min scores. These ligands were then used as the initial conditions for the optimization process. As shown in Table 12 the optimization outcomes are slightly influenced by the quality of the initial ligands. However, regardless the quality of the initial ligands, DECOMPÔPT can consistently improve the quality of the generated ligands.
Table 12: Comparison of optimization with initial ligands of different quality.
High Vina Min Scores Med.
Low Vina Min Scores
A (high low) Avg.
Avg.
Avg.
Med.
Initial ligands
-8.54
-8.48
-7.08
-7.04
-1.46
DECOMPPPT
-9.12
-8.96
-9.00
-8.96
-0.12
C.6 INFLUENCE OF NUMBER INITIAL LIGANDS ON PERFORMANCE.
To study the influence of the number of initial molecules on the performance of structure-bases molecular optimization, we further run the experiments with initial arm lists of and molecules generated by DecompDiff. As Table 13 indicates, the initial number of molecules has modest impact on the optimization outcomes, with a higher number molecules generally leading to improved performance. Notably, even when starting with single molecule generated by DecompDiff, DECOMPÖPT demonstrates a considerably high success rate.
Table 13: Summary of results using different number of molecules to initialize arm lists. (t) denotes larger / smaller number is better.
Vina Score (1)
Vina Min (1)
Vina Dock (1)
High Allinity (f)
QED (1)
SA (1)
Diversity (?)
Success
Methods
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Ave.
Med.
Avg.
Med.
Rate
init num
-5.41
-6.61
-7.12
-7.51
-8.78
-8.82
70.4%
88.9%
0.47
0.45
0.64
0.63
0.61
0.61
47.0%
init num 5
-5.11
-6.71
-7.25
.7.8
..86
-897
71.8%
93.3%
0.49
0.46
0.65
0.64
0.60
0.61
49.4%
init nam 20
-3.87
-6.81
-7.35
-7.72
-8.8
-9.01
73.5%
93.3%
0.48
0.45
0.65
0.65
0.60
0.61
52.5%
D EXTENDED RESULTS OF CONTROLLABILITY
D.I R-GROUP OPTIMIZATION
We provide additional R-group Optimization experiment on protein 4G3D, as shown in Figure 13
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Reference Ligands
DecompOpt for R-group Optimization
4G3D
Vina Mi16
Vina Min:
Min
HO
Figure 13: Additional R-group optimization result. The left column is reference binding molecule, the middle and right columns are molecules generated by DECOMPOPT with 30 rounds of optimization on protein 4G3D. Optimized R-group are highlighted in red.
Table 14: R-group optimization results generated using Decompdiff and DECOMPÔPT on protein 3DAF and 4FIM. DECOMPOPT was optimized over 30 rounds towards high Vina Min Score and evaluated using the final round results. Both targets were assessed with 20 generated molecules and the mean of properties are reported.
3DAF Tanimoto Sim. (f)
4FIM
Model
Vian Min (1)
Complete. (f)
Vian Min (L)
Tanimoto Sim. (t)
Complete. (1)
Decumpdiff
-8.44
0.15
60.0%
-5.90
0.15
65.0%
DECOMPÖPT
-9.39
0,23
95.0%
-6.32
0.49
55.0%
D.2 FRAGMENT GROWING
Enhancing the binding affinity drug candidates through combination of R-group optimization and fragment growing effectively leverage capabilities of DECOMPOPT. The quantitative results shown in Table 14 For our case study, we perform R-group optimization and fragment growing on SAEH. Starting from high binding affinity drug candidate, first optimize R-group for 30 rounds same as workflow in Section 4. Subsequently, we design the new arms prior and atom num with expert guidance, and expand fragments using DECOMPÔPT. As Figure 14 shows, DECOMPOPT ultimately generates molecules with Vina Min Score more than 4 kcal/mol better than the reference.
Reference Ligands
R-group Optimization
Fragment Growing
5AEH
Vina-Min: -9.869
Vina-Min: -10.645
-13.077
Figure 14: Example of R-group optimization and fragment growing conducted using DECOMPÔPT on 5AEH. The reference ligand, the best R-group result, and the best fragment growing result based on R-group optimization are displayed from left to right. The selected R-group is highlighted in red, while the newly extended arm is highlighted in orange.
D.3 SCAFFOLD HOPPING
Additional Evaluation Metries In addition to evaluation metrics discussed in Section 4, we evaluated Validity, Uniqueness, Novelty, Complete Rate, and Scaffold Similarity to measure models' capability in scaffold hopping. Detailed calculation of these metrics as follows:
Validity is defined the fraction of generated molecules that be successfully sanitized.
Uniqueness measures proportion of unique molecules among the generated molecules.
Novelty measures the fraction of generated molecules that not presented in training set.
Complete Rate measures the proportion of completed molecules within the generated results.
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Scaffold Similarity Following Polykovskiy et al. (2020). Bemis-Murcko Murcko scaffolds extracted using rdkit function MurckoScaffold. We count the occurrences of scaffolds in all generated and reference molecules, creating vectors G and R, where each dimension represents the count of a specific scaffold. The scaffold similarity is calculated as the cosine similarity between vectors G and R.
More Examples of Generated Results For scaffold hopping, we provide more visualization of ligands generated by DECOMPOPT and DecompDiff on protein 273H, 4AVW, 4QLK, and 4BEL,, which are shown in Figure [5
Reference Ligands
DecompOpt Scaffold Hopping
Decompdiff Scaffold Hopping
P
iee
Figure 15: More examples of Scaffold Hopping results. The left column shows reference ligands. Scaffold Hopping results generated by DECOMPÔPT are shown at the second and the third rows, and results generated by DecompDiff are shown the fourth and the fifth rows. Scaffold are highlighted in green.
Changes in Molecular Properties After Scaffold Hopping Scaffold hopping aims at finding scaffold structures that can connect existing functional groups without disrupting their interactions with the target protein. The main purpose of this is to find novel scaffolds which are not protected by existing patents while maintaining comparable properties as the original molecule. Therefore, we did not implement property optimization mechanisms in scaffold hopping tasks and solely focusing designing scaffolds that can connect existing arms. We provide the property comparison before and
after scaffold hopping in Table 15 As the result shows, the properties of the ligands remain relatively consistent before and after the process of scaffold hopping.
Table 15: Summary of properties of reference molecules and molecules generated through scaffold hopping using DECOMPOPT. (f) (4) denotes larger smaller number is better.
Vina Score (L)
Vina Min (1)
Vina Dock (L)
QED (1)
SA (f)
Methods
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Reference
-6.36
-6.46
-6.71
-6.49
-7.45
-7.26
0.48
0.47
0.73
0.74
Scaffold Hopping by DECOMPOPT
-5.89
-6.46
-6.28
-7.28
-7.48
0.48
0.71
23


Reviews:
[{"review_id": "mYKv7Wj9JM", "reviewer": "Reviewer_Tgrc", "summary": "Through this paper, the authors aim to establish a structure-based molecular optimization model that can be applied to both *de novo* molecular design and controllable generation. To accomplish this, the authors propose to train a diffusion model with decomposed ligands.", "questions": "- What is the specific difference between DecompOpt and DecompDiff? One of the claimed contributions is that the authors designed a unified framework via a decomposed diffusion model (the 3rd bullet point in the introduction), but DecompDiff has already proposed and applied this to SBDD.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The writing is easy to follow. The concept figure also aids the understanding.\n- The experimental results show the effectiveness of the proposed method and ablation studies were also conducted. The experiments about controllability (R-group optimization and scaffold hopping) seem interesting.", "weaknesses": "- The authors did not provide the codebase to reproduce the results.\n- The authors used the term *controllable generation* to indicate tasks like R-group design and scaffold hopping. However, *controllable* is a widely used expression with a general meaning and *de novo* molecular design can also be controllable in a broad sense. There is some lack of rigor in the choice of wording.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "wfOBgbYc1v", "reviewer": "Reviewer_eZ5C", "summary": "This paper introduces a controllable and decomposed diffusion model for de novo molecular optimization. More specifically, the paper presented a method for molecular optimization while maintaining the constraint that the crucial binding region undergoes minimal alteration. The author conducts a comprehensive benchmarking of their work against numerous existing baselines, revealing strong performance across a wide range of quality-related metrics, although it does exhibit a lower score in terms of diversity.", "questions": "1. How similar is your generated ligand to the reference ligand?\n2. Can you demonstrate the influence of the reference ligand's quality on performance?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The motivation is evident and firmly grounded. \n2. The paper provides a great tool for chemistries to design the molecular and it is expected to be highly practical and beneficial.", "weaknesses": "I observed that you employed the reference ligand as the input for optimization, while most of the baseline methods, except RGA, did not. Moreover, the reference ligand exhibits exceptionally high quality, surpassing all the Gen-based baselines in terms of success rate. This leads me to question whether this comparison might be somewhat unfair to these baseline methods. I acknowledge that the primary focus of the method lies in optimization, making this kind of bias understandable. In light of this, I wonder whether it is necessary to include the Gen-based methods as baselines.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "shszpBwfMn", "reviewer": "Reviewer_SQ7r", "summary": "The paper focuses on the task of conditional generation in structure-based drug design, aiming to generate drugs with specific properties. The proposed method is an optimization approach based on a controllable and decomposed diffusion model, offering fine-grained control and local optimization. The method introduces a mechanism for precise control over the arms of the generated ligands. Subsequently, the ligand molecules, including atom coordinates, atom type, and bond type, can be generated by conditioning on certain arms and the target pockets using the diffusion model. Once a ligand molecule is derived, it is treated as a reference molecule and further optimized using evolutionary algorithms. The author presents the results from two perspectives: the generation perspective and the optimization perspective  to evaluate the target binding affinity and molecular properties.", "questions": "1. Why can solely maximizing the likelihood of training data mislead SBDD models?\n2. What is your novelty in section 3.1 comparing to DecompDiff?\n3. How is diversity achieved in the generated ligand molecules without explicitly introducing regularization over the representation space of conditions?\n4. Have you try multiple time experiments with differnet random seeds to avoid the randomness?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "The paper gives a decomposed method on drug design, generation on arms and scaffold. DECOMPOPT combines the advantages of diffusion models and optimization algorithms, utilizing diffusion models to extract molecular grammar and optimization algorithms to effectively optimize desired properties.", "weaknesses": "The method section containing diffusion part also used in the previous tasks while the author does not point out their novelty. The implementation detail is hard to reproduce", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "FPnfp6DNiP", "reviewer": "Reviewer_ewuH", "summary": "This paper aims to address the problem of generating 3D molecules with desired properties by introducing a controllable and decomposed diffusion model. Specifically, this paper proposes a model DECOMPOPT, which learns molecular grammar by iterative molecular optimization.The approach decomposes the molecules into scaffolds and arms, aiming to replace underperforming arms with new arms that exhibit improved properties.", "questions": "(Updated) Thank you for providing additional experimental details and clarification. I appreciate that my main concerns have been mostly addressed, especially the results for conformation optimization. I would raise the score from 3 to 5.", "limitations": "", "rating": 5, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.\tThe paper is well-written and easy to follow.\n2.\tThe experiment results are comprehensive.", "weaknesses": "1. My main concern regarding this article is the lack of alignment between the motivation and the approach. While the article acknowledges the importance of the property, it doesn't directly address it.\n\n   a) Which part of the article is designed to address QED or easily synthesizable compounds?\n\n   b) The Vina score from Table 1 appears to be subpar. Although I understand that the Vina score may not be the most suitable metric due to its weak correlation with affinity, the authors use it for optimization and as an indicator for data analysis(Figure 1). This raises the question of why they emphasize the results of Vina min and but not reporting the median or some other indicator.\n\n2. I am curious about the inference efficiency of the diffusion model. Since diffusion models are not known for their efficiency during inference, could the authors compare the generation efficiency of the proposed method with that of other models?\n\n3. Did the authors evaluate the rationality of the generated conformations? For instance, did they assess the energy difference before and after force field optimization? As diffusion-based models like DecompDiff has problems with this.\n\n4. The second case in Figure 3 seems questionable or may be difficult to interpret. I recommend redrawing it for clarity.\n\n5. Scaffold hopping is an interesting aspect, but the authors have not considered the potential changes in molecular properties (vina score, for example) after the hopping process.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "c8U0Q7a5Nf", "reviewer": "Reviewer_dt3J", "summary": "The paper proposes DecompOpt, a framework for de novo design and optimisation of ligands in protein binding sites conditioned on the pocket and a set of templates for arms and scaffold. The method is trained on the CrossDocked2020 benchmark and applied to de novo design, R-group optimisation and scaffold hopping.", "questions": "- Criteria for success rate seem arbitrary. How were these thresholds chosen?\n- Where does the difference for the DecompDiff results between Tabs 1 and 3 stem from?\n- Is DecompOpt applicable if no/only few reference ligands are available? How does the performance depend on the number / performance of initial reference ligands?\n\nUpdate:\nI thank the authors for the extensive answers to my questions and the additional experiments and clarifications. I raised my score accordingly.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "- DecompOpt is a flexible framework that is applicable to practical use cases in drug design\n- SOTA results on CrossDocked2020 benchmark", "weaknesses": "- Confidence intervals in evaluation are missing.\n- The overall clarity of the text should be improved (typos/grammar/…). \n- The complex framework is not described very well and is hard to grasp. For example, the “model architecture, training loss etc” is taken from DecompDiff and only referenced. An overview figure might help to better show the overall framework and identify novel contributions. \n- It is not clear what the arm / subpocket conditioning exactly encodes: Is this just guiding towards similar arms, or is the sub-pocket important here? An additional ablation using only the arms, A_k = Enc(A_k), would be informative.\n- It is unclear / not evaluated, how much the method relies on the availability of high-quality reference ligands vs the generative capabilities of the diffusion model. For example, a simple 2d baseline that recombines arms of different reference structures might already perform very well if already a large set of references is available.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (poster)