Reprogramming Pretrained Target-Specific Diffusion Models for Dual-Target Drug Design
Authors: Xiangxin Zhou
Jiaqi Guan
Yijia Zhang
Xingang Peng
Liang Wang
Jianzhu Ma
Venue: NeurIPS 2024 poster (2024)
Keywords: dual-target drug design
drug discovery
diffusion model
structure-based drug design
Primary area: machine_learning_for_other_sciences_and_fields

Abstract: Dual-target therapeutic strategies have become a compelling approach and attracted significant attention due to various benefits, such as their potential in overcoming drug resistance in cancer therapy. Considering the tremendous success that deep generative models have achieved in structure-based drug design in recent years, we formulate dual-target drug design as a generative task and curate a novel dataset of potential target pairs based on synergistic drug combinations. We propose to design dual-target drugs with diffusion models that are trained on single-target protein-ligand complex pairs. Specifically, we align two pockets in 3D space with protein-ligand binding priors and build two complex graphs with shared ligand nodes for SE(3)-equivariant composed message passing, based on which we derive a composed drift in both 3D and categorical probability space in the generative process. Our algorithm can well transfer the knowledge gained in single-target pretraining to dual-target scenarios in a zero-shot manner. We also repurpose linker design methods as strong baselines for this task. Extensive experiments demonstrate the effectiveness of our method compared with various baselines.

Reprogramming Pretrained Target-Specific Diffusion Models for Dual-Target Drug Design
Xiangxin Zhou 1.2
Jiaqi Guan
Yijia Zhang'
Xingang Peng
Liang Wang1.2
Jianzhu Ma
1 School of Artificial Intelligence, University of Chinese Academy of Sciences New Laboratory of Pattern Recognition (NLPR),
State Key Laboratory of Multimodal Artificial Intelligence Systems (MAIS),
Institute of Automation, Chinese Academy of Sciences (CASIA)
DDppatment of Computer Science, University of Illinois Urbana- trbaan-Chammaain
Department of Electronic Engineering, Tsinghua University
Institute for Artificial Intelligence, Peking University
Institute for Al Industry Research, Tsinghua University
Abstract
Dual-target therapeutic strategies have become a compelling approach and attracted significant attention due to various benefits, such as their potential in overcoming drug resistance in cancer therapy. Considering the tremendous success that deep generative models have achieved structure-based drug design in recent years, we formulate dual-targe drug design as a generative task and curate a novel dataset of potential target pairs based on synergistic drug combinations. We propose design dual-target drugs with diffusion models that are trained on single-targed protein-ligand complex pairs. Specifically, we align two pockets 3D space with protein-ligand binding priors and build two complex graphs with shared ligand nodes for SE(3i-eqiivariant composed message passing, based on which we derive a composed drift in both 3D and categorical probability space in the generative process. Our algorithm can well transfer the knowledge gained in single-target pretraining to dual-target scenarios in zero-shot manner. We also repurpose linker design methods as strong baselines for this task. Extensive experiments demonstrate the effectiveness of method compared with various baselines.
Introduction
A promising paradigm of rational drug design is structure-based drug design (SBDD) [. which uses computational chemistry tools in which the 3D structure of a protein target is used as the basis to identify design new chemical entities. The foundation of structure-based drug design has been grounded in the lock-and-key hypothesis, positing that an optimal ligand molecule should possess structure that is complementary to design "one key" for "two locks", has attracted significant attention. Precisely, dual-target drug design [4] is strategy in pharmaceutical research that aims design single ligand molecules capable of interacting with two different biological targets simultaneously. dual-target drug can potentially lower the odds of resistance developing 62 and effectively manage the disease which involve complex biological pathways with multiple proteins 44). Recent years have witnessed noticcable
the target site. Recently, dual-target drug design, which aims
"Correspondence to: Jianzhu Ma <majianzhueeeeee tsinghua.edu.ccm
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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increase in the FDA's approval of dual-target drugs [32 34]. Please refer to Appendix A for a more
comprehensive understanding of motivation, significance, and current practices of dual-target drug
design.
Deep learning, particularly deep generative models [X]] and geometric deep learning 46
has been
introduced to SBDD and achieved promising results. Peng et al. [45]. Zhang et al. to sequentially generate atoms or fragments using auto-regressive generative models conditioned
65
proposed
on a specific protein binding site. Guan et al. [9]] Lin et al. 33. Schneuing et al.
5
proposed
to generate ligand molecules with diffusion models and achieved high binding affinity. However, due to the scarcity of data resources and high computational complexity, there is limited progress on introducing powerful generative models into dual-targer drug design. Besides, there also lacks a comprehensive benchmark and dataset for evaluating the dual-targer drug design, which also hinders the community from developing Al Al-powered computational tools for dual dual-target drug design.
To overcome the aforementioned challenges, we first propose a dataset for dual-target drug design. The design of dual-target drugs for arbitrary target pairs lacks substantive purpose. Inspired by the concept of drug synergism [58], where the combined effect of two drugs surpasses the effects of each drug when used individually, we carefully select pairs of targets from combinations of drugs that demonstrate significant synergistic interactions. The effectiveness of such combination therapy has demonstrate significant efficacy in tumor eradication both cellular level and in vivo study. Designing dual-target drugs for the paired targets may further improve the efficacy and reduce side effects. Additionally, we also provide a reference ligand for each target and the 3D structure of each protein-ligand complex in our dataset. Besides, we formulate the dual-target drug design as generative task, based on which we further propose to reprogram pretrained target-specific diffusion models as introduced by Guan et al. [19] for the dual- setting in zero-shot manner. More specifically, we first align dual pockets in 3D space with protein-ligand interaction priors that encapsulate the intricate features of the pockets. We compose the predicted drift terms in both 3D and categorical probability space in the reverse generative process of the diffusion model to generate dual-target drugs. We name this method as COMPDIFF. We further improve this method by building two complex graphs with shared ligand nodes for -quuieqquiaaiian composed message passing, In this method, we compose the -qqivvaaaa message at each layer of the equivariant neural network instead of only on the output level. We name this method as DUALDIFF. Our approach effectively transfers the knowledge acquired from pretraining on single-target datasets, cireumventing the challenging demand for extensive training data required for dual-target drug design. We also as strong baseline for this task. We outline strategies to identify potential fragments from the synergistic drug combinations, serving as input for these linker design methods. We highlight our main contributions as follows:
39 50
repurpose linker design methods 22 17
We present a meticulously curated dataset derived from synergistic drug combinations for dual- target drug design, offering new opportunities for Al-driven drug discovery.
We propose
composed message for compositional generative sampling to repro- gram pretrained single-target diffusion models for dual-target drug design in a zero-shot way. We propose fragment selection methods from synergistic drug combinations for repurposing linker design methods as strong baselines for dual-target drug design.
Our method can be viewed as a general framework where any pretrained generative models for SBDD can be applied to dual-target drug design without any fine-tuning. We select TargetDiff as demonstrative demo in our work.
2
Related Work
Structure-based Drug Design Structure-based drug design (SBDD) aims to design ligand molecules that can bind to specific protein targets. The introduction of deep generative models has marked a paradigm shift, yielding noteworthy outcomes. Ragoza et al. 48 utilized variational autoencoder to generate 3D molecules within atomic density grids. Luo et al. [2), Peng et al.
[4), Liu et al. [36] employed an autoregressive model to sequentially construct 3D molecules atom by atom, while Zhang et al. [65] introduced method for generating 3D molecules by successively predicting molecular fragments in an auto-regressive way. Guan et al. 19, Schneuing et al. [53] Lin
et al. [3 introduced diffusion models [1] to SBDD, which first generate the types and positions
of atoms by iteratively denoising with an SE(3)-equivariant neural network [52 [8] and then de-
termine bond types by post-processing. Some recent studies have endeavored to further improve

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the aforeementooed methods through the integration of biochemical prior knowledge. Guan et al. [00 proposed decomposed priors, bond diffusion and validity guidance to improve the quality of ligand molecules generated by diffusion models. Zhang and Liu [64] augmented molecule generation through global interaction between subpocket prototypes and molecular motifs. Huang et [23] incorporated protein-ligand interaction prior into both forward and reverse processes to improve the diffusion models. Zhou et al. [66] integrated conditional diffusion models with iterative optimization to optimize properties of generated molecules. The above works focus structure-based single-target drug design, while our work aims at dual-target drug design.
Molecular Linker Design Molecular linker design, which enables the connection of molccular fragments to form potent compounds, is an effective approach in rational drug discovery. Approaches like DeLinker [66 and Develop 27 design linkers by utilizing molecular graphs with distance and angle information between anchor atoms, but they lack 3D structural information of molecules. More recent techniques, such as 3DLinker [22] and DiffLinker [25], generate linkers directly in 3D space using conditional VAEs and diffusion models, respectively, but they assume known fragment poses. LinkerNet 117 relaxes this assumption by co-designing molecular fragment poses and the linker, making it applicable in cases where fragment poses are unknown, such as in the linker design of PROTACs (PROteolysis TArgeting Chimeras). Since pharmacophore combination strategy to design dual-target drugs, repurpose linker design methods as strong baselines for dual-target drug design. Please refer to Appendix B for extended related works.
traditional
3 Method
In this section, we will present the pipeline of our work, from dataset curation to method. In Section 3.T, will introduce how curate the dual-target dataset based synergistic drug combinations and how we derived the pootein-ligane complex structures. In Section3.22 we will show how we reprogram the pretrained target-specifie diffusion models for dual-target drug design and we will show how we repurpose
introduce two methods, COMPDIFF and DUALDIFF. Section 3.3 linker design methods for dual-target drug design.
(a)
P1
Componitional Sampling
Align Protein
by
Composed Eqqiivaraia Message
Equivariant
Aligned Dual Targets
Protein- Protein-Ligand Binding Prior
(b)
P1
Linkr
Dock
Selected Fragments
Designed Drug
Figure 1: Overview of our method for dual--trget drug design. (a) Illustration of COMPDIFF and DUALDIFF, We first align two pockets 3D space with protein-ligand binding prior and build two complex graph with shared ligand nodes. We then compose the (equiv-aqa message to derive the drift on output level (COMPDiFF) or at each layer of the equivariant neural network (DUALDiiFF) Based on the composed drift, we can generate dual-target ligand molecules by compositional reverse sampling. (b) Illustration of repurposing linker design methods for dual-tare target drug design. first identity binding-related fragments from the reference molecules for each of the dual targets and then apply linker design methods link fragments and derive a complete molecule that can bind to the dual targets separately.

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3.1 Data Curation
Designing -taret drugs for random pairs of targets lacks significant intent. However, by taking cues from drug synergy, where two drugs together deliver an impact greater than the sum of their separate effects (58), we carefully select target pairs to ensure the dataset holds practical significance for drug discovery.
Drug Synergy To collect drug combination pairs, we start from DrugCombDF CombDB is comprehensive database devoted to the curation of drug combinations from various data sources including high-th high-throughhut screening (HTS) assays, manual curations from the literature, FDA Orange Book and external databases. DrugCombDB comprises a total of 448,555 combinations of drugs, encompassing 2,887 unique drugs and 124 human cancer cell lines. Particularly, Drug- CombDB has more than 6,000,000 quantitative dose responses, from which we determine whether drug combination is synergistic or not. Specifically, a drug combination with positive zero interaction potency (ZIP), Bliss, Loewe and the highest single agent (HSA) scores simultancously in at least one cell line is supposed to be a synergistic one. Please refer to Appendix foor a comprehensive understanding of these scores.
35 Drug-
Drug Information After collecting synergistic drug combinations, we need to collect other neces- sary information (c.g., SMILES and targets) according to their drug names provided by DrugCombDB. Before this procedure, we collect synonyms and grass-natching ID (c.g. CAS Number and ChEBI ID) mainly from DrugBank [0) and Therapeutic Target Database (TTD [67] This step facilitates comprehensive literature reviews, ensuring that all relevant data sources that may use alternate names for a drug is considered. We then collect SMILES or structures (if possible) also mainly from DrugBank and TTD. To identify drug targets, also utilize DrugBank and TTD as the primary
data sources, and supplement these with manual curation from the literature (e.g.. (28)) ). For drugs for which we cannot find either SMILES targets, exclude them from previously collected dataset of positive drug combinations.
Complex Structures For certain drug-target pairs, we incorporate their complex structures directly into our dataset if they are available in PDnBind (38), a repository of protein-ligand binding structures sourced from the Protein Data Bank (PDB) 22. For drug-target pairs not present in PDBBind, we initially attempt to retrieve the target structures from PDB; if the structures are unavailable, we
then source them from the AlphaFold Protein Structure Database (AlphaFold DB) [59] and exclude those whose confidence scores, referred to as pLDDT which provide an assessment of the structures predicted by AlphaFold 2 (29), are less than 70, For these protein targets with structures from PDB or AlphaFold DB, we first utilize P2Rank (3). program that precisely predicts ligand-binding pockets from a protein structure, to find the most possible pocket given the target structure, and use AutoDock Vina 12 to obtain the protein- protein-ligand complex structures. For each drug, there may exist more than one targets. in which case we use AutoDock Vina to measure the binding affinity and selected the target with the best binding affinity. Finally, we obtain 12,917 postive drug combinations with protein-ligen ligand complex structures, among which there are 438 unique drugs. The 12,917 pairs of targets can be used to evaluate the ability of methods for dual-target drug design. And the binding ligands can be used for reference molecules.
3.2 Reprogramming Target-Specific Diffusion Models for Dual- Marget Drug Design
Diffusion models 21
56 have been introduced to ttructure-based drug design and achieved
33 20 We will first revisit the background of diffusion models for SBDD 19 and then introduce how we apply diffusion models trained on single-target protein-ligan ligand datasets to dual-target drug design in zero-shot manner. Our method is illustrated in Figure [ (a).
promising results 19
53
Diffusion Models for single-target SBDD E R and the coordinate of an atom as E RR3, where K is the number of atom types of our interest. For single-target drug design, given a protein binding site denoted as a set of atoms
In this following, we denote the type of an atom as
http:// wenglab. crtiaaiirrr//miiin
httpe://ddrblab.net//e

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P ")) ) where Np is the number of protein atoms, our goal is to generate binding up
molecules M- ( L I For brevity, we denote the molecule as M = [x, v], where [: denotes the concatenation operator and x E RN x3 , E R. x denote the coordinates in 3D generative models to model the conditional
space and one-hot atom types, respectively. So distribution p (P).
In the forward diffusson process of the diffusion model, noises are gradually injected into the data sam- ple (i.e., small molecule Mo ~ p(M PP) and lead to a sequence of latent variable M1, .M...., Mr. The final distribution p(MrlP) (P), also known prior distribution, is approximately standard normal distribution for atom positions and uniform distribution for atom types. The reverse generative process learns to recover data distribution from the noise distribution with neural network parameterized by 0. The forward and reverse processes are both Markov chains defined as follows:
T
T
(Ma Mo. P)= II
(M and (M P) 2=1
II
po po (M P). (1)
t=1
More specifically, the forward transition kernel in Guan et al. 19 are defined as follows:
P)
v 1, C(v. - 8ev + Bt/K),
(2)
where {,817-1 are fixed noise schedule. The above diffusion process can be efficiently sampled directly from time step & as follows:
((x, -x(xi dx (1 ax) and ((v./vo) C(v.lārvo + (1 (1-ār/) aā,K))
where 02 := 1 - 3t and āe= == IT ag.. The posterior can be easily computed via Bayes theorem as:
xo) = (xx-13 1; (x), B.I) and g(v:/Vo) C(v. (v (1 k.)/K), (4)
where 3. 1- St, t& xo) Xx)
Vār-T& 2. = c² / ox and e² (viv, vo) = [aeve+ +
(1 -x,)/ K] ④ T-6;
1-a: 1Vo (1 kr-1)/Kj.
Accordingly, the reverse transition kernel are defined as follows:
Po M, P) = (o vr), 4, P),oo( C(ve-1lco((x,, ve),4,)),
(5)
Guan et al. 19 use SE(3) -qquivaraa neural networks [52 18 to parameterize en ([x,, vi), t, P) and co ca([x, [xx, vel. t, P). More specifically, the [xo, vol are first predicted using neural network fe. i...
[Ko. vnl = fo( x vel.t. P) and then substitute in the posterior as in Equation (4). At the I-th layer of for the hidden embedding h and coordinates x of each atom updated alternately as follows:
h+1= = h +
Σ jEV,ijj
for (h', h's d'y. ciy),
++1
x
Σ JEV.
(x]
-x{-x1a x,) (h/+1, h/411 d.y. eij) I ligand,
where is a k-nearest neighbors (knn) graph, dij = ||, - x, is the Fuclidean distance between two atoms i and j. eij is an additional feature that indicates the connection is between protein atoms, ligand atoms or protein atom and ligand atom, and ligand is a mask for ligand nodes since only coordinates of ligand atoms are supposed to be updated.
The diffusion model is trained to minimize the KL-divergence between the ground posterior ((M,-1/Mo. Mr. P) and the estimated posterior Pe MM, P). After being trained, given specific pocket, the ligand molecule can be generated by first sampling from prior distribution and sequentially applying the reverse generative process defined above.
Problem Definition of Dual- TurleT Drug Design The goal of dual-target drug design is to design a ligand molecule M that can bind to both given pocket Pi and pocket Ps. The problem can be also formulated generative task which models the conditional distribution p( [P,, TP2). Notebly, we introduce a transformation operator T here. This is because protein pockets exhibit wide variety of shapes and chemical characteristics and it is necessary to achieve spatial alignment of the dual pockets when modeling the conditional distribution with both of them as conditions. To maintain a neat but siginificant setting, we restrict the transformation to encompass solely translations Tr and
rotations TR. i.e., T = Tr o TR. To be more precise,
(Tr o TR) = {RR R E SO(3) represents the rotation and E RR3 represents the translation.
(i) p2 + t), up Jer, where
(.)
5

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Aligning Dual Targets with Protein-Ligand Binding Priors Protein pockets can have intricate 3D structures with varying depths, widths. and surface contours, and distinct chemical properties. including differences in surface electron potentials, hydrophobicity, and the distribution of functional groups. The complex nature of pocket characteristies hinder us from directly aligning two pockets. Nevertheless, the binding mode is determined by the complex nature of pocket information, thus the
priors can effectively summarize the essential information needed for aligning prober to implicitly
the two pockets. This motivate us propose use a ligand molecule reflect the spatial arrangement of the two pockets and then align them with the protein-ligand binding priors. More specifically, we first dock ligand molecule pocket P1 and pocket P2 separately. We can then compute R and by aligning the two docked poses of the ligand molecule. Experiments have demonstrated that even ligand molecules capable of approximate binding to the two pockets can effectively indicate specific spatial alignment between them. Further details are provided in Section 4
SE(3)-Equivariant Composed Message and Compositional Generative Sampling Inspired by compositional visual generation 9 37 we can model the dual- ttrget drug design with the following composed distribution:
P(M x pp
(8)
Following Liu et al. [37], for the atom position prediction, we can reparameterize [ vr], 4, P) with x; EØ [xx, vel, P), that we can rewrite the transition kernel of the reverse generative
process as follows:
pu( P) = (x 1o (v), P) = -xx--i;xxxx - - v)),
(9)
The reversed transition kernel corresponds to a step as follow:
= co ( vel.t, + +(0,
(10)
where eg ([x,, vel, P) can be viewed as a drift term and (0, can be viewed as a diffusion term. As Liu et al. (37 points out, this is analogous the Langevin dynamies [T] that used to
sample from Energy- Energy-Based Models (EBMs) 10 55), which can be formulated as follows:
X
2 V Eo(x,, vel. t,,,,P) P) + +N 1
(11)
The sampling procedure produces samples from the probability density pe (x() xx where (x) is a energy function parameterized by model 0. Thus, accordingly, the composed distribution of atom positions can be written as:
p(x|P1, TP2) (o(x(Pi))po(x(PP) x cxp (- (Eo((x,, vel,t,P:) Eo([x,, vel,t, TP2))
This composed distribution corresponds to Langevin dynanmics as follows:
X A Vx (Ex( t, Pi) + Eo([x,, vel, TP2)))
(12)
Accordingly, each step in the compositional reverse generative sampling process can be defined as:
x xx - ( (Ee((x), vo), + co c vel, P2)).
(13)
where we additionally introduce hyperparameter 7) here to control the strength of the drift. In theory, this is equivalent to making more flexible assumption that p( TP2) & [Po (x In this case the transition kernel is defined as 1 P1, TP2) [x Pi)pe (x; 1 TP2)]". In practice, we set 1 = 1/2 by default. This composition operation equivalent to averaging two x predicted on two complex graphs, i.e. V and V2. Sim- ilarly, for the atom types which are discrete variables, we can also compose the transition kernel as follows:
po (v, v Vr. Pi, TP2) x po(v.-I|V.. Iv., Pi )poo(v-ilve TP2). Note that vo(vv-1|ve Ve. Pi) is categorical distribution and its dimension (i.e., the number of atom types of our interest) is K, which small in practice. So compositional reverse sampling with composed transition kernel (i.c., composed drift) COMPDUFF
Pı, TP2) can computed analytically. We name the

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We further improve the compositional reverse sampling by introducing the composition into each layer of the equivariant neural network in the pretrained diffusion model. For brevity. we denote the SE(()-equivariant message at the 1-th layer for the i-th atom of the complex graph Ve (v = 1,
introduced in Equation 7 as follows:
Ab((V)) = E
fex (h', hý, dl,.di., dig. eiy),
(14)
jEVeNEfj
Ax(O)) = Σ
(x (b/+)) .iftt dlys exj) ligand-
(15)
JEVon'y)
The above SE(3)-cquivarian message can also be interpreted drift in 3D and latent space. Thus we can also compose them as follows:
h - ht + (A + Ab( and = + (Ax + Ax (V2))/2. (16)
We name the compositional reverse sampling with the above SE(3) message at each layer as DIFF The proof of -quivvaeqi can found in Appendix G composition is supposed to lead to higher-quality samples.
This more meticulous
3.3 Repurposing I Linker Design Methods for Dual-Targe Drug Design
Pharmacophore combination a prevalent strategy in traditional dual-target drug design, requiring the specialized knowledge of chemists. To automate this procedure, We design a strategy to identity crucial fragments from reference molecules of dual targets in our dataset and apply linker design methods (25] 17 to link the fragments and obtain complete molecules. Please refer to Appendix D for a more detailed justification for the choice of baselines.
Specifically, we break all rotatable bonds of reference molecule M1 (resp. M2) of target P1 (resp. P2) to obtain fragments. Since DiffLinker [25] requires relative positions of fragments as input, we dock all fragments derived from Mi and M2 to P2 (or P1) and select the pair of fragments which has the best sum of binding affinity and no physical conflicts (i.e., the minimum between atoms from the two fragments is large than 1 1.4Å). We then apply DiffLinker to link the two fragments, considering the existence of the pocket P2 (or Pi). Since LinkerNet [17] models the translation and rotation of fragments by neural networks and does not require relative position of fragments as input, we directly dock all fragments derived from Mi (resp. M2) to Pi (resp. P2) and select their respective fragment with the best binding affinity. And we then link them using LinkerNet to obtain complete molecules.
4 Experiment
4.1 Experimental Setup
All 12,917 pairs of targets (including 438 unique targets) are used for evaluation. For each target, there is associated reference molecule that can be considered a benchmark for high-quality ligand molecules and utilized linker design methods.
Dataset We use our dataset introduced Section 3.1
Baselines We compare our method with various baselines: Pocket2Mol molecules atom by atom in autoregressive manner given specific protein binding site. Tar- getDiff 19 is a diffusion-based method which generates atom coordinates and atom types in a non-autoregressive way. Note that Pocket2Mol and TargetDiff are both proposed for structure-based single-target drug design. DiffT iinker (25) is a diffusion-base model for linker design with given frag- ment poses. LinkerNet (17) is diffusion-baai based model for co-designing molecular fragment poses and the linker, DiffLinker and LinkerNet are repurposed for dualetarget drug design as we introduced in Section 3.3 The code is available at
generates 3D 45
com/ ztoziioouiiannaa wtt.urriaaaignnnn//////aaa0
Evaluation
We evaluate generated ligand molecules from the perspectives of target binding affinity
and molecular properties. We employ AutoDock Vina [12 to estimate the target binding affinity, following Peng et al. [45), Guan et al. [19]. We first evaluate Pocket2Mol and TargetDiff under the
7

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Table I: Summary of different properties of reference molecules and molecules generated by baselines and our methods under the dual-target setting. (t) (C) denotes a larger smaller number is better. Top 2 results highlighted with bold text and underlined text, respectively.
Methods
P-1 Vina Dock (.)
P-2 Vina Dock (
Max Vina Dock (1)
Dual High AGE
QED (f)
(1)
Divensity (?) Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Mal
4.82
4.76
4.63
-4.6 64
.442
0.2%
0.0%
0.48
0.88
0.82
0183
TaretDiff
-8.62
-8.61
-6.89
-7.67
-6.57
-7.39
29.0%
20.07%
0.50
0.51
0.58
0.58
0.70
0.71
DifLLinker
-7.05
-7.87
-7.27
-7.92
-5.87
-7.18
24.6%
0.0%
0.43
0.42
0.30
0.29
0.52
0.51
LinkerNet
-8.0
-8.37
-8.13
-7.17
-7.72
35.7%
0.0%
0.63
0.72
0.37
COMP
DUALDIFF
:441
:8.51
-8.48
-8.55
-7.66
-7.88
36.3%
30.2%
0.56
0.58
0.59
0.59
0.67
0.67
single-target setting as a preliminary verification (see Appendix Dp. For dual-ttrget drug design, we use each method design 10 molecules for each pair targets, denoted Pi and Ps. (For reference molecule, Pocet2Mol and TafgetDiff, the ligand molecule is generated for Pi but the target binding affimity is evaluated on both P1 and P2.) We then collect all generated molecules across 12,917 pairs of targets and report the mean and median (denoted as "Avg." and "Med." respectively) of affinity-related metrics (P-1 Vina Dock, P-2 Vina Dock, Max Vina Dock, and Dual High Affinity) and property-related metrics Edrug-likeness QED 3 synthesizability SA [14], and diversity). Vina Dock incorporates re-docking step to assess the highest binding affinity achievable. Here we introduce P-1 Vina Dock and P-2 Vina Dock to represent the Vina Dock score evaluated on P1 and P2, respectively. Besides, we introduce Max Vina Dock, which represents the maximum Vina Dock of a given molecule towards PI and P2. The Vina Dock will be low if and only if the molecule can bind to both targets simultaneously, which is the goal of dual-target drug design. Additionally, we report Dual High Affinity (abbreviated as Dual High Aff.) which represents the proportion of generated molecules that exhibit binding affinity that exceeds that the reference molecules on both the respective targets. This reflects the success rate in achieving higher binding affinities simultaneously both targets in dual-target drug design. We also evaluate the RMSD between docked poses towards dual targets.
4.2
Main Results
We compare all methods under the dual-target set- ting. The results reported in Table Our meth- ods, COMPDIFF and DUALDIFF, significantly out- performs other methods, especially in terms of bind- ing affinity. Notably, DUAL achieves the high- Dual High Affinity among all methods. In line with our expectations, for the single-target drug de- sign methods (c.g., Pocket2Mol and TargetDiff), we
Method
observe a significant decline in performance accord- ing to P-2 Vina Dock compared to P-1 Vina Dock, which shows their inability in dual-target drug de- sign. LinkerNet also achieves promising results ex- cept diversity. Note that DiffLinker and LinkerNet are provided with reference molecules while COM- PDIFF and DUAL.DIFF are not. This indicates the strong generative abilities our methods. Finally, DUALDIFF outperforms COMPDIFF, which shows that composition of SEuuveqqivaaian message at each layer is more effective than only at the output level.
[5. 13) 111 20
23/ps,
301
30)
155,
400
45) 50
atoms
Figure 2: RMSD between docked poses to- wards dual targets of different methods.
As shown in Figure 2 DUALDIFF performs better than LinkerNet the RMSD between docked poses towards dual targets. This indicates that the molecules generated by DUAL can bind dual targets with smaller conformation change. We also benchmark the inference time of baslines and our methods Appendix[H H Additionally, we provide visualization of examples of generated molecules in Figure See more examples in Appendix F

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Reference
TargetDiff
LinkerNet
DualDiff
P18507
Vina:
Vina:-8.809
Vina: -7.998
Vina: -9.206
Q9UBS5
Vina: -6.318
Vina: -1.972
Vina: -8.027
Vína: -8.056
Figure 3: Reference molecules and examples of ligand molecules by different methods generated for the dual targets (UniProt ID: P18507 (top) and Q9UBS5 (bottom)).
Table 2: Ablation different ways of aligning dual targets.
Methods
P-1 Vina Dock (1)
P-2 Vina Dock ())
Max Vina Dock (i)
Dual High AfT.
QED
SA
Diversity (f)
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Mod.
Avg.
Med.
Avg.
Med.
Avg.
Med.
COMPDIPF Center
8.10
-8.26
-.08
8.26
-7.33
-7.60
30.8%
22.0%
0.52
0.53
0.60
0.59
0.73
0.73
COMPDIT-RMSD
-8.29
-8.44
-8.35
8.46
-747
-7.78
35.6%
30.0%
0.55
0.36
0.59
0.59
0.72
0.72
COMPDIFF
35.9%
0.72
DUst DIFF-Center -8.12
-8.29
-8.12
-8.28
-7.32
-7.66
30.0%
22.2%
0.52
0.54
0.59
0.59
0.69
0.69
DUALDIEF-MMS RMSD
-8.40
-8.51
8.45
88.3
-7.63
-7.87
35.8%
30.0%
0.55
0.57
0.59
0.59
0.67
0.67
-8.55
0.67
Table Ablation on different strategies of identifying fragments for linker design methods.
Methods
P-1
(1)
Vina (i)
(.)
High (f)
QRD (?)
SA (?)
Divessity (f)
Avg.
Med.
Med.
Avg.
Mod.
Mol.
Avp.
Med.
Avg.
Med.
Avg.
Mod.
5
.6.11
0.32
DiftLinker-pocket.
-7.35
-7.74
-7.20
-3.75
4.25
-7.14
20.2%
0.0%
0.45
0.45
0.31
0.30
0.58
0.62
DiffLinker-
-7,22
-7.32
-7.49
-7.99
6.65
-6.86
15.7%
0.0%
0,61
0.63
0.32
0.32
0.49
0.51
-7.05
-7.87
-3.27
-7.92
-5.87
-7.18
24.6%
0.0%
0.43
0.30
0.29
0.52
0.54
LinkerNet-
-7.54
-7.54
-7.56
-7.58
.6.98
-7.05
19.9%
0.0%
0.69
0.72
0.77
0.79
0.46
0.46
LinkerNet-self.5
-7.55
LinkerNet-8
-8.09
-8.23
-8.23
.3.29
-7.63
34.0%
0.0%
0.62
0.65
0.72
0.74
0.38
0.35
LinkerNet-self-8
-8.20
-8.37
-8.13
-7.17
-7.72
38.7%
0.0%
0.61
0.63
0.72
0.73
0.37
0.34
4.3
Ablation Studies
Effects of Alignment of Dual Targets We perform different methods align the pockets of dual targets for COMFDIFF and DUALDIFF. See the results in Table Naively, we can align two pockets by their geometric centers (denoted "-Center")). In our method, we propose align pockets with protein-ligand binding priors. We select the ligand with minimum RMSD between docked poses (resp. minimum sum of Vina Dock scores) towards dual targets as the anchor align the dual targets, which is denoted as "-RMSD" (resp. "-Score"). DUALDIFF-SCOr achieved the best performance among all variants, demonstrating the effectiveness of the alignment method.
Different Strategies of Identifying Fragments for Linker Design Methods We conduct ablation on different strategies of identifying fragments for DiffLinkee and LinkerNet for dual-target drug design. Since we use Vina Dock to select fragments, we have tried different box sizes for docking, i.e., 5Á and 8A. For DiffLinker, since the relative poses of fragments are required as input, we dock fragments derived from Mj and M2 target P1 (or P2). We then apply DiffLinker both with and without considering the pocket. The corresponding methods are denoted as ShiffLinkee-5/-88 8----pckkee- 5/-pocket-8". For LinkerNet. the relative poses of fragments are not required. So we try two setting: dock fragments from Mi and M2 to target Pi (or P2); dock fragments from Mi (resp. M2) to target Pi (resp. P2). The difference is that all fragments are docked the same pocket in the former setting while the fragments from two ligand molecules docked to their respective pockets. The

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corresponding methods are denoted as S/ The results are reported in Table The results show that larger docking box size allows for better selection of fragments. As we expected, DiffL with consideration of pockets achieves better performance. Among all variants, "LinkerNet-seff-8" achieves best performance, which implies that adjusting relative poses of fragments may play crutial role in linker deisgn. This feature of LinkerNet allows for selecting the most important fragments for each pockets of the dual targets.
Conclusion
In this work, introduced novel dataset for dual-target drug design. We formulate this problem a generative task and propose compositional reverse sampling to reprogram pretrained target-specific model for dual-target drug design, which successfully generate dual-target ligands and outperform all baselines, including repurposed linker design methods. Our research lays the groundwork for dual-target drug design using generative methods, with future progress expected.
Acknowledgments
This work is supported by the National Science and Technology Major Project (2033DD120000) and the National Natural Science Foundation of China No. 62377030. We also thank the reviewers for their valuable feedback.
10

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A Motivation, Significance, and Current Practices of Dual-Target Drug Design
Motivation and significance of dual-target drug design The reviewers and audicnce can refer to Giordano and Petrelli [16), Boran and Iyengar [5] and [4]] for the concept of dual-target (or multi- target) drugs. Dtal-target drugs have various advantages, especially in aspects such anti-tumor and overcoming drug resistance.
It has been revealed that single-targe drugs may not always induce the desired effect on the entire biological system even if they successfully inhibit or activate a specific target [47] One reason is that organisms can affect effectiveness through compensatory ways. Another reason is the development of resistance either by self-modification of the target through mutation or by the adoption of new pathways by cancer cell, for the growth and multiplication [47]. Cancer and those nervous and cardiovascular system diseases are complicated, thereby promoting the mulli-targeted therapies as a better pathway achieve the desired treatment. For example, the multiple tyrosine kinase inhibitor imatinit induces better anti-cancer effects compared with that of gefitinit which involves a single target, further indicating that drugs with multiple targets may exhibit better chance of affecting the complex equilibrium of whole cellular networks than drugs that act on a single target. Refer to Lu al. [1] for more examples. Notably, combination therapy also performs well in overcoming drug resistance [5]. However, under some circumstances, the combination therapy might have additive and even synergistic effects in theory; however, it often leads some unpredictable side effects, such as increased toxicity. Thus, multi-target drugs are a better choice.
Current practices for dual-target drug design Refer to Sun et al. [57 for a comprehensive review. The mainstream strategies are drug repurposing, skeleton modification. and linked/mergee//fuee pharmacophores, which involve complicated pipelines and require domain knowledge from experts. To the best of our knowledge, are the first one to formulate dual-target drug design as a generative task and provide simple yet effective solutions.
B Extended Related Works
Our work is also relevant to neural model reprogramming" We will discuss the connections as follows:
Elsayed et al. [33 proposed adversarial reprogramming. Specifically, given model trained on a task which maps x to ((x), the adversary aims repurpose the model for new task which maps g(ā)
for inputs &. by learning mapping functions (-; f) and (= 9) to make hy (f (f(h) approximate g()). They successfully demonstrated their methods on image classification tasks. For example, a trained adversarial program can cause a classifier trained on ImageNet to an MNIST classifier.
Yang al. [61] reprograms acoustic models for time series classification, through input transformation learning and output label mapping, which are similar to (.) and (-).). respectively. The motivation is that data scarcity hinders researchers from using large-scale deep learning models for time-series tasks while many large-scale pre-trained speech processing models are available. Melnyk et al. (43 also follows this paradigm reprogram pretrained language models, BERT trained on English corpus, for the antibody sequence infilling task.
The above works all aim to reprogram model trained task perform new task. Our work also falls into this paradigm, since we focus on reprogramming models trained for single-target drug design to design dual-targe drugs. And also have similar motivation of Yang et al. [6]] and Melnyk et al. 43 because there is no training data for dual-target drug design. Differently, we focus on reprogramming a diffusion model equipped with SE(3)-equivaring explored in previous works due to its complex sampling process during inference. And, notably, all the above works require additional training to learn the additional parameters of input transformation (i.e., ( 0) in Elsayed et al. (13) for reprogramming. However, our framework works in a zero-shot manner, which means only need modify the sampling process of the diffusion model to perform
which has not been widely
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httpp://ee www.wwwiiiiiiia org/vik://effiiini
Note that the reprogramming here is not relevant to the biological concept "cell reprogramming" 6
15

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the novel task without any additional training. Specifically, our proposed pocket alignment resembles the "input transformation", i.e., hy)-). and the compositional sampling resembles the "output label mapping", i.e., (,))), but no learnable parameters are introduced for reprogramming. Yang et al. [6]] provided theoretical results on selecting a pre-trained model for reprogramming. but it not easy to directly apply the results to our case due to the intricate properties of diffusion models.
C Term Definitions in Drug Synergy
Drug Synergy Drug synergy refers to the phenomenon where two or more drugs used in com- bination, produce more therapeutic effect than the sum of their individual effects. When drugs with distinct binding targets are strategically paired, they can leverage each other's strengths and compensate for respective weaknesses, which enables lower individual drug doses, thereby reducing the risk of adverse effects. This characteristic is usually used cancer and HIV treatments, and has been proven to be new but promising way combat complex diseases
Zero Interaction Potency (ZIP) Yadav et al. 60 proposed ZIP score to describe the drug interac- tion by comparing the alteration in the potency of dose-response curves in the context of single drug administration versus their concurrent use in combinations. In the two-drug combination scenario, will refer to drug A and drug B, respectively. The effects of these drugs defined as EAD for combination, E and En for individual situations (0 < E < 1). The ZIP score can be defined as follows:
SZP = EAR - (Ex Ep EA En).
(17)
The ΣAB in Equation 17 is the average response values obtained by fitting dose-responss curves independently in each dimension of the measured combinatorial data sub-tensor, the explanation for other variables are the same.
Bliss The Bliss independence model [24] assumes stochastic process where the two drugs elicit their effects independently. In this model, the expected combination effect can be calculated based on the probability of the independent events occurring:
Syuss EAB - (1- (1- - EB)).
(18)
Equation (8) is similar Equation 17 the difference between which is that Equation 17
employs
fitted drug responses instead of observed ones.
Loewe The Loewe score [1 forecasts the dose combination that will produce specific effect, it calculates the expected response as if both drugs are the same. Assume drug A can produce effect FA dose AA and drug B can produce effect EB dose JB, then the loewe affinity states that the expected effect FoLoww can be determined by:
FA
JB 1
(19)
XA
XB
where XA and XB are the doses drug A or B alone that produces effect EL The Loewe score is then defined follows:
Stoewe
EAB
ELoewe-
(20)
Highest Single Agent (HSA) The HSA is straightforward scoring system for estimating drug synergy, which determines the incremental effect of combining drugs by comparing the enhanced combined effect to their individual effects 660 The HSA score be caleulated as follows:
SHSA EAR max EA, Ep)
(21)
The ZIP score is the most prevalently utilized metric in the assessment of drug synergy. Furthermore. these scores can be collectively analyzed to identify optimal drug combinations for targeted therapy.
D Justification for the Choice of Baselines
One of the traditional strategies for dual-target drug design (refer to Sun at. 57 as a comprehensive review) is linking pharmacophores by domain experts, such chemists or pharmaceutical scientists.
16

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We use SOTA deep-learning based linker design methods (DiffLinker [25] and LinkerNet [T9] to mimic this procedure. Since each target pocket has a corresponding ligand molecule our curated dataset, we can break the ligand molecule into fragments and select the ones critical for binding as pharmacophores. In this case, given respective critical fragments of dual pockets, we can design linkers and resemble them into complete molecules. Ideally, the designed molecules contain critical pharmacophores that account for binding to dual targets and serve as a potential candidate for dual-target drugs.
E Preliminary Verification on Single- Taaget Setting
We evaluate Pocket2Mol and TargetDiff under the setting of single-target drug design on 438 unique targets in dataset preliminary verification. We each method generates 10 molecules for each target and collect all generated molecules across 438 proteins and report the mean, trimmed mean (i.e., averaging that removes 10% of the largest and smallest values before caleulating the mean) and median (denoted as "Avg.". "T-Avg." and "Med." respectively) of affinity-related metrics (Vina Score, Vina Min, Vina Dock, and High Affinity) and property-relatee metries -drue-likeness QED 31, synthesizability SA [14), and diversity). Vina Score assesses binding affinity directly based on the generated 3D molecules. Vina Min carries a energy minimization over the local structure before estimation. Vina Dock incorporates a re-docking step to assess the highest binding affinity achievable. Meanwhile, High Affinity evaluates the proportion of generated molecules that have stronger binding affinity than the reference molecule for each protein tested.
The results are shown in Table where molecules generated by TargetDiff exhibits binding affinities that are either comparable to or slightly greater than those of the reference molecules. Pocke12Mol achieves strong performance in terms of QED, SA, and diversity but fails in Vina-related metrics. Therefore, TifgetDiff can be regarded as an effective molecular generative model on our dataset.
Table 4: Summary of different properties of reference molecules and molecules generated by baselines under the single-target setting. (1) (4) denotes a larger / smaller number is better. Considering outliers significantly affect the mean, we ignore some abnormal values of Vina Score and Vina Min.
Methods
Vina Score ())
Vina Min (.)
Vina Dock (])
High Affiait (f)
QED (7)
SA (t)
Diversity th)
T-Avz
Med.
Med.
Avg.
T-Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg. Mad.
Reference
-8.02
-7.96
-8.99
-8.37
0.54
0.55
Pockei2Moll
33.14
-3.19
-3.16
3381
-3.77
-3.76
-1877
-1.86
-185
2.1%
0.0%
0.49
0.49
0.87
0.89
0.83
0.85
TargetDiif
-1.88
-1.88
-7.99
.788
4.77
8878
8875
56.0%
55.0%
0.51
0.53
0.58
0.58
0.89
0.70
F Visualization of More Examples
Here we provide visualization of more examples as shown Figure
17

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Reference
TargetDiff
LinkerNet
DualDiff
P11388
Vina: -9.730
Vina: -8.800
Vina: -10.132
Vina: -10.360
P42345
Vina:-7.714 -7.714
Vina: -5.467
Vina: -8.747
Vina: -9.541
Q16739
Vina: -8.380
Vina: -8.978
Vina: -7.875
Vina: -9.133
P48735
Vina: -5.466
Vina: -2.611
Vina: -7.565
Vina: -8.846
Figure 4: Visualization of more reference molecules and examples designed by TargetDiff, LinkerNet and DUALDIFF.
G Proof of SE(3)--qivarraace
We denote the global SE(3) transformation as Tg. and which means the transformation as (x,, Ryx; + b, where Ry E 3x3 is the rotation matrix and E R3 the translation vector. In line with define the composed message passing as follows:
Section 3.2
Ab((V)== := Σ for (b/, h/. dig. exj)
(22)
SEV
Ax((). =
Σ
(xf - xxxx x)) (h!"! .nt,1 d. cij) Iigand
(23)
jEV..
h(d1 h + (Ah) +bb((2))
(24)
x = x(x)) x } (Ax((1)) Ax((1a)
(25)
It is easy to that the atomic distance d' ||, - xyy1 and e₁ feature both invariant to SE(3) transformation The hidden embedding h is also invariant since the its updates (as shown in Equation (22) and Equation (4)) are only related to invariant features.
18

---

We define ATg (x((V)) as
ATg (x)())) =
Σ (Tg(2)) - To (x,)) fo. (h.
[+ _// dig.. eij) ligand
JEVone#
Σ
(Rgx; + b - R.x - fo. for (h/+1, n//t dij. ciy) .1 Ligand
JEV. (t
Σ
[ x,) So. (b h diis eij)
ligand
JEV
After apelying Tg to x, the updated position x = o(xx) can be written as (using the above results):
o(Tx(x)) = [x(x) + (
-, +
Σ
Σ
(x x)) S0 (b/+) 1+1 _n//t ddiy. 1rgand
vE
JEV..
= R + R Σ
Σ
(x fo. (h, 1 .nft' dij. eij) Ingand
+
2
DEI,2 VEV..
HE
Rgx, + Ry (xx (Vi) + (1s) +
2
Rg x 2 (Ax( + Ax(()2)) +
2
1
Tg TT (o(x))
x + 2
(A) ax((1))
The above equation shows the SE(3) eqquivaraae of the atom position update formula Equation (25). Based on the fact that Equation (2 is SE(3)-invarian and Equation (25) is SE(3)-equivariant, can say that the composition operation of our method is -E(3)venqivariant.
H Computational Efficiency
We test the time for generating 10 molecules by TargetDDiff (single-target drug design) and DiffLinkerr LinkerNet, CompDiff, and DualDiff (dual-target drug design). The results are shown in Table
Table 5: Time Cost for generating 10 molecules by TargetDiff Lingle-target drug design) and DiffLinker, LinkerNet, CompDiff, and DualDiff (dual-target drug design).
Setting
Method
Time (seconds)
Single-Targe
TargetDiff
220
DiffLinker
31
LinkerNet
30
Dual-Targer
COMPDIFF
395
DUALDIFF
493
Linker design methods (DiffLInker and LinkerNet) are faster than de novo design methods. The reasons twofold: 1. For linker design, parts of the molecules are provided; thus, it is only necessary to generate the remaining part (i.e., the linker). 2. For DiffLinker, only one of the dual targets
the input of the model. For linkerNet, it cannot pockets conditions. Thus, the computational cost lower.
As the table shows, the inference time of CompDiff and DualDiff (dual-target drug design) is about twice as that of TargetDiff (single-target drug design). This as expected because there are two heterogencous graphs and the messages the two graphs processed and aggregated separately
19

---

(sequentially in our implementation) and then composed as described in our paper. There is space for optimizing the inference speed CompDiff and DualDiff by parallelling the peessag--psssingg operations over the two graphs (when GPU memory is sufficient). This code optimization will only speed up the inference and not change the generated results. Ideally, this will make the inference time of CompDiff and DualDiff almost the same as that of TargetDiff.
Though the computational cost of our method is higher than the baselines, is still acceptable in practice.
General acceleration methods (e.g.. pruning, quantization, and distillation) for deep learning models can be applied to the models used in our framework. Besides, fast diffusion sampling solvers can also be applied to our framework, with DPM-Solver [40] one of the most representative works, which can significantly reduce the number of sampling steps without sacrificing the quality of generated samples.
I Discussion, Limitation, and Future Work
Our work provides a novel dataset and a general framework for dual-target drug design to the community. And our method can be casily adapted the multi-target scenario. Our work is the first step towards generative dual-target drug design. There are still limitations in our work. For example, we not consider flexibility of proteins in our work, which is more practical setting, though this is also an issue for most works in SBDD. Another limitation of our work is the lack of validation through wet-lab experiments. will leave these as future work.
Societal Impacts
Our research holds the promise of significantly advancing the pharmaceutical industry by aiding in the development of potent dual-target drugs. This could potentially streamline the path to new treatments, making efficient drug discovery more attainable goal. Moreover, emphasizing the ethical implementation of our methods is of paramount importance. It is also needed to ensure that these scientific achievements are utilized for social good, safeguarding against any misuse that could lead to negative consequences for society.
20

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Reviews:
[{"review_id": "D1atytui5s", "reviewer": "Reviewer_xVLn", "summary": "This work studies a dual-target drug design using diffusion models trained on single-target protein-ligand complex pairs. \n\nThere two proposed methods, COMPDIFF and DUALDIFF, both are aim to align and generate dual-target ligands using SE(3)-equivariant composed message passing. The paper also introduces a curated dataset based on synergistic drug combinations to evaluate the effectiveness of these methods. \n\nIn general, I like this work and its perspective from single-cell / bio-system reprogramming to drug design tasks.\n\nOn interesting point is, for pre-trained models, there are also neural model reprogramming works [A,B] and some theoretical studies on selecting pre-trained model for mis-tasks alignment in [B]. \n\nIt would be attracting more audience by adding some related neural model-level reprogramming in the related works or future theoretical analysis. \n\n***\n**References**\n\nA. Adversarial reprogramming of neural networks, ICLR 2019\n\nB. Voice2series: Reprogramming acoustic models for time series classification, ICML 2021\n\nC. Single-cell expression analyses during cellular reprogramming reveal an early stochastic and a late hierarchic phase. Cell 2012", "questions": "1. Would the authors provide more details on detailed justification for the choice of baselines?\n\n2. How would be challenges on reprogramming other generative model different from diffusion based model?", "limitations": "- Not previous, some limitation on the wet labs perhaps.", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- overcoming drug resistance and improving therapeutic efficacy by using diffusion models for dual-target drug design\n\n- alignment of dual pockets using protein-ligand binding priors is interesting and novel\n\n- The creation of the dataset based on synergistic drug combinations is a good contribution", "weaknesses": "- the alignment side, there are more depth to studies motivated by measurement theories or so.\n\n-  illustrations to explain the methodology, e.g., the process of SE(3)-equivariant composed message passing would be a plus", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your positive feedback. Please see below for our responses to the comments.\n\n**Q1: Further studies of the alignment motivated by measurement theories or so.**\n\nA1: \nThe alignment of the dual pockets is dependent on the molecule selected to compute the alignment transformation (i.e., the anchor molecule that we mentioned in line 313-319). Thus, we provided ablation studies on various alignment algorithms based on different types of anchor molecules (see Section 4.3 and Table 2). The results show that the performance of various alignment methods (CompDiff/DualDiff-RMSD/Score) is consistently superior to the baseline (CompDiff/DualDiff-Center).\n \nOur paper focuses on the application, i.e., dual-target drug design instead of theory, which is out of our scope. We would like to leave it as future work.\n\n**Q2: Illustrations to explain the methodology, e.g., the process of SE(3)-equivariant composed message passing.**\n\nA2:\nWe have illustrated our method in Figure 1. To be more clarified, we would add more detailed legends and captions to promote understanding. As for SE(3)-equivariant composed message passing, see the content inside the dashed box in Figure 1, where the gray / red / green nodes represent atoms of ligand molecules being generated / pocket P1 / pocket P2, respectively. The arrows in red and green represent the messages (or drifts) computed over two heterogenous knn graphs with dual targets P1 and P2, respectively. (Specifically, one graph is built upon the gray and red nodes, and the other is built upon the gray and green nodes.) Then the messages are further composed and the dark arrow represents the SE(3)-equivariant composed message. Notably, the compositional operation preserves the SE(3)-equivariance (see Appendix D for the proof). The composed message is used to update the atom positions and types of ligand molecules being generated. The complete reverse sampling process consists of a series of such operations (1000 steps in practice).\n\n**Q3: More details on detailed justification for the choice of baselines.**\n\nA3: Considering the strict page limit of the submission, we describe the choice of baselins in Section 3.3. We will elaborate on the justification in the appendix in the revision. Here, we provide more detailed justification as follows: One of the traditional strategies for dual-target drug design (refer to [1] as a comprehensive review) is linking pharmacophores by domain experts, such as chemists or pharmaceutical scientists. We use SOTA deep-learning-based linker design methods (DiffLinker [2] and LinkerNet [3]) to mimic this procedure. Since each target pocket has a corresponding ligand molecule in our curated dataset, we can break the ligand molecule into fragments and select the ones critical for binding as pharmacophores. In this case, given respective critical fragments of dual pockets, we can design linkers and resemble them into complete molecules. Ideally, the designed molecules contain critical pharmacophores that account for binding to dual targets and serve as a potential candidate for dual-target drugs. \n\n**References:**\n\n[1] Sun, Dejuan, Yuqian Zhao, Shouyue Zhang, Lan Zhang, Bo Liu, and Liang Ouyang. \"Dual-target kinase drug design: Current strategies and future directions in cancer therapy.\" European Journal of Medicinal Chemistry 188 (2020): 112025.\n\n[2] Igashov, Ilia, Hannes Stärk, Clément Vignac, Arne Schneuing, Victor Garcia Satorras, Pascal Frossard, Max Welling, Michael Bronstein, and Bruno Correia. \"Equivariant 3D-conditional diffusion model for molecular linker design.\" Nature Machine Intelligence (2024): 1-11.\n\n[3] Guan, Jiaqi, Xingang Peng, Peiqi Jiang, Yunan Luo, Jian Peng, and Jianzhu Ma. \"LinkerNet: fragment poses and linker co-design with 3D equivariant diffusion.\" Advances in Neural Information Processing Systems 36 (2024).\n\n**Q4: Challenges on reprogramming other generative models different from diffusion-based models.**\n\nA4:\nAs pointed in line 66-68, our method can be viewed as a general framework where any pretrained generative models for structure-based drug design (SBDD) can be applied to dual-target drug design without any fine-tuning.\n\nOne example is reprogramming the autoregressive models for SBDD, e.g., Pocket2Mol [1] and GraphBP [2]. They are GNN-based methods that generate 3D molecules by sequentially placing atoms into a protein binding pocket. In our framework, the alignment procedure is independent of the type of generative models. We only need to compose the conditional distribution at each step of autoregressive sampling, which is actually straightforward and much simpler than the compositional sampling of diffusion models.\n\nWe have tested the performance of Pocket2Mol for single-target drug design (see Table 4 in Appendix B). The average high affinity ratio of Pocket2Mol is only 2.1%, far behind TargetDiff (56.0%). Thus, we do not reprogram it in practice, considering its unsatisfactory performance.\n\n**References:**\n\n[1] Peng, Xingang, Shitong Luo, Jiaqi Guan, Qi Xie, Jian Peng, and Jianzhu Ma. \"Pocket2mol: Efficient molecular sampling based on 3d protein pockets.\" In International Conference on Machine Learning, pp. 17644-17655. PMLR, 2022.\n\n[2] Liu, Meng, Youzhi Luo, Kanji Uchino, Koji Maruhashi, and Shuiwang Ji. \"Generating 3d molecules for target protein binding.\" arXiv preprint arXiv:2204.09410 (2022).\n\n**Q5: \"Some limitation on the wet labs perhaps.\"**\n\nA5:\nWe have discussed the limitations of our work in Appendix E. We would like to validate our methods by wet-lab experiments in the future, if possible. And we will add this point in Appendix E as you suggest.", "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": "2gyQd5IlKG", "reviewer": "Reviewer_aLWE", "summary": "The paper presents a comprehensive approach for dual-target drug design by reprogramming pretrained single-target diffusion models. It introduces a curated dataset derived from synergistic drug combinations, and two methods, COMPDIFF and DUALDIFF. The experimental results demonstrate the outperformance of the proposed methods compared to the baselines.", "questions": "None", "limitations": "The authors clearly discussed the limitations and potential improvements of the methods.", "rating": 7, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The experimental setup is rational, including multiple appropriate baselines and comprehensive evaluation metrics. In addition, this proposed method can serve as a general framework where any pretrained generative models for SBDD can be applied to dual-target drug design without fine-tuning.", "weaknesses": "The generalization of this framework could be discussed in more detail.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your positive feedback. Please see below for our responses to the comments.\n\n**Q1: Discussion about the generalization of this framework.**\n\nA1: \nOur proposed framework is **general** and **any types of pretrained generative models** for structure-based drug design can be applied to dual-target drug design without any fine-tuning. In our work, we use TargetDiff as a demonstrative case. Additionally, as a representative example, Pocket2Mol can also be reprogrammed. See our response to reviewer xVLn for details (Q4 & A4).\n\nOur methods can also be easily applied to **multi-target drug design**, though we focus on dual-target drug design in the experiments in our paper. Specifically, for the pocket alignment procedure, we can select a pocket and align all other pockets to it. \n\nSince we focus on reprogramming single-target diffusion models for dual-target drug design in a **zero-shot manner**, there are two different tasks and datasets for training (single-target) and inference (dual-target), which require strong generalization ability of our methods. The promising experimental results show that our reprogrammed model can effectively design drugs that bind to dual targets, demonstrating the generalization ability of our framework.", "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": "NUOLh0wuDt", "reviewer": "Reviewer_em5U", "summary": "This paper addresses the challenge of designing dual-target drugs, a promising strategy in overcoming drug resistance in cancer therapy. The authors propose leveraging the success of deep generative models in structure-based drug design, formulating dual-target drug design as a generative task. They introduce a novel dataset of potential target pairs derived from synergistic drug combinations and propose a method using diffusion models trained on single-target protein-ligand complex pairs. Their algorithm effectively transfers knowledge from single-target pretraining to dual-target scenarios in a zero-shot manner. Multiple experiments show the effectiveness of their approach compared to various baselines.", "questions": "How does the computational efficiency of your method compare with the baselines? Are there specific optimizations that can be applied to reduce computational demands?\nCan you provide more detailed comparisons and analyses of the repurposed linker design methods used as baselines? How do they perform relative to your proposed method?", "limitations": "The paper mentions repurposing linker design methods as strong baselines but does not provide detailed comparisons or analyses of these methods.\n\nThe scalability of the proposed method to larger datasets and more complex protein-ligand interactions needs to be explored further.", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "The formulation of dual-target drug design as a generative task using diffusion models is novel and addresses a significant challenge in cancer therapy. The curation of a dataset with potential target pairs based on synergistic drug combinations provides a valuable resource for the research community. The use of SE(3)-equivariant composed message passing to align two pockets in 3D space and build complex graphs is a strong point, leveraging advanced geometric deep learning techniques. The ability to transfer knowledge from single-target pretraining to dual-target scenarios in a zero-shot manner is impressive, showcasing the model’s flexibility and generalization capability.\nThe extensive experimental validation against various baselines highlights the robustness and effectiveness of the proposed method.", "weaknesses": "The proposed method involves complex geometric deep learning techniques, which may pose implementation challenges for researchers less familiar with these methods.\nThe computational demands for training and inference using diffusion models and SE(3)-equivariant message passing could be significant, potentially limiting the method’s accessibility.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your detailed feedback. Please see below for our responses to the comments.\n\n**Q1: \"The proposed method involves complex geometric deep learning techniques, which may pose implementation challenges for researchers less familiar with these methods.\"**\n\nA1: \nTo understand our method, researchers need to have a background in both geometric deep learning [1] and diffusion models [2]. To help researchers who are less familiar with these concepts use our method in practice, we will open-source both the code, curated dataset, and generated molecules upon acceptance of this paper and provide a user-friendly interface.\n\n**References:**\n\n[1] Bronstein, Michael M., Joan Bruna, Taco Cohen, and Petar Veličković. \"Geometric deep learning: Grids, groups, graphs, geodesics, and gauges.\" arXiv preprint arXiv:2104.13478 (2021).\n\n[2] Yang, Ling, Zhilong Zhang, Yang Song, Shenda Hong, Runsheng Xu, Yue Zhao, Wentao Zhang, Bin Cui, and Ming-Hsuan Yang. \"Diffusion models: A comprehensive survey of methods and applications.\" ACM Computing Surveys 56, no. 4 (2023): 1-39.\n\n**Q2: \"The computational demands for training and inference using diffusion models and SE(3)-equivariant message passing could be significant, potentially limiting the method’s accessibility.\"**\n\nA2: \nOur framework allows for transferring the knowledge gained in single-target pretraining to dual-target scenarios in a zero-shot manner. More specifically, the open-sourced diffusion model checkpoints (e.g., DiffSBDD [1], TargetDiff [2]) can be directly used in our framework for inference without any additional training or fine-tuning, which can save the computation demanded for training. Actually, the computational demand for training a diffusion model for single-target drug design is acceptable. For example, the training of TargetDiff converges within 24 hours on one NVIDIA GeForce GTX 3090 GPU.\n\n**References:**\n\n[1] Schneuing, Arne, Yuanqi Du, Charles Harris, Arian Jamasb, Ilia Igashov, Weitao Du, Tom Blundell et al. \"Structure-based drug design with equivariant diffusion models.\" arXiv preprint (2022).\n\n[2] Guan, Jiaqi, Wesley Wei Qian, Xingang Peng, Yufeng Su, Jian Peng, and Jianzhu Ma. \"3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction.\" ICLR (2023).\n\n**Q3: \"How does the computational efficiency of your method compare with the baselines? Are there specific optimizations that can be applied to reduce computational demands?\"**\n\nA3: We test the time for generating 10 molecules by TargetDiff (single-target drug design) and DiffLinker, LinkerNet, CompDiff, and DualDiff (dual-target drug design). The results are shown as follows:\n\n| setting | method | Time (seconds) |\n|---|---|---|\n| single-target | TargetDiff | 220 |\n| dual-target | DiffLinker | 31 |\n|  | LinkerNet | 30 |\n|  | CompDiff | 395 |\n|  | DualDiff | 493 |\n\nLinker design methods (DiffLInker and LinkerNet) are faster than de novo design methods. The reasons are twofold: 1. For linker design, parts of the molecules are provided; thus, it is only necessary to generate the remaining part (i.e., the linker). 2. For DiffLinker, only one of the dual targets can serve as the input of the model. For linkerNet, it cannot use pockets as conditions. Thus, the computational cost is lower. \n\nAs the table shows, the inference time of CompDiff and DualDiff (dual-target drug design) is about twice as that of TargetDiff (single-target drug design). This is as expected because there are two heterogeneous graphs and the messages on the two graphs are processed and aggregated separately (sequentially in our implementation) and then composed as described in our paper. **There is space for optimizing the inference speed of CompDiff and DualDiff by parallelling the message-passing operations over the two graphs (when GPU memory is sufficient).** This code optimization will only speed up the inference and not change the generated results. Ideally, this will make the inference time of CompDiff and DualDiff almost the same as that of TargetDiff. \n\nThough the computational cost of our method is higher than the baselines, it is still acceptable in practice.\n\nGeneral acceleration methods (e.g., pruning, quantization, and distillation) for deep learning models can be applied to the models used in our framework. Besides, fast diffusion sampling solvers can also be applied to our framework, with DPM-Solver [1] as one of the most representative works, which can significantly reduce the number of sampling steps without sacrificing the quality of generated samples. \n\n**References:**\n\n [1] Lu, Cheng, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu. \"Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps.\" Advances in Neural Information Processing Systems 35 (2022): 5775-5787.", "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": "m5t6LeuKaY", "reviewer": "Reviewer_7yyK", "summary": "This is an interesting and promising work that combines state-of-the-art techniques in structure-based drug design, such as diffusion models, to address the challenging but important problem of dual-target drug design. The main contributions of the paper are:\n\n1.Carefully curated a dataset based on synergistic drug combinations for the dual-target drug design task, offering new opportunities for AI-driven drug discovery.\n2. Proposed SE(3)-equivariant composed message passing to reprogram pretrained single-target diffusion models for dual-target drug generation in a zero-shot manner.\n3. Proposed fragment selection methods from synergistic drug combinations to repurpose linker design as baselines for dual-target drug design.\n4. The method can be viewed as a general framework where generative models for single-target SBDD can be applied to dual-target design without fine-tuning.", "questions": "1. What are the current practices and needs for dual-target drug design in industry? The authors could discuss the importance of this task in drug discovery, as well as the limitations and future directions of this work.", "limitations": "1. The motivation and significance of dual-target design need to be further emphasized. The current discussion in the Introduction about the advantages of dual-target drugs is not sufficiently convincing. More references should be added to support the advantages of dual-target drugs, especially in aspects such as anti-tumor and overcoming drug resistance.\n\n2. The novelty of the proposed generative models need to be further enhanced. Compared to the existing approaches, the proposed methods has no inspiring contributions except SE(3)-equivariant modeling, which is also a common idea in this field.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The paper addresses an important and challenging problem in drug discovery, namely dual-target drug design, which has the potential to overcome drug resistance and manage complex diseases more effectively.\n2. The authors curate a novel dataset based on synergistic drug combinations, providing a valuable resource for AI-driven dual-target drug discovery.\n3. The proposed method, which reprograms pretrained single-target diffusion models for dual-target drug design using SE(3)-equivariant composed message passing, is innovative and has the potential to transfer knowledge from single-target to dual-target scenarios without the need for extensive training data.\n4. The authors repurpose linker design methods as strong baselines for the dual-target drug design task and propose strategies to identify potential fragments from synergistic drug combinations, demonstrating a comprehensive approach to the problem.", "weaknesses": "1. The method description is unclear in several aspects:\na) The formal definition of the dual-target drug design problem, especially the pocket alignment, is lacking.\nb) The specific approach for aligning two pockets is not well explained, leaving questions about the consideration of different ligands and the quality of the alignment.\nc) The composed reverse process in the generative model is not described in sufficient detail, making it difficult to understand how it is defined and sampled.\n2. The experimental results are not presented in the paper, making it impossible to assess the effectiveness of the proposed method. The authors should include detailed quantitative and qualitative results and compare their method with baseline approaches to demonstrate its advantages.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your feedback. Please see below for our responses to the comments.\n\n**Q1: Formal definition of the dual-target drug design problem, especially the pocket alignment, and consideration of different ligands and the quality of the alignment.**\n\nA1: We have provided the definition of the problem in line 184-192. Here we discuss it in more detail:\n\nFor single-target drug design, it can be formulated as a generative task. Specifically, following Pocket2Mol and TargetDiff, the goal is to model the conditional distribution $P(M|\\mathcal{P})$, where $\\mathcal{P}$ is a protein pocket with its 3D structure and $M$ is the ligand molecule with its 3D structure. Autoregressive models (e.g., Pocket2Mol) and diffusion models (e.g., TargetDiff) are developed for the 3D molecule generation task.\n\nIntuitively, the dual-target drug design can also be formulated as a generative task and the goal is to model the conditional distribution $P(M|\\mathcal{P_1}, \\mathcal{P_2})$, where $\\mathcal{P}_1, \\mathcal{P}_2$ are the two different pockets. However, this formula is ill-defined when considering the 3D structures, because $\\mathcal{P}_1$ and $\\mathcal{P}_2$ do not lie in the same coordinate system and any geometric operations are meaningless. Thus, we need to introduce a transformation $\\mathcal{T}$ to align the two pockets so that they lie in the same coordinate. In this case, the goal is to model $P(M|\\mathcal{P}_1, \\mathcal{T}\\mathcal{P}_2)$. \n\nConsidering that single-target model is trained on protein-ligand complex datasets, to alleviate the gap between training (single-target) and inference (dual-target), we propose to align the two pockets by the protein-ligand interaction prior. Specifically, this alignment ensures the ligand molecule being generated can stay in a spatial position that is suitable for both pockets. We have described how to obtain such $\\mathcal{T}$ in practice in line 201-205. Here we provide a more mathematical description: We first select a molecule $M_1$ that binds to pocket $\\mathcal{P}\\_1$ and then we dock it to pocket $\\mathcal{P}\\_2$ to obtain $M_2$. Note that $M_1, M_2$ are the same molecule with different 3D poses. The transformation can be defined as  $\\mathcal{T}:= \\text{argmin}_{\\mathcal{T}} \\text{RMSD}(M_1, \\mathcal{T}M_2)$.\n\nThen we provided ablation studies on how we choose the anchor molecule $M_1$ for obtaining the transformation. See Section 4.2 and Table 2 for details. The results show that our proposed alignment methods can ensure the model generates valid molecules and consistently surpass the baseline.\n\n**Q2: \"The composed reverse process in the generative model is not described in sufficient detail, making it difficult to understand how it is defined and sampled.\"**\n\nA2: We have described the composed reverse process in detail in line 206-239 of the paper.\n\nIn the paper, we describe the process from the perspective of energy-based (or score-based) generative models and Langevin dynamics, which are the motivation of the compositional operation. The description explains why the compositional operation at each step in the process can generate samples from the distribution $P(M|\\mathcal{P}_1)\\cdot P(M|\\mathcal{T}\\mathcal{P}_2)$ in theory.\n\nThough the theoretical justification seems complicated, the practical implementation of our method is actually simple yet effective. In the following, we provided a simplified description from the perspective of diffusion models to help the audience less familiar with diffusion models (or score-based generative models) better understand the operation.\n\nThe step at time $t$ of the reverse process is as follows (refer to Equation (4) in the paper for definition of notations):\n$$q(\\mathbf{x}\\_{t-1}|\\mathbf{x}\\_{t},\\hat{\\mathbf{x}}\\_0)=\\mathcal{N}(\\mathbf{x}\\_{t-1};\\hat{{\\mu}}\\_t(\\mathbf{x}\\_t,\\hat{\\mathbf{x}}\\_0),\\tilde{\\beta}\\_t\\mathbf{I})$$\n$$q(\\mathbf{v}\\_{t-1}|\\mathbf{v}\\_t,\\hat{\\mathbf{v}}\\_0)=\\mathcal{C}(\\tilde{{c}}\\_t(\\mathbf{v}\\_t,\\mathbf{v}\\_0))$$\n\nwhere $\\hat{\\mathbf{x}}\\_0, \\hat{\\mathbf{v}}\\_0$ are the atom positions and types predicted by the SE(3)-equivariant neural network based on $\\mathbf{x}\\_{t},\\mathbf{v}\\_{t}$. In the dual-target setting, there are two graphs, based on which two sets of $\\hat{\\mathbf{x}}\\_0, \\hat{\\mathbf{v}}\\_0$ are predicted. The compositional operation composes the two sets of prediction to obtain a composed version of $\\hat{\\mathbf{x}}\\_0, \\hat{\\mathbf{v}}\\_0$. CompDiff directly composes the final outputs of the neural network. DualDiff composes them at each layer of the neural network. By analysis in Section 3.2, the composition is equivalent to 'average' operation over drifts in Euclidean space for atom positions and logorithms of categorical distribution for atom types, which can ensure correct sampling from the target distribution.", "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:

Meta-review: Dual-Target Drug Design is an important problem in drug discovery for which authors present a solution based on diffusion models and SE(3) equivariant GNNs. Reviewers raised some concerns regarding the reporting including computational time and efficiency, choice of baselines, need for the method in industry, and other minor concerns. Authors have satisfactorily addressed these comments. It is recommended that the additional results and new insights that came of the discussions are added in the camera ready version of the manuscript.
Decision: Accept (poster)