FlexSBDD: Structure-Based Drug Design with Flexible Protein Modeling
Authors: ZAIXI ZHANG
Mengdi Wang
Qi Liu
Venue: NeurIPS 2024 poster (2024)
Keywords: Structure-based drug design
Generative models
AI for Science
Protein Modeling
Steric Clashes
Protein-ligand Interactions
Primary area: machine_learning_for_other_sciences_and_fields
TL;DR: FlexSBDD is a deep generative model capable of accurately modeling the flexible target protein structure for ligand molecule generation.

Abstract: Structure-based drug design (SBDD), which aims to generate 3D ligand molecules binding to target proteins, is a fundamental task in drug discovery. Existing SBDD methods typically treat protein as rigid and neglect protein structural change when binding with ligand molecules, leading to a big gap with real-world scenarios and inferior generation qualities (e.g., many steric clashes). To bridge the gap, we propose FlexSBDD, a deep generative model capable of accurately modeling the flexible protein-ligand complex structure for ligand molecule generation. FlexSBDD adopts an efficient flow matching framework and leverages E(3)-equivariant network with scalar-vector dual representation to model dynamic structural changes. Moreover, novel data augmentation schemes based on structure relaxation/sidechain repacking are adopted to boost performance. Extensive experiments demonstrate that FlexSBDD achieves state-of-the-art performance in generating high-affinity molecules and effectively modeling the protein's conformation change to increase favorable protein-ligand interactions (e.g., Hydrogen bonds) and decrease steric clashes.

FlexSBDD: Structure-Based Drug Design with Flexible Protein Modeling
Zaixi Zhang 12.33 Mengdi Wang", Qi Liu
1: School of Computer Science and Technology. University of Science and Technology of China 2:State Key Laboratory of Cognitive Intelligence, Hefei, Anhui, China
3:Princeton University
mixi@@mall.ust..edd... mengdiw princeton.edu, qutiugl@utc.edu..n
Abstract
Structure-based drug design (SBDD), which aims to generate 3D ligand molecules binding to target proteins, a fundamental task drug discovery. Existing SBDD methods typically treat protein as rigid and neglect protein structural change when binding with ligand molecules, leading to a big gap with real-world scenarios and in- ferior generation qualities (e.g., many steric clashes). To bridge the gap, we propose FlexSBDD, a deep generative model capable of accurately modeling the flexible protein-ligand complex structure for ligand molecule generation. FlexSBDD adopts an efficient flow matching framework and leverages E(3) E(3)-equivariamt network with scalar-vector dual representation to model dynamic structural changes. Moreover, novel data augmentation schemes based on structure relaxation/sidechann repacking are adopted to boost performance. Extensive experiments demonstrate that FlexS- BDD achieves state-of-the- art performance in generating high-affinit molecules and effectively modeling the protein's 's conformation change increase favorable protein-ligand interactions (e.g.. Hydrogen bonds) and decrease steric clashes.
Introduction
Deep generative models are profoundly impacting drug discovery, particularly within the challenging subfield of structure-based drug design (SBDD) [ 54 36). SBDD focuses on generating drug-like ligand molecules conditioned on target-binding proteins, necessitating precise modeling of complex geometric structures and detailed protein- ligand interactions. Some early attempts adopt autore- gressive models to generate 3D ligand molecules atom atom-by-atom by-atom 53 57
or fragment-by trraammetby-- To overcome the limitations of autoregressive methods (e.g., error accumulation), recent works
(85.
28 29 leverage -arratrrrrrrssvve diffusion-baatt models [31] to predict the distribution of ligand
atom types and positions via denoising and have achieved the state-of-the- performance.
Despite the remarkable success, most existing SBDD models treat target proteins as rigid and neglect the conformation change. However, according the "induced fit" theory in biochemistry (3). proteins are flexible structures that undergo structural changes upon ligand binding, leading to enhanced interactions and binding affinity. In structural biology, the protein structure that has a bound small molecule is referred to as ligand-bound or holo conformation, and the protein structure without bound small molecule called ligand-free or apo conformation [16]. For example, Figure. (b)&(b) shows the aligned apo and holo-structures of two proteins, and the extent of structural change influenced by the specific properties and structures of the proteins and ligands. The neglect of protein flexibility in SBDI leads to several significant drawbacks: (1) The generated protein-ligand ligand complexes are prone to have sub-optimal protein structures and steric clashes as the protein cannot adaptively adjust structures according to different generated molecules 30 (2) The chemical search
"Q Liu is the corresponding authors.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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space is overly restricted by existing holo data, limiting the exploration of diverse high-quality drugs. As result, SBDD models tend to produce molecules that are similar to those fitting the predefined pocket space 53 62 (3) A large gap between real-world physical binding process and computational simulations, which may lead to high false positive rates real-world drug discovery applications i.e.,
most computationally designed drugs do not have real therapeutic effects (2).
However, several challenges exist for flexible protein modeling in existing SBDD models. Firstly, proteins are macromolecules with thousands of atoms, which brings formidable high degrees of freedom for flexible structural modeling [3]] Secondly, there lack apo-holo structure pair datasets for learning structural changes [16]. Finally. the widely used diffusion- based models are conssconnu for exploring the huge space of flexible protein-ligand complexes (28).
To address the aforementioned challenges, we propose new method FLeXSBDD capable of modeling the flexibility of target protein while generating de novo 3D ligand molecules. To reduce the computational complexity, we focus on the key degrees of freedom in protein structure (i.e., C. coordinate, the orientation of the backbone frame, and the sidechain dihedral angels to determine the full atom structure) inspired by previous works [67 77 [1. As for the dataset, we employ the Apobind dataset 3 with additional Apo data generated by OpenMM relaxation 21 and Rosetta repacking 18 as data augmentation. For efficient and stable generation, we adopt a flow-matching framework that defines multimodal conditional flows for different components in protein protein-ligand complex and use equiivarrr network with scalar-vector dual representation for learning the chemical and geometrie information. The input to FlexSBDD is the initialized protein structure (e.g., apo structure). FlexSBDD learns to iteratively update protein-ligand structures and ligand atom types from time- = to and finally outputs both the generated 3D ligand molecule and the updated protein structure (holo). Extensive evaluations on benchmarks and case studies show the advantage of FIeXSBDD in generating structurally valid protein-ligand complexes with high affinity, more favorable non-covalent interactions, and fewer steric clashes. The code of the paper is provided at We highlight our main contributions as follows:
49
https://gg www..tt.....a.aii...ooto
We propose flw-mmttching-basel generative model FlexSBDD, capable of modeling protein flexibility while generating de novo 3D ligand molecules.
FlexSBDD not only achieves wate-of-the-art performance on benchmark datasets (e.g., -9.12 Avg. Vina Dock score), but also learns to adjust the protein structure to increase favorable interactions (e.g., 1.96 Avg. Hydrogen bond acceptors) and decrease steric clashes.
With concrete case study on KRACGI2C promising target of solid tumor, we demonstrate FlexSBDD's potential discover cryptic pockets for drug discovery.
2 Related Works
2.1 Structure-Based Drug Design
pruuttue--bssed drug design (SBDD) 87 aims to directly generate 3D ligand molecules inside target protein pockets. LiGAN (62 first uses 3D CNN to encode the protein-ligane ligand structures and generate ligands by atom fitting and bond inference from the predicted atom densities. Several follow-up works have adopted autoregressive models for atom-wise [53 50
57
79
78
or fragment-wist
[57 adopts the geometric vector perceptrons [40] as the context encoder and autoregressively predicts the atom types, atom coordinates, and bond types until the generated molecule is completed. FLAG (85) and DrugGPS [82] predict the next molecular fragment and add it to the partially generated molecule in each round. Recently, powerful diffusion models have started to make significant impact in SBDD, demonstrating promising results with non-autoregressive sampling 665 28 29 46). They usually represent the protein-ligane complex as 3D atom point sets, and define diffusion and denoising processes for both continuous atom coordinates and discrete atom types. For instance, TargetDiff
27
60
78 generation of 3D molecules. For example, Pocket2Mol
28 proposes a target-aware molecular diffusion process with SE(3)-equivariant GNN denoiser. While there has been significant progress, existing approaches often neglect the critical aspect of protein flexibility. To address this gap, we explicitly model the conformational change of protein in FDcX

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Provin
Residoe type Lysie
Co postion a
Ligand mobecale
Aton type a! Alom postion an-)
Frumc orianiationn
(a)
(b)
(c)
Figure I: Aligned apo (ligand-free) and holo (ligand-bound) examples of (a) Human Glutathione S-Transferase protein (PDB ID: 10GS) and (b) Human Menkes protein (PDB ID: 2KMX) (3] Apo structures are colored in "magenta" and holo-structures "cyan" with the bounded ligand in "orange". (c) Illustration of the protein structure and ligand molecule parameterization.
2.2 Flexible Protein Modeling
Proteins are intrinsically dynamic entities and flexibility is critical factor affecting protein's function and behavior in biological systems [72 37). The dynamic properties are traditionally modeled with physics-based methods such as Molecular Dynamics simulation (MD) [33]. To overcome the computationally demanding drawback of MD, some deep learning-based methods have been recently proposed, e.g., DynamicBind [51), FlexPose [20). SBAlign (68, NeuralPlexer [6]] and
DiffDock-Pon Pookktt (59] consider protein flexibility in protein-ligand docking. However, these methods can hardly extended to the challenging de novo ligand generation, leaving it an unsolved problem.
3 Preliminaries
Notations and Problem Formulation: We model pegtein-ligand complex C C (P. G)
84 86
[6,88]] The objective of FlexSBDD to learn a conditional generative model P(PP', .PP that generates ligand molecule conditioned on the target protein and meanwhile updates the structure of the target protein (P'). Proteins are composed of a sequence of residues (amino acids), each containing backhone atoms (i.e., Ca, N, C, O) and sidechain that identifies the residue type. In this paper, the residue types are assumed known and the full atom structure of an amino acid can be represented by its Ca coordinates æ; E IR3 the frame orientation ( E 50(3), and maximally 4 sidechain dihedral angles x = {xx] il x"2 x x²* E [0, 2TT²* where E {1, ........ Np} and N₂ is the number of residues protein. The backbone structure of the residue can be determined according their
ideal local coordinates relative to the C, position (+) and the orientation O (4) 23 The sidechain
conformations can be derived with the dihedral angles (ii as the bond length/angles are largely fixed [8.. With the above notations, protein structure with Np residues can compactly represented
as P = (()(0, (+), x ( J==1 (see the illustration in Figure. C)). Following previous works (74). we treat each amino acid as a node and integrate backbone orientation and sidechain dihedral angles as node features. Such method enjoys the advantage of fewer nodes and less computational cost. The generated ligand molecule can be represented as set of atoms: G = (a(*), a (6) Ni /==1, where
(1) n indicate the atom type (n,, is the total number of atom types we consider) and () e R denotes the atom coordinate. In the constructed protein-ligand complex 3D graph, we use ((1) to denote both C, coordinates and the ligand atom coordinates for conciseness.
Flow Matching (FM) 49 4 a simulation-free method for learn- ing continuous normalizing flows (CNFs) [15], has shown better performance and efficiency than diffusion-banee models on series of biomolecular tasks 9 77 69). To model the complicated protein- -igand complex structures, manifolds [14]. Let M be the manifold space with metric g. q is the probability distribution of data M. and p be the prior distribution. The time-dependant probability path on M is defined as Pr M + Ry0 satisfying Po = P and P1 = (xx) E T.M is the corresponding gradient vector the path on æ at time t. Flow Matching aims to learn a neural network 0g (z to approxi- mate the target vector field u,: (0) (x,) [0 () uy (x))l However, ue is intractable in practice and alternative is to use conditional density path (z(z1) with conditional gradient
Riemanian Flow Matching:
need to apply the general flow matching the Riemannian
3

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fime-1
Initiaiiod
Update structure
Ligazd
Updated protein structure
10
Flex- SBDD
0
0
Flet-
0
Add chemical bonds with post- processing
SBDD
Acedd
00
ar
Figure 2: Overview of FlexSBDD. The flow matching-based generative process starts from apo protein structure and the initialized ligand molecule. each time step, FlexSBDD updates C, to Cl+ and finally obtains the holo ppptiinliggant structure at f 1. In the illustration, the gray dots indicate protein residues and the other dots indicate ligand atoms with different element types.
field (x(arr)) and use Conditional Flow Matching (CFM) objective as:
(CF = (e)p t) ur (1)22)))
(I)
because LrM and LCFM have the same gradients according previous works [1 49 is sampled from the uniform distribution between 0 and Once the gradient field my is learned, we can integrate (x)), t) with do(x) = I, (x) = 2, and ODE solvers 10 to push data from prior distribution po to the data distribution pl. Specifically, a data point from the prior distribution Po C. (Po. Go), where Po is the initialized protein structure (e.g., the apo conformation) and Go is the initialized ligand molecule. The number of ligand atoms is sampled from the reference dataset distribution; the atom types are initialized with uniform distributions; the atom coordinates initialized with Gaussian distributions inside the protein pocket The target data distribution P1 is the holo protein-ligand complex C₁ from datasets.
ordinary differential equations (ODE): _ (x)
following 28
4 FlexSBDD
Figure. shows the overview of FlcxSBDD. Given the initialized target protein structure, the goal of FlexSBDD is to generate the binding ligand molecule well the adjusted protein structure. In other words, the output is the generated protein-ligand complex. Given the complexity of the protein-ligand system, first introduce flow matching the protein backbone (Sec. (41)), side chain
(Sec. 4.2 and ligand atom type (Sec. 4.3) respectively. Then we show E(3)-oquivariant network in Sec. 4 Finally, we discuss the training and generation procedure of FlexSBDD (Sec. 4.5)
4.1 FlexSBDD Protein Backbone and Ligand Coordinates
Following previous works 9 77], The backbone atom positions of each residue protein can be modeled as rigid frame T (x, O) e SE(3), consisting of Ca coordinate to denote coordinates in the rest of this paper) and the frame orientation matrix O E SO(3). For simplicity, the following deduction focuses on single residue/frame and can be generalized to all the residues in the protein. The conditional flow of frame T, is defined to be along the geodesic path connecting To (apo frame) and Tj (holo frame): T, exPr, (t log (Ti)), where exp, represents the exponential map and logr denotes the logarithmic map at 777 99. Specifically, the conditional flow for the Euclidean coordinate vector æ, and the orientation matrix O, are defined as:
R (we use
Coordinates (Ieaattees(R3)) (IR3): (1 t) + tx
(2)
Orientations(SO(3)) O, = expo, (ogo, (O,)). (O,))
(3)
Both R and 50(3) are simple manifolds and their closed-form geodesics can be derived. The exponential map exPo, can be computed using Rodrigues' formula and the logarithmic map logo, is similarly easy to compute with its Lie algebra so(3) [77]. protein-ligand complex, the ligand atom coordinates have the same data modality and probability path as C., The loss function of FlcXSBDD

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for protein backbone and ligand coordinates is the summation of the following two terms:
N₂
1
(1)
(2) (6)
(coord(0) Et (o No + No
11 (It .t) xi 2
(4)
N,
log 0 (0f²) 12
(0) E 00pp:00)))m0000)1000000000000000
Σ
(1) Up (0 .t)
(5)
1
(50(3)
where the superseript (i) in (x and O is the index of the residues/ligand atoms. For conciseness, we use Equ. 4 to represent the coordinate loss with respect to Np a-Carbon and N; ligand atoms.
4.2 FlexSBDD on Sidechain Torsion Angles
In FlexSBDD, define sidechain torsion angles the torus space to model the protein sidechain structures. There are maximally four sidechain dihedral angels for each residue i.e., (0) {x"1, x x= x²* { E 2x)² and there are totally 4N,, torsion angles [8I]. Since each torsion angle lies in [0, 2T). the 4N, torsion angles of sidechains define hypertorus TAN, The manifold of the hypertorus is parameterized as the quotient space RAN, // leading to the equivalence relations X ()...... X (4N,)) (x + 2 X (4M,) (x(1),, .................... ..... (4N,) +2x
39 8T.
We use the linear interpolation paths and the conditional flow for x is defined as:
X = (1 x)xx + t reg(x: - Xu),
(6)
where reg(.) means regularizing the torsion angles by reg (x + T) mod (2r) - m. This leads to the closed-from expression of the loss to train the conditional Torus Flow Matching:
Up (x." reg(xi ( - xo -eg(xx" x0")
(0) (xppptaaassooxxoopxxxxxxxxxxxx N
-
(7)
4.3 FlexSBDD on Ligand Atom Types
The ligand atom types are denoted as a = (a()) N==1 where ( the i-th atom probability vector with n, dimensions: (1) E R To build a path, we define ag as uniform distribution over all atom types and aı as the one-hot vector indicating the ground truth atom type. The probability path
is define as a; = ta + (1 t) and u, (a (alan, a aj ag- a, is a probability vector because its summation over all types equals 1. Following 47
70 12]
we use Cross-Entropy loss CE(.,) to
directly measure the difference between the ground truth type and the predicted one:
Ni CE
Catom (0)
( a
(1
(al t), af)) (8)
We also note the recent progress of sequential flow matching methods seamlessly integrated into FlexSBDD and are left for future works.
71 12
which can be
4.4 Model Architecture
FlexSBDD is parameterized with an E(3)-Equivariant Neural Network with scalar-vector dual feature representation effectively capture the geometric attributes [40 57 The scalar features contain basic biochemical knowledge (c.g., residue/atom types), and the vector features contain geometric knowledge of the structure (c.g., direction the geometric center). The basic building blocks include geometric vector linear (GVL) and geometric vector perceptron (GVP). We also incorporate the geometric vector normalization (GVNorm) and the geometric vector gate (GVGate) for the model's stability and better performance. There are mainly two modules: an encoder that is responsible for encoding the protein-ligand complex 3D graph (see details Sec. D.2p and a decoder that updates both the coordinates, frame orientation, atom types, and side-chain torsion angles (see details in Sec. DD3).. Similar to previous works [57] the update process satisfies the F())-equivariance, More model details are in the Appendix. D.5
5

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4.5 Training and Generation
Training with Data Augementation: For protein-ligan complexes from the training set, we associate them with apo conformations from Apobind [ to create apo-holo pairs. Additionally, we create synthetic apo conformations as data augmentation. This done by first removing the ligands from the holo proteins, followed by applying OpenMM [21 relaxation and Rosetta repacking [18] to these proteins. For each holo-structure, we generate total of 9 additional structures: 3 only with sidechain repacking. 3 with both structure relaxation and repacking. and 3 with additional random perturbations with up to 30 degrees to the sidechain angles. In each training iteration, we randomly sample from the corresponding pool of apo structure Co of the holo-structure Ci and interpolate to obtain C,. The overall loss function is the weighted summation the above four loss functions:
Watom Catom + Weosed Gowsed Wari foo + Use Luss
where Watom, Wooord, Woris and Use are the loss weights and set 2.0, 1.0, 1.0, and 1.0 in the default setting. We adopt Adam 42 optimizer for the optimization and finish training on a Tesla A100 GPU.
Generation:
Starting with the apo structure and an initialized ligand molecule, denoted as Co. the generation process of FlexSBDD is the integration of the ODE dC, with an Euler solver [[O]. Specifically, for each component in C₁, we have:
va(Ce, t) from & to t
de
i+ = xz + vo(2)) A)
(
(1)
t4A = =O, exp 20 (O) .t)tt)
(10)
(8) Xita = reg
( Xt
+ vo (x
( t))():
(0) a++ norm ( + ro ra 10 .)Ar):
(11)
where At is the time step. norm()) means normalizing the vector probability vector such that its summation is 1, and reg(-) means regularizing the angles by reg(r) = (r + T) mod (2Tr) π.
5
Experiments
5.1 Experimental Setup
Datasets:
Following previous works 665|57 we use two popular benchmark datasets for ex- perimental evaluations: CrossDocked and Binding MOAD. Binding MOAD dataset (34] contains around 41k experimentally determined protein-ligand complexes. We further filter and split the Binding MOAD dataset based on the proteins' enzyme commission number [77. resulting in 40k ligain pairs for training, 100 pairs for validation, and 100 pairs for testing following previous work [65]. CrossDocked dataset (25) contains 22.5 million mrolein-molecule pairs generated through cross-docking. We use the same data preprocessing and splitting as [52), only high-quality docking poses (RMSD between the docked pose and the ground truth < IÅ) are kept and 30% sequence identity dataset split is adopted. This produces 100, 000 protein-ligand pairs for training and 100 proteins for testing. We regard the piggein-ligand structures in the datasets as holo-structures. The corresponding apo structures are obtained from Apobind and the generated apo structures as described in Sec. 4.5 We note that it is fair to compare FlexSBDD with other baseline methods as the additional apo structures contain no ligand molecules and cannot be used by baselines for training.
We compare FlexSBDD with five representative methods for SBDD. LiGAN [62] is conditional VAE model that represents protein-ligand complex as an atomic density grid. AR (52) and Pocket2Mol (57) are autoregressive schemes that generate 3D ligand molecules atom- by-atom.
Baseline Methods:
Tifget 28 and DecompDiff (2 are state-of-the-art diffusion- models.
Evaluation: We comprehensively evaluate the generated molecules from three perspectives: bind- ing affinity and molecular properties, molecular structures, and protein-ligand interactions: (1) Following previous work [28]22 (2], we use AutoDock Vina [22 to calculate and report the mean and median of binding affinity-reattd metrics, including Vina Score, Vina Min, Vina Dock, and High Affinity. Vina Score directly measures the binding affinity based on the generated 3D molecules; Vina Min performs local structure relaxation before calculation; Vina Dock includes an extra step of re-docking, which serves to reveal the optimal binding affinity achievable; High affinity measures the percentage of generated molecules with higher binding affinity than the reference molecule in the

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Vina Score (1)
Vina Min (p)
Vina Dock (3)
High Aftinity (f)
QED
(T)
Diversity (T)
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Reference
6.36
4644
-6.71
-6.49
-7.45
-7.26
0.48
0.47
0.73
0.74
LIGAN
-6.33
-6.20
21.1%
11.1%
0.39
0.39
0.59
0.57
0.66
0.67
AR
.575
-5.64
-6.18
-5.88
-6.75
-6.62
37.9%
31.0%:
0.51
0.50
0.63
0.63
0,70
0.70
Pocket2Mol
-5.14
-4.00
-6.42
-5.82
-7.15
-6.79
48.4%
51.0%
0.56
0.57
0.74
0.75
0.69
0.71
TargetDiff
-5.47
-6.30
-6.64
-6.86
-7.80
-7.91
58. 1%
19.1%
0.48
0.48
0.58
0.58
0.72
0.71
DecompDii
-5667
6.04
.7004
.6.1
.8.39
-8.3
64.4%
71.0%
0.45
0.43
0.61
0.60
0.68
0.68
FlexSBDD
-6.64
-7.25
-8.27
-8.46
-9.12
-9.25
78.5%
84.2%
0.58
0.59
0.69
0.73
0.76
0.75
Table 1: Overview of properties of the reference dataset and the molecules generated by different methods on the CrossDocked dataset. (1) / (L) denotes the larger/smaller, the better. The best results marked with bold and the runner-up with underline.
Poceataa
(a) Runtime
(b) Clashes
(c) HB Donors
(d) HB Acceptors
(e) Hydrophobic
Figure 3: Computational Efficiency and Interaction Analysis on CrossDocked. (a) The average time required by different methods to generate 100 ligand molecules for a protein target. (b) The number of steric clashes. (c) The number of hydrogen bond donors in the ligand molecules. (d) The number of hydrogen bond acceptors in the ligand molecules. (e) The number of hydrophobic interactions.
test set. As for the other molecular properties, we consider QED, SA, and Diversity. QED measures how likely a molecule is a potential drug candidate; SA (synthesize accessibility) represents the difficulty of drug synthesis; Diversity is computed as the average pairwise dissimilarity between all generated molecules for binding pocket. (2) terms of molecular structures, we calculate the Jensen-Sin -Shann-Shannon divergences (JSD) in bond length/angle distributions between the reference molecules and the generated molecules following [29] (3) We adopt PoseCheck (D) to evaluate whether methods can establish favorable interaction between protein and ligand. The interactions include Hydrogen bonds and Hydrophobic interactions. We also conduct Steric clashes analysis to examine unphysical structures/interaction.
5.2 Main Results
In Table. [ and 4 we show the binding affinity and the drug-related properties of the generated molecules on benchmarks. We can observe that our FlexSBDD outperforms baselines by large margin in affinity-related metrics. For example, FlexSBDD surpasses the strongest baseline DecompDiff by 0.73 and 0.82 in Avg. and Med. Vina Dock on CrossDokeed and 0.92 and 1.03 respectively on Binding MOAD. These gains indicate the strong capability of FlcxSBDD to explore high-affinity drug molccules and adjust protein structures for tight binding. As for molccular properties QED and SA, FlexSBDD also achieves competitive performance with baselines. As discussed in 229 these properties are usually employed as preliminary screening criteria in real drug discovery scenarios as long as they fall into a reasonable range. Finally, the high diversity indicates that FlexSBDD can explore larger chemical space with flexible protein modeling, which is important for early drug discovery. Generation efficiency is also a key factor to consider when sampling large batch of molecules for screening. A major drawback of widely-used diffusion models their inference speed, which may require 1000 time steps to produce high-quality samples. In contrast, flow matching methods remove stochasticity from the sampling path and can achieve stable and high-quality generation with much fewer steps (e.g., 20 steps in FlexSBDD). In Figure. 3 we observe that FlcxSBDD can generate molecules much more efficiently than autoregressive- based methods such AR [52] and diffusion-based methods such as TargetDiff (28) and DecompDiff (2)..
We further consider steric clashes, hydrogen bonds, and hydrophobic interactions. Steric Clashes happens when two neutral atoms come into closer proximity than the combined extent of their van der Waals radii [63], indicating energetically unfavorable and physically unrealistic structures. Hydrogen bonds (HBs) (58) and Hydrophobic interactions are polar interactions that significantly contribute to the binding affinity between proteins and ligands (More details Appendix (. Figure. 3 show the average number of steric clashes, hydrogen bond donors, acceptors, and hydrophobic
7

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interactions in the generated ligands (without redocking), We observe that FlexSBDD can generate ligands introducing fewer clashes and more favorable interactions. For example, the average steric clashes for DecompDiff and FlexSBDD are 6.43 and 1.39 respectively. The average number of HB Acceptors for DifompDiff and FlexSBDD are 1.18 and 1.96 respectively. This could be attributed to the flexible protein adjustment capability of FlexSBDD, which could adaptively adjust protein and ligand conformations to reduce clashes and increase favorable protein- interactions.
In Figure. we show examples of the generated ligand molecules for target proteins. Especially, We colored the original holo protein structure green and the updated structure with FlexSBDD cyan for comparison. Firstly, we observe FLe can generate ligand molecules with higher affinity and comparable QED and SA compared with reference complexes from datasets and molecules generated by DecompDiff. Morcover, the protein structures of FlexSBDD are adjusted to accommodate the generated ligand molecules. Consistent with the prior knowledge in biology [8) we generally observe that the loop regions in protein structures exhibit greater flexibility, whereas the alpha-helix and beta-sheet regions display more rigidity. To further evaluate the validity of the updated protein structure, we employ self-consistency Template Modeling (scTM) following [48) (more details in Appendix(A22 A.2)). scTM score ranges from to and a larger scTM score indicates better structural validity. On average, the updated protein structures by FD have scTM score of 0.964, comparable to the score of the original structures from the datasets (0.975). Moreover, to evaluate the validity of sidechain structure, compute the Mean Absolute Error (MAE) of sidechain angles following previous works [8]. In Table. 6 we observe FlexSBDD achieves better performance in sidechain structure prediction. These results indicate FlexSBDD has learned the protein flexible changes and maintains the structural validity. More results are included in the Appendix
5.3 Sub-structure analysis
Bond
BGAN
AR
Pocket2 Mal
Target
Dxft
Docomp
Diff
SBDD
Flex
We further conduct sub-structure analysis to evaluate whether FlexSBDD can generate valid molecular conformations. In Table. and Table. 5 in Appendix [ we compute different bond distance and bond angle distributions of the gen- erated molecules and compare them against the corresponding reference empirical distributions following [28. 22)] We can observe that our model has a comparable or better performance on all the bond distances and angles, demon- strating the strong capability of FleXSBDD to generate realistic 3D molecules directly.
C C
0.601
0.609
0.496
0.369
0.359
0.367
C=C
0.665
0.620
0.561
0.505
0.537
0,280
C-N
0.634
0.474
0.416
0,363
0.344
0.277
C-N
0.749
0.535
0.629
0.550
0.584
0.384
C-O
0.656
0.492
0.454
0.421
0.376
C=O
0.661
0.558
0.516
0.461
0.374
0.245
C:C
0.497
0.451
0.416
0.263
0.251
0.193
C.N
0.638
0.552
0.487
0.235
0.269
0.189
Table 2: Lensen-Shanmen divergence between bond distance distributions of reference and generated ligands (the lower, the better). "_", "=", and "." denote single, double, and aromatic bonds.
5.4 Rediscover Cryptic Pockets with FlexSBDD
The dynamic nature of proteins frequently results in the forma- tion of cryptic pockets, which can reveal novel druggable sites not found in static structures and make previously "undrug- gable" proteins into potential drug targets (55]. To study the capability of FlexSBDD explore cryptic pockets, we take KRAS012C for case study, which is a promising target in the treatment of solid tumors, and over 3 decades of efforts have been devoted discovering its inhibitors (drug molecules) [7 (3). The binding mode of ARS-1620 (green, PDB id 5V9U) represents the typical binding pocket exploited by pre- vious research, which limits the exploration of high-affinity inhibitors. Here, we take the protein structure of ARS- as the apo structure and generate ligand molecules. By comparing and filtering the generated molecules according to recent literature 45
Figure 5: The predicted side chain rotation of residue H95 (marked with the red rectangle) is consistent with experimental observation (45
we managed to rediscover the cryptic pockets with FlexSBDD. In Figure. [5] the updated structure is colored cyan and the generated ligand molecule is colored orange. We observe that the side chain rotation of residue Histidine-99 95 (marked with the red rectangle) consistent with the report in (45 (PDB id 6P8Z), which forms new subpocket and contributes lot to binding affinity. This case
8

---

4yhj
2v2r
Reference
DecompDift
FlexSBDO
Reference
DecompDit
Flex5BD0
Wesi 4.50 QED:
642 Vhn 5.34 GED 0.13 SA 8.5
Ving: 24 QED: 253
Wie DRDI 6as BA: 6:00 Vizi -.33 GED: 047 SA 0.79
Vina: 42.11 GED: 6A:3.57
1fmc
1a2g
Reference
DecompDiff
FlexSBDO
Reference
DecompDiff
FlexSBOO
Vhs 40.38 DED: 6.70 SK: 0.53 Vina: 4:72 QCD-851 851--11554 SA: 846
Vita 11.65 DED.EEEED..... 3.:3..3
Wia:: 4-47 GED: 6.58 SA: E40 Vha 4.55 DEC: 0.55 SAC 0.73
Vita: -11 OED: SA:
Figure 4: Examples of the generated ligand molecules for target proteins (PDB ID: 4yhj. 2v3r, Ifme, la2g). We colored the original holo-structure from the dataset green and the updated protein structure with FlexSBDD cyan (structures are aligned). The Carbon atoms in Reference, DecompDiff, and FlexSBDD ligands are colored green, yellow, and orange. Vina Score, QED, and SA are reported.
study demonstrates FlexSBDD's capability accurately model flexible protein structure, update sidechains to reduce steric clashes, and explore cryptic pockets for drug discovery.
5.5 Ablation Studies
We conduct a series of ablation experiments to study the effect different modules on the generation
capability of FlexSBDD: (1) ExpO: In model training, remove the data augmentation mentioned in Sec. [. (2) Expl: we replace the geometric vector modules with EGNN (64] adopted [65],
which only has scalar features without vector features, (3) Exp2: we do not update the backbone structure of the protein (i.e., æ, O) (4) Exp3: we do not update the sidechain dihedral angles of the
protein (i.e., X). (5) Exp4: we fix the whole protein structure in ligand molecule generation. We
retrain all the FlexSBDD variant models for comparison. The results are present in Table. 3
By comparing results from ExpO and FlexSBDD, we can find that data aug- mentation indeed helps boost perfor- mance by introducing more diverse apo structures. In comparing Expl with FlexSBDD, it is obvious that scalar-vector dual feature representation can benefit ligand molecule generation by well capturing geometrical features. When comparing EXP2, 3, and 4 with FlexSBDD. we observe that the model- ing of flexible protein structures includ- ing backbone and sidechains is important for FlexSBDD. Specifically, we find modeling the flexibility of sidechain angles is more important than backbone structure as the backbone is more rigid. For example, the average Vina Dock drops to -8.86 for Exp3 (FlexSBDD w/o flexible sidechain) while only drops to -9.05 for Exp2 (FlexSBDD w/o flexible backbone). According to [43] the sidechains are critical "induced fit", where they adjust positions to accommodate the ligand and enhance binding affinity. Overall, the FlexSBDD variants still demonstrate competitive performance, showing the advantage of flow-matching architecture.
Methods
Vina Scure (1)
Vina Min (L)
Vima Dock (.)
QED
Avg.
Med.
Avg.
Med.
Avg.
Med.
Avg.
Med.
Expo
Expl
-.50
4.85
-7.91
-8 10
-8.95
-9.03
0.55
0.58
Exp2
.6.7
.3.9
-8.14
.8.31
.9.05
.9.20
0.56
0.57
Exp3
Exp4
-6.32
4.88
-7.80
-7.91
-8.82
-8.85
0.52
0.55
FlxxSBDD
-6.64
-7.25
-8.27
-8.46
-9.12
-9.25
0.58
0.59
Table 3: Effect of different modules on the generation performance of FlexSBDD. The best results are marked with bold and the runner-up with underline. The original FlexSBDD incorporated for comparison.
5.6 Hyperparameter Analysis
We investigate the influence of two important hyperparameters on the performance of FlexSBDD, the hidden dimension size and the total number of iteration steps T in flow matching. In Figure.

---

observe the trend of generating higher-quality molecules with larger hidden dimension sizes and more iteration steps. In the default setting, we the node scaler feature size to 256 and total iteration steps to 20 to achieve balance between the computational complexity and the generation quality.
6 Conclusion
In this paper, we propose FlexSBDD, deep generative model capable of modeling the flexible protein structure for ligand molecule generation. FlexSBDD adopts a flow matching framework for efficient ligand generation and leverages E(3)-equivariant network with scalar-vector dual feature representation effectively model dynamic structural changes. Extensive experiments show its state-of-the-an performance in generating high-affinity molecules with less steric clashes and more favorable interactions. Potential future works include leveraging FlexSBDD to discover more cryptic pockets and modeling other functional proteins such as antibodies, peptides, and enzymes.
7
Acknowledgements
This research was supported by grants from the National Natural Science Foundation of China (Grant No. 623B2095) and the Fundamental Research Funds for the Central Universities.
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14

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A Data Analysis
A.1 Protein-ligand Interaction Analysis
We consider steric clashes, hydrogen bonds, and hydrophobic interactions in protein-ligand interaction analysis with PoseCheck [30]. Steric Clashes happens when two neutral atoms come into closer proximity than the combined extent of their van der Waals radii 63], indicating energetically unfavorable and physically unrealistic structures. In PoseCheck, a clash is counted when the pairwise distance between protein and ligand atom falls below the sum of their van der Waals radii, allowing clash tolerance of 0.5 Á. Hydrogen bonds (HBs) represent form of molccular interaction where a hydrogen atom, covalently linked to an element of high electronegativity like nitrogen, oxygen, fluorine, engages with another electronegative atom [58] These bonds crucial in numerous protein-ligand interactions [3] and necessitate precise geometric alignments to form 11. HBs are directional, bestowing distinct roles the atoms involved: the hydrogen covalently bonded to the electronegative atom acts as a "donor", while the atom that receives the HB known as an "acceptor". Hydrophobic interactions are type of non-covalent bonding that occurs among hydrophobic molecules or moieties within an aqueous setting. Driven by water's propensity to hydrogen bond with itself, these interactions result in the segregation of non-polar entities, compelling them cluster together away from the water-rich environment [56]. This behavior significantly contributes to the binding affinity between proteins and ligands.
A.2 Protein Sturcture Analysis
Following 48 scT'M takes generated structure and feeds it into ProteinMPNN [19], state-of- the-art structure-conditionna sequence generation method. With a sampling temperature of 0.1, we generate eight sequences per input structure and then use OmegaFold [75] to predict the structure of each putative sequence. We follow [48] that substitutes AlphaFold2 with OmegaFold for better sequence prediction performance. Finally, scTM is measured by computing the TM-score [80], a metric of structural congruence of the
structure and the original updated structure by our FlexSBDD. scTM scores range from 0 to 1, with higher numbers corresponding to the increased likelihood that an input structure is designable (higher structural validity).
B More Results and Analysis
Table. 5 7 and Figure. show the additional results on substructure analysis, and hyperparameters analysis.
B.1 Benchmark Results on CrossDocked
In Table.
we show the additional results on the Binding MOAD dataset.
Vina Score (
Vina Min (
Vina Dock (i)
High Affinity
QED
SA
Diversity (f)
Methods
Med.
Avg.
Med.
Avg.
Med.
Med.
Avg.
Med.
Avg.
Med.
Med.
Reference
-6.8
-6.66
-7.62
-7.47
-8.21
-8.16
0.60
0.58
0.33
0.34
LIGAN
0.37
0.37
0.40
-7.65
-7.61
32.6%
31.9%
0.42
0.36
Packer2Mol
-7.69
-7.74
37.1%
0.60
0.35
TargetDiff
-6.85
-6.92
-7.95
-7.94
40.3%
39.7%
0.50
0.33
0.71
DecompDiff
-6.37
-6.41
-7.52
-7.31
-8.46
-8.51
56.4%
58.3%
0.60
0.61
0.32
0.34
FexSBBD
-7.04
-7.20
-8.36
-8.73
-9.38
-9.54
74.5%
76.9%
0.63
0.64
0.42
0.41
0.73
0.74
Table 4: Overview of properties of the reference dataset and the molecules generated by different methods on Binding MOAD dataset. (t) (4) denotes the larger/smaller, the better. The best results marked with bold and the runner-up with underline.
B.2 Bond Angle Distributions
In Table. 5 we show the Jensen-Shanme divergence between bond angle distributions of the reference molecules and the generated molecules.
15

---

Bond
liGAN
AR
Pocket2
Target
Decomp
Flex
Mol
Diff
Diff
SBDD
CCC
0.598
0.340
0.323
0.328
0.314
0.285
CCO
0.637
0.442
0.401
0.385
0.324
0.316
CNC
0.604
0.419
0.237
0.367
0.297
0.226
OPO
0.512
0.367
0.274
0.303
0.217
0.210
NCC
0.621
0.392
0.351
0.354
0.294
0.283
CC=0
0.636
0.476
0.353
0.356
0.259
0.270
COC
0.606
0.459
0.317
0.389
0.339
0.320
Table 5: Jensen-Shannow 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.
B.3 Validity of Side Chain Prediction
In FlexSBDD, the sidechain torsion angles predicted and the sidechain conformations derived based on the dihedral angles and the ideal bond length/angles. To evaluate the validity of sidechain structure, compute the Mean Absolute Error (MAE) of sidechain angles (degrees) following previous works [8] in Table. 6 We also compare the results with NeuralPlexer [61]. the state-of-the- protein-ligand complex structure prediction. In the table, report the average MAE and can observe that FlexSBDD achieves better performance in generating valid sidechain structures.
Method
X1
X2
X3
X4
NeuralPlexer
15.40
18.77
44.83
50.24
FlexSBDD
12.95
17.80
32.18
46.71
Table 6: The MAE NeuralPlexer and FlexSBDD on sidechain torsion angles.
B.4
More Results on Abation Studies
In Table.
we show the average number of interactions in the ablation studies.
Methods
Steric Clashes (4)
Donors (f)
HB Acceptors (f)
Hydrophobic (f)
Exp0
1.56
1.38
1.74
4.79
Expl
1.77
1.35
1.77
5.40
Exp2
1.45
1.23
1.85
5.75
Exp3
1.92
1.11
5.23
Exp4
1.90
1.09
1.58
5.29
FlexSBDD 1.39
1.40
1.96
6.12
Table 7: Effect of different modules on the generation performance of FlexSBDD. We show the aver- age number interactions here. We highlight the best two results with bold text and underlined text, respectively.
B.5 Evaluation of Binding Affinity with GlideSP
Besides Vina Scores, we also try to leverage other docking methods to evaluate the binding affinity 24.. In Table. 8, we further leverage Glide (26) to evaluate the generated ligand molecules, which demonstrates superior ability in filtering active compounds. Specifically, we calculate the min-in- place GlideSP score following (24,, where the ligand structure undergoes force-field-bar based energy minimization within the receptor's ' field before scoring. In the table below, we observe that FlexSBDD can also achieve the best score on Glide, demonstrating strong performance generating protein- binding molecules.
16

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Table 8: Comparison of Average Min-in-Plas Place GlideSP Scores on CrossDocked.
Methods
Avg. min-in-place GlideSP score (J)
Reference
-6.32
LiGAN
-6.14
AR
-6.20
Pocker2Mol
-6.71
TargetDiff
-6.86
DecompDiff'
-7.09
FlexSBDD
-7.55
B.6 Hyperparameter Analysis
In Figure. 6 flow matching.
we show hyperparameter analysis for the hidden dimension size and the total steps of
-8.8
-8.7
Vina Dock
Vina Dock
-8.9
-8.8
-9.0
-9.1
-9.1
64
128
256
512
20
Hidden Dimension Size
lteration Steps
(a)
(b)
Figure 6: Hyperparameters Analysis with respect (a) the hidden dimension size (the node scaler features) and (b) the node scaler features, the other features scaled proportionally.
total iteration steps of flow matching. When varying the dimension size of the
C More Details of FlexSBDD Training and Generation
C.1 Hyperparameters settings
To construct the protein-ligand KNN graph, we A as 8 (each node is connected its nearest neighbors). In the default setting, we use hidden size of 256, 128, 128, and 64 for the scalar features of nodes, scalar features of edges, vector features of nodes, and vector features of edges, respectively. The Encoder and Decoder have 6 layers respectively with the number of attention heads set as 4. The number of integration steps in flow matching is 20 for FlexSBDD. The hyperparameters for selected based on grid search ((0.5, 1.0, 2.0, 3.0)). Watom Weaards Woii and Use are set 2.0, 1.0, 1.0, and 1.0 in the default setting. To train FlexSBDD. we use the Adam [42 as our optimizer with learning rate of 0.001, betas (0.95, 0.999), and batch size for 500k iterations. takes around 36 hours on n one NVIDIA GeForce GTX A100 GPU to complete the training.
the loss function: Watom; Wccord, Wori and
C.2 Pseudo Algorithms
We show the pseudo codes of FlexSBDD training and generation in Algorithm |
and
D More Details of Neural Network Architecture
D.1 Overview
series of previous works on biochemistry tasks nodes and edges in 3D graphs with scalar-vector dual features greatly improve performance. In
have shown that representing the
17

---

Algorithm 1: Training algorithm of FlexSBDD
Holo data distribution pr, FlexSBDD model up, Apobind and generated apo structures while Training do
Input:
C1 pr; (0, 1];
Sample Co from the corresponding apo structure pool (Apobind and data augmentation)
2; 20 + t.:; O expo.
(t logo, (O1)) Xr (1 Xo + reg(Xi Xo); a, laj + (1 - t) // Interpolation
Watom Catom Wooodd Worl Cori Wse Lic/ calculate loss according Equ.
0 <
Update(0, VoLFM);
return
Algorithm 2: Generation algorithm of FlexSBDD
Input: Total number of integration steps T, and trained model steps t 0, 0, At 1/L':
Initialize Co with the apo structure and sampled ligand atoms;
while steps < 7 1 do
(+ zt (i)
(2)
H+ = of exp (wo(O,)) (t)2t) + vo(a (2) ,t)t;
O (i)
X+tat reg(xi" (t) + 00 (xi (1) ,)A();;
(1)
attar norm a (1) + (a (9) .1)A1);
(i)
t ++ At;
return C1
FleXSBDD, all nodes and edges in the target protein P and the generated molecules G are assigned with both scalar and vector features better capture the 3D geometric information. The scalar features contain basic biochemical knowledge (e.g., residue/atom types), and the vector features contain geometric knowledge of the structure (e.g.. direction the geometric center). In the of this paper, we use "." and "-"" overheads to explicitly indicate scalar features and vector features (e.g.. and v).
We adopt the geometric vector linear (GVL) and the geometric vector perceptron (GVP) as the main building blocks to enhance the information flows between the scalar features and the vector features and achieve -quivviiree [40]. The details of GVP and GVL are shown in Appendix [D.5] Briefly, they propagate the vector features into the scalar features by row-wise norm and propagate the scalar features to the vector features through gating. The GVP further applies extra non-linear transformations to both the scalar and vector features, following the output of GVL.:
(v'
GVL(V, V),
(12)
NonLinear NonLinearTTannffmmi Transform( v
where (v. v) could be any pair of scalar-vector features. Incorporating vector features is essential for our model's ability to directly and precisely update the positions of atoms and model the conformation change of the flexible protein. In our model, we also incorporate the geometric vector normalization (GVNorm) and the geometric vector gate (GVGate) for model's 's stability and better performance. Specifically, GVNorm combines the layer normalization with the vector normalization [40]; GVGate performs skip connection and fuses features from different blocks.
D.2 Encoder
In FlexSBDD, represent the protein pocket-ligand complex as a k-nearest neighbor (KNN) graph in which nodes represent protein residues or ligand atoms and each node is connected to its nearest neighbors. The imput scalar features of residues are onehot embeddings of residue types and the input scalar features of ligand atoms are initialized with uniform distribution over all atom types. The input vector features of residues are computed based on coordinates of backbone and sidechain atoms, while the vector features of ligand atoms are the Fuclidean vectors pointing to the geometric center of the ligand molecule (see Appendix [.4).. The scalar edge features are the radial basis function (RBF) distance encodings [66] and the vector edge features are the relative coordinates. In
18

---

the flow matching model, to further incorporate time step information, we embed time with sinusoidal embedding [73 and concatenate it with the input scalar node features following 22
Generally, the encoder of FBeX follows the message-passing paradigm to update the features. Denote the feature of node at the I-th layer (v; v(") and the edge feature between node and
as (o)) oiy) (we use subscript here for the index of nodes instead of time step in the main paper).
Each layer consists of a message-passingg module M, and an update module Ut:
M ( M (111 ((l-1)
(13)
(v()
= Ui(V 11-1)
(
where we use M = (m m and M. (m..) .j: m ij to denote the calculated messages for node and the edge between node i and j. The message-passian
module is based on an attention mechanism [73]. The query (ds, q)), key (k,, ky), value (ú,, ūj), and edge bias (bij. bij) are first calculated with GVLs (the layer superseripts are omitted here for simplicity):
d: q: = GV (1-1) )
ky, kj. ú U = GV
(14)
(-1) (l"1)), bij: bi = G
Then the attention weights for the scalar are computed as:
å q o k2 @ bij. àig E R
(15)
dzj = softmax,
V/ 1
Similarly for the vector features:
ā.j = q 2 kj + bij, ā. E x3
1 v3h
(16)
d.j = softmax;
where @ denotes the Hadamard product, 1 is the vector with all entries as 1, he and ht denote the hidden dimension size of the scalar and vector features respectively. softmax, means perform softmax
over the j index. ā.j and â. are the attention weights (scalar and vector channel) between node and The message is obtained as:
(m
(1) m (0) GVL Σ رراúد Σ رis ū,);
(17)
(m By: ()) = GVL (a.y,, K.y)
where the message features with respect node are obtained by applying GVL to the weighted summation of the neighboring value features. Finally, the update module U₁ is formulated as:
"VNorm(GVGate (
(t-1) -
))
(18)
GVNorm(GVGatee é (1-1) (1-1
)),
where the GVGate fuses the information from the (1 1) layer and the calculated messages from the 1-th layer. GVNorm is appended to normalize the features.
D.3 Decoder
The node/edge features of the decoder are initialized from the output of the encoder and are updated the same as the encoder. The decoder of FlexSBDD further updates the protein C₂ and ligand atom coordinates follows:
50
f!!
GVL(GVP( Σ Czj.y Σ Eayū,))
(1-1)
x. (1-1)
(1)
Σ
x
MLP(concat(a;, (ā., || 16 )),
(19)
(1-1) 1)
x (1-1) 111
(1 (11)) (() (1)
x
19

---

where ii is the node i's coordinate at the I-th layer and -112 denotes the row-wise L2 norm. The attention weights (ā:y. å.g. a.j. a.y) and features (ù,, ūj) are calculated similarly Equations 14 and 15 Finally, we apply MLPs on last layer representations (v!-)) v(D)) (totally I. layers) that capture the chemical and geometric attributes for ligand atom type a residue sidechain dihedral angles ( and the residue backbone orientation O prediction. For the efficient encapsulation of three-dimensional rotations for O we predict a unit quaternion vector [38]. The quaternion can be easily transformed into rotation matrix and is a more concise representation of rotation in 3D. The protein-ligand structure is then adjusted based on the updated coordinates, orientation, and the sidechain dihedral angles. Similar to previous works [57], the update process satisfies the -qquiiarrrie
D.4
Feature Initialization
Protein node vector features Following (2). the vector feature for protein nodes in FIexSBDD consists of three parts with a total dimension of [Np, 24, (Np is the total number of protein nodes).
(I) Euclidean vectors between the C. CA, N. CB (CA for GLY) atoms for given residue (shape: [Np, 16, 3).. It encompasses various combinations like C to C, C to CA. C to N, C to CB, CA to C, and so forth.
(2) Euclidean vectors between atom j and atom k in for all side-chain dihedral angles (shape:
[Np. 4, 3).. For instance, an amino acid like Arginine (ARG), the side-chain angles (denoted as X1, X3. X4) defined by specific sequences of four atoms (i-j-k-l) according Rosetta: Xi: N-CA-CB-CG, X2: CA-CB-CG-CD, X3: CB-CG-CD-NE, X4: CG-CD-NE-CZ Then the Euclidean vectors can be obtained by combining vectors of CA CB, CB to CG, CG to CD, and CD NE. For residues with less than 4 sidechain angles, the corresponding vectors are assigned
(3) Euclidean vectors between CA and atom k in all side-chain dihedral angles (shape: 4,,, 3)). For example, the vectors for ARG can be obtained by combining Euclidean vectors of CA to CB, CA to CG, CA CD, and CA to NE, For residues with less than sidechain angles, the corresponding vectors are assigned 0.
Ligand node vector features The vector features for ligand nodes are initialized as the Euclidean vectors between ligand atoms and the geometric center of the ligand molecule (shape: [N1, 1,3).. Ni the number of ligand atoms.
D.5 Geometric Vector Modules
In Algorithm 3 and we show the Geometric vector linear (GVL) and the Geometric vector perception (GVP) modules in FlexSBDD. In Algorithm and show the GVNorm and GVGate modules for the stability and better performance of FlexSBDD.
Algorithm 3: Geometric Vector Linear (GVL)
Input: Scalar and vector features (v, V)
Output: Updated scalar and vector features (v", (y'v" V
Function GVL (v, v):
V' LinearNoBiast VV:
V |
V"
+ concat (v. v²):
4 Linear( v
V"
+ LinearNoBias(
" sigmoid v v"
return (v",v");
20

---

Algorithm 4: Geometric Vector Perceptron (GVP)
Input: Scalar and vector features (v, v)
Output: Nonlinear transformed scalar and vector features (v", v
Function CVP (v, v):
v¹, V <- GVI((v, v):
V loaky (aakkyrelu(v))
V" & LincarNoBiasí
dott (V' @ 1:
Vmaak <- 1 if V dot 2 0, else 0:
Vact f Vdtt Ø V
1 @ v; // ? is element-wise division
4u f- aV + (1- a)) maak ① v' + maskk) O (V' Vact)); // 0.01
return (v", v");
Algorithm 5: Geometric Vector Normalization (GVNorm)
Input:
Scalar and vector features (v, v) Output: Normalized scalar and vector features (v", V Function GVNorm (v, v):
Th LayerNorm(v):
V'
[V, v): 4" V + B: // E e
// v' Rxx3
R R' are trainable parameters
return vv",
Algorithm Geometric vector gate (GVGate)
Input: Scalar and vector features (v, v)
Output: Updated scalar and vector features (v", 4*)
Function GVGate (vrr Vq:: Vp v,):
Ve < concal ( (Vps Vas p
Vg
Ve concat
Vay
Vg):
Vg, V, + GVL (Ve: V.)i
g, sigmoid (Vg);
go sigmoid (1Vv
v Bs ① Vp
gs
V
V" + ge ① Vp + (1 g.) Vgi return (v" v²)
E Limitations and Broader Impact
One limitation of FlexSBDD is that it only considers small molecule design. Recently, other drug modalities such as antibodies, peptides, and nucleic acids have played critical roles in drug discoveries and bio-engineering. We would like to build a generalized version of FlexSBDD for other drug modalities. Another limitation is the limited dataset size, which restricts the scaling of the proposed models. In the future, we may benefit from the generated protein- protein-ligand interaction data from generative AI models e.g.. AlphaFold
[T] and RoseTTAFold All-Atom 44
As for the broader impacts, there are many potential applications of our work, e.g., discovering cryptic pockets and generating drugs cure various diseases. We acknowledge the necessity for regulatory oversight of our Structure-Based Drug Design (SBDD) technique to prevent the creation of harmful molecules. Overall, believe the positive influence of work outweighs the potential negative impacts.
21

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Reviews:
[{"review_id": "fZVYuzlqAf", "reviewer": "Reviewer_QC25", "summary": "In this paper, the authors focus on the flexible protein setting in the structure-based drug design task. They propose a method named FlexSBDD, which is based on flow matching and utilizes E(3)-equivariant neural networks. The experiments show the advantages of the proposed FlexSBDD.", "questions": "See the weaknesses. Additionally, I noticed a work [1] that is closely related to this paper, also employing flow matching. However, the authors have not cited or discussed the differences between their work and this one.\n\n\n**Minor Concern:**\n\nLine 240 \"Table.\": Since \"Table\" is written in full without abbreviation, there is no need to add a period after \"Table\". This issue occurs in multiple places.\n\n\n\n**Reference:**\n\n[1] Schneuing, Arne, et al. \"Towards Structure-based Drug Design with Protein Flexibility.\" ICLR 2024 Workshop on Generative and Experimental Perspectives for Biomolecular Design.", "limitations": "The authors have discussed the limitations of FlexSBDD.", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. This paper focuses on an interesting setting where the proteins are flexible.\n2. The presentation is good, and the paper is well-organized.", "weaknesses": "1. The method does not explicitly model the interaction between the ligand and the protein, especially the pocket. The authors might consider building an external interaction graph between the residues in the pocket and the atoms of the ligand.\n2. I would like to see more focused results on the binding interface.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the valuable comments!\n\n**Comment 1**: The method does not explicitly model the interaction between the ligand and the protein, especially the pocket. The authors might consider building an external interaction graph between the residues in the pocket and the atoms of the ligand.\n\n**Response1**: As indicated in lines 666-668 of the submitted paper, in FlexSBDD, we represent the protein pocket-ligand complex as a k-nearest neighbor (KNN) graph in which nodes represent protein residues or ligand atoms and each node is connected to its k-nearest neighbors. Therefore, the interactions between the ligand and the protein are considered as edge representations in the constructed protein-ligand graph. \n\nWe can also incorporate an additional interaction graph to emphasize protein-ligand interactions. For instance, we may train interaction/binding affinity predictors based on protein-ligand graphs and use these trained predictors to guide the sampling process of FlexSBDD, similar to the approach described in [1]. These only require minor modifications to the FlexSBDD framework. We will include these additional discussions in our revised paper.\n\n[1] Qian H, Huang W, Tu S, et al. KGDiff: towards explainable target-aware molecule generation with knowledge guidance[J]. Briefings in Bioinformatics, 2024, 25(1): bbad435.\n\n**Comment 2**: I would like to see more focused results on the binding interface.\n\n**Response 2**: Thanks for the valuable comments! Besides the common benchmark metrics adopted by previous SBDD papers such as Vina scores, QED, and SA, we also focus on investigating the interactions on the binding interface. **In Figure 3, we consider steric clashes, hydrogen bonds, and hydrophobic interactions at the protein ligand binding interface.** Steric clashes happens when two neutral atoms come into closer proximity than the combined extent of their van der Waals radii, indicating energetically unfavorable and physically unrealistic structures. Hydrogen bonds (HBs) and Hydrophobic interactions are polar interactions that significantly contribute to the binding affinity between proteins and ligands.\nWe observe that FlexSBDD can generate ligands introducing fewer clashes and more favorable interactions. For example, the average steric clashes for DecompDiff (baseline) and FlexSBDD are 6.43 and 1.39 respectively. The average number of HB Acceptors for DecompDiff (baseline) and FlexSBDD are 1.18 and 1.96 respectively. These results indicate that FlexSBDD can adaptively adjust protein and ligand conformations to reduce clashes and increase favorable protein-ligand interactions.\n\nThese analysis are included in lines 257-268 of the paper. We will include more comprehensive analysis in the revised paper.  \n\n**Comment 3**: I noticed a work [2] that is closely related to this paper, also employing flow matching. However, the authors have not cited or discussed the differences between their work and this one.\n[2] Schneuing, Arne, et al. \"Towards Structure-based Drug Design with Protein Flexibility.\" ICLR 2024 Workshop on Generative and Experimental Perspectives for Biomolecular Design.\n\n**Response 3**: Thanks for mentioning the related paper. The ICLR24 workshop paper represents a pioneering work to consider structure-based drug design with protein flexibility. However, it only considers side chain flexibility while keeping backbone atoms fixed. The authors said the full-fledged induced-fit requires backbone movement modeling. Moreover, it only trains on protein-ligand binding complex structures and did not consider apo-holo structure pairs to learn structural transitions. Therefore, the performance of FlexFlow from the ICLR24 workshop is quite limited, even worse than its counterpart without flexible sidechain modeling.\n\nIn comparison, FlexSBDD is able to model both sidechain and backbone flexibility of the protein while generating de novo ligand molecules. To better learn the transition between apo and holo structures, we associate data from the training set with apo structures from Apobind. We also create synthetic apo conformations with OpenMM relaxation and Rosetta repacking. As for the performance, FlexSBDD not only achieves state-of-the-art performance on benchmark datasets (e.g., -9.12 Avg. Vina Dock score), but also learns to adjust the protein structure to increase favorable interactions (e.g., 1.96 Avg. Hydrogen bond acceptors) and decrease steric clashes.\n\nWe will cite and include the discussions in our revised paper.\n\n**Comment 4**: Line 240 \"Table.\": Since \"Table\" is written in full without abbreviation, there is no need to add a period after \"Table\". This issue occurs in multiple places.\n\n**Response 4**: Thanks for the valuable comments! We have corrected the typos in our paper and would like to update the submitted paper in the final version.", "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": "RvOdjAo6gq", "reviewer": "Reviewer_jwrm", "summary": "The author identified an important missing factor in current SBDD modeling, i.e. protein structural change upon binding, and proposed an E(3)-equivariant flow matching framework named FlexSBDD that jointly models protein flexibility and molecule generation. This paper augmented apo structures for each holo protein in the training set via structure relaxation, Rosetta repacking and random perturbations. FlexSBDD achieves SOTA binding affinities, QED and diversity benchmarked on CrossDocked2020 and Binding MOAD dataset, together with fewer clashes and more HB donors and acceptors.", "questions": "- How would FlexSBDD behave if applied to an inpainting scenario (with ground truth holo-protein)?\n- For a fair comparison, I would recommend the authors to try some flexible docking tools that also take the protein flexibility into account, and see how the performances of FlexSBDD and other baselines change.\n- The authors could elaborate a bit more on the evaluation of protein structures. For example, why is FlexSBDD superior to SOTA protein-ligand complex structure prediction method? Under what setting are they being evaluated and compared?", "limitations": "N/A", "rating": 7, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- This paper is well-motivated and generally easy to follow (except for model architecture and training). \n- The authors raise an important question for SBDD, i.e. holo-structures are an induced fit for ligand molecules, which is a novel contribution. \n- The results on two benchmarks are convincing and highlight the importance of modeling protein flexibility.", "weaknesses": "- Typo: (Line 90-91) However, these methods can hardly [be] extended to the challenging de novo ligand generation, leaving it an unsolved problem.\n- Typo: (Line 591) Protein Sturcture Analysis => Protein Structure Analysis\n- Ablation studies suggest that the biggest performance gain come from data augmentation. However, I feel that augmentation shouldn't matter that much, since the whole pipeline only implicitly utilizes the protein structural change and the explicit outcome is the generated ligand itself. Could the authors explain the role of data augmentation in your method?\n- Since apo (unbound) and holo (bound) state proteins are of great focus in this paper, it seems to me that more reasonable metrics for protein analysis would be based on some molecular dynamics, instead of scTM or something that are not guaranteed to output holo proteins for given ligand molecules.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for valuable comments and appreciation!\n\n**Comment 1**: Ablation studies suggest that the biggest performance gain come from data augmentation. However, I feel that augmentation shouldn't matter that much, since the whole pipeline only implicitly utilizes the protein structural change and the explicit outcome is the generated ligand itself. Could the authors explain the role of data augmentation in your method?\n\n**Response 1**: Thanks for the insightful comment! Data augmentation plays important roles in FlexSBDD and the protein structural changes are considered explicitly in the whole pipeline. As indicated in lines 186-195 of the submitted paper, we take apo-holo structure pairs for training. In each training iteration, we sample the apo structures $\\mathcal{C}_0$ and holo-structures $\\mathcal{C}_1$ and interpolate to obtain $\\mathcal{C}_t$, i.e., FlexSBDD is supervised to learn the protein structural changes and the data play critical roles. However, existing apo-holo data pairs from Apobind are quite limiting (~10K data points) and directly training FlexSBDD on it leads to severe overfitting according to our experiments. The low-quality of the generated protein structure would directly lead to inferior Vina scores because of steric clashes and few protein-ligand interactions. **Therefore, we propose to use data augmentation to increase the training dataset size, cover more apo-holo transition paths, and boost FlexSBDD’s generalization capability.** The ablation studies show that the data augmentation contributes a lot to FlexSBDD’s performance. \n\nWe will include more detailed discussions and analysis of the role of data augmentation in our revised paper. \n\n**Comment 2**: Since apo (unbound) and holo (bound) state proteins are of great focus in this paper, it seems to me that more reasonable metrics for protein analysis would be based on some molecular dynamics, instead of scTM or something that are not guaranteed to output holo proteins for given ligand molecules.\n\n**Response 2**: Thanks for the constructive suggestion! We follow DynamicBind to conduct a comprehensive analysis six distinct conformational changes **across the picosecond level to millisecond level (molecular dynamics)**, each exemplified by a case from PDBbind. In the following table, we report Δpocket RMSD of DynamicBind and FlexSBDD, which measures the relative decrease in pocket RMSD (crystal structure as reference) compared with the AlphaFold structures. **A negative Δpocket RMSD indicates that the predicted aligns more closely with the crystal structure compared with the AlphaFold prediction.** We observe that FlexSBDD achieves competitive performance although it is not specifically designed for dynamic docking. \n\n| Methods    | 6QGF | 6PGO | 6N8X | 6UWV | 6ROT | 6S9X | \n|------------|--------------------|------|------------------------|------|---------------|------|\n| DynamicBind  | -0.669     | -1.140| -2.297    | -0.465| -2.327      | -5.245 |\n| FlexSBDD| -0.680    | -0.976| -1.159  | -0.504| -1.148   | -3.083 | \n\n\n**Comment 3**: How would FlexSBDD behave if applied to an inpainting scenario (with ground truth holo-protein)?\n\n**Response 3**: Thanks for the question! We agree it is a good comparison to apply FlexSBDD to the inpainting scenario (with ground truth holo-protein), which is the same setting with the baseline methods (LiGAN, AR, Pocket2Mol, TargetDiff, and DecompDiff). We show the results below and observe that FlexSBDD still behaves well in the inpaint setting, showing the generalizability and flexibility of FlexSBDD’s architecture. \n\n| Methods    | Vina Score (↓) Avg. | Med. | Vina Min (↓) Avg. | Med. | Vina Dock (↓) Avg. | Med. | High Affinity (↑) Avg. | Med. | QED (↑) Avg. | Med. | SA (↑) Avg. | Med. | Diversity (↑) Avg. | Med. |\n|------------|---------------------|------|--------------------|------|--------------------|------|------------------------|------|---------------|------|-------------|------|--------------------|------|\n| **Reference**   | -6.36               | -6.46| -6.71              | -6.49| -7.45              | -7.26| -                      | -    | 0.48          | 0.47 | 0.73        | 0.74 | -                  | -    |\n| LiGAN       | -                   | -    | -                  | -    | -6.33              | -6.20| 21.1%                  | 11.1%| 0.39          | 0.39 | 0.59        | 0.57 | 0.66               | 0.67 |\n| AR          | *-5.75*             | -5.64| -6.18              | -5.88| -6.75              | -6.62| 37.9%                  | 31.0%| 0.51          | 0.50 | {0.63}      |{0.63}| 0.70               | 0.70 |\n| Pocket2Mol  | -5.14               | -4.70| -6.42           | -5.82| -7.15              | -6.79| 48.4%                  | 51.0%| **0.56**      | **0.57** | **0.74**  | **0.75** | 0.69            | *0.71*  |\n| TargetDiff  | -5.47               | *-6.30*| -6.64            | -6.86| -7.80              | -7.91| 58.1%                  | 59.1%| 0.48          | 0.48 | 0.58        | 0.58 | 0.72               | *0.71*  |\n| DecompDiff  | -5.67               | -6.04 | *-7.04*           | *-6.91*| *-8.39*          | *-8.43*| *64.4%*             | *71.0%*| 0.45         | 0.43 | 0.61        | 0.60 | 0.68               | 0.68  |\n| FlexSBDD (inpaint)| **-6.69**           | **-7.16**| **-8.24**      | **-8.50**| **-9.06**      | **-9.12**| **75.9%**         | **82.1%**| **0.58**    | **0.58** | *0.70*    | *0.71* | **0.74**          | **0.72**  |\n\n- **Bold**: Best results\n- *Italic*: Second best", "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": "XoQp91PNim", "reviewer": "Reviewer_Y45d", "summary": "In this research paper, the authors introduce FlexSBDD, a novel model that employs flow matching for the generation of flexible protein-based molecules. Initially, the model sample a noisy ligand based on an empirical distribution. Subsequently, it conducts flow matching, performing on both geometric characteristics and atomic types. Through comprehensive experimentation, FlexSBDD has demonstrated superior performance compared to previous methodologies, including TargetDiff, Pocket2Mol, and DecomDiff.", "questions": "1. In the evaluation using Vina dock metrics, it remains unclear which protein structures were utilized for benchmarking. Could you specify whether the benchmarks employed the initial holo structures or those updated by FlexSBDD?\n2. Could you elaborate on the statement made in lines 216-217? “We note that it is fair to compare FlexSBDD with other baseline methods as the additional 217 apo structures contain no ligand molecules and cannot be used by baselines for training.” I do not fully understand the points here. \n3. The code provided with the submission appears to lack both training and inference components, which undermines the credibility of the reported results. Could you address this omission?\n4. Regarding the prediction of side-chain conformations, it appears that the analysis is limited to the mean squared error (MSE) of chi angles without considering the orientation within the residue frame prediction. Could you discuss the rationale behind this methodological choice?", "limitations": "The limitations and broader impacts are well discussed in Appendix E of the main paper.", "rating": 5, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1. FlexSBDD explores a new avenue, flexible structure-based conditional molecular generation, which is quite novel. \n2. FlexSBDD demonstrates superior performance through well-recognized benchmarking and ablation studies, adhering to rigorous research practices.\n3. FlexSBDD discussions have many chemical insights, which is commendable.", "weaknesses": "1. As discussed in the Dynamic-Bind, many flexible aspects of protein residues involve changes in backbone atoms, such as transitions from DFG-in to DFG-out conformations. The current implementation of FlexSBDD does not demonstrate its capability for conformational search in more rigorous settings, such as when the apo pocket exhibits substantial dissimilarity from the holo pocket.\n2. Although FlexSBDD represents a commendable effort, it fails to address a fundamental issue in flexible-pocket generation: evolving the appropriate atomic number through the generation process. FlexSBDD initializes ligands from an empirical distribution without considering pocket structures, resulting in a somewhat stochastic generation process: sampling a large number of ligands may artificially expand the pocket, leading to an increase in biased docking scores. The illustration provided with the 1a2g example supports this observation.\n3. The model architecture of FlexSBDD, which includes flow matching on various geometries, has been previously implemented in other works such as PPFlow, diminishing the architectural novelty of FlexSBDD.\n4. The illustrations in Figure 4, including the structures from 4yhj and 1fmc, display unusual bond topologies in molecules generated by FlexSBDD, such as a ring containing two double bonds. This issue may stem from an oversight in bond modeling within the architecture.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the appreciation and valuable comments!\n\n**Comment 1**: As discussed in the Dynamic-Bind, many flexible aspects of protein residues involve changes in backbone atoms, such as transitions from DFG-in to DFG-out conformations. The current implementation of FlexSBDD does not demonstrate its capability for conformational search in more rigorous settings, such as when the apo pocket exhibits substantial dissimilarity from the holo pocket.\n\n**Response 1**: Thanks for the insightful comment! FlexSBDD has the capability to model both the backbone and the sidechain structural changes. During rebuttal, we perform a comprehensive quantitative study on proteins with DFG-in/out confirmations to evaluate whether FlexSBDD can perform conformational searches on proteins with substantial structure variability. **As shown in the uploaded pdf (https://openreview.net/forum?id=4AB54h21qG&noteId=Jo1MWV179v), the majority of the predicted protein structures show a lower pocket RMSD compared to the initial ones**, verifying FlexSBDD’s strong capability for conformational search. \n\n**Comment 2**: Although FlexSBDD represents a commendable effort, it fails to address a fundamental issue in flexible-pocket generation: evolving the appropriate atomic number through the generation process. FlexSBDD initializes ligands from an empirical distribution without considering pocket structures, resulting in a somewhat stochastic generation process: sampling a large number of ligands may artificially expand the pocket, leading to an increase in biased docking scores. The illustration provided with the 1a2g example supports this observation.\n\n**Response 2**: Thanks for the insightful comment! In FlexSBDD, the number of ligand atoms is sampled from the reference dataset distribution. \nAccording to related works [1-2], the flexible pocket can adaptively adjust structures to accommodate ligand molecules with different sizes. Therefore, sampling ligand molecules with different sizes help explore different binding modes, e.g., discover cryptic pockets. Pre-determining the ligand atom numbers may restrict the diversity and novelty of the generated molecules. \nWe also report the average number of ligand atoms below. Generally, the average num of atoms of FlexSBDD is comparable to the reference and other baseline methods. DecompDiff has more Avg. Num of Atoms than FlexSBDD. \nAs for the case study examples, we select the best generated ligand molecules for each target protein and FlexSBDD and DecompDiff have roughly the same number of atoms in most of cases. \n\n| Methods    | Reference | LiGAN | AR | Pocket2Mol | TargetDiff | DecompDiff | FlexSBDD|\n|------------|--------------------|------|------------------------|------|---------------|------|------|\n| Avg. Num of Atoms  | 22.8     | 19.9| 17.7   | 24.2| 29.4     | 23.0 |\n\nThere are also some other promising techniques such training neural networks to predict the number of ligand atoms. We will include the discussions in our revised paper.\n\n[1] Lu W, Zhang J, Huang W, et al. DynamicBind: Predicting ligand-specific protein-ligand complex structure with a deep equivariant generative model[J]. Nature Communications, 2024, 15(1): 1071.  \n[2] Qiao Z, Nie W, Vahdat A, et al. State-specific protein–ligand complex structure prediction with a multiscale deep generative model[J]. Nature Machine Intelligence, 2024, 6(2): 195-208.\n\n\n**Comment 3**: The model architecture of FlexSBDD, which includes flow matching on various geometries, has been previously implemented in other works such as PPFlow, diminishing the architectural novelty of FlexSBDD.\n\n**Response 3**: Thanks for the comment! Both FlexSBDD and PPFlow are based on Riemannian Flow Matching [3,4] proposed by previous works. Different from PPFlow that focus on peptide design, we propose a flow-matching-based generative model FlexSBDD, capable of modeling protein flexibility while generating de novo 3D ligand molecules. To work well on the challenging flexible SBDD scenario, FlexSBDD has unique designs on sidechain flow matching, scalar-vector dual representation architecture, and training with data augmentation. \nWe will cite and discuss more related works in our revised paper. \n\n[3] Yaron Lipman, Ricky TQ Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le. Flow matching for generative modeling. arXiv preprint arXiv:2210.02747, 2022.  \n[4] Chen R T Q, Lipman Y. Riemannian flow matching on general geometries[J]. arXiv preprint arXiv:2302.03660, 2023.  \n\n**Comment 4**: The illustrations in Figure 4, including the structures from 4yhj and 1fmc, display unusual bond topologies in molecules generated by FlexSBDD, such as a ring containing two double bonds. This issue may stem from an oversight in bond modeling within the architecture.\n\n**Response 4**: In FlexSBDD, the bonds are modeled with scalar/vector edge representations in the protein-ligand graph. The details of graph construction, feature initialization, message passing, and feature/structure update are included in Appendix D. We will provide more detailed and clear description in our revised paper. Actually, rings containing two double bonds are common in drug molecules, such as Metronidazole [5], Omeprazole [6], Pyrantel Pamoate [7], and Celecoxib [8]. The sub-structure analysis (Sec. 5.3) further validates that FlexSBDD generates valid bond distance/angle distributions.\nIn the future, the bond modeling can be further improved with e.g., generating the bond types along with FlexSBDD sampling. \n\n[5] FINEGOLD S M. Metronidazole[J]. Annals of Internal Medicine, 1980, 93(4): 585-587.  \n[6] Maton P N. Omeprazole[J]. New England Journal of Medicine, 1991, 324(14): 965-975.    \n[7] Rim H J, Won C Y, Lee S I. Anthelmintic effect of oxantel pamoate and pyrantel pamoate[J]. The Korean Journal of Parasitology, 1975, 13(2): 97-01.    \n[8] Puljak L, Marin A, Vrdoljak D, et al. Celecoxib for osteoarthritis[J]. Cochrane Database of Systematic Reviews, 2017 (5).", "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": "JClIeWuVf0", "reviewer": "Reviewer_7REV", "summary": "This paper presents a new deep generative model, FlexSBDD, which advances the field of structure-based drug design (SBDD) by accounting for the flexibility of proteins when generating 3D ligand molecules. This approach addresses the shortcomings of traditional SBDD methods that assume proteins are rigid, leading to less effective drug interactions. To obtain apo-holo data pairs, this paper utilizes Apobind to generate apo strutures from known holo structures. This paper adopts advanced flow matching to learn the apo-holo dynamics of protein and generate 3D molecules in surprising 20 steps. Experiments on CrossDocked and Bingding MOAD show that FlexSBDD can generate drug-like molecules with highest affinity compared to auto-regressive and diffusion-based baselines.", "questions": "1. The reviewer believes FlexSBDD may generate different holo structures than ground-truth (GT). 1. The generated molecules should have higher affinities on generated holos than GT holos, right? 2. How different are the generated and GT holos? 3. If the GT ligand is provided, can the model generate accurate GT holos?\n2. In Table 2, FlexSBDD shows much better bond length distribution than other baselines. How is bond generated? And why is it so good? And why is bond angles (Table 5) not much better?\n3. In Table 3, why data augmentation boosts so much (and the most) on performance? It's hard to understand the connection between apo structures and affinity in fixed holos.\n4. Affinity and other metrics have strong correlation with atom numbers. Please include atom numbers in Table 1 for fairer comparison.\nI will raise my score if the questions are properly answered.", "limitations": "see weakness above", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. For task, this paper focuses on protein flexibility, which is a crutial shortcoming of current SBDD methods. From the data aspect, this paper utilizes Apobind to generate apo strutures from known holo structures. From the evaluation aspect, this paper presents a case study which analyzes the predicted structure in 5.4. For normal SBDD evaluation, this paper includes 2 datasets and adopts Glide scores.\n2. For methodology, this paper respects characteristics of different modalities, and utilizes continuous, Riemanian, torus, and discrete flow matching for different modalities. Benefits from optimal transport path of flow matching, this paper achieves quite surprising sampling efficiency.\n3. For technical innovation, this paper proposes, 1. data augmentation, 2. a good composition of geometric NN modules, both of which boost the performance.\n4. The results look good. Congratulations, this paper makes it work.", "weaknesses": "This paper focuses on protein flexibility for SBDD. However, the evaluation (except for a case study in 5.4) mainly follows normal SBDD, while the readers may concern more about: 1. Quality of Apobind-generated apo structures and model-generated holo structures, which is not fully discussed and evaluated, 2. Why protein flexibility can help improve affinity for fixed holo structures? Thus, the reviewer concerns the thoroughness and presentation of the experiments. And the reviewer encourages the authors to elaborate on further evaluation and more discussion specific to protein-flexible SBDD.\nI will raise my score if more flexible SBDD evaluations and discussions are presented.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the appreciation and valuable comments! We hope our following responses can properly address your questions.\n\n**Comment 1**: Quality of Apobind-generated apo structures and model-generated holo structures, which is not fully discussed and evaluated\n\n**Response 1**: Thanks for the question! We use self-consistency TM (scTM) scores to evaluate the quality of apo/holo structures. The average scTM of apo structures from Apobind is 0.957 and the model generated holo is 0.964. We have a brief discussion in lines 276-282. We will make the discussion clearer in the revised paper. \n\n**Comment 2**: Why protein flexibility can help improve affinity for fixed holo structures? Thus, the reviewer concerns the thoroughness and presentation of the experiments. And the reviewer encourages the authors to elaborate on further evaluation and more discussion specific to protein-flexible SBDD.\n\n**Response 2**: Thanks for the valuable comment! According to the induced fit theory in biochemistry, proteins are flexible structures that undergo structural changes upon ligand binding, leading to enhanced interactions and binding affinity. Technically, modeling protein flexibility can help reduce steric clashes and adjust structure to establish more protein-ligand interactions such as hydrogen bonds to improve affinity. During rebuttal, we have done a series of further evaluations **including DFG-in/out structure prediction (uploaded pdf), distinct conformational search with respect to time/space scale (response 3), and comparing FlexSBDD with SBDD+flexible docking (response 4 to reviewer jwrm)**. These flexible SBDD specific evaluations shows the effectiveness of FlexSBDD. We will include these results and discussions into our final version.\n\n**Comment 3**: The reviewer believes FlexSBDD may generate different holo structures than ground-truth (GT). 1. The generated molecules should have higher affinities on generated holos than GT holos, right? 2. How different are the generated and GT holos? 3. If the GT ligand is provided, can the model generate accurate GT holos?\n\n**Response 3**: Thanks for the insightful comments! \n**Firstly**, it is true that the generated molecules have higher affinities on generated holos than GT holos. For example, the Avg. Vina Dock on generated holos is -9.12 while on GT holos is only -8.78. **Secondly**, the average RMSD between the generated and GT holos is 0.895, indicating the generated and GT holos are largely aligned. \n**Finally**, if the GT ligand is provided, FlexSBDD can generate accurate holos close to GT holos.\nWe perform a comprehensive quantitative study on proteins with DFG-in/out confirmations to evaluate whether FlexSBDD can perform conformational searches on proteins with substantial structure variability. As shown in the uploaded pdf, the majority of the predicted protein structures show a lower relative pocket RMSD (better) compared to the initial ones, verifying FlexSBDD’s strong capability for ligand-specific conformational search.\n\n**Comment 4**: In Table 2, FlexSBDD shows much better bond length distribution than other baselines. How is bond generated? And why is it so good? And why is bond angles (Table 5) not much better?\n\n**Response 4**: In FlexSBDD, the bonds are generated with post-processing similar to TargetDiff. The powerful flow matching framework and well-designed model architecture contribute to the better bond length distribution. As for the bond angles, FlexSBDD still achieves competitive performance. The advantage over baselines methods may not be that much because bond angles are more complicated and FlexSBDD does not explicitly learn the bond angles (the bond representation are learned and updated in FlexSBDD). It will be our future work to design more powerful model architecture to learn the representations of bond angles.", "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:
Thanks for the insightful comments and appreciation from all the reviewers! 

FlexSBDD has the capability to model both the backbone and the sidechain structural changes. During rebuttal, we perform a comprehensive quantitative study on proteins with DFG-in/out confirmations to evaluate whether FlexSBDD can perform conformational searches on proteins with substantial structure variability. As shown in the uploaded pdf, the majority of the predicted protein structures show a lower relative pocket RMSD (better) compared to the initial ones, verifying FlexSBDD’s strong capability for ligand-specific conformational search.

As for the specific questions, our responses are included in the following paragraphs. Thanks!

Meta-review: This work explores the use of dynamic information in molecular design, introducing a method called FlexSBDD based on flow matching and utilizing E(3)-equivariant neural networks. Experimental results demonstrate that the model achieves state-of-the-art performance across multiple benchmarks. After a thorough rebuttal, the reviewers found this work to be universally innovative and timely, given the growing capabilities in exploring protein dynamics for drug discovery. Despite some minor concerns, this is a good paper that I recommend for acceptance to NeurIPS.
Decision: Accept (poster)