Integrating Protein Dynamics into Structure-Based Drug Design via Full-Atom Stochastic Flows
Authors: Xiangxin Zhou
Yi Xiao
Haowei Lin
Xinheng He
Jiaqi Guan
Yang Wang
Qiang Liu
Feng Zhou
Liang Wang
Jianzhu Ma
Venue: ICLR 2025 Poster (2025)
Keywords: flow matching
structure-based drug design
protein dynamics
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: The dynamic nature of proteins, influenced by ligand interactions, is essential for comprehending protein function and progressing drug discovery. Traditional structure-based drug design (SBDD) approaches typically target binding sites with rigid structures, limiting their practical application in drug development. While molecular dynamics simulation can theoretically capture all the biologically relevant conformations, the transition rate is dictated by the intrinsic energy barrier between them, making the sampling process computationally expensive. To overcome the aforementioned challenges, we propose to use generative modeling for SBDD considering conformational changes of protein pockets. We curate a dataset of apo and multiple holo states of protein-ligand complexes, simulated by molecular dynamics, and propose a full-atom flow model (and a stochastic version), named DynamicFlow, that learns to transform apo pockets and noisy ligands into holo pockets and corresponding 3D ligand molecules. Our method uncovers promising ligand molecules and corresponding holo conformations of pockets. Additionally, the resultant holo-like states provide superior inputs for traditional SBDD approaches, playing a significant role in practical drug discovery.

Published as a conference paper at ICLR 2025
INTEGRATING PROTEIN DYNAMICS INTO STRUCTURE- BASED DRUG DESIGN VIA FULL-ATOM STOCHASTIC FLOWS
Xiangxin Zhou? 2.2 Yi 2.4 Haowei Lin Xinheng He Jiaqi Guan?
Yang Wang' Qiang Liu² Feng Zhou" Liang Wang! 1.2 Jianzhu Ma
School of Artificial Intelligence, University of Chinese Academy of Sciences NNew Laboratory of Pattern Recognition (NIPR).
State Key Laboratory of Multimodal Artificial Intelligence Systems (MAIS),
Institute of Automation, Chinese Academy of Sciences (CASIA)
3 Schooo of Information and Communication Technology, Griffith University
"Beijing Wise Technology Co Ltd
Innttitute for Artificial Intelligence, Peking University
6 "Inttitute for AI Industry Research, Tsinghua University
7 "Department of Computer Science, University of Illinois Champaana *Dparrment of Electronic Engineering, Tsinghua University
ABSTRACT
The dynamic nature of proteins, influenced by ligand interactions, is essential for comprehending protein function and progressing drug discovery. Traditional structure-based drug design (SBDD) approaches typically target binding sites with rigid structures, limiting their practical application in drug development. While molecular dynamics simulation can theoretically capture all the biologically rel- evant conformations, the transition rate is dictated by the intrinsic energy bar- rier between them, making the sampling process computationally expensive. To overcome the aforementioned challenges, we propose to use generative model- ing for SBDD considering conformational changes of protein pockets. We curate a dataset of apo and multiple holo states of protein-ligand complexes, simulated by molecular dynamics, and propose full-atom flow model (and a stochastic ver- sion), named DynamicFlow, that learns to transform apo pockets and noisy ligands into holo pockets and corresponding 3D ligand molecules. Our method uncovers promising ligand molecules and corresponding holo conformations of pockets. Additionally, the resultant holo-like states provide superior inputs for traditional SBDD approaches, playing significant role in practical drug discovery.
INTRODUCTION
Modern deep learning is advancing several areas within drug discovery. Notably, among these, structure-basee based drug design (SBDD) (Anderson) 2003) emerges as a particularly significant and challenging domain. SBDD aims to discover drug-like ligand molecules specifically tailored to target binding sites. However, the complexity of chemical space and the dynamic nature of molecule conformations make traditional methods such high throughput and virtual screenings inefficient. Additionally, relying on compound databases limits the diversity of identified molecules. Thus, deep generative models, such autoregressive models (Luo et al. 2021 Peng al. 2022) and diffusion models (Guan et al. 2023 Schneuing et al. 2022). have been introduced as a tool for de novo 3D ligand molecule design based on binding pockets, significantly transforming research paradigms.
However, most SBDD methods based deep generative models assume that proteins are rigid (Peng et al. [022] Guan et al.) 2024). The dynamic behavior proteins is crucial for practical drug discovery (Krrllina et al. 2023 Boehr al. (2009). Thermodynamic fluctuations result in proteins existing as an ensemble of various conformational states, and such states may interact with different drug molecules. The interconversion between these states often leads the formation of cryptic
"Equal Contribution.
1 Corresponding Author; Jianzhu Ma (majiarzhu@tsigghuu..d....

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pockets, which are closely tied to the biological functions of the protein. During binding, the pro- tein's structure may undergo fine-tuning, adopting different conformations to optimize its interaction with the drug, a phenomenon referred to induced fit (Sherman et al.) 2006). This binding can af- fect the protein's s function by inhibiting the biological signaling pathway associated with a disease.
The underlying mechanism might involve blocking the binding of a natural sub- strate or shifting the protein's 's conforma- tional distribution. For instance, kinases, which catalyze phosphorylation reactions by transferring phosphate groups from ATP to substrates, exist primarily two conformations with different mainchain conformations: active (DFG-in) and in- active (DFG-out) (Panjarian al., 2013). As illustrated Fig. [ the Abl kinase ex- ists in both active and inactive apo states (6XR6, 6XR7), which differ in their DFG conformations. Type kinase in- hibitors, such as Dasatinib (2GQG), bind and stabilize the DFG-in conformation. In contrast, type II inhibitors like Ima- tinib (2HYY) stabilize the inactive con- formation by occupying the ATP-binding pocket. Considering these dynamic con- formational shifts is crucial for designing compounds that precisely target this ki- nase, such structural nuances directly influence binding and efficacy.
Transtorm
Apo active conformation
Apo inactive confomation
Imatinio
DFG-in
Dasatinib
Transform
DFG-out
Holo conformation
ligand
Holo inactive confomationn ligand 2
Figure 1:
Comparison of Abl kinase domain conforma- tions. In the top panel, the transition between the apo active and apo inactive conformations is shown. In the bottom panel, the active conformation with Dasatinib bound (DFG-in state) is compared to the inactive con- formation with Imatinib bound (DFG-out state). The transformations between these states highlight the struc- tural shifts critical for ligand binding.
We take step towards integrating protein dynamics into structure- drug design. First, we cu- rate a dataset based on a large collection of molecular dynamics traces of protein-ligand complexes. Our dataset comprises both apo and multiple holo states of each protein-ligand complex. We propose an -qq3i-equivariant full-atom flow model, named DYNAMICFLOw, that simultancously transforms the apo state of protein pockets and noisy ligands into holo states and their corresponding binding ligand molecules. Our method integrates insights from both machine learning and biology, utilizing the flow model's ability to transport one arbitrary distribution to another. We employ apo and holo state pairs as natural coupling for conditional flow matching train our flow model, making learn the dynamics of both backbone frames and side-chain torsions of protein pockets. Simulta- neously, we use continuous and discrete flow matching model the distribution of atom positions, atom types, and bond types of ligand molecules. Additionally, we propose a stochastic version of our flow further promote the robustness. Notably, to comprehensively capture the protein-ligand interaction, we meticulously design a full-atom model that incorporates both -Eu()--quivarrian ge- ometrical message passing layers and residue-level Transformer layers. The experimental results demonstrate the ability of our method to discover biologically meaningful protein conformation and promising ligand molecules. Interestingly, we find that the conformation states of protein pockets discovered by our method can serve improved input for SBDD methods that treat proteins rigid entities. We highlight our main contributions as follows:
We present a meticulously curated dataset consisting of both apo and multiple holo states of protein-ligand complexes derived from molecular dynamics simulation, offering new opportu- nities for Al-driven drug discovery.
We propose a full-atom flow model and a stochastic version that transform apo states of protein pockets to holo states and generates the corresponding 3D ligand molecules simultaneously.
We design full-atom model with both atom-level SE(3)-equivarian) geometrical message passing layers and residue-level Transformer layers, which captures comprehensive protein-ligane inter- actions and flexibly models protein backbone frames and side-chain torsions.
Our method generates meaningful protein conformation shifts and promising ligand molecules with high binding affinity. The discovered conformations also further enhance SBDD methods with rigid pockets input.
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2 RELATED WORK
Structure-based Drug Design. Structure-based drug design (SBDD) aims to develop ligand
molecules capable of binding to specific protein targets. The advent of deep generative models
has revolutionized the field, producing significant results. [Luo et al.] (202T): :PPng et al. (2022): Liu
et al. (2022a) and Zhang et al. (0222) employed an autoregressive model to generate atoms (and
bonds) or fragments of a ligand molecule given specific binding site with 3D structure. Guan et al.
(2023) Schneuing et al.] 2022); Lin et al. (2022) integrated diffusion models (Ho et al. 2020) into
SBDD. These models initially generate the types and positions of atoms through iterative denoising, followed by determining bond types through post-processing. Some recent studies have sought to enhance these methods by incorporating biochemical prior knowledge. For an representative ex- ample, |Huang et al. (2023) integrated protein-ligand interaction priors into both the forward and reverse processes to refine the diffusion models. While these studies have shown promising results in in silico evaluations, their disregard for protein dynamics limits their applicability in practical drug development. Please refer to App. for extended related works.
Generative Modeling of Protein Structures. Deep generative models, especially diffusion models (Ho al. 2020) (also known as based generative models (Song al. (021) and flow models (Lipman et al. 2022 Liu et al. 20226 Albergo & Vanden- Mijnden- (0222) have been widely utilized in modeling distributions of protein structures and attained impressive results. Protein structures are usually described with frames, which can be represented with elements of the Lie group SE(3), and
side-chain torsion angles, which can be represented with elements of the Lie group SO(2) (Jumper
iet 2002 Watson et al. 2003).. Both diffusion (De Bortoli et al. [2022] Huang et al. 2022) and flow
(Chen & Lipman| 2023) models have been well extended to Riemannian manifolds, theoretically providing complete tools for modeling protein structures. These techniques have been extensively
applied various tasks related to protein structure modeling. Watson et al.] (2023); Yim et al.)
(2023b a Bose et al. (2024) employed diffusion and flow models for protein backbone generation. Yim al. 2024) and Lu et al. (2024a) further utilized these models for motif scaffolding and protein conformation sampling, respectively. Zhang et al.) (2024a); Lee & Kim (2024) applied diffusion and flow models to protein side-chain packing. Plainer et al. (2023): Zhu et al. (2024); HHann et al. (2024b) proposed protein-ligand docking with fiexibility on protein side-chain torsion under the framework of diffusion models. [u et al. (2024b) considered flexibility on both protein backbone structure and side-chain torsion in protein-ligand docking. The above works inspire us to consider the complete degrees of freedom of proteins in the scenario of structure-bar -based drug design.
3 METHOD
In this section, we will present our method, named DYNAMICFLOW, as illustrated in Fig. 2 Section 3.1, we provide a clear statement about our problem setting and notations about SBDD considering protein dynamics along with a background on flow matching. In Section 3.2, we show the details about the training and inference of the full-atom flow, named SYNAMICFLOW-ODE for this novel task. In Section 3.3 we show how to extend this flow model to a stochastic version, named DYNAMICFLOW-SS SDE, to improve its robustness. Finally, in Section 3.4, we introduced details about the multiscale full-atom architecture design of our flow model as shown in Fig.
In
3.1 BACKGROUND AND PRELIMINARIES
We aim to generate a holo state of protein pocket and its binding ligand molecule given its apo state. The ligand molecule can be represented as a set of Nm atoms M
((xa, Vm.
(i) (8) (11) )i.nee
The apo state of a protein pocket can be represented in atom level Np
as set of Np atoms Pu {(x v(t))
(1)
1-1-- It can also be represented in residue level as length-
po:
Dp sequence of residues So [(ab))
(6) (0) (6) (6) (4) (8) (t) < For the holo state, the
,ro X00 Xio X20 X30 X40
R is the atom type, b E R is the bond type, a E R is the amino acid type, t E R is the translation of the residue frame, E SO(3) is the rotation of the residue frame, Xo E SO(2) is backbone torsion angle that governs the position of atom O, and X1, X2, X3, X4 E SO(2) are the side-chain torsion angles (1)
first digits in all subscripts change from 0 to 1. Here
R is the atom position,
(6) (see definitions in App. C) Note that a al and vn ( for all i since protein conformation changes do not impact the amino acid types and atom types. The SBDD task, incorporating protein dynamics, can be formulated as modeling the conditional distribution (P
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(a)
MD simulation
Apo
Holo
Holo
Holo
Ligund
Protein pocket
Simu lation time
Initialization
(Stochastie) Flow
AMA
ODE
SDE
wwm
Aminno
Netry ligand
Apo
Www
MA
Tumiion angles
Holo
Dupel Ouzat duaud sea
Oate Dusel
N00037
Rozdon
tye opc
Framc reprosettation
Lipard repreettaiiss
Venilla conformation
Data structure for pocket-ligand complex
Samplal confemmtton
Holo
Figure 2: Overview of DYNAMICFLOW. (a) Our dataset consists of apo and multiple holo states of protein-ligand complexes derived from molecular dynamics simulation. (b) Our flow mod- els, DYNAMICFLOW-ODE and DYNAMICFLOW-SDER the generative process of ligand molecules along with the protein dynamics from apo to holo. The protein pocket represented as both (i) residue frames and side-chain torsions and (ii) full atoms. The ligand molecule is represented as atom types, bond types, and atom positions.
We will use flow models to model the above conditional distribution. In the following, we provide
background on flow matching for modeling both continuous (Lipman al., [0022] Liu al. [002bb] Albergo & Vanden- which we will use in the following sections.
2022) and discrete (Campbell et al. 2024 Gat et al. 2024) variables,
We start with the continuous case. In flow matching, we consider predefined marginal probability path Pt that interpolates prior distribution and data distribution P1 = to train a generative model that transports source sample Xo Po target sample X₃ ~ Q1 We denote the joint distribution of and as IT (X,, X1) (also known as the data coupling). The probability path corresponds to time-dependent flow the [0, 1] R IRd and an associated vector field u, (0, 1] T Rd. which can be defined via the ordinary differential equation (ODE) as X, (xx) where (xo). One could use a neural network Ue (Xe, to regress the ground truth vector field wx,)). However, the flow matching objective is intractable since have no knowledge about the closed- form of the vector field ut that generates marginal distribution path Pt- The key insight (Lipman et al. 2022 Liu et al. 2022b)
regress 29 against the conditional vector field un (x [X., X1 (1). whhcc generates the conditional probability path (x(x, Xn, x1). and use it to construct the target marginal path Pr (x,) Jx0.x, Pe (x( Xo, X1 X1)T(( (xo, ; X1 ]dxodx1. The corresponding marginal vector field can also be constructed as un (xx)= Sxo.x; de (XxxXXX. x1) flow matching loss as follows:
Pe be, (x..,x)) dxjdxx. Pc(X))
1 The conditional
L=
t) (x,
For modeling discrete variables, we follow the framework of Discrete Flow Matching (Camp- bell et al. 2024) which based on Continuous- -ime discrete Markov Chain (CTMC). Here E [l,...,,1] ST is random discrete variable, e.g., a length-D sequence where each element takes on one of states, and we denote as specific state of x. We first introduce the con- cept of rate matrix R, E RS8 which plays similar role to the vector field in the contin- different state j is (xx. after an infinites-
uous case. The probability that x, jumps imal time step dt is R(x,,)dd i.e., Pt+aaje(]xx) = 6(x;, j} Ri (xe, (xXes))d dt where 8(i,j) is element-wise Kronecker delta which in dimension d when id j" and O otherwise. To
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build a discrete flow, also use the conditional probability path construct the marginal one as (x,) =
We define R (xxx, as a conditional rate matrix that gener- ates Pe (x(xx())) x1). Notably, (x, can usually be in a simple formula. For example, it can be that (x. x11 = (ix1j]]0f M) t) where M is the mask token. It can be proved that the marginal rate matrix (x), = (x. (xx. j|x1]] corresponds to the marginal probability path px(x)) which we have defined above, where p(x1{x;) = pe (x |xi (xp.x))))(x))) We can use a neural network pf (x1|x;) to approximate the posterior pe (xe). We denote R2 (xe:)) == E (xtx)))))) (R, (R( -xx)).
We can generate sample by iteratively sampling from the
process
Px xx) 0xxx+dde, x1} + Rf Xitii + o(dt).
3.2 FULL-ATOM FLOW FOR SBDD WITH PROTEIN DYNAMICS
One advantage of flow models is their ability to transport any arbitrary distribution another, with- out imposing constraints on the source or target distribution. Fully leveraging this advantage to model the conditional distribution q I, MP)), that transforms apo to holo states and generates ligand molecules from a noisy prior distribution simultaneously. The apo state Po and holo state PI naturally serve as samples from the source and target distribution for flow matching. Formally, we define the source distribution po as
build flow, named DYNAMICFLOw-ODD
Nm
No
Po (PP) = Po)
0 m M.) II (x :CM(())) I
II 8(b w==
(3)
1=1
where 5(,, -) is the Dirac delta function, 8(:: is the discrete Kronecker delta function, CoM(-) is the function that calculates center of mass, and M, (resp. Ms) is the token for atom (resp. bond) type. This means that the pocket directly starts with the apo state, atom/bond types of ligand molecules start with mask tokens, and atom positions of molecules start with normal distribution around the CoM of the apo pocket. The target distribution pi (P, MM ) is the data distribution q. Specifically, we use the multiple holo states and binding ligand molecules that correspond to apo state Po in our training dataset as the data coupling (Muu Pa. M1, . P1 (Po) and use the predefined conditional probability path (MM,, Mo. Po, M1, P1) to sample "interpolant" to train our flow model.
Next, we show how to derive the vector field ue for the continuous variables (i.e., pocket residues' translation, rotation, torsion angles, and ligand molecules' atom positions). Both pocket residues' translation t and ligand molecules' atom positions X., live in 3D Euclidean space. Taking t as an example, given samples from source and target distribution, i.c., to and ti. we define the conditional probability path as the linear interpolant between these two samples and derive the conditional vector field as follows (t in superscript stands for "translation" and in subscript stands for "time"):
(1)
(1 (1) 100 5 -111--(1-10 -1-((1))) and wii(t,
(2) (1) [t , (6")=t)) -
0
(4)
Instead of directly predicting the vector field, we to (t.²) (t) to predict the "clean" sample at time Please note that
and express the predicted vector field as Ug (t(²) = 1111
while the complete context (M,, P.) is indeed input into the network parameterized with 0, we omit here for simplicity. This convention is maintained throughout the entire paper. The conditional flow matching (CFM) objective for translation of residue frame at time & can be formulated as:
C EE (t)to.t))) (66". (I))(t))) ,t) (tl
(5)
For the rotation of residue frames, we the geodesic interpolant to define the conditional proba- bility path and conditional vector path as follows:
. --/)== log,te (a (f(*) 1-t
(r - exp,c0 (t (oog (I(9)) and (r(r("1100
(6)
Similar to the case for translation, we use rg (r.)) t) to predict the "clean" sample at time and express the predicted vector field SO(3) manifold as vo (x.")) t) = log, (ra(x()) (4) ,t)) t).
The CFM objective for rotation of residue frame at time t can be formulated as:
log, (o) (r(2)
( C = E (a (9)))) va (r( (r( ,,))
(S03)
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Torsion angles of protein pockets lie high- high-dimensional tori. Note the slight abuse of notation that we use M to represent both the manifold and the molecule. For a torus M == [0, kT (h = 1,2), the exponential and logarithm maps are follows Chen & Lipman (023):
expu(x) = (a ())( and log, (v)
arctan2
- x), cos x))
(8)
where x, y E M and u E M. Following Li et al. (002)) we define wrap(u) = (u+ ( -
While we model 5 torsion angles, here we use x for brevity. The conditional probability path and
conditional vector field can be defined as follows:
(xt XD Xt ) = 8 xt
(6)
(8)
(6) + twrap(xi (0) - xo (6))))((+)))
(9) ( x wrap(x1 (() - Xo (0)) wrap(xi (0) Xt (e(xt XU
(10)
1-6
Here we introduce ls = 1111 to handle the special cases where some side-chain torsion angles of certain residues exhibit x-rotation-sye -symmmtryyyyyetty (e.g., X2 of ASP). For other general cases, k = 2. Refer
to App- C for details. We use Xo(xi
(i) t) to predict the "clean" sample at time 1 and express the
predicted vector field on tori as vo (Xi
(6) .t) == wrap(xe(xe" (6) .) - x/)))(( - t). Also following Li
et al..0 (2024), we use the flat metric on tori in CFM objective as follows:
C E x (xxxxx)))P((xx 1x6 xx()))
wrap
(e0 (x(( (t)
X0
(11)
So far, We have now covered all cases of the continuous variables. The sampling (i.e., inference) procedure of these continuous variables is solving ODEs defined on the corresponding space.
Next, we show how we model discrete variables, i.e., atom types and bond types of ligand molecules.
We take bond types b(6²) of ligand molecules as an example. In the following, we omit the subscript m that stands for "molecule" for brevity without ambiguity. We define the conditional probability path and the conditional rate matrix as follows:
(b
(15) (15)) b(())) = (at(15(b by (10) + (1- - (0-(())8())) (9) M)),
(12)
(b .nb (8) 5(b, (6) m]j[b (6) M]
(13)
1-t
where n E (1....; B} is specific bond type. A straightforward interpretation of the above condi- tional discrete flow is that we linearly interpolate between a probability mass concentrated entirely on the mask token and the data distribution. As introduced in Section 3.1 we train neural network (it)) with simple cross-entropy loss as follows:
(b
c E (bo.
(b( ( b,00, log (b ).
(14)
The estimated marginal rate matrix can be expressed as
(b (4)) bb,
(15)
(b (1) n) E (3 (oo) [R (b. (i)) .nb[[")]]
(0)
M).
(15)
1-t
During sampling, the transition step from / to L di is
(65)) ar (n) b( d(b] (i)) .n + (b( (10) n)dd.
(16)
To better capture interactions between atoms, we propose an interaction loss that directly regresses the distances between predicted atom pairs and the ground-truth distances in local space. For time t, we denote the predicted "clean" holo state and ligand molecule as
$, :==1(aa) [(a)) to .ra .199 X29 X39. 1139:X44111 10)) and Mi = (( 1
(1) (8) (6) (6) (4) (4)
(17)
where we denote ro (r (r, t) as (,4) for brevity and similarly for other variables. Note that here we omit the bond types in M₁ because we do not use it in the interaction loss. The frame repre- sentation is then converted to atom representation P. = [(*{1) " FrameToAtom($.). See details about (otom)) in App. B We denote all predicted atoms in the protein-ligand complex as Ai = {xx
P. U U,, and the corresponding ground truth as A == (xx(( (1) (0) ) N = Pi MM. The interaction loss can be formulated as follows:
(3) (00)
>> N.mm
Chm Σ E
D,y. NN Σ
Ejmtt
NotNun |ld(()) - d(t0) 1 (aft) < 3.5} 1 > 0.65).
(18)
1=1
where 2(t0) |x((0 x( d(())) ||x(0) xx"1|, ||. and 1 {.) is the indicator function.
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Complex gruph
Complex messuge
Protein embedding
passing
incariant Reature
Protein
(KNN graph. kw32))
BGNN
Ligund incariani feature
Atom type
type
Ligand
Ligund message passingg
Ligand embedding
Ligund SEC() equivariant fenture
Atom coordinates
Atum-wise node embhelding
(fully connected graph)
Heterogenous graph
(b)
Protein SE(31
atom37 residue aggregation
Residue level feature
Torsion angles
invariant feature
Invariant Point Attention (IPA)
representation
Residue rotation
angles
Updoted frome
Residue translation
Figure 3: Illustration of multiscale full-atom model architecture: equivariant graph neural network; (b) residue-level Transformers.
(a) atom-level SE(3)-
3.3 EXTENSION TO STOCHASTIC FULL-ATOM FLOW
The probability path induced by linear interpolant between apo and holo state of pocket has limited set-theoretic support, thus potentially leading to inferior robustness. This motivates us to build stochastic flow, named DYNAMICFLOW-SDDE since SDEs offer the significant advantage of being more robust to noise in high-dimensional spaces compared to ODEs (Tong et al. 2023 Shi et al,
2023 Liu al.) 2023). Based on the way that build DYNAMICFLOW--DEE
introduced
in Section 3.2 we can easily extend to SDEs via simply updating the conditional probability paths (2024) offers theoretical justification that conditional flow matching loss and original flow matching loss remain equivalent with respect to optimization.
in training and sampling. [ose
For variables lie in Euclidean space, i.c., the translation of residue frames (+) and the atom positions
(6), we can update the conditional probability path from Eq. to:
(6) tt = it (1-11)) 721(1 t)1),
(19)
where y is constant hyperparameter that controls the noise scale.
For variables lie on SO(3) manifold, i.e., the rotation of residue frames ((), we update the condi- tional probability path in Eq. (6) to an efficient simulation- approximation of correct conditional
stochastic flow on SO(3) suggested by Bose et al. (0024):
= IG (rl
exp,,o ; (oog (T(+) 711 -))-))))
(20)
where IGso0) denotes the isotropic Gaussian distribution on SO(3) NNkolaaev & SSayolovv
1900
For variables lie on tori, i.e., the torsion angles of residues (+), we update the conditional probability path in Eq. (10) to:
IIxe" (xo" +twrap(xi" (())) (kT)) kmdd k
pt (x 1x
&
Σ
dEz exp
(21)
dez
2y -
which is wrapped normal distribution. This be sampled directly (Jing et al. 2022
3.4 MULTISCALLF FUL.I-ATOO MODEL. ARCHITECTURE
Our flow models employ multiscale scheme as shown in Fig. 3 which is comprised of two main parts: (a) atom-level SE(3)-equivariant graph neural network: (b) residue-level Transformers.
In the atom-level GNN, inspired by Guan et al. (004)), we maintain both node-level and edge-level hidden states in the neural network by modifying widely used EGNN (Satorras et al., 2021). During training, for time f, build k-nearest neighbors (knn) graph Go upon the atoms of the protein- ligand complex to capture the mrotein-ligant interaction:
Ahlo < EjENs (c(())) ho), ||x(0) - x001 F000)
(22)

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where h is the atom-level hidden state, NN(i) is the neighbors of i in Ge. E(0) indicates the edge 2j is protein-provt protein, ggaad-liggand, or protein-ligant edge. We also build a fully connected ligand graph Gm upon all ligand atoms to model the chemical interaction inside the ligand molecule:
m 6m (1x -x x (5)
and
Ab
(y)N.. om (h h() m t),
(23)
where e is the bond-level hidden state. We then update the atom and bond's hidden state as follows:
h (0) t (1) + (Ah 1 + )
(24)
( ExEN. (h(" h (K), m (ik) m (5ا)) .),
(25)
Then we update the SE())-eqiivarian features (i.e. positions of ligand molecules) as:
( 0 (h (0), h(), d( (), Ax + Σ d o (1 h()) d(d)) m (0) ,t) (26)
jEN((()
JENm(()
where =00==(()) -x(0 and d = || We only update ligand atom positions in the atom-level part as (() +- (() (Ax!" + +xxx)) ( 1m
m (i). where 1m (i) is an indicator of ligand atom, and leave the pocket update in the residue-level part. The output equivariant (resp. invariant) hidden states of
ligand nodes used to predict atom positions (resp. atom/bond types) of ligand molecules.
We aggregate the final protein atom hidden states h output by the above full-atom GNN into residue level according to the atom37 template (Jumper al., 2021). The aggregated residue-level hidden states along with amino acid type a. 5 torsion angles X. and frame (t,r) are input into residue- Transformer model which composed of node embedding layer, edge embedding layer, multiple Invariant Point Attention (IPA) blocks, following Jumper et al. (2021): Yim et al. (2023b). In each IPA block, residue-level hidden state h and frame (t, r) are updated. The final updated frames are used predictions. Torsion angles are predicted based on the final residue-level hidden states.
4 EXPERIMENTS
Data Curation. We curate our dataset based on MISATO dataset (Siebenmorgen et al. 2024) The original dataset contains approximately 20,000 protein-ligand complexes with associated 8ns molecular dynamics (MD) simulation trajectories. We filter out complexes where the ligands are oligopeptides, yielding 12,695 complexes for further processing. For each complex, we efficiently use the data by clustering the holo-ligand conformations with RMSD threshold of 1.0 Á. Finally, to filter out the invalid MD simulation results, we select complexes whose averaged RMSD between the ligand conformations simulated by MD and native ligand structures is less than 3 Á. The above procedure results in a dataset containing 5,692 complexes with 46,235 holo-ligand conformations and corresponding apo structures. More details can be found in App.
Baselines. We compare our models with three representative baselines for SBDD: Pocket2.Mol (Peng et al.) 2022) generate 3D molecules by sequentially placing atoms around a given protein pocket; TafgetDiff (Guan et al. (202)) generates atom coordinates and atom types based sion model and bonds are determined with post-processing algorithm; IPDiff (Huang et al. 2023) incorporated protein-ligand interaction priors into both the forward and reverse processes to enhance the diffusion models. Since diffusion models require the number of atoms in the ligand molecule input, we align TargetDiff and IPDiff with methods based the number of ligand atoms, denoting them as Tiff and IPDiff". We also compare our methods on the ability of pocket conformation sampling with two baselines: a simple method that injected appropriate noise into
diffu-
Table 1: Summary of properties of reference molecules and molecules generated by our model and other basclines. (1) / (4) denotes larger / smaller number is better.
Vina Score (4) QED (t) SA (?) Linpiski (1)
logP
High Afti (t) Comp. Rate (1)
Reference
-7.84&3.11
0.5340.19 0.67=0.15
4.45+0.77
1.64+2.17
N/A
N/A
Pocket2Mol
1.25
0.54+0.12 0.83#0.10
1.70=1.52
4,98+0.14
28.6%
N/A
TargetDiff
-5.09+4.81
0.42+0.18
0.
3.20=2.39
4.32+0.81
44.0%
68.2%
TifgetDiff*
-5.53+4.09
0.39+0.21
0.
3.02+2.75
4.11+1.10
45.7%
62.4%
IPDift
-7.55+5.59
0.38+0.17
0.50=0.14
4.10=0.77
5.07+2.94
51.0%
67.8%
I
-6.2345.26
0.40+0.20
05
3,94+1.00
5.04+3.34
49.5%
67.3%
DYNAMICFLOW-ODD
-7.28+1.98
0.53+0.20
0.61
3.1342.62
4.45+0.81
51.0%
70.2%
DYNAMICHLOW-SDE
-7.65+1.59
0.53+0.15
0.53+0.17
4.34+2.58
4.25+0.90
52.5%
73.6%
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Table 2: Performance of SBDD methods with rigid pocket inputs on apo/our pockets, where "our
pockets" refers to the pocket structures generated by our method.
Vina Score (1)
QED (1)
SA (1)
Linpiski (1)
log!
High Affi. (1) Comp, Rate (t)
Pocket2Mol
-5.50=1.25
0,54=0.12
0,83=0.10
1.70=1.52
4.98+0.14
28.6%
N/A
Pocket2Mol + Our Pocket
-5.92=0.88
0.57=0.07 0.88+0.10
2,09=1.24
5.00+0.00
28.6%
N/A
TargetDiff
-5.09=8.81
0.42+0.18
0.53+0.13
3,20+2.39
4.32+0.81
44.0%
68.2%
TargetDift Our Pocket
-9.00=3.19
0.44=0.18
0.53=0.14
3,82+2.29
4.22+0.91
61.2%
79.6%
TargetDiff*
-5.53=44.09
0.39=0.21
0.55#0.15
3.02+2.75
4.11=1.10
45.7%
62.4%
TargetDiff+ Our Pocket
-7.82+3.50
0.48=0.22
0.58+0.14 14
3.65
4.14
51.0%
79.72%
IPDiff
-7.55+5.59
0.38+0.17
0.50
4.10=0.77
5.07+2.94
51.0%
67.8%
IPDiff Our Pocket
-11.0443.76
0.40=0.16
0.46#0.15
3.84
6.97+3.33
83.7%
83.4%
IPDiff
-6.2345.26
0.40=0.20
0,55=0.15
3,94=1.00
5.04+3.34
49.5%
67.3%
IPDi Our Pocket
-9.7143.66
0.42+0.16
0.52+0.13
4.00=0.83
5.9243.67
81.6%
82.1%
apo
2 d9b
apo mean: 0.202
mean: 0.482
0.522
Ape
Our
Density
apo mean: 0.586
apo mean: 0.04 our mean: 034
our mean:
2.0
4.0
0:2
0.4
0.5
1.0
1.5
0.0
Hydrophobic interaction Hydrogen bond
Salt bridge
It-1t stack
It cation
Figure 4: Distribution of differences in protein-ligand non-covalent interaction numbers of apo/our pockets and ligands designed by TargetDiff' from those of ground-truth holo-ligand complexes.
apo structures; Str2Str (Lu et al. 2024a) that repurposed the protein backbone generation model, FrameDiff (Yim et al. 2023b), for protein conformation sampling by first injecting noise into apo structures and then denoising by diffusion models.
Evaluation. We select 50 complexes that have no overlap with the training set as the test set. We evaluate both the generated lig- and molecules and the pocket conformations. For ligand molecules, we evaluate the binding affinity with AutoDock Vina (Eberhardt et al. 202I]. There are three modes in AutoDock Vina: "vina score.scoe..ee score.only", "vina minimize", and "vina dock". We use minimmizni as re- ported Vina Score because this mode performs slight local structure energy minimization with- out disregarding the generated molecular con- formations before estimation. We find an issue with the Vina Score for the complex 6SD9, so we exclude it from the 50 test samples. For each test target, we generate 100 molecules and se- lect the one with the best Vina Score as the final design. For a fair comparison, all methods are provided with apo pockets as input. We collect the designed ligand molecule of all the test targets and report the mean and standard derivation of Vina Score and the following molecular properties: likeness QED (Bickerton et al. (012). synthesizabilityy SA (Ertl & Schuffenhauer 2009). the octanol-wate partition coefficient log? (values ranging from -0.4 to 5.6 indicate good drug candi- dates) (Ghose et al. 1999), number of molecules that obeys Lipinski's rule of five Lipinski (Lipinski et al. 2012), the ratio of design molecules that exhibit higher binding affinity than the reference lig- and in the test set High Afli. (High Affinity). We also report the ratio of generated molecules that are valid in valency and form single connected graph as Comp. Rate (Complete Rate) for the diffusion-based methods. Since autoregressive models filter out the invalid entities during sampling and always form connected graph, we do not report their Comp. Rate. For pocket conformation, we compute the minimum RMSD between the generated pocket conformation and ground-truth holo conformations for each target and report the average value over all the targets. We compute
1.
60
17
Cover Ratio (9))
-.6
40c coral rack
1.5
40
1.4
0uth 340
30-
1.3
122
20-
0
20
40
60
80
100
Number of samples
Figure 5: Cover Ratio and minimum RMSD
against holo states along the number of samples.

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Published as a conference paper at ICLR 2025
Apo Volumes 150. 9.024)
Fole Volumes
Protein
Ligand
Hydrogen Bond
Interaction
Cation
Hydrophobic Interaction
Our volumes Q50: 0.005)
Density
2500 2000 Volume (A')
Figure 6: Distribution of apo / holo / our pocket volumes and Jensen- Shannon divergence (ISD) between apo our and holo volumes.
Figure 7: Visualization of the protein- ligand non-cov non-covalent interactions of molecules generated by TargetDiff and apo (left) pockets refined by our methods (right). Only inter- acted residues visualized.
the maximum RMSD between holo conformations for each complex, whose average is 1.42 A. A ground-truth holo conformation is considered covered when at least one generated pocket conforma- tion has an RMSD less than 1.42 Á against it. We compute the ratio of covered holo conformations for each target and report the average of this value all the targets Cover Ratio. We also compute the pocket volume using POcket Volume MEasurer (POVME 3) (Wagner et al. 2017) and compare the distribution of volumes between apo/our pockets and ground-truth holo pockets. To further test the generated pocket conformations, for each target, we select the predicted pocket conformation corresponding the designed ligand molecule with the best Vina Score among 100 candidates as "our pocket". We then use TargetDiff to design ligand molecules for "our pocket", summarize the properties of the designed molecules, and also profile the protein-ligand interactions using Logten- Interaction Profiler (PLIP) (Salentin et al. 2015).
PDB ID: 652)
PDB ID: 652)
PDB ID: 6UL8
QED:
QED:
QED: 0.78
SA: 0.65
SA: 0.60
SA: 0.67
1.38
logP: 1.75
lagP: 4.93
Upiinkis
Lipinski:
Lipinski:
Vina Score: -7.36
Vina Score: -7.98
Vina Score: -7.1
Figure 8: Examples of ligands and holo pockets generated by our model. The green surfaces are the holo pockets and the white surfaces with transparency are the apo pockets.
Main Results. We report the properties of designed ligand molecules in Table [ The molecules designed by our method show high binding affinity and also exhibit satisfactory drug-likeness and synthesizability. The performance of the baselines might be affected by the apo structures, which may not be suitable for designing a binding ligand. Fig. 5 shows the Cover Ratio and minimum RMSD against holo states along the number of samples. DYNAMICFLOW-OL ODE shows the best per- formance RMSD, while DYNAMICFLOOW -OD-EDE shows the best performance Cover Ratio due to the diversity enhanced by SDEs. Str2Str performs even worse than the naive perturbation baseline, possibly because designed for whole proteins rather than pockets and does not use sequence information as methods do. Fig. show the distribution of apo/holo/our pocket volumes. Our pocket volume distribution more closely resembles holo pockets than apo pockets, Table 2 shows that refined pocket conformation can effectively improve the performance of SBDD methods with rigid pocket inputs. Fig. [ shows the distribution in number differences NCIs of apo/our pockets and molecules designed by Targetdiff (see example in Fig. 7 against those of holo pock- ets along with the mean differences in NCI numbers. These results demonstrate that our method effectively transforms apo states into holo-like states. Examples of generated examples are shown
in App. G More ablation studies can be found in Fig. 8 and App.
5
CONCLUSION
In this work, we introduce generative modeling approach, DYNAMICFLOW, effectively transform- ing pockets from apo holo states and generating ligand molecules simultaneously. Our method uncovers promising ligands and provides enhanced inputs for traditional drug discovery, advancing practical applications in the field. Our research lays the groundwork for integrating protein pocket dynamics into structure-based drug design, with future progress expected.
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ACKNOWLEDGMENTS
This work was supported by the National Key Plan for Scientific Research and Development of China (2033YF33043300) China's Village Science and Technology City Key Technology funding and Wuxi Research Institute of Applied Technologies, Tsinghua University under Grant 20242001120.
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A DATASETS DETAILS
A.1 INTRODUCTION OF MISATO DATASET
The limited availability of protein-ligand interaction data has significantly hindered the progress of artificial intelligence in biological domains Yang et al. 2020). Most of existing datasets either lack molecular dynamics information relevant to pooeiin-lgaand interactions (Wang et al. al. [2005] Liu al.) 2007). The absence of kinetic information for protein-ligand complexes makes it challenging for Al to fully capture and model these biological processes. The development of the MISATO dataset has, to some extent, alleviated the shortage of kinetic data for
complexes.
The MISATO dataset (Siebenmorgen et al. 2024) contains the largest molecular dynamics simu- lation data to date for protein-ligand complexes, along with recalculated QM properties of small molecules. Our work utilizes the complex structures and the associated MD simulation results as the primary data source, with further processing to tailor the data for in-depth modeling.
The development of MISATO dataset is based the PDBbind database (Wang al. 2005) which contains around 20,000 complexes structures and experimental binding affinities measurement. A total of 19,443 complexes are collected from PDBBind for further processing, Some important properties during the binding process, such as the binding affinity and the interaction energy are recalculated. Most importantly, the MISATO dataset performs 10ns MD simulations for 16,972 -igiin complexes" with 8 ns of MD trajectory recorded. These extensive MD results can provide additional kinetic information in the protein-ligand interaction process which is crucial for drug discovery and design research (Vajda et al. 2018).
A.2 HOLO POCKET CONSTRUCTION
Holo Pocket Definition. We exclude the complexes in MISATO where the ligands are oligopeptides, resulting in a total of 12,695 different complexes MD data. To capture different binding pocket conformations from the MD simulation trajectories, we locate residues within a cutoff distance of 7 A around each ligand and extract them from the 100-frame MD results. We then define the pocket as the union set of all extracted residues from each frame. To select representative holo-state pocket conformations that appear with higher probability in the interaction process, we cluster the 100- frame complexes conformations from the 8 ns MD simulations using GROMACS (Van Der Spoel ct al. 2005). with an RMSD threshold of less than 1 Á between the heavy atoms of both the proteins and the ligands. We then retain the top 10 clusters (or fewer if the total number of clusters smaller than 10) as different holo conformations in our training dataset. The statistics of clustered conformations and pockets are shown in Fig.
Additionally, we refer to the MD trajectory analysis results of the complexes, including the buried solvent- surface area (SASA) (Lee & Richards] 197I), the center-of-mass distance be- tween ligands and receptors. RMSD Ligand (the root-mean- square deviation of the ligand after protein alignment with the native structure), and the molecular mechanics generalized Born surface area (MMGBSA) (Wang et al. 2019). These labels provide global description of the dynamic prop- erties of the complexes and can be used as evaluation metrics for the binding process. We use the record of RMSDrigand in the following processing.
Structural File Alignment. The PDB files in the MISATO dataset contain unusual three-letter-code representations for residues. This is due to the requirement of the force field calculation, where needs to consider the special states of amino acid such protonation and deprotonation for better simulation accuracy (Case et al. 202T). However, for the training data points in our structure-bass drug design model, it is necessary uniform the representations of residues with the 20 types of three-letter codes for standard amino acids. Consequently, we correct the CYX (Cystine). which denotes the CYS (Cysteine) that forms disulfide bond with another CYS, and the HIE, which represents the default protonation state of HIS (Histidine) in Amber's pre-processing (Case et al.) 2021). We also examine the atom names within residues and find that some atoms in ASP, GLU, PHE, TRP, TYR occasionally have inconsistent atom naming, which could lead to mismatch in atve- alignment. Additionally, the Amber adds terminal cappings for the missing residues before MD
AAcordiin to Siebenmorgen et al. 2024), structures from PDBbind were excluded whenever non- standad ligand atoms or inconsistencies in the protein starting structures were encountered, resulting in 16972 com- plexes for MD simulation.
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0.04
2500
Number of samples
2000
0.03
Density
1500
0.02
1000
0.01
500
0.00
20
40
100
20
80 100 120 number pocket residues
60
number conformations
Figure 9: The statistics the number of conformations (left) and the number of pocket residues (right) in our clustered complexes.
simulations, affecting atom naming in N-terminus and C-terminus residues. These naming issues have been corrected in our processed holo-pocket data. Finally, the residues all holo proteins are idealized with determined bond lengths and angles according to Engh & Huber (2006).
A.3 APO POCKET CONSTRUCTION
Apo Protein Prediction. In order obtain the apo apo-pocket structures as the input of our model, we consider the SalaaaFod2--rrdicctt (Jumper et al. (2021) structures as apo-like conformations and extract the corresponding pocket residues to generate apo-like pockets.
One challenge of folding structures directly from current sequences is the lack of chain annotations in the original MISATO files, which causes residues to be indexed continuously from start to finish. This can lead incorrect folding structures during single-chain folding. Moreover, missing residues in PDB records can further decrease the prediction accuracy of folding models.
Instead, we retrieve Database where proteins identified using UniProt IDs (Consortium 2019). We perform ID mapping from Protein Data Bank (PDB p to UniProt using the mapping tools provided by the UniProt API. In total, successfully map 12,695 PDB IDs 13,775 UniProt IDs, with 203 PDB IDs failing to find associated UniProt records. Among the successful mappings, 991 entries lack ApphaFold2-predicee structures in the database. Finally, we download AlphaFFold2-prediited struc- tures for 2,639 unique proteins and align these structures with the corresponding MISATO holo proteins.
structures from the AlphaFold Protein Structure
Apo Pocket Alignment. To identify the pocket residue indices in apo proteins, first extract quences from both the MISATO PDB files and the AlphaFold2-prediceee establish residue index-mapping relationships. We the Bio. pairwise2
structures, then perform
sequence alignment module with the Smith-Waterman algorithm (Smith et al. 1981) for local sequence alignment (Cock al., 2009). Using the residue mapping results, we extract the aligned residues from the apo-protein files to generate what we refer to as apo pockets. Through this workflow, we success- fully obtain 7,528 atom-level aligned apo pockets. Alignment failures are primarily due to missing residues, mutations, and aligning sequences for multimers where the pocket consists of residues from different chains. In our curated dataset, the residues forming the pocket all originate from single chain. Finally, the residues of all holo proteins are idealized with determined bond lengths and angles according Engh Huber (2006).
A.4 LIGAND DATA PROCESSING
The RMSDLigand is used to evaluate the conformational stability of complexes during MD simu- lations. To ensure the reliability of MD results for our training data, we filter the clustered holo structures based the average RMSDLigund of 3 À is applied, resulting in selection of 5,692 holo and apo structures for training dataset. Additionally, we use RDKit (Landrum et al.] 2020) to recalculate the bond connections and bond types in ligands ensure that all ligands can successfully loaded and featurized.
the 100-frame MD simulation results. A threshold
https::/aalphafold.ehh
https: wwwp://wwwwwmmm wwwb.
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The protein-ligand complex conformations in training dataset count for 46,235. The distribution
of RMSD Ligand and the number of remaining complexes after each key processing step are illustrated
in Fig. 10
17500
0.4
Number of complexes
15000
0.3
Density
12500
0.2
10000
0.1
7500
0.0
5000
2
3
6
9 10
B
LMSDdd (A)
Data Processing Stages
Figure 10: Left: Statistics of RMSD Ligand for complexes in MISATO; Right: Statistics dataset size after each processing step. (A-B) Filtering out complexes of where ligands are peptides; (B- C): Sequence aligmment and apo-pocket extraction; (C-D): Filtering conformation ensembles with RMSDrigund smaller than 3
A.5 VISUALIZATIONS OF DATASET
We provide visualizations of apo pockets and holo conformations from processed dataset in Fig. [3] In each row, the left figure shows the apo pocket and the right two figures are different holo pockets with the same ligand. We also visualize the main chain and side chains residues surrounding the ligand. Additionally, we evaluate the ligands in our dataset with QED, SA, logP, Lipinski and their binding affinity with apo and holo pockets using vina score and vina min. The results are presented in Fig. 11 and Fig. 12
1.75
3.5
0.20
1.50
1.50
3.0
1.25
1.25
Denaly
1.00-
2.0
Deralty
1.00
0.75
1.5
0.10
0.75
0.50
1.0
0.05
0.50
0.25
0.00
0.2
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
6.0
-3.0
3.0
6.0
0.0
1. 3.0 50 60 Ligand Lipinski
QED
SA
Lag?
Figure 11: The distribution of molecular properties (QED, SA, logP, and Lipinski) for ligands in our dataset.
apo score_only apo
vina setss_coorooooeee only holo vina_min
0.150
0.20
Density
0.15
0.100
0.050
0.05
0.025
0.000
0.00
-2
-10
-2
10
vina score
vina score
Figure 12: The distribution of oonl and vina_min of apo/holo complexes in our dataset.
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Figure 13: Examples of apo pockets and holo complexes from our processed dataset. The left yellow regions represent the apo pockets in the form of protein surfaces. The right two green regions show different holo conformations of the same proteins and ligands. The PDB IDs for these examples are 3FUP, 3D74, 3A3Y, 2F2B, 1PMU, 1FQ8, and 5TT7.
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B ALL ATOM COORDINATES COMPUTING
We adopt a coordinates computing and updating method similar to those employed in previous works (Camphell et al., 2024 Jumper al. 2021 Yim al. 2023b). The residue-specifie frames are first constructed to describe the idealized atom positions in every type of amino acid. Then we will predict the backbone and side-chain frames update and map the updated frames back atom coordinates. We will explain the details of this process in the following paragraphs.
Backbone Parameterization. To simplify the expressions, we specify that all subsequent expres- sions refer the residue at index i. We begin by constructing the frame centered C. for every residue using their position of Ca. C and N, represented by bold letters. The residues are idealized with determined bond lengths and angles according to Engh & Huber (206)). Based on this setting, the rigid frame is built with the Gram-Schmidt process:
C Ca.
V2 = N Ca.
v1/llvill e3 C1 ez-
U2 V2 eie V2),
C2 u2/l /u2ll
(27)
Then we can generate backbone amino acid frame To (to, with to C. = and ro concat(e1, e2, 03) = I.
Backbone Frame Update. According to Jumper et al. (021), the rotation and translation of back- bone expressed using a predicted quaternion (a, b, C, d,d) and vector t.. The rotation matrix is calculated from the predicted quaternion as follows:
a + 122 -22 d²
2bc 2nd
2bd 2ac
r=
2hc + 2ad
a² 12 + c² d2
2cd 2ob
(28)
2bd 2ac
2nd + 2ab
a
b2 e² + d2
Note that the quaternion need normalization before the calculation of The backbone frame update can thus be expressed as Tis = (t, r).
The position the O atom in the backbone is constrained to circle that rotates around the x- axis (defined by C.-C bond) with the C-O bond. We predict the torsion angle of the backbone Xo = [Xo1, X02| E SO(2) that determines the position of the O atom and calculate the rotation with:
1
0
p-o
0
Xo1
X02
(29)
0
X02
X01
where (1xoo)2 )2 + (xo2)²11 = 1, the C-O bond length which defines the translation txo is specified at 1.23 Using Txo = rxo) with backbone frame update, we can update the position of the O atom in backbone.
ToAtom Mapping. The updating of full atom positions involves the backbone rotation and translation with side-chain torsion a = (X1 X2, X3, Xx). X3) chain frame is built to ensure that the torsion occurs around the x-axis within the current frame @Jumper et al. 2021). The definitions of the side-chain torsion angles for the 20 types of amino acids are shown in Table 3 The side-chain frames updated hierarchically follows:
For each torsion angle, an additional side-
(xx Ti Tis To +66)
X1
o o T2 = Ti o Ta (x2+xx)
T3 = T₂ o Th (x)+ 0 orx
T4 T3 T
(x4+ orx4
1
r =
0
a1
- 02
(30)
02
01
Here, 7 (x- -66) denotes the transformation from the X1 frame to the backbone frame for an idealized amino acid of type a. The same hierarchical updating process is applied from Xı to X4- r represents the rotation of the four types of torsion angles around z-axis where ([())) [1 1. Using the
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Table 3: Definition of the torsion angles (X1, X2, X3. X1) and their corresponding rigid groups for the 20 types of residues. We frame the torsion angles that are r-symmetric and list the required torsion angles to fix the side-chain atom positions.
Residue Type
X1
X2
X3
X4
Atom position fixed
ALA (A)
ARG (R)
N, N.C C C
C C,
C.C.C,,,
C². C,CCs.N.CC'
X1. X2. X3. X4
ASN (N)
A.C,CC,C
C C².C C7.00
X1.
ASP (D)
N,C". C
c..cr.om
X1. X2
CYS (C)
N,C S?
X1
GLN (Q)
N,C", C
C C, C,, c C
C C
X1. 12. Xa
GLU (E)
N,
C P, C,
X1. X2
GLY (G)
HIS (H)
N.C
No
X1xX2
ILE (I)
N,C
X1xX2
LEU (L)
N.C
X1x
LYS (K)
N,C
c
C CS.
X1. X2, Xa. X4
MET (M)
N,C
C S c
X1, X2. Xa
PHE (F)
N.C
X1
PRO (P)
N, A.C" C
SER (S)
N, C. C. O
THR (T)
N, CO, C O
X1
TRP (W)
N, C C*
Co C C
X1s
TYR (Y)
N,C*, C
C C C²
X1. X2
VAL (V)
N.C*.C².C
X1
above frame transformations and updating rules, we can mapping the idealized atom positions from the frames to coordinates, also referred to as Frame'ooAtor in the main paragraph:
a
concat,, ((Tyo
(31)
where i the updated atom position, Jy.'' represents the idealized position of atom v in residue with amino acid type a under frame f defined by different rotations and translations in Eqs. (28)
to (30)
C DEFINITION OF TORSION ANGLES
In Table we present the compositions of all the side chain torsion angles in the 20 types of amino acids that used to compute atomic coordinates. The side-chain torsion angles that show m-- symmetric are highlighted with black boxes.
D ILLUSTRATION OF THE OVERALL WORKFLOW
We illustrate the overall workflow in Fig. 14]to enhance understanding, particularly of how different components of the multi-scale model relate to the training loss.
E NOTE ON EVALUATION METRICS
From distribution learning standpoint, generated ligands with more similar statistics (e.g., mean and median of QED, SA, Vina Score) to reference ligands indicate a superior model. In our work, we followed conventions from other studies (Guan et al. (223)) by using "f" or "J"" to denote preferences in drug design. From the distribution learning perspective, our methods outperform others across nearly all metrics, they most closely approximate the reference molecules in terms of property statistics.
F ABLATION STUDIES
Effect of Interaction Loss. We perform ablation studies to verify the effect of interaction loss that
introduced in Section 3.2 The related results reported in Table The results demonstrate that the proposed interaction loss can effectively improve the performance of both ODE and SDE versions of DYNAMICFL.CC especially the binding affinity.
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Multi-Scale Architecture
Residue Frames
Translation
Apo State
Pockel time
Residual-level
Holo
Rotation
Transformer
State
Torsion Angles
predict
Framn To Atom37
Alom37
To Frame
predict
Noisy Ligand from Prior Distribution
Ligand at time
SE(3)-Equivariant
Alom-level
Atom Position
Atom Type
Flow Matching Loss
Binding
Ligand
Network
Interaction Loss
Type
Trainiing Loss
The illustration of the overall workflow. The model inputs are the protein-ligand com- plexes at time t. (Notably, the apo state and noisy ligand sampled from the prior distribution repre- sent the protein-ligand complex time 0, while the holo state and its binding ligand correspond to the complex at time 1. During training, the complex at time is interpolated between the samples at times 0 and 1. During sampling. the complex at time is derived by solving the ODE/SDE defined by the flow model.) The pocket and ligand are first input into the atom-level SE(3)-equivarian neu- ral network. The output features corresponding type, atom position, and bond type. Meanwhile, the output features related to the pocket, along with the original residue-level features of the pocket (such as residue type), are input into the residue- level transformer to predict residue frames' translation, rotation, and torsion angles. Ultimately, all of these predictions contribute to computing the training loss.
Figure 14:
the ligand are used to predict the ligand's 's atom
Table 4: Summary of properties of reference molecules and molecules generated by our model and the variants without interaction loss. (1) / (4) denotes larger smaller number is better.
Vina Score (1) QED (1) SA (t) Linpiski (1)
logP
High Afti. (1) Comp. Rate (1)
DYNAMicFI.ow-ODS wfo interaction loss
1.928
0.53+0.20 0.61#0.14 3.13+2.62
4.45+0.81
51.0%
70.2%
-6.76*1..39 1.39
0.54+0.22 0.60#0.15
3.20+2.48
4.36+0.93
37.4%
72.2%
DYNAMICFLOw-SDD
-7.65+1.59
0.53+0.15
0.53=0.17
4.34+2.58
4.25 90
52.5%
73.6%
w/o interaction loss
-7.00
0.48+0.21 0.56#0.16 1.3533554
4.06+ 1.48
43.4%
78.0%
Effect of Multi-Scale Model Architecture. We conduct ablation studies to evaluate the impact of different architectural components on model performance. We implement baseline denoted as "w/o residue-level Transformer". which uses only atom-level SE(3)-equivariant geometrical message- passing layers. In this setup, atom-level output features are aggregated into residue-level features without employing residue-level Transformer for further extraction, and these aggregated features are used to predict the residue frames' translation, rotation, and torsion angles.
Additionally, we develop a baseline referred to as "w/o atom-level EGNN", which transforms the atom-level pootein-ligand complex graph into heterogeneous graph, where each node represents either a residue (with C-alpha coordinates, rotation vectors, and torsion angles as input features) or a ligand atom. In this variant, since we do not explicitly reconstruct the full atom representation of the pocket, the atom interaction loss is not applied.
Table 5: Summary of properties of reference molecules and molecules generated by our model and the variants with different model architectures. (t) (4) denotes larger / smaller number is better.
Vina Score (L)
QED (1)
SA (t)
DYNAMICFLOW-OPD w/o interaction loss w/o residue-level Transformer
-7.28 + 1.98
0.53 z 0.20 0.61 # 0.14
-6.76 + 1.39
0.54 0.60 # 0.15
-6.23 1.68
0.22 0.59 0..14
w/o atom-level EGNN
-6.02 + 1.63
0.54 0.113
DYNAMICFL.OW -OD w/o interaction loss
-7.65 + 1.59
0.15 0.17
-7.00 + 1.15
0.48
0.116
w/o residue-level Transformer
-6.50 + 1.22
0.52
0.114
w/o atom-level EGNN
-6.13 1.31
0.49
0.16
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The results shown in Table The results indicate that proposed architecture significantly enhances binding affinity and is vital for effectively modeling protein- ligand interactions and protein dynamics.
Both variants ('w/o residue-level Transformer" and "w/o atom-level EGNN") are more computa- tionally efficient due to their reduced model sizes. However, despite using both residue-level and atom-level models, our method maintains acceptable inference speed because our flow model can generate qugh-qualtty ligand molecules in fewer steps.
G VISUALIZATION OF GENERATED SAMPLES
Visualization of Generated Complexes. Here, we list more examples of generated ligands and holo-like pockets in Fig. 13 The ligands demonstrate promising binding affinity, indicated by their Vina Scores.
PDB ID: 6T6A
PDS ID: 6T6A
PDB ID: 6SLG
QED: 0.72
QED:
QED: 0.61
SA: 0.78
SA: 0.49
lagP: 1.68
log2: 1.68
loge: 3.13
Lipinski5
Lipinski55
Upinski:
Vina Score: -7.27
Vina Score: -7.27
Vina Score: -10.75
PDB ID: 6ULB
PDB ID: 6ULB
PDB 6UL8
QED:
QED: 0.85
QED: 0.71
SA: 0.67
SA: 0.68
logP:
log2:
logP: 0.33
Lipinskt: 5
Lipinskt:
Liiinktt
Vina Score:
Vina Score:
Vira Score: -8.02
Figure 15: Examples of our generated ligands and corresponding holo pockets. The green surfaces the holo pockets and the white surfaces with transparency are the apo pockets.
Visualization of Sampling Trajectories. We sample from the generation trajectories and illustrate the ligand generation process along with the conformational changes of the pocket in Fig, T6 The reference apo pockets are from 6SZJ (top) and 6UL8 (bottom). From left to right, the ligands are reconstructed from random noise, represented by the nodes. The apo pockets also undergo conformational changes, transitioning from the apo state to the holo state in response to the generated ligands.
QED: 0.86 SA: 0.79 logP: 4.89 Lipinski: 5 Vina Score: -7.37
QED: 0.84 SA: logP: 2.69 Lipinski: Vina Score: -8.35
Figure 16: Examples of our generation flow. The ligand is initialized at the CoM of the apo pocket terms of random noise. The white node corresponds to the mask token of atom type.
H EVALUATION ON POCKET VOLUME
We use POVME3 (Wagner al. 2017) to estimate the volumes of generated pockets and make comparison with the volumes of apo and holo pockets. РOVME3 is a receptor-centric method for pocket analysis. It defines pocket volume by occupying the surrounding region the receptor with equidistant points. Points that are near or outside of receptor atoms are removed and the volume calculated based on the remaining points. Following this approach, we define the pocket region the spherical area with 15 Á radius centered the pocket's geometric center, excluding points within the van der Waals radius (plus the hydrogen atom radius) of receptor atoms. Compared with the apo pockets, (randomly selected) generated pockets more similar the reference holo
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states with smaller volume differences. The results shown in T We also show example of the volume occupation of our generated pocket and the corresponding apo/holo pocket Fig. 17
Holo Pocket
Generated Pocket Volume = 204 A3
Apo Pocket
Volume = 267 A
Volume 117 A
Figure 17: Example of volume calculation from РOVME3 using Aradius. We select the apo (purple) and holo (red) pocket from PDB file 6UDI, alongside the generated pocket (cyan). Com- pared to the apo pocket, our generated pocket more resembles the real holo structure in terms of pocket volume.
Table 6: Volume difference (A") between apo/our pockets and holo pockets.
Avg. + Std.
Med.
Apo states Our Pocket (DYNAMICFLOW-ONK 50.08 35.05
83.84 + 61.20
71.20
41.75
Our Pocket (DYNAMICFLOW-SD)
68,56 55.51 59.20
I BINDING AFFINITY EVALUATION CONSIDERING PROTEIN DYNAMICS
Incorporating molecular dynamics in evaluation is also important. However, relying on MD trajectory-based methods such as MMGBSA or MMPBSA (Wang et al.) 2019) can be highly cum- bersome. These approaches employ different solvation models and require extensive computational resources, with MD simulations often taking months to complete for thousands of systems. There- fore, as alternative, to achieve reliable and scalable evaluation.
opt for deep-learning-base approach for flexible docking and scoring
Specifically, for each generated ligand designed by the baselines and our methods, we employ Dy- namicBind (Lu et al.) 2024b), geometric deep generative model tailored for "dynamic docking", to generate 10 protein- ligand complex structures. DynamicBind also includes a model that predicts "affinity" score, which estimates the negative logarithm of the binding affinity in concentration units. We then calculate the weighted average of these predicted binding affinities to derive the final "affinity" score, where higher "affinity" score indicates better binding potential.
For each target, assess the affinity of randomly selected generated ligand (single), the highest affinity among 10 generated ligands (Best over 10), the best affinity over all 100 generated ligands (Best over all), and the average affinity over all 100 generated ligands (Avg. over all). We port the mean, standard deviation, and median of these affinities across 50 targets. The results are summarized in Table
INFERENCE TIME
We benchmark the inference time of baselines and methods for generating 10 ligand molecules given the same pocket on Tesla 1100-XXM--32GB The default number of function evaluations (NFE) 1000 for TafgetDiff and IPDiff and 100 for our method.
As Table shows, methods capable of generating high-quality ligands while simultaneously modeling protein dynamics at a fast speed, demonstrating a significant advantage in computational efficiency.
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Table 7: Binding affinity evaluation based on DynamicBind.
Single
Best over 10
Best over All
Avg. over All
Avg. + Std. Med.
Avg. + Std.
Med.
Avg. # Std. Med.
Avg. # Std. Med.
Pocket2Mol
3.64 + 1.26
3.31
4.90 1.15
4.81
5.70 + 1.22
5.68
3.74 + 0.92
3.41
TargetDiff
6.00 1.14
6.19
7.30 = 0.70
7.46
7.81 + 0.71
7.91
6.14
6.29
TifgetDiff*
6.19 + 0.97
6,38
7.16
7.54
7.64 0.73
7.79
6.08 + 0.92
6.21
IPDiff
6.15
6,45
7.05
7.18
7.68
0.90
7.82
6.05 +
6.19
IPDiff
5.96 + 1.31
5.83
7.10:1009
7.14
7.63 0.97
7.72
6.10
6.12
DYNAMICFLOW-ODE
6,46 1.00
6.69
7.40 0.94
7.62
7,91 0.90
8.07
6.37
6.38
DYNAMICFLOW-SDD
6.21 # 1.19 6.09
7,53 # 0.86
7.67
7.95 + 0.83
8.12
6.39 + 0.87 6.37
Table 8: Inference time of baselines and our methods for generating 10 ligand molecules.
Time (s) Default NFE
Pocket2Mol
980
N/A
TargetDiff
156
1000
TafgetDiff*
154
1000
IPDiff
334
1000
IPDiff*
343
1000
DYNAMICFLOWW-DD
35
100
DYNAMICFLOW-SDD
36
100
K IMPLEMENTATION DETAILS
In this section, we provided details the implementation of our methods.
Featurization. Protein and ligand embeddings (as shown in Fig. 3 are derived from the encodings of protein atom features and ligand atom and bond features, respectively, through an embedding layer (i.e., learnable linear transformation). The protein atom feature contains its atom37 represen- tation and residue type. Atom37 is an all-atom representation of proteins where each heavy atom corresponds to a given position a 37-dimensional array. This mapping is non amino acid specific, but each slot corresponds to atom of given name. Note that atom37 is widely used in protein modeling (Jumper et al. 2021). We concatenate the one-hot encodings of these two features (whose dimensions are 37 and 20, respectively)
derive the protein atom encodings (whose dimension is 57). We use the one-hot encoding of the atom type as the ligand atom encoding. We only consider explicitly modeling N, O. F, P. S, CI, Br" in ligands, so the dimension is 8. For ligand bond types, we consider "non-bond, single, double, triple, aromatic", so the dimension of ligand bond encoding The protein and ligand atom features are used the initial node features in the complex graph. And ligand atom and bond features are used as the initial node and edge features, respectively. in the ligand graph. The above encodings are common in modeling protein and small molecules.
Hyperparameters. There are 7 individual losses: 4 continuous flow matching losses for residue frames' translation (Eq. (5)) rotation (Eq. (7). torsion angles (Eq. (8) and ligand atom position (same Eq. 55. 2 discrete flow matching losses for ligand atom and bond types (Eq. (4)). and interaction loss (Eq. (T8). There are first averaged across all residues or atoms in a training sample
and then simply weighted summed with weights: 2.0, 1.0, 1.0, 4.0. 1.0, 1.0, 0.5.
We use AdamW (Loshchilov] 2017) the optimizer with learning rate 0.0002, betal 0.95, and beta2 0.999. r controls the stochasticity of the stochastic flow (see Eqs. (19) to (T)). We use 2.0, 0.005, 1.0, 2.0 the values of yy for residue frames" translation, rotation, torsion angles, and ligand atom positions.
Model Architecture. Our model consists an atom-level SE(3)--quivariant graph neural network and residue-level Transformers. The number of total parameters is 15.9 M. The total estimated model parameter size is 63.401 MB. We include more details about the model architecture in Table
L EXTENDED RELATED WORKS
In this section, we discuss more related works in addition those mentioned in Section 2
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Table 9: Details of our model architecture.
Layer name
Number layers
Protein atom embedding layer
Ligand atom embedding layer Ligand hond embedding layer
Atom-level Model
Time embedding layer
EGNN block
6
Ligand atom type prediction head
Ligand bond type prediction head
Protein residue embedding layer
Time embedding layer
Residue-level Model
Transformer block with IPA
Torsion angle prediction head
There are several research efforts that also focus on structure-based drug design with rigid pock- ets. We discuss these works as follows: Ragoza et al. (2022) applied a variational autoencoder to generate 3D molecules within atomic density grids. (Guan et al. (2024) introduced decomposed pri- ors and validity guidance to improve the quality of ligand molecules generated by diffusion models. Zhang& & Liu (2023) enhanced molecule generation through global interactions between subpocket prototypes and molecular motif's. Zhang et al. (2023a) promoted ligand molecule generation based on the principle of parallel multiscale modeling. Lin et al. (2023) employed diffusion models to generate ligand molecules by denoising the translation and rotation of 3D motifs. Qu et al. (2024) introduced an SBDD model that operates in the continuous parameter space, equipped with a noise- reduced sampling strategy. [Huang et al. (2024c) proposed to adaptively extract essential parts of binding sites to enhance the quality of ligand molecules generated by diffusion models. [uunn al. (2024d) leveraged curated set of ligand references, i.c., those with desired properties such as high binding affinity, to steer the diffusion model towards synthesizing ligands that satisfy design criteria. Zhou et al. (2024a) integrated conditional diffusion models with iterative optimization to optimize properties of generated molecules. [ee et al. (2024) proposed to simultaneously denoise non-covalent interaction types of protein-ligand edges along with 3D graph a ligand molecule. Zhou et (2024b) and Cheng et al. (2024) proposed to fine-tune diffusion models by policy gradient (Sutton et al. 1999 Lillicrap et al. 2015) and direct preference optimization (Rafailov et al. 2023), respectively, to generate ligand molecules with desired properties. Huang et al. (2024a) represents a standard SBDD method with rigid-pocke input. Although molecular dynamics were mentioned in this work, they refer dynamics induced by the forward process of the diffusion model. There are other settings for structure- based drug design. For instance, Zhhou et al. (2025) proposed to reprogram single-target diffusion models to design dual-target ligands in zero-shot manner.
A recent work (Schneuing et al., 2024) considers protein flexibility in terms of side-chain torsions in SBDD. Our work differs in that our method models the dynamics of both the protein backbone structure and side-chain torsion, and utilizes rigorous discrete flow matching for modeling atom and bond types of ligand molecules. Importantly, our model employs an apo-holo transformation paradigm, offering biologically informative prior for the flow model. In contrast, |Schneuing et al.) (024) focuses on denoising side-chain torsions from a non-informative prior derived from a static protein-ligand complex dataset.
Another recent research work, FlexSBDD (Zhang et al. 2024b), and our work both integrate protein flexibility or dynamics into SBDD but present differences various aspects. We developed our methods independently from FlexSBDD. The key distinctions between work and FlexSBDD include:
Motivation: FlexSBDD primarily seeks to incorporate protein flexibility into SBDD for optimizing complex structures and ligands. However, it overlooks the role of thermody- namic fluctuations that govern protein flexibility and conformational shifts, leading di- verse conformations with different ligands. In contrast, our work delves into the physics underlying these dynamics. We illustrate this by examining the DFG-in and DFG-out states of Abl kinase (see Fig. D. emphasizing our motivation to integrate comprehensive protein dynamics into SBDD, beyond merely addressing flexibility.
Data: FIxX derives most of its apo data by augmenting holo data through relax- ation/sidechain repacking. In contrast, we use AlphaFold2 to predict apo data, poten-
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tially resulting in greater conformational changes. Additionally, our holo states are diverse, providing multiple states for each -igtid pair through molecular dynamics simula- tions, enabling more thorough exploration of pocket conformational changes. This aligns with our motivation.
Methodology:
FlexSBDD employs a residue-level model for the protein pocket, whereas we utilize both residue-level and atom-level models simultaneously. lever- aging atom37 mapping. This approach allows us to more precisely capture protein- ligand interactions at the atomic level, enhancing the accuracy and detail of our mod- cling.
Protein Modeling:
Ligand Modeling:
On the ligand side, we construct flow models for atom positions, atom types, and bond types simultaneously in an end-to-end manner. In contrast, FLcxSBDD does not incorporate bond modeling within its flow model, instead gener- ating bonds through empirical post-processing rules. Our approach allows for more integrated and cohesive modeling of ligand structures.
Discrete Variable Modeling: FlexSBDD uses continuous vectors to represent dis- crete variables (i.e., atom types) and utilizes standard flow matching for continuous variables, employing "norm" for seff-normalization to mimic probabilities. This in- troduces a lack of rigor due to the inference gap created by "norm". Conversely, we apply rigorous discrete flow matching using continuous-tima Markov chains (CTMC) to model both atom and bond types, ensuring a more precise and theoretically robust representation. For detailed mathematical insights, see Section [3.] and Section 3.2]
For torsion angles, both FlcxSBDD and our approach employ flow matching on the manifold of hypertorus, originally proposed for full-atom peptide de- sign by Li et al. (2024). However, given the amino acid sequence in SBDD, we can explicitly address cases where certain residues have side-chain torsion angles with -rotation symmetry (e.g., of ASP). This is a more natural choice than FlexSBDD's method, which overlooks symmetry-indiee tails, see Section 3.2 and App. B
Torsion Angles:
angle period differences. For more de-
SDE Variants: Both DYNAMICFLOW-ODD (ours) and FlcxSBDD use ODEs to model transitions between apo and holo states and the ligand generation process. However, also introduce SDE variant to enhance robustness, with experi- mental results demonstrating that the DYNAMICFLOW-SDD DYNAMICFLOWWOOD For more details, refer to Section 3.3
variant outperforms the
Interaction Loss: FlexSBDD models predict the vector field directly, while our ap- proach predicts "clean" samples and reparameterizes them into vector fields. This allows us to introduce an interaction loss focused on atom distances, enhancing the learning of protein-ligand interactions from ground-truth data. Our experiments show that this interaction loss improves the model's understanding of these interactions and enhances the binding affinity of generated ligands.
FlexSBDD assesses generated small molecule ligands based on QED, SA, Binding Affinity (measured by Vina), and profiles of protein- ligand interaction. We evalu- ate baselines and our methods from these perspectives, and also add an evaluation of how similar the generated pocket structures are to actual holo states by comparing pocket vol- ume and RMSD. For details, see Section especially Fig. and Fig.
Evaluation:
The above differences underline our unique approach to incorporating protein dynamics in SBDD.
In addition our focus on structure-baset based drug design, an alternative and widely utilized approach in drug design is ligand-based drug design. This method does not explicitly use the 3D structures of target proteins. Instead, it optimizes ligand molecules for specific properties, such as binding affinity to certain targets, using various algorithms. The ligands themselves are modeled, while target infor- mation is incorporated implicitly. We list several representative examples in the following. Xie et al. (2021) employed Markov chain Monte Carlo sampling (MCMC) molecules with GNN-based adaptive proposal model to optimize molecules towards multiple desired properties. Bengio et al. (2021) proposed flow network for modeling distribution that is proportional to the rewards, from which the molecules can be sequentially sampled. Fu et al. (2022) proposed a differentiable scaf- folding tree for molecular optimization. FREED YYang al. 2021 and FREED++ (Telepov al.)
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2023 utilized fragment-based molecule generation models combined with reinforcement learning algorithms, leveraging desired properties as rewards for designing molecules.
There are also extensive works focused on other tasks instead of (small molecule) drug design but also modeling protein-ligane complexes. Notably, the imput conditions (i.e., known information) and the output goals (i.e., the components to be generated) differ from those of our task. Our focus on structure-base drug design (SBDD) considering protein dynamics, where we start with the apo state (initial pocket structure) and aim to generate the holo state and binding ligands. detailed ligand information, including both topology graphs and 3D structures, is not provided. We will discuss the differences of these related works, using representative examples to illustrate them, follows: Pocket Design: Zhang et al. (2023b) concentrates pocket design where the topology graph and initial 3D structure of the ligand are provided and the goal is to generate a compatible pocket for binding. Protein-Ligand Complex Structure Generation: Gao al. (2024) focuses on protein-ligand complex structure generation where the protein sequence and the topology graph (i.e., 2D graph) of the ligand molecule are provided and only their 3D structures need be generated. Pocket Representation Learning: Nakata et al. (2023) focuses on pocket representation learning via pretraining on pseudo-ligand pooc-- complexes instead of SBDD.
our case,
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Reviews:
[{"review_id": "3GmuX3JlqT", "reviewer": "Reviewer_gwDc", "summary": "Summary: \n1. This paper tackles the problem of flexible proteins in small molecule structure based drug discovery to account for protein's conformational changes during binding. \n2. The authors propose a full-atom model based on continuous flow matching for pocket residues' translation, rotation, torsional angles and ligand molecule's atom position) and discrete flow matching for atom and bond types of ligand molecules. \n3. They finally present a stochastic version of their flow matching objective for increased robustness.", "questions": "I found certain parts of the paper difficult to follow. Particularly in section 3.4, the details of  each of the $\\phi_i$ are mising. Are they all EGNNs? I also struggled to understand how this parametrization relates to the final flow matching objective to be used. Furthermore, some parts in this section feel hand-wavy. For example, how were the hidden states used to predict atom positions and atom/bond types. Similarly in residue-level transformer, L412, final updated frames were used as predictions - for what? It was again unclear how torsion angles were predicted based on final residue level hidden states.", "limitations": "", "rating": 6, "confidence": 2, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "Strengths:\n1. The protein flexibity problem is critical in drug discovery with no good computationally efficient insilico methods. Hence, the proposed method (if works as advertised) could be paradigm shifting. \n2. The flow matching components in the paper are generally well explained. \n3. The structural features of protein and ligands are carefully considered and appropriately modeled.", "weaknesses": "Weaknesses:\n1. I have concerns about the reproducibility of this work with no code or the curated dataset (mentioned as a key contribution) not provided. Moreover access to the code would have helped understanding the complex workflow in the paper better. \n2. In table 2, where are the results for dynamic flow?\n3. In figure 1, what are protein and ligand embeddings, where are they computed in the proposed workflow and how are they being used in complex graph and ligand graph respectively? Given the number of components in the workflow, I would suggest including an aggerated workflow figure with end to end pipeline starting from the apo state input to the molecule and holo state output, complete with the final flow matching loss. \n4. The overall loss for this work is unclear, while individual losses for structural features for protein and ligand are provided, how are they aggregated is not mentioned. \n5. Hyperparameter and other architectural details are also not provided.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "F57MYcLCC5", "reviewer": "Reviewer_FBxC", "summary": "The authors propose a new dataset of apo/holo proteins and a new model to solve the mapping task between apo protein pockets and holo protein pockets/ligand complexes.", "questions": "## Questions and remarks\n1. How did you transition from 19437 proteins to 16972 complexes? How are ligands selected, and why was the original number of proteins reduced?\n2. What does \"100-frame\" mean? Every 100th frame of the MD trajectory? Or 100 frames from each MD simulation? If the second is true, how were the 100 frames selected from the MD trajectory?\n3. Do you filter the protein-ligand complexes depending on the average RMSD throughout the trajectory? Please explain Figure 10 b.\n4. Please add the DynamicsFlow models to Table 2 for easier comparison.\n5. FREED [6] and FREED++ [7] are not cited.\n6. Line 214: string repetition.\n7. line 848: mistake (are can).\n\n## Closing remarks\n\nOverall, I find the paper important for drug design. The idea that the pocket changes upon the introduction of the ligand is well physically motivated. The generative model itself is impressive, as it combines various flow-matching modules. However, the experimental evaluation raises serious concerns about the validity of the comparison with the baselines. I would consider raising my score if the authors propose a better evaluation strategy or resolve concerns with the current evaluation.\n\n[1] Zhang, Z., Lu, Z., Zhongkai, H., Zitnik, M., & Liu, Q. (2023). Full-atom protein pocket design via iterative refinement. Advances in Neural Information Processing Systems, 36, 16816-16836.\n\n[2] Gao, B., Jia, Y., Mo, Y., Ni, Y., Ma, W. Y., Ma, Z. M., & Lan, Y. Self-supervised Pocket Pretraining via Protein Fragment-Surroundings Alignment. In The Twelfth International Conference on Learning Representations.\n\n[3] Nakata, S., Mori, Y., & Tanaka, S. (2023). End-to-end protein–ligand complex structure generation with diffusion-based generative models. BMC bioinformatics, 24(1), 233.\n\n[4] Huang, L., Xu, T., Yu, Y., Zhao, P., Chen, X., Han, J., ... & Zhang, H. (2024). A dual diffusion model enables 3D molecule generation and lead optimization based on target pockets. Nature Communications, 15(1), 2657.\n\n[5] Wang, E., Sun, H., Wang, J., Wang, Z., Liu, H., Zhang, J. Z., & Hou, T. (2019). End-point binding free energy calculation with MM/PBSA and MM/GBSA: strategies and applications in drug design. Chemical reviews, 119(16), 9478-9508\n\n[6] Yang, S., Hwang, D., Lee, S., Ryu, S., & Hwang, S. J. (2021). Hit and lead discovery with explorative rl and fragment-based molecule generation. Advances in Neural Information Processing Systems, 34, 7924-7936.\n\n[7] Telepov, A., Tsypin, A., Khrabrov, K., Yakukhnov, S., Strashnov, P., Zhilyaev, P., ... & Kadurin, A. FREED++: Improving RL Agents for Fragment-Based Molecule Generation by Thorough Reproduction. Transactions on Machine Learning Research.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "- A new dataset derived from the MISATO dataset and AlphaFold Protein Structure Database, which includes 5,692 complexes with 46,235 holo-ligand conformations and corresponding apo structures.\n- A new task to map apo protein pockets to holo protein pockets/ligand complexes.\n- A new generative model, DynamicFlow, with a stochastic variation, which is based on the combination of discrete and continuous Flow Matchings, that simultaneously generates a ligand and adjusts a protein pocket.", "weaknesses": "- The dataset collection process is not very clear; see the questions below.\n- The dataset is simulational, which makes it less representative than the PDB.\n- The paper lacks the baselines for joint pocket and ligand generation or the motivation for their absence  [1, 2, 3, 4].\n- The evaluation pipeline seems unfair and may be misleading: baseline models are designed to work with holo-state pockets, whereas, in the experiment, they are utilized to generate ligands for apo-state pockets.\n- Unlike the baselines, DynamicFlow-generated ligands are evaluated inside the generated pockets, which also affects the comparison. From our point of view, a valid way to compare different settings for baselines and DYNAMICFLOW is to use MD trajectories-based methods, such as MMPBSA [5].\n- Moreover, the fact that a ligand binds well to a generated pocket may not imply that the real affinity is good. The validity of the generated pockets is not assessed. For example, the AF PLDDT may be used. \n- Table 2. shows that the diffusion methods work better for the ligand prediction given the generated pocket than the proposed model itself, which increases the concern about the lack of comparison of the model’s architecture with the other known models", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "UPAlEI3wgL", "reviewer": "Reviewer_7Up8", "summary": "The paper proposes Dynamic Flow, a flow-matching-based method designed for structure-based drug discovery (SBDD) with a focus on protein flexibility. Specifically, Dynamic Flow models the mappings between apo (unbound) and holo (bound) protein conformations, as well as between an ideal normal distribution and the actual ligand conformation distribution. To effectively train the model on meaningful mappings between apo and holo conformations, the authors introduce a new dataset that includes molecular dynamics (MD)-modeled apo-holo protein conformations paired with ligand conformers.", "questions": "I was wondering, how did the author select the 50 test pockets other than having no overlap with the training set? Are they uniformly sampled from the whole dataset", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1) The curated dataset, where each apo protein pocket is mapped to multiple holo pockets, is novel and well-suited for the SBDD task involving protein flexibility.\n2) The paper is clearly written and supported by well-designed figures, which enhance comprehension of the proposed method.", "weaknesses": "1, The curated dataset in the paper is slightly different from the commonly used benchmark dataset in SBDD which are bindingMOAD and crossdock2020 and also the datasize is smaller compared with those two, I’m curious why not start with crossdock2020 and BindingMOAD before moving into new dataset?\n\n2, About baseline: As far as I know, there is another work on SBDD with protein flexibility via flow matching that published or submitted ahead of this work FlexSBDD[1] on Neurips 2024, I would suggest author to benchmark with their number on vina results and illustrate the novelty and improvement compare with this previous work.\n\n3, The paper lists “atom-level SE(3)-equivariant geometrical message-passing layers and residue-level Transformer layers” as contributions; however, there is no ablation study showing the impact of these architectural changes on model performance. Providing an ablation to assess their effects on sample quality (e.g., Vina score) or computational efficiency (e.g., FLOPs) would strengthen the evidence of these improvements.\n\nRef:\n[1]FlexSBDD: Structure-Based Drug Design with Flexible Protein Modeling", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "VOMHJKmBSR", "reviewer": "Reviewer_JxBu", "summary": "Authors developed the 3D pocket conditioned generative model, named DynamicFlow, for small molecule drug discovery. Compared to existing 3D generative models that require HOLO pocket structures, the proposed model can generate protein-ligand binding HOLO structures from the APO protein structure predicted by protein structure prediction models such as AlphaFold.", "questions": "1. **Page 8, Table 1.** The proposed models and baselines are distribution learning-based models. Therefore, QED, SA, Lipinski, logP should be similar to Reference ligands. (No $\\uparrow$ or $\\downarrow$.)\n2. What is the generation time scale?", "limitations": "", "rating": 8, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The authors extend the 3D structure-based ligand binder design problem to an Apo pocket structure setting.\n2. They demonstrate that the predicted protein Holo structures can be utilized as input structures for existing 3D molecular generation models.\n3. The authors perform not only docking but also non-covalent interaction analysis. This will likely serve as a desirable experimental analysis design for future 3D molecular generation model works.", "weaknesses": "**Overall comment.**\n\nThe authors effectively address protein flexibility relative to small molecules using state-of-the-art flow matching techniques.\nI'm not very interested in the 3D molecular generative models due to its unproven practicality; however, setting this bias aside, I consider this paper an important milestone in this field. However, questions remain regarding the quality of generated samples and the real-world applicability of the proposed methodology.\n\n*\\* The issues are sorted in the order they appeared in the manuscript.*\n\n**Issue 1: Bias in the training data.** Page 8. Section 4. Data curation.\n\nThis work relies on training datasets constructed from MD simulations, which may lead the model to learn the simulated physics of MD rather than capturing real-world structural distributions. While various 3D generative models ([1-2]) utilized simulation datasets (e.g., CrossDocked2020), I think it would be a minor issue. For future work, authors might consider leveraging true experimental datasets PDBbind [3] to enhance reliability [4].\n\n**Issue 2: Bias in the predicted pocket structure selection for analysis.** Page 9. Table 2, Page 10 Figure 6.\n\nIn the paper, authors selected the pocket structure (\"our pocket\") among the predicted pocket conformations based on Vina score, so the distribution of selected structures is biased from the training dataset. I suggest adding the analysis about randomly selected conformations, too. If the performance of SBDD methods (Table 2) or Volume distribution (Figure 6) are similar when using true holo structure and randomly selected structure, this would be strong evidence that the model has learned the distribution of holo structures.\n\n**Issue 3: Questions about applicability in real-world applications.** Page 16. Line 835. \"we locate residues within a cutoff distance of 7Å around each ligand and extract them from the 100-frame MD results.\"\n\nAs I understand it, this study define the pocket using the atom coordinate informations of known active binders in holo structures.\nHowever, I wonder whether these pocket definitions are directly applicable to Apo protein structures generated in AlphaFold.\nFor high usability, the pockets should be easily defined, e.g., defining pocket using the center and radius (or box length) in an Apo structure.\nThis process has been used in existing 3D generative models [1-2], but this is because they do not account for the flexibility of the pockets.\nIf I misunderstood the process, let me know.\n\n\n---\n**Reference.**\n1. Peng, Xingang, et al. \"Pocket2mol: Efficient molecular sampling based on 3d protein pockets.\" International Conference on Machine Learning. PMLR, 2022.\n2. Guan, Jiaqi, et al. \"3d equivariant diffusion for target-aware molecule generation and affinity prediction.\" arXiv preprint arXiv:2303.03543 (2023).\n3. Wang, Renxiao, et al. \"The PDBbind database: methodologies and updates.\" Journal of medicinal chemistry 48.12 (2005): 4111-4119.\n4. Zhung, Wonho, Hyeongwoo Kim, and Woo Youn Kim. \"3D molecular generative framework for interaction-guided drug design.\" Nature Communications 15.1 (2024): 2688.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "VhNCMReDHt", "reviewer": "Reviewer_vrce", "summary": "The paper curate a dataset of apo and multiple holo states of protein-ligand complexes, simulated by molecular dynamics, and propose a full-atom flow model (and a stochastic version), named DynamicFlow, that learns to transform apo pockets and noisy ligands into holo pockets and corresponding 3D ligand molecules. The experimental results seem to demonstrate that the model significantly improves the inputs for SBDD methods and enables the generation of ligand molecules with high binding affinity.", "questions": "What challenges does this method have in dealing with protein flexibility? How can we learn from the direction of the solution?", "limitations": "", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The results indicate that the proposed method is effective in enhancing the binding ability between ligands and proteins, with the Vina score reflecting a strong binding affinity.​\n2. The concept of incorporating dynamic adaptability into drug design is uncommon in the existing literature and demonstrates a high level of originality.", "weaknesses": "1. The results pertaining to the main proposed evaluation algorithm appear to align with previous studies. Several algorithms referenced are well established in the literature. The authors should:\n\n- Clearly specify which algorithms are original and unique to this study.\n\n- Explicitly indicate which algorithms are derived from existing works, rather than from the authors' own proofs.\n\n2. The paper employs various professional terms and abbreviations; however, the backgrounds and specific definitions for these terms are not adequately clarified. For example, the term \"stochastic full-atom flow\" within the model lacks a clear explanation of its exact meaning and implementation methods.\n  \n3. Regarding the dynamic adaptation of ligands and proteins, although relevant mathematical models are provided, there is a lack of essential intuitive explanations. Additionally, the logical relationships and technical details of certain steps are not distinctly articulated.\n\n4. The analysis and treatment of different states (apo and holo) in the dataset are not sufficiently explored. Moreover, the specific reasoning behind the ratio of the various states (apo to holo) remains unclear.\n\n5. There is a notable absence of baseline methods presented. It would be beneficial to consider comparing a broader range of graph-based generative models to conduct a thorough evaluation of the model's performance.\n  \n6. Reviews of computer science papers typically encourage the inclusion of anonymous code, accompanied by straightforward and easily testable data. Furthermore, it is recommended to incorporate a Jupyter Notebook, facilitating readers' understanding of the method presented.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)