DynaPhArM: Adaptive and Physics-Constrained Modeling for Target-Drug Complexes with Drug-Specific Adaptations
Authors: Diya Zhang
Mengwei Sun
Xingdan Wang
Cheng Liang
Qiaozhen Meng
Shiqiang Ma
Fei Guo
Venue: NeurIPS 2025 poster ()
Keywords: Target-drug complex dynamic modeling
Physics constraints
Denoising diffusion probabilistic model
Flexible docking
Primary area: machine_learning_for_sciences

Abstract: Accurately modeling the target-drug complex at atom level presents a significant challenge in the computer-aided drug design. Traditional methods that rely solely on rigid transformations often fail to capture the adaptive interactions between targets and drugs, particularly during substantial conformational changes in targets upon ligand binding, which becomes especially critical when learning target-drug interactions in drug design. Accurately modeling these changes is crucial for understanding target-drug interactions and improving drug efficacy. To address these challenges, we introduce DynaPhArM, an SE(3)-Equivariant Transformer model specifically designed to capture adaptive alterations occurring within target-drug interactions. DynaPhArM utilizes the cooperative scalar-vector representation, drug-specific embeddings, and a diffusion process to effectively model the evolving dynamics of interactions between targets and drugs. Furthermore, we integrate physical information and energetic principles that maintain essential geometric constraints, such as bond lengths, bond angles, van der Waals forces (vdW), within a multi-task learning (MTL) framework to enhance accuracy. Experimental results demonstrate that DynaPhArM achieves state-of-the-art performance with an overall root mean square deviation (RMSD) of 2.01 Å and a sc-RMSD of 0.29 Å while exhibiting higher success rates compared to existing methodologies. Additionally, DynaPhArM shows promise in enhancing drug specificity, thereby simulating how targets adapt to various drugs through precise modeling of atomic-level interactions and conformational flexibility.

DynaPhArM: Adaptive and Physics-Constrained Modeling for Target-Drug Complexes with Drug-Specific Adaptations
Diya Zhang',
Mengwei Sun', Xingdan Wang', Cheng Liang** Shiqiang Ma";
Qiaozhen Meng";
Fei Guo
CCentall South University Shandong Normal University
Xiangtan University
*Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences
{diya. zhang, 234711070, 244711083, guofei feeei.iccuuueee edu.
ALCS417@sdnu, eew.eddduueuuuee.e.. cn qiaozhenm@xtu edu. sq www.iaat.accc. ac. on
Abstract
Accurately modeling the target-drug complex at atom level presents a significant challenge in the computer-aided drug design. Traditional methods that rely solely rigid transformations often fail to capture the adaptive interactions between targets and drugs, particularly during substantial conformational changes in targets upon ligand binding, which becomes especially critical when learning target-drug interactions in drug design. Accurately modeling these changes crucial for understanding target-drug interactions and improving drug efficacy. To address these challenges, we introduce DynaPhArM, an SE(3)- EEuiiaanqi Transformer model specifically designed to capture adaptive alterations occurring within target- drug interactions. DynaPhArM utilizes the cooperative scalar-vector representation, drug-specific embeddings, and a diffusion process to effectively model the evolving dynamics of interactions between targets and drugs. Furthermore, we integrate physical information and energetic principles that maintain essential geometric constraints, such as bond lengths, bond angles, van der Waals forces (vdW), within multi-task learning (MTL) framework enhance accuracy. Experimental results demonstrate that DynaP achieves state-of- ffte-off-hhe-rr performance with an overall root mean square deviation (RMSD) 2.01 Á and Sc-RMSD 0.29 Á while exhibiting higher success rates compared to existing methodologies. Additionally, DynaPhArM shows promise in enhancing drug specificity, thereby simulating how targets adapt to various drugs through precise modeling of atomic-level interactions and conformational flexibility.
1 Introduction
Accurate modeling of the 3D structures of target-drug complexes provides essential insights into the molecular binding modes and interaction mechanisms between drugs and their target proteins 2 Furthermore, enhances our understanding of inter-individual variability drug metabolism and pharmacodynamic responses. The insights gained from simulating target-drug interactions establish a robust theoretical foundation for the development of personalized therapeutic strategies, thereby improving drug selectivity and specificity while minimizing adverse effects [3].
Corresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Traditional methods, such as AutoDock 4,, AutoDock Vina [1 ZDOCK 66 and RDOCK 77]. often rely on rigid assumptions or static representations of target structures. These approaches fail to account for adaptive conformational changes. Such conformational alterations are not merely incidental. They are integral to the binding process, significantly influencing the strength, specificity and overall efficacy of interactions. Consequently, these methods become inadequate when targets undergo substantial conformational changes upon binding with various drugs. To address this challenge, there is pressing need for more sophisticated modeling techniques that can accommodate both target flexibility and drug adaptability 9].
Recent advancements have concentrated on the development of adaptable representations for target- drug complexes. Techniques such as Transformers are increasingly employed due to their capability to capture long-range dependencies and structural relationships, particularly in the modeling of target-drug complexes [10]. Approaches like ProteinBERT [11] and MolTrans 12 underscore the efficacy of self-attention mechanisms in encoding both target and drug structures. However, Transformer-basse methods face challenges in accurately modeling local target-drug structures and capturing critical geometric and spatial relationships for the purpose of modeling natural poses.
Furthermore, through pessaage-pssing mechanisms, Graph Neural Network (GNN) effectively model both local and global dependencies, enhancing the representation of local interactions while preserving Recent studies have utilized GNN address
a comprehensive view of complex systems 13 [5].
the limitations inherent in Transformers 16 17 Nevertheless, GNN may encounter challenges
in capturing rang-range dependencies and lack explicit mechanisms for rotational and translational invariances, which are essential for accurately modeling the adaptive nature of target-drug binding
within tiree-dimensiona space 18 20
To address these challenges, we propose DynaPhArM, a method specifically designed for drug- aware target-drug complex modeling. DrM introduces specialized encoding module that captures dual-layer representations of target backbones, side chains and drugs via cooperative scalar-vector mechanism. For target backbones, we apply embedding quantization discretize representations into informative token spaces. These representations are then integrated using constcs-cn interaction module based on attennint,,,,,,, modulated by atomic-level docking scores to capture structurally grounded target-drug interactions. To model the adaptive nature of binding, we employ Diffusion Denoising Probabilistic Model (DDPM) to generate latent joint embeddings that reflect conformational flexibility. Finally, DynaPhArM integrates physical constraints through a multi-objeccive loss function designed balance structure reconstruction and denoising, promoting physically realistic and informative representations of target-drug complexes. Experiments demonstrate that DynaPhArM enables more accurate 3D conformation reconstruction and improves binding affinity prediction performance.
The contributions of this paper are summarized as follows:
We introduce DynaPhArM, method that accurately and adaptively models the target-drug complex using an
framework.
DynaPhArM captures adaptive joint embeddings of the target-drug complex through the physics-comstrained interaction module and diffusion module, effectively reflecting diverse conformations during the binding process.
DynaPhArM enforces physical plausibility of 3D) conformations by integrating atomic interaction constraints into the loss.
Related work
2.1
Flexible docking
Early key-lock bheory-based docking methods initially assumed rigid target structures 21 over- looking the importance of conformational flexibility (2). Over time, flexible docking approaches have emerged to address these limitations by incorporating the conformational flexibility of targets, drugs, or both during the docking process. As early as the 1960s, advances such as nuclear magnetic resonance (NMR) spectroscopy [23 and the first molecular dynamics (MD) simulations 24 began to reveal the inherent flexibility of proteins and its crucial role in ligand binding. These insights laid the groundwork for modern flexible docking strategies. FlexPose [20] is graph neural network-

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based model designed for target-drug structure reconstruction. It employs attention-basee blocks to adaptively update features, allowing for adaptation complex environments. PackDock [25] is two-stage model that integrates conformation selection and induced fit mechanisms, which facilitate adaptive adjustments of side-chain conformations. FATR [26] enhances the full-atom coordinates of both the pocket and drug while adaptively updating residue types, backbone configurations, and flexible side-chain structures within the target. EDM-Dock [27] utilizes a dynamic graph neural network to predict distance matrices and variances between target-drug nodes for generating flexible docking poses.
2.2 Denoising difffusion probabilistic models
DDPM 28 is a generative model that learns to produce samples by progressively reversing diffusion process that introduces noise into data, which manages complex data distributions and generate realistic structural representations positions [29]. DiftDock-Pocker [30] employs DDPM to regenerate the translation, rotation, and torsion angles of the drug, along with the torsion angles of the side chains, effectively simulating the flexible alterations occurring during the binding process. a joint denoising process involving four variables in tangent space, thereby generating adaptive binding conformations. SurfDock [32 enhances initial random pose through denoising via DDPM, which captures complex distributions and enables the generation of adaptive drug poses within a flexible spatial framework. DynamicBind (33 utilizes DDPM to optimize conformational changes in both apo targets and drugs, modeling target flexibility through side-chain torsions and residue movements.
DiffBindFR [I]] conceptualizes structure reconstruction
3 Method
We introduce DynaPhArM, a transformer-based diffusion model (illustrated in Figure I designed for drug-specific target-drug complex modeling. The model consists of three principal modules: representation encoder with a cooperative scalar-vector encoding module (3.T). adaptive joint embedding generation module (3.2) and loss function integrating physics and geometry constraints (3.3) The decoder architecture and inference procedure are provided in Appendix and
3.1
Representation encoding module
As shown in Figure T DynaPhArM employs representation encoding module (target side-chain Encoder,, target backbone Encoder; and drug Encoder composed of two main components: cooperative scalar-vector representation and target embedding discretization to represent both the drug and target molecules. Both target and drug are represented graphs. We utilize hicrarchical encoding for the target by dividing it into the backbone G = (V", 8d) and the side chain Go = (V*, (V*,E*). All nodes and edges are jointly parameterized by scalar and vector features (as shown in Appendix C
Cooperative scalar-vector representation. To overcome the decoupling of scalar and vector channels in the original Transfrereee (34] devise dynamic bidirectional update mechanism (Algorithm in Appendix [D that tightly couples geometric (vector) and semantic (scalar) features. At each iteration, the passing of the node-node and edge-edge message is enhanced by gated updates: for each node v, we compute directional messages h, from neighbors Uy that fuse its scalar descriptor, edge scalars and learned encoding of the edge vector; Attention weights oij then modulate their aggregation into a residual message m;- The node scalar feature is updated by an multi- perceptron (MLP), while its vector feature undergoes an SE(3) Eqqivvraaa correction via another MLP. Edge features are likewise refined: spherical harmonics-bars geometric embeddings genmetric augment edge scalars through edge-MLP, and the edge vector is shifted by learned function of its incident node vectors.
Finally, an interaction module executes scalar-vector inner product at each node to produce a cross-modal message hinteract. which is fed back both channels, adding squared norms of the other channel as residual boosts, to enable true bidirectional flow. We apply this cooperative encoding to the drug graph Gd, as well as the target backbone Go and side-chain G graphs. After T iterations, spatially aggregated features (via global average pooling over nodes and edges) are passed through task-specific MI.P to yield three embeddings: the backbone embedding e² (global fold topology), the side-chain embedding e (local conformational variability), and the drug embedding ed.
3

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a. Overall diagram.
Potentials
Residun
Side chain
Encoder,
Physics
Target
Pre- dock-o
Rackbone
Incodery
Embedding Discretization
Interaction Module
Diffusion Module
Decoder
Geametry gguided Loss
Module
1.0-25A
Encoder
102 120
Drug
Cooperative Scalar-vuctor Representation Module
b. Cooperative retelaa-veecooreepeeeenttttt module.
Target embedding discretization module.
Node Scalar Feat.
Node Vector Feat.
MLP
Cooperative Scalar Vectur
Updated Node Scalar Feot.
edgo Scalar Fost
Update
Updated Node Vector Peat
Representation
Updated Edge Scalar Feat.
Edge Vector Peal.
MLP
Module
- Updated Edge Vector Feat.
Node Features
SH:: Spherical Harmonic Punction
Edge Features
d. constraec interaction module. Diftusion module.
Physics and geometry-guide loss.
Lennard-jones Potentials
((cle--1) :) - (ees (o Valeo 1 aad
Lees
Docking Guided
Score Matrix
Lboud
Froona
frangle
Latedrrat
Lyst
Pole, all) (e,,, rimole o) o)
Letectro
Distance
Figure 1: DynaPhArM pipeline outlines key modules for representing and modeling target-drug complexes. The overall framework of DynaPhArM. The model encodes target-drup features via scalar-vector and discretization modules, integrates them with physics-aware attention, and generates 3D structures using diffusion model under multi-task loss enforcing structural and physical consistency. b The cooperative scalar-vector representation module serves to dynamically integrate geometric and semantic features of targets and drugs. The discretization module facilitates the quantization of backbone embeddings into discrete tokens. The physics-constrained interaction module is designed generate embeddings for backbones, side chains, and drugs. The diffusion module models adaptive complex structures based on the joint embedding derived from the physics- constrained interaction module. The physics and geometry-guided loss function ensures that the predicted complex structures adhere to physically realistic interaction potentials and geometric constraints.
Target embedding discretization. After obtaining the enhanced embedding via scalar-vector cooperation, the target representation discretized using the pre-trained FoldToken4 codebook 355 This discrete encoding has been shown to more effectively capture recurring structural motifs, reduce representational variance, and minimize redundancy in the learned embeddings. Using the inherent regularity of the backbone structures compared to the conformational diversity of the side chains, we map the continuous geometric embedding e" into a discrete semantic space through vector quantization. Specifically, the high-dimensional continuous representation e is compressed into discrete semantic token e::
e² Tokenizo(e") arg min ||eb - ( ill2 ozEc
by minimizing the Euclidean reconstruction error between the backbone embedding and the codebook vectors C = {cr, ... ).). cN). This discretization mechanism achieves dimension-reducce encoding of 3D structures while preserving backbone topological features, significantly enhancing storage efficiency and computational tractability of target representations.

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3.2 Adaptive joint embedding generation
In this section, we adopt the cesstssconnttaiiee interaction module and diffusion module generate adaptive joint embedding for the target-drug complex.
chestae-con interaction module. To capture the adaptive nature of target-drug interactions in a drug-specific manner, we incorporate docking-derived interaction priors into the attention computation. Specifically, we extend the conventional cross-attention formulation by integrating Chysics-constraiin interaction matrix that reflects atomic-level docking scores, shown in Equation
QiKq vdx
head; = Softmax
V
Here, Qi -== K; - W and V; e where x, v, E {b, d) denote the backbone (b), side-chain (s), and drug (d) embeddings respectively, depending on the directional pair under consideration. Let E Rl e² E Rr and ed E R. be the corresponding input features, with W.O. W.K W.V E Rdd denoting learnable projection matrices. Ia, represents the number of nodes in the protein backbone. Each node in the backbone graph corresponds to a single residue. L, represents the number of nodes the protein side-chain. In our atom-level graph for the side-chain, each node corresponds to a single heavy atom. de represents the dimensionality of the node feature embeddings. is hyperparameter that defines the length of the feature vector used represent each node, whether it is residue in the backbone or an atom in the side-chains or the drug. The learnable scalar 7 controls the influence of the physical prior on the final attention distribution.
The interaction matrix S.) is computed by using Lennard-Jones (IJ) potentials of target-drug
conformation modeled by AutoDock tool. For each directional pair 2, E {b, 8, d], we define
ay
12
JEM Fj
67
SoY 4
Tij
where ri = Ipp - Pyll is the Euclidean distance. Sty serves as an interaction- prior that modulates the raw attention logits. By adding 7 to Q,K,T the model is guided to emphasize spatially and chemically plausible interaction sites, promoting more meaningful attention across drug-targe pairs. And the LJ parameters are computed via Borentz-Berthellt rules:
oij = (a: Eij Ve,ej
where o; and o, the LJ size (collision-diameter parameters of atom and atom j. e, and Ey the IJ energy-well depth parameters of atom and atom j.
To account for the full interaction landscape, we compute attention over six directional combinations:
+ 8, s + b, + d, + b, s + d, and + s. Each head output has shape xdd, Concatenating all six directional outputs along the feature dimension yields tensor of shape B x (6d,), which is then passed through trainable MLP to project it back into R xd, to produce a compact fused embedding e/. By integrating these interaction-aware priors, the model generates adaptive, drug-specific representations that reflect diverse structural or functional responses across target environments.
Diffusion module. To model the adaptive nature of protein- ligand binding, we employ a conditional DDPM to generate refined latent embedding. This module transforms an initial fused embedding, ef, into final conformation-awat embedding, Crefined, which captures structural flexibility.
The diffusion model consists of forward process and reverse process operating on a latent variable 2. The forward process, q. progressively adds Gaussian noise to the ground-trun -tuuth embedding, Egt. over T timesteps. We define the starting point of this process as 20 = egti
T
( = II 1=) where g( ((=x/z=-)) = N(zi /1 1,,
(5)
5

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The reverse process is modeled by neural network that learns to iteratively denoise noisy variable 2,, critically conditioned on the fused embedding e!:
T
pa(za.Tle = p(=r) II
where p(2r) = (2r; ([2r;0,1 0,
(6)
During inference, the refined embedding crefined is generated by starting from a noise vector 2T (0, I) and iteratively applying the learned denoising steps po for t= ,,,., 1, The final output of this process is frefined = 2g- Conditioning on ef at each step ensures that the resulting embedding accurately reflects the interaction patterns specific to the protein- pair.
3.3 Physics and geometry-guided loss design
To ensure the biophysical plausibility the generated target-drug conformations, we integrate fundamental physics and geometric information constraints to loss function Lphy-geo- The feasibility of generated structures enforced through seven geometrically regularization terms: bond lengths, bond angles, dihedral angles, vdW radius, electrostatic interaction, hydrogen bonding interaction and æ ı interaction, details of which can be found in Appendix Then, the physics and geometry- guided loss is the sum of the above seven items:
pphy- Lbond
Langle Ldihedral + LudW Lelectro + Litoond + CT-
In addition, we consider the objective of complex modeling task, which focuses modeling the all- atom coordinates f; of the predicted complex derived from the decoder relative their ground-truth positions which is defined as:
1 M
Latructure
Σ
A -
where M represents the number of atomic coordinates in the complex.
Within the embedding space, the noise prediction task is critical for the diffusion- denoising process, aiming minimize the error between predicted ég and true noise, conditioned the corrupted embedding e, and the time step t:
Luoise = Eg,elllc - éo(ce, 1)
(9)
The total loss defined as a weighted sum of three objectives:
Lotal = ai Cnoise Ct 0r3 cpa
(10)
where a1, 02 and ag dynamically adjusted weights that balance the contributions of each task during training. The detailed adaptive weight adjustment method can be found in Appendix F
Experiments and results
In this section, comprehensively evaluated DynaPhArM's performance across multiple bench- marks (Section assessment (Section 4.2) and conformational ensemble docking performance in Appendix G We also did a few ablation studies to show the functions of main modules in Section 4.3 Then, we conducted the study to validate the drug-specific binding in Section 4.4 and its ability to capture target adaptive changes in the drug binding process in Appendix H We finally analyzed the model's sensitivity the physical priors (Appendix lt
complex structure modeling binding affinity prediction, cross-docking
4.1 Experimental setup
Dataset. We curated a comprehensive dataset of 21,762 high-quality target-drug complexes from the Protein Data Bank (PDB) and 2,417 validated drugs from DrugBank. Each drug was standardized and structurally validated. grouped by 30% sequence identity, with entire clusters assigned to either the training (80%) or validation (20%) sets, guaranteeing no sequence overlap between subsets. The details of the curated data and other datasets used can be found in Appendix
prevent data leakage and ensure generalizability, complexes were

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Baselines. We evaluated our model against GNN-based methods (FlexPose 20) TankBind
[3]). diffusion-based models (PackDock [25], DynamicBind [33, DiftDock 2 DiftBindFR [I],
DifiDock-Pocket 30), SurfDock [32] and conventional docking tools (Glide [37 Rosettal.igand
38
and AutoDook (39))
Evaluation metrics. The proposed method evaluates both structural and functional performance. For structural accuracy, we compute the RMSD of the entire target-drug complex (overall RMSD), the ligand's 3D coordinates (L-RMSD), and the side-chain conformations (sc-RMSD). Corresponding success rates are reported as the percentage of cases with RMSD values less than 2 A, including overall success rate, ligand success rate, and side-chain success rate, which respectively reflect the reconstruction fidelity of the full complex, the drug molecule, and side-chain positioning. For functional performance, we assess binding affinity prediction accuracy using the Pearson correlation coefficient (PCC), root mean square error (RMSE), Spearman correlation coefficient (Spearman) and mean absolute error (MAE) between predicted and experimental affinities.
4.2 Main results
Complex structure modeling. We evaluated the performance of DynaPhArM complex structure modeling and compared with range of baseline methods as shown in Table [ Among all the methods, DynaPhArM achieved the best overall performance, with the lowest overall RMSD, sc- RMSD and L-RMSD. Moreover, it demonstrated the highest success rates, achieving 61.60% for L-RMSD <2 A, 70.50% for sc-RMSD <2 Á and 65. 55.30% for overall RMSD <2 Å, which highlight DynaPhArM's ability to effectively model both global and local structural details of target-drug complexes. These results demonstrate that DynaPhArM provides significant advantages over existing methods in modeling accurate and physically plausible target-drug complexes, particularly in cases requiring adaptive flexibility. The running time in reconstructing task of all of these methods can be found in Appendix
Table I: Performance of different methods in reconstructing complex structures within the test set, evaluated by RMSD (A) and success rate.
Method
RMSD (L)
(1)
Overall
Side-chain
Ligand
Overall RMSD < 2
sc-RMSD < 2
L-RMSD < A
Glide
37
11 11.20=4.92 92
9,37e4.32 32
15:01 48
18.79%
19.73%
10.31%
RosetaLigandd
38
9.83+-1.01
9.1924.13
19.3244.84
20.97%
21.02%
8.33%
AutoDock
39
8.601-4.73
7.05a4.011
13.29a4.556
21.06%
22.80%
12.56%
TankBind
36
5.36Gt.11
4.48
14.66+5.08 0.8
23.51%
29. 10%
11.34%
DiflDock
3.77a2.85
2.53&1.40
57.50%
DiADock Pocket
x
1.19&1.40
1.27+1.56
6.24=4.22
39. 10%
67.20%
25.65%
DynamicBind
3.01+1.88
1.36+0.67
3.25=2.67
70.
51.77%
DiffBindER
31
2.98+1.35
0.61=0.38
2.73=1.30
50.98%
55.30%
57.22%
SurfDeck 32
2.55+2.35
0.55&1.37
4.59=2.46
58.23%
70.00%
46.16%
PackDock 25
2.52+1.44
0.52&0.37
2.80=1.42
56.54%
68.10%
57,89%
FlexPose 20
2,44+2.80 83
0.44+0.34
3.48=2.20
60%
70.20%
30.24%
DynaPhArM
65.30%
70.50%
(4) demotess higher/ lower is better: Top 1 and Top 2 are highlighted with bold and underlined, respectively.
Cross-docking assessment. Cross-docking serves as a stringent, application-oriented benchmark by placing ligands into non-cognate receptor conformations, thereby probing docking model's ability to generalize beyond crystallographically aligned complexes. In the apo-holo scenario (CDK2, EGFR, CASS2001-Drug' ligands must navigate collapsed or misaligned binding sites in ligand-fre free receptors, demanding that the model infer plausible induced-fit rearrangements of side chains and backbone to reconstruct binding-competent geometries. The holo-holo setting (DUDE27-HoloEn)) removes the apo bias but introduces geometric mismatch among pockets induced by different co-crystallized ligands, so success hinges on recognizing invariant physccccla interaction patterns across diverse induced-fit landscapes. Finally, the ANN docks into honelogy-modeled modeled or unrelated receptor structures plagued by backbone shifts, rotamer errors, and absent waters or cofactors, imposing extreme structural noise. Traditional rigid-body algorithms falter under these out of distribution challenges, whereas DynaPhArM leveraging an (E(3)--quivarrint, cooperative scalar-vector architecture and learned joint target-drug embedding, which bridges conformational
7

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Table 2: Performance of different methods various cross-docking datasets, evaluated by overall success rate and overall RMSD (A).
Overall Success Rate
Overall RMSD 4
Mathod
CDK2
EGER
DUDE27- HoloEEs
CASE2016
ANN
CDK2
EGER
DUDE27- Holotins
CASF2016 ANN
Drug
Drug
AutoDock 39
5.92%
3.11%
11.37%
18.47%
15.29%
6.12
6.37
6.04
4.37
5.37
Glide X7
15.17%
9.38%
13.10%
16.32%
13.38%
6.87
5.72
4.86
DifiDock 2
29.83%
33.55%
34.78%
32.72%
21.40%
4.06
5.46
3.17
3.46
4.02
TankBind
2.21
3.14
DiffBindFR 31
39.45%
41.05%
14.24%
63.02%
$4.56/%
1.85
2.58
3.28
2.23
2.43
Diffeeck-Pocket
44.28%
30.75%
29.05%
40.81
1.82
5.50
3.91
PackDock (25
50.64%
28.37%
20.46%
61.13%
42.63%
1.73
4.02
4.36
2.31
2.94
HeexPsse (20
48.56%
33.22%
26.81%
69.24%%
36.74%
1.80
3.13
5.13
1.38
3.05
DynaPhArM
56.01%
43.46%
40.52%
70.06%
60.85
2.14
2.80
1.05
2.28
(4) denote that higher/lower is better. Top and Top results are highlighted with bold and underlined, respectivoly.
Table 3: Performance of different methods in predicting target-drug binding affinity, evaluated by
PCC, RMSE, Spearman, and MAE.
Method
PCC t
RMSE +
Spearman 1
MAE
KDEEP
40
0.734
1.50
0.725
1.12
ECIGGraph::M--oloo
0.781
1.42
0.765
1.08
FlexPose
20
0.793
1.39
0.780
1.06
Interformer
42
0.802
1.27
0.790
1.04
ELGN
43
0.805
1.31
0.795
1.07
GIGN
44
0.807
1.34
0.800
1.10
WaterWat
45
0.814
1.28
0,810
1.05
DynaPhArM
0.820
1.20
0.815
1.00
( (4) denotes higher lower number is better; Top and Top 2 results are highlighted with bold and underlined, respectively.
gaps, disentangles ligand- and srreptor-specife features, and maintains high accuracy and low RMSD even in the most distorted scenarios.
Binding affinity prediction. We evaluated DynaPhArM's performance in the downstream bind- ing affinity prediction task. KDEEP [40] is based on the Convolutional Neural Network (CNN). ECIFGraph:HHM-Holo -olo-Appo [41 and GraphWater-Ne. 455 are GNN-base methods. FlexPose (0 and Interformer 42) are transformer-basee
methods. ELGN [43] and GIGN [44] are EGNN- based methods. As shown in Table 3 DynaPhArM achieved the highest PCC of 0.820 and the lowest RMSE of 1.20, outperforming the second best method by 0.006 and 0.07. This superior performance validates DynaPhArM' efficacy not only modeling and structure prediction but also as a robust tool for affinity prediction, making it a versatile and powerful model for structure- based drug design.
4.3 Ablation experiments
To evaluate the contributions of key components in model, conducted ablation experiments by systematically removing pre-docking strategy, physical features, cooperative scalar-vector repre- sentation module, target embedding discretization module, physics-constrained interaction module, diffusion module and physical constraints, as illustrated in Table
Criticality of the pre-docking strategy. The pre- pre-docking strategy initializes drug poses to avoid local energy minima. Adding a pre-docking strategy modestly improves the drug success rate by 14%, demonstrating that accurate geometric initialization acts synergistically with structural modeling to preserve global conformational fidelity, preventing pose divergence during refinement.
Importance of physical features. Physical features (e.g., atomic mass, charge) offer intrinsic molecular descriptors. Removing them caused notable rise in sc-RMSD from 0.29 to 0.31 Á and decrease drug success rate by 1.04%, which highlights that explicit physical priors enhance local structural alignment and enhance atomic-level discriminability.

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Effectiveness of the cooperative scalar-vector representation module. The cooperative scalar- vector representation module is designed to model the structural interdependencies. Removing the cooperative scalar-vector representation module significantly degraded side-chain prediction accuracy, increasing RMSD from 0.29A to 2,04A, while the drug success rate dropped by 17.47%, highlighting the critical importance of this module in maintaining accurate structural predictions.
Role of the target embedding discretization module. Discretization encodes local geometric details fine resolution. Its removal resulted in substantial degradation: the overall RMSI) increased from 2.01 3.34 and the success rate dropped from 61.60% to 41.34%. These results emphasize that discretized spatial encoding is indispensable for capturing spatial granularity critical for precise structure generation.
Effect of the physics-constrained interaction module. inter-molecular force priors. Eliminating this component increased the overall RMSD from 2.01 Á to 2. 1Â and reduced drug success rate by 8.69%. This suggests that energy-awars modeling facilitates spatial compatibility between target and drug, contributing to biologically valid predictions.
Physics-constrained interactions impose
Contribution of the diffusion module. Diffusion modeling introduces denoising dynamics to capture conformation flexibility. Removing led to severe performance loss, with overall RMSD increasing by 2.98Å and drug success rate dropping by 30.79%. This underlines that the generative denoising process is fundamental for modeling complex structural distributions in a physically consistent manner.
Necessity of physical constraints. Physical constraints include seven physical and geometrical terms to ensure structural plausibility. Adding these constraints significantly mitigates deviations, the overall RMSD decreases by 0,79Å, and overall success rate rises by 14.76%, which demonstrates that physical constraints prioritize local atomic realism over global sampling, leveraging physicochemical principles to refine modeling.
Table Experimental results on ablation study, which summarizes the performance models with various components (V/ X), highlighting the impact of each element. a: pre-docking strategy, b: phys- ical features, c: cooperative scalar- vector representation module, target embedding discretization module, e: physics- physics-based interaction module, f: diffusion module, g: physical constraints.
Components
RMSD
Success Rate
Overall
Side-chain
Ligand
Overall RMSD) <2Å
sc-RMSD <2Å
L-RMSD <2Á
2.01 Á
0.29 Á
2.17 Á
65.30 %
70.50
61.60% %
2.07 Á
0.48 Á
2.31 Á
64.17%
69.17%
58.46%
2.05 Á
0.31 Á
2.73 Á
64.66%
70.15%
60.56%
3.22 A
2.04 Á
4.96 Á
49.72%
62.01%
44.13%
3.34 Á
1.89 Á
5.13 Á
47.01 16
67.8 67.88%
41.34%
2.11 Á
0.59 Á
2.70 Á
60.87%
57.45%
52.91%
4.99 Á
3.72 Á
4,08 Á
40.45%
36.67%
30.81%
2,80 Á
1,93 Á
5.42 A
50.54%
66.21%
43.02%
4.53 A
3.65 Á
3.81 Á
41.08%
38.90%
35.27%
4.60 À 3.06 Á
4,26 Á
37.19%
37.12%
30.78%
5.01 Á 5.17 Á
6.11 Á
29.23%
25.45%
26.09%
/1) (L) denotes higher lower is better. Top I and Top 2 results are bold and underlined.
4.4
Case study
We evaluate DynaPhArM through two case studies: drug-specific binding conformations on a shared target (3APW) using drugs and reconstruction accuracy compared to baselines (Appendix H)
Disopyramide an antiarrhythmic agent used to treat ventricular arrhythmias by stabilizing cardiac electrical activity 4Б and 3APW is experimentally validated target for this drug. As illustrated in Figure for Disopyramide binding to the target, DynaPhArM achieved high structural accuracy, with an overall RMSD of 0.92 Á, which underscores its capacity to reconstruct the precise spatial organization of the complex, including critical molecular interactions governing therapeutic action.

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Figure The case of DynaPhArM on one target 3APW and different drugs, The 2D representation of the drug molecule Disopyramide (DPO). b The 2D representation of the drug molecule Zolpidem (R5R). c, The experimental grey and predicted (green target surface and yellow DPO sticks) structures of complex forming by DPO and 3APW, respectively. d The predicted structure of (green target surface, yellow R5R sticks and red collision region) complex forming by R5R and 3APW.
In contrast, Zolpidem is redative-hypnotie drug used for short-term management of insomnia by modulating GABA-A receptor activity (47). which is not naturally binded to 3APW. DynaPhArM accurately predicted structural rearrangements, including side-chain closure around the ligand, which a hallmark of specific engagement, demonstrating both structural fidelity and adaptive sensitivity.
5
Conclusion
In this study, we present DynaPhArM, framework based on SE(3)-Equivarian) Transformer designed to simulate the flexible and adaptive nature of target-drug interactions. DynaPhArM utilizes a cooperative scalar-vector representation approach and discretazation mechanism that facilitates efficient and scalable modeling. By integrating adaptive embeddings with physics-constrainee MTI. framework, DynaPhArM guarantees the generation of chemically accurate and physically plausible 3D structural models of target-drug complexes. DynaPhArM provides deeper insights into target-drug interactions, enabling the development of more effective and individualized therapeutic strategies. Extending DynaPhArM to complex, multi-target systems could boost discovery efficiency and accuracy but risks overfitting, higher validation costs, or biosecurity.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (62322215, 62532017, 62402488, 62372279), the Hunan Provineial Natural Science Foundation of China (20251160387), and the Natural Science Foundation of Shandong Province (ZR2025QB62, ZR2023MFI (1002MMF1199 19), This study was also supported in part by the High- Righ-Perfforance Computing Center of Central South University.
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Justification: All datasets used in our experiments are publicly available and used under their respective licenses. We cite the original sources the paper and confirm that we comply with their terms of use.
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Answer: [Yes]
Justification: We curated and released novel dataset comprising 21,762 high-quality target-drug complexes from the PDB and 2,417 validated drugs from DrugBank in Section
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Institutional review board (IRB) approvals or equivalent for research with human subjects
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Question: Does the paper describe potential risks incurred by study participants, whether such risks were disclosed to the subjects, and whether Institutional Review Board (IRB) approvals (or equivalent approval/review based on the requirements of your country or institution) were obtained?
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A Decoder architecture
The decoder fdee is responsible for transforming the final diffusion-denoisse fused representation of E Vxd wwhih jointly encodes physics-aware target-drug interaction semantics- physi- cally plausible 3D structure Ö = (+z E 1= atoms).
) where N denotes the number nodes (residues and
The decoder is implemented as an L-layer SE(3)-Equivariant graph transformer, where each node i initialized with the latent feature h via a pre-docking strategy:
0. from diffusion and an initial coordinate (0) obtained
Ef
h
ri = r
(11)
At each layer& & = 1,...,, L, the decoder performs the following operations:
A.1 Equivariant attention
At each layer f, the decoder refines node-level representations through self-attention mechanism that integrates contextual information across the target-drug interaction embedding. Specifically, each node i with scalar feature h (t-1), Rd computes attention weights over its neighbors by projecting its embedding into a query vector:
Q
14 (4- w(o
(12)
where Q E Raxd is a learnable projection matrix at layer l.
Similarly, all other nodes j are projected into key and value vectors:
Kf n ww
Vj = h (f---11 w
(13)
where w ( E gaxd are the key and value projection matrices, respectively, K The attention weight between node i and node is computed via scaled dot-product attention:
exp (Q. K.O/vO
(
(14)
E exp (Q. k
where d is the hidden dimension and dig defines the normalized attention score assigned to node when updating node i.
Using these weights, node aggregates contextual information from all neighbors:
N
(
(15)
where 1(00 represents the aggregated semantic message from the neighborhood of i.
Finally, the new node representation is updated using residual connection followed by layer normalization:
LayerNorm (ng (e(1-) + R(()),
(16)
where (2) is the refined embedding at layer &.
A.2 Message passing
To incorporate distance-aware relational information into node-level reasoning, we employ a message passing mechanism that explicitly encodes pairwise Fuclidean distances into high-dimensional edge features. each layer f, for each node pair (i,j), we first compute their spatial distance based on current coordinates:
21

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d l|r (e- -r -r
----1111 112.
(17)
where ri ((-1) E R is the coordinate of node at layer 1, and dg denotes the Euclidean distance between nodes i and j.
The scalar distance d is then passed through radial basis function (RBF) expansion to obtain smooth, high-dimensional representation:
Φu (diy) exp (- Bx pa }2))))
K,
(18)
where μa and 8x are the center and bandwidth of the k-th Gaussian kemel, respectively. The output (du(d) is K K-ddimensional vector encoding the relative spatial proximity between nodes and j.
Finally, we compute the adge-wise message mij (!) and the geometric encoding:
by integrating both node-level semantic information
(2) mij dm (n/², n for (d;())))
(19)
where h E Rd and h Rd are the current scalar embeddings of nodes and j. and dm denotes a learnable MLP that fuses semantic and geometric inputs into unified message representation.
A.3
Coordinate update
To refine the atomic coordinates in an SQuii-Equivariant manner, we apply direction-aware coordi- (9) computed in A.2 For each node pair (i, j), scalar weight
nate update based on the message m.
(t) is first predicted via learnable neural function:
Wij
(E)
2b (m)
(20)
where (.) is an MLP that maps the message mij ( geometric influence of node j on node i.
into scalar attention score that modulates the
Next, the coordinate displacement for node is computed by aggregating normalized directional vectors weighted by w!?!
(f-1)
(e-1) dig
Ari 10 Σ
(2) wif
(21)
where (((-1) E 3 and r (t-1) Euclidean distance as previously defined. The term (ra (v2-r,) -ry)/ds is the unit direction vector pointing from j to i, ensuring the update direction is geometrically meaningful and rotation naation-equivariant.
RR3 are the coordinates of nodes and j at layer f 1, and d:ş is their
Finally, the coordinates of node are updated via residual addition:
r
r (f-1) + Ar!
(22)
producing refined coordinates 1 at layer The additive update formulation allows gradual correction of initial positions while preserving SE(3) equivariance, as the entire update depends only on relative positions and scalar weights.
A.4 Final prediction
After L layers of equivariant updates, each node is associated with a refined coordinate r((4) g3 To ensure that the final predicted structure is invariant to global translations, we subtract the centroid of all node positions before output:
A -( (L)
(L)
Ò= (A.j.
(23)
j=1
22

---

where N denotes the number of nodes, and é E I is the final translation translation-normalize coordinate of node i. The term N/2 أー= 1, represents the centroid of the entire structure at the final layer, and its subtraction centers the predicted coordinates around the origin.
This normalization step guarantees that the predicted structure Ö remains invariant under global translations of the input coordinate frame, preserving the Squii-Eqiv property of the overall architecture.
A.5
Multi-Objective loss and physical geometry constraints
The coordinate predictions C are supervised under multi-objective loss function that enforces physical plausibility, which can be found in 3.3
B Inference algorithm
Algorithm Structure Refinement via Diffusion and Geometric Constraints
1: Input: Target structure P. drug SMILES S
2: Output: Predicted binding pose (3D coordinates)
3: Convert S to 3D drug structure D via RDKit
4: Generate initial pose Co by docking P and D with AutoDock
5: Build backbone graph Gb side-chain graph G from P
6: Build drug graph G from D
7: e + ShccoeebackbonelC (G))
8: ed Eneoderarug (GD)
9: e < Encoder,ide- chain (g*)
10: e + Tokenize(e" )
11: ef + PhysicsAttentionne ed)
12: e, + Linear(e').
13: Sample pure noise vector: 2T (0,
14: for T down do DenoisingNett(2e:. e,) (Conditioned ey
15:
16: Æt Val
1-01 Eo VI-ai
17: end for
18: Crefined 2u
Ö Decoder((reefinal)
C
Graph feature construction
Both target and drug represented graphs. We utilize hierarchical encoding for the target by dividing it into the backbone gh = (V*, Eh) and the side chain g* (V*, E.). All nodes and edges jointly parameterized by scalar and vector features. For target, the backbone graph encodes the global structural scaffold, preserving its rigid tertiary folding through continuous peptide bond connectivity. For each node, scalar features include amino acid type, residue ID from the sequence, hydrophobicity and secondary structure, while vector features incorporate geometric information including Cartesian coordinates of the C, atom, dihedral angles and four direction vectors. Foe each edge, scalar edge features include Euclidean distance between two adjacent residues and bond type. Vector edge features include the direction vector of two adjacent residues. Meanwhile, the side-chain graph g* (V*, E*) of target captures localized chemical environments at binding sites, representing rotatable bonds and functional group orientations critical for molecular recognition. Scalar features include atom type, atom number, B-factor, functional groups type, implicit valence electrons, aromaticity, electrostatic charge and hybridization state, while vector features include atom coordinates and five dihedral angles, which are represented by their sine and cosine values. Scalar edge features are same as the backbone. The atomic graph G (V*,E*) explicitly models conformationally flexible side-chain atoms (c.g., X -angle rotations in tyrosine residues), focusing
23

---

on their spatial rearrangements during drug binding [31] Additionally, the atomic graph gd is also represented by physical and chemical properties and geometric features, such as element type, partial charge, hybridization state, chirality, aromaticity, atomic mass.
D
Cooperative scalar-vector representation algorithm
Algorithm 2 Scalar- Vector Feature Interaction with SE(3)- (eqii--qqia Update
1: Input:
2:
Node scalar features fucalar (U:), vector features fvecuur (1z) for all 2s E V
3: Edge scalar features Ryealar (ecala((ss)) vector features fvector (Gis) for all esj E &
4: Output: Updated facalar (U)). Evector (et), facalar (eiz) ) Evector (ei))
5: Initialize iteration +- 0, maximum iterations
6: repeat
7: for each node v; E do
8: for each neighbor vj E (vx) do
9:
fueetor( (v:) Fij - (vecto(
Ozj. Øij SphertiallCoordinte((r....)
11:
hig Concat Sscalar (1a), (et): M..P(fescor(et)))
Osj f- Softmax (WT hig + b1)
13:
end for
m; < EjeN(m) Olsj hij
15:
Eacata((1e (ve) f- MI.P mode (fecator (U:): m:) Evector (1/) frecto (1:) ML. (m):)))(m))
16:
17:
end for
for each edge Ejj do
19:
h goometric +- Et=o Ei==1 Wim New Pin (cos Oig )e emory
Escalar (e1z) MdLPaggo (Lealar(ei))) h geometric
20:
21:
Evector (Ei)) t frectur (eij) + MLP vee edge (frector (bector(())) (vi), (U))
22:
end for
23:
Interaction Module:
for each node "1 do
25:
Dinteract f- MLP((scalar (1:)) fvector
26:
Escular (v)) f fscator (U;) + f Evector (v)
27:
Evector (w:) +- Evector Us)) + Dinerratt
Secator (1:)l12
28:
end for
29:
t + t ++1
30:
until
E
Detailed formulation of geometry and physical loss functions
Bond lengths penalize deviations from reference covalent bond distances (1.0-2.5 Á):
||:
r, pel
Loond
Σ
(24)
yef
(U))S
ij
where B denotes the set of bonded atom pairs, and dief are experimentally derived bond lengths.
Bond angle consistency maintains directional geometry by constraining angles (102"-1209) between consecutive bonds:
(r; - rj) (Ik - rz)) -r,) [r: ry r r -r gref
Gangle
Σ (Kd.)Edd
cos
(25)
24

---

where A represents valid bond angle triplets.
To preserve the higher-order structural stability of the molecule, dihedral angle consistency constrains the torsional rotation between four sequentially bonded atoms, capturing the flexibility of the target and drug conformation:
Σ (1.i,K,)) ( Piykt
Laihedral
Pijkt
(26)
where denotes the set of dihedral angle quadruplets, pred is the predicted dihedral angle formed by atoms i, J. k and and o represents the true torsional angle.
Steric exclusion enforcement prevents atomic overlaps using vdW radius thresholds:
Cvaw
E ReLU (ri (reaW i<
1 Tj 112)
(27)
2dd is the sum of atomic vdW radii. where "i
To account for long-range Coulombic effects in the target-drug complex, we introduce dipole-dipole interaction term based on the leading order of multipole expansion. This term enforces electrostatic plausibility by penalizing deviations from physically consistent dipole alignments:
Pi P, -3ppi rij) rij)
Celectro (1,j)) EP
(28)
r; ry
where P denotes all relevant dipole dipole pairs, p; and Py are the atomic dipole moments, and Piş is the unit vector from atom to atom j.
Hydrogen bonding geometry is regularized reflect canonical interaction patterns, enforcing appro- priate donor-acceptor distances and angles between participating atoms:
Lbbond
Σ
ReLU((ra - ral ral-aal -3.2)² ReLU - Ira ral)²
(d.,,))HH
ReLUU1100000 - 0)2 + Re - 180)3
(29)
where is the set of donor- www---hydroonn-ccpppee triplets, Ta and Fa are the coordinates of the donor and acceptor respectively. 0 is the angle between the donor, hydrogen and acceptor atoms.
π- stacking geometry regularized to promote favorable aromatic ring interactions by enforcing appropriate inter-centroid distances and planarity constraints between participating rings:
Lyoggoo
Σ
ReLU - 5.0)² + Re. dz,)² 2 + ReRLR - 30
(KJ))T pairs
(30)
+ (eLLU((Azy) 3.5)²
-
n. nj (15) n;
Cxn-aliign =
ReLLUddy 3.5)
(31)
C--x= L geo
Laz-align
(32)
where π π pairs is pairs of aromatic systems involved in म a interactions. dy and 0,g are distance and angle between the centroids of the i-th and j-th systems respectively. Ary is the lateral displacement between the centers of the क - n systems. n,, and n, are normal vectors the planes of the i-th and j-th systems.
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Adaptive weight adjustment
In MTI frameworks, the design of loss weightings critically influences how the model balances its optimization trajectory across competing objectives. In our model, the total training loss comprises three core components: the structural loss Lsmesture the diffusion denoising loss Lnoise and the physies and ecodeery-guiiedd loss Lphy-geo- pointty supervising the complex modeling.
Traditionally, scalar weights statically assigned each loss component. However, such static weighting cannot adapt to the non-stationary nature of training. Different tasks may converge at different rates present varying levels of difficulty throughout training. Improper weighting may result in biased gradient updates, overfitting to easier tasks, or neglecting harder ones. To overcome this, introduce dynamically adaptive inverse proportional weighting strategy based instantaneous loss magnitudes.
F1 Theoretical motivation
From a theoretical point of view, our strategy can be interpreted under Min-Max loss balancing framework. Specifically, we seek minimize the largest normalized task loss at each training step, formulated as:
max (E{a,d,p)
(33)
where é, denotes the instantancous scalar loss,a, represents the corresponding adaptive weights.
Under our inverse proportional weighting rule, this ratio is approximately constant across all loss terms:
1/8, = const. E 1/Ex
(
~ > 4.
(34)
This normalization implies that the optimizer perceives all tasks as having equal scaled difficulty, thus promoting fairness in multi-objective convergence and avoiding task imbalance.
F.2 Formulation of Inverse Proportional Normalization
At each training step t, observe the instantaneous (i.e., per-batch) losses:
siucture = t.. dilfusion = la.
(t)
(t)
(t)
phy-geo Ep-
(35)
where l, Eu lp E R500 are the current magnitudes of the structure, diffusion, and physical geometry losses, respectively.
We then define the adaptive weights using the inverse proportional rule:
1/4
a, =
Eje(ed,e) I/l,
for each i {s, ds.
(36)
This ensures that the sum of weights satisfies E, a, 1, while favoring tasks with smaller loss magnitudes by reducing their weight, and increasing the weight on larger-loss terms that need more attention.
The final total loss is as follows:
(1) = a, l, O.g la + a E
(37)
where each term is adaptively scaled to counteract imbalance across sub-tasks.
F.3
Empirical Results
We evaluate the impact of adaptive weighting in Table 5
comparing fixed scalar weights to our adaptive strategy. Notably, the adaptive scheme achieves the best performance across all evaluation metrics, demonstrating superior capability in fine-grained structure modeling.
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Table 5: Experimental results different weight adjustment strategies of the loss function. the weight of the structure term. b: the weight of the diffusion term. c: the weight of the physical and geometry term.
Weight
RMSD +
Success Rate 1
a
b
c
Overall
Side-chain
Drug <2Å
Overall <2
1.0
1.0
1.0
2.22A
1.04À
49.13%
51.32%
0.5
1.0
1.5
2.43A
1.65Ä
45.27%
49.48%
dynamic
dynamic
dynamic
2.01Å
0.29Å
61.60%
65.30% %
/ (1) denote higher / lower is better. Top results are bold.
G Conformational ensemble docking performance
The heatmap in Figure 3 further emphasizes the consistency of DynaPhArM across structurally heterogeneous targets. The L-RMSD distributions across the DUDE27 benchmark illuminate core mechanistic divergences in how docking methods address receptor flexibility, conformational selec- tion, and induced-fit coupling. DynaPhArM achieves the lowest L-RMSD in 18 out of 27 targets. By leveraging long-range coupling, which is critical for targets with substantial loop or helix remodeling, such BRAF (2.70 A), where DFG-out to DFG-in transitions are necessary for accurate binding pose prediction.
optimization, DynaPhAr.M resolves steric conflicts and captures
In contrast, igid-receptor docking methods like AutoDock and Glide systematically underperform on conformationally adaptive proteins. For example, in EGFR, the kinase C-helix undergoes a pronounced shift upon ligand engagement, transition not accounted for by static scoring protocols, resulting in marked deviation (AutoDock: 6.36 À vs. DynaPhArM: 3. 3.02 Å). These methods are intrinsically limited by their reliance on a single, often non-native receptor conformation. TankBind demonstrates reasonable performance when structural homologs are available but degrade significantly on divergent folds allosteric pockets (e.g., GRIA2: 10.33 Å), highlighting their dependency on prior ali alignment and conformational priors. While DiffDock demonstrates strong performance when docking to protein conformations that closely resemble those encountered during training, its ability to generalize deteriorates in extrapolative scenarios involving rare or unseen structural variations. This limitation is exemplified by the MET target, where DifiDock achieves relatively high L- RMSD of 7.91 Á. The underlying issue stems from the model's reliance on implicit geometric representations learned from training data, which tend to favor commonly observed backbone and side-chain configurations. As result, DifiDock often fails to accurately model rare but functionally important conformational states, such as the loop opening events observed in MET, due to insufficient exposure to such structural diversity during training. Hybrid approaches such DiffBindFR, which integrate learned priors with restrained physics-base based refinement, show moderate success in flexible regions (c.g., CDK2: 2.71 Å) but are still limited in sites requiring long-range conformational propagation, such as TGFRI (3.61 Å), where allosteric activation involves distal loop dynamics and solvation effects. Tragment-basee flexible methods like FlexPose capture local side-chain and loop adjustments (THRB: 3.49 Å), but are insufficient for large-scale domain or backbone reorganization.
H Case study on reconstructing accuracy
The study of Aceclofenac binding to the 6Y3C target structure carries important real-world implica- tions for anti-inllammatry drug design. Aceclofenac a widely used nonsteroidal anti-inflammttory drug [48]. and 6Y3C corresponds to the crystal structure of cyclooxygenase- (COX-2), a crucial enzyme involved in prostaglandin synthesis and inflammation. Given the clinical relevance of COX-2 selectivity in minimizing gastrointestinal side effects while preserving therapeutic efficacy, accurate modeling of the binding interaction between Aceclofenac and 6Y3C is paramount pharmaceutical interest. What makes this case particularly meaningful is due to the intricate nature of their binding mechanism, which presents significant challenges for structure reconstruction and pose prediction. Aceclofenac binds to COX-2 through combination of hydrogen bonding, stacking, and hy-
27

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1RY1
MMAM
MAFK2
TOPR
RRAF
RXRA
HSPA
BACH
1894
6B
TekKal
Dilbbl Aole
DysRKMM
Figure 3: Performance of different methods reconstructing complex structures within the DUDE27 test set, evaluated by L-RMSD.
drophobic interactions within a highly adaptive and conformationally flexible active site. The induced fit nature of COX-2, characterized by local rearrangements of the side chains (particularly in the hydrophobic channel and the T380, L384 and V423 residues), often leads to substantial deviations between the apo and holo states. These conformational changes, coupled with the drug's non-rigid scaffold and multiple rotatable bonds, introduce a high degree of uncertainty into conventional docking methods. By using this system, we aim to highlight nuanced drug-ing gruu-induced conformational adaptations and accurately reconstruct the binding pose in a physically plausible manner, thus demonstrating its superior capacity to handle real-world flexible docking scenarios.
model's 's ability capture such
As shown in 4 DynaPhArM achieves the lowest L-RMSD and the best reconstruction performance comparing to the other methods. According to b in 4 the drug engages in a complex network of interactions with several key residues, including T380, M367, H422, V423, Q179, and L384. which collectively orchestrate the formation well-defined binding pocket, characterized not merely by static complementarity but by conformational plasticity, especially within the receptor's side-chain architectures. DynaPhArM demonstrates a profound understanding of this induced-fit paradigm by accurately capturing the side-chain reorganization necessary for stable drug accommodation. In particular, DynaPhArM predicts a significant conformational shift V423, which subtly reorients to alleviate steric hindrance and permit favorable der Waals and hydrophobic contacts with Aceclofenac's chlorophenyl and phenylacetic moieties.
In contrast, FlexPose, despite achieving comparable RMSD, fails resolve critical steric clash between V423 and the drug, which highlights the limitations of RMSD as sole metric, as FlexPose's predicted pose superficially resembles the native binding mode but lacks the microscopic interaction fidelity required for biological plausibility. The clash at V423 indicates FlexPose's insufficient modeling of side-chain entropy compensation.
Traditional metrics such as RMSD provide coarse assessment of geometric alignment, they often obscure deeper deficiencies in interaction fidelity and physical plausibility. The above analysis reveals that accurately capturing side-chain flexibility and resolving steric particllllp residues like V423, which is essential for modeling biologically valid binding poses. DynaPhArM's superior performance stems not merely from pose prediction accuracy, but from its ability to model the energetic and structural consequences of induced fit at atomic resolution, which enables it to
key
28

---

discriminate between superficially correct and mechanistically correct solutions a capability critical for drug design applications where small structural inaccuracies can lead to large functional errors.
DrugRMSD:
DrugRMSD.O.Bll
Drug RMSD: 1.97
3990
ME67
L384
H122
V423
Q179
Clash
DynaPhArM
DynaPhArM
FlexPose
LrugRRASD:2.0AA
Doug RUSD:M
PrUgRMSD:S.OU A
DiffBindER
Glide
AutoDock
The case of different methods on the reconstructing the structure of the complex which is consist of the drug Aceclofenac and the target 6Y3C from PDB. d-f The comparative figures illustrating DynaPhArM, DiffBindFR, Glide and AutoDock predicted structure (cyon target cartoon, pink drug sticks) alongside the experimental structure in grey from PDB, respectively. b The detailed illustration of a, which shows the key residues (purple) in the binding pocket and the interaction forces between key residues and drugs in dashed lines. The comparative figures illustrating FlexPose (the second best method) predicted structure (cyon target cartoon, pink drug sticks) alongside the experimental structure in grey from PDB, which also identified key residues in purple.
Figure 4:
Sensitivity Analysis of Priors
To evaluate the model's robustness to potential inaccuracies in priors, we conducted a sensitivity analysis the pre-computed IJ matrix. To measure the degradation in model performance, added Gaussian noise with an increasing standard deviation (Noise Level) to the IJ matrix, with results summarized in Table
Table 6: Sensitivity analysis of the model to noise the LJ prior. Performance is evaluated across different noise levels added to the LJ matrix.
Noise Level
Overall RMSD (A)
Side-chain RMSD (A)
Ligand Success Rate (<2A)
0.0
2.01
0.29
61.60%
1.0
2.07
0.38
58.10%
2.0
2.10
0.49
54.20%
5.0
2.21
0.55
53.17%
No Prior
2.11
0.59
52.91%
At low noise levels, performance changed very little, as the model's 's learned data-driven patterns and the adaptive "/ effectively compensated for minor inaccuracies.
At very high noise levels, the prior became actively misleading. The performance degraded, but did not collapse entirely. The performance plateaued at level comparable to that of the model trained without any prior, demonstrating that the model could learn effectively ignore a completely useless prior.
29

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In conclusion, the model is not overly sensitive to enrors in the AutoDock AutoDock-generatee LJ potential and can effectively mitigate its impact.
J Details of Datasets
We have performed a detailed analysis of our full learnable dataset. The results summarized in Table confirm that the dataset is sufficiently large and diverse support the learning of generalized principles of protein-ligand interaction.
Table 7: Statistics of our curated dataset.
Category
Metric
Value
Total Complexes
21,762
Overall Dataset Size
Unique Protein Targets
3,673
Mean Unique Ligands per Target
6.57
Median Unique Ligands per Target
3.0
Ligand Diversity
Targets with > 5 Unique Ligands
917
Targets with 10 Unique Ligands
444
Targets with 20 Unique Ligands
200
Targets with Co-crystal Structures
609
Structural Diversity
Targets with > 10 Co-crystal Structures
318
Targets with > 20 Co-crystal Structures
148
HYDROLASE TRANSFERASE
16.6%
16.0%
Protein Family Diversity
HYDROLASE/NHHIIITR
10.3%
TRANSFERASEENHHIBBTOO 10.1% %
TRANSCRIPTION
3.6%
In our evaluation of DynaPhArM's performance on the cross docking task, we compared with variety of baseline methods using several benchmark datasets, including CDK2, EGFR, DUDE27- HoloEns, Astex Non-Native (ANN), and CASF2016-Drug. The CDK2 and EGFR datasets are curated collections of high-resolution, inhibitor-bound protein-ligand complexes from the PDB [49] The CDK2 set includes 11,317 Cyclin-Dependent Kinase complexes, emphasizing ATP. competitive interactions in both rigid and flexible kinase active sites. EGFR comprises 67 wild- type and mutant kinase-inhibinn inhibitor pairs, challenging algorithms to accommodate subtle shifts in the activation loop and ah-helix. The DUDE27-HoloER
dataset (50) is curated ensemble-docking benchmark comprising 27 DUD-E targets for which multiple holo structures have been experimentally determined. Each target's ensemble includes all available high-resolution co-crystal complexes, yielding 268 pairs of complexes. The ANN dataset [51] comprises 65 protein- ligand systems, each represented by native holo complex and
more non-native receptor conformations into which the cognate ligand is re-docked. Designed specifically for cross-docking, challenges algorithms to recover the correct binding pose despite backbone and side-chain rearrangements present in the ligand's original crystal structure, thereby gauging a method's robustness to receptor conformational variability. The CASF2016 dataset a refined subset of the widely used CASF2016 benchmark (52), focusing exclusively on drug-like ligands and their corresponding protein targets, and the original CASF2016 dataset comprises 65 distinct targets and 195 unique ligands. The curated subset emphasizes biologically and pharmacologically meaningful interactions, providing a more targeted benchmark for evaluating models in drug target cross docking and structure- based virtual screening. The PoseBusters (PB) dataset [53] and toolkit form a comprehensive benchmark suite specifically designed to evaluate the structural plausibility and physical validity protein-ligand complex models, which includes 428 high-quality crystal structures of protein-ligan complexes. By highlighting not only how close predicted pose is, but also whether makes chemical and physical sense. The detailed results on PB dataset can be found in Appendix L
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K Time consuming in reconstructing task
Our proposed method, DynaPhArM, achieves the fastest average reconstruction time (2.39 per complex NVIDIA RTX 4090) by virtue of an integrated. end-to-end adaptive embedding framework that collapses what are traditionally multiple, disjointed pipeline stages into a single monolithic operator. Our approach fuses every stage from SMILES to 3D conversion and coarse docking to graph construction, encoding, quantization, and coordinate regression into single, zero-copy GPU pipeline. By embedding drug conformer generation and rough docking directly in GPU memory, we eliminate file I/O and CPU-GPU handoffs. A unified CUDA kernel then builds backbone, side-chain, and drug graphs in parallel, computing all scalar and vector features without repeated memory allocations or host transfers. We pack GNN inference, codebook distance computation, and embedding quantization into the same kernel launch on the fly reeovnng intermediate tensor copies. Cross-modal multi-head attention merges target and drug embeddings, which immediately flow into diffusion noise/denoise network in one continuous stream. Finally, coordinate regression decodes the denoised embeddings in-place, avoiding reshape operations and extra kernel calls and eliminating redundant data transformations and minimizing CPU-GPU synchronization overhead.
fusion, diffusion denoising,
In contrast, many existing approaches fragment the reconstruction task into discrete modules, each incurring its own latency. Packlock's exhaustive conformational sampling spawns a combinatorial explosion of rotamer states requiring successive scoring rounds, SurfDock's fine-grained surface tessellation enforces sequential mesh generation and probe- based mapping, and Tank dual- attention cross-correlation between ligand voxels and receptor grids introduces non-trivial dependency chains that stifle mntra-kernel parallelism. DiffDock and DynamicBind, while streamlined for infer- ence, nevertheless traverse multiple graph and volume-based passes, each demanding separate tensor allocations and synchronization barriers. FlexPose augments sampling agility with energy minimization, but each iteration triggers back propagation like recalculation of forces and gradients.
When DynaPhArM is deployed on the RTX 4090, it sustains throughput exceeding 1500 complexes per hour, opening new avenues for large-scale drug discovery campaigns. Its capacity to deliver sub-3- second reconstructions near-experimental accuracy makes it particularly attractive for applications such as: (1) Ultra large virtual library screening, where millions of candidate compounds must be evaluated for plausible binding conformations; L2)Lead optimization loops, enabling rapid in silico iteration over substitution patterns and intformmationactviin relationships; (3) Drug repurposing efforts, where existing pharmacopeia can be exhaustively reassessed against emerging targets with minimal computational investment; (4) Fragment- based drug discovery, facilitating real-time scoring of fragment assemblies during interactive fragment linking.
In sum, by harmonizing algorithmic depth with GPU-native efficiency, DynaPhArM promises to transform the computational throughput frontier, making true real-time, large-scale ligand screening not only feasible but routine.
L Structural rationality verification
L.1 Evaluation metrics
Te PB success rate reflects the proportion of predicted complexes that meet key biophysical and geometric criteria evaluated by the PB toolkit, including steric clashes, bond geometry, hydrogen bonding, and conformational strain energy, thereby excluding physically implausible poses.
L.2 Experiments results
As shwon in Figure 6 on PB dataset, traditional regid-receptor dockers such as Glide, RosettaLigand and AutoDock occupy the lower end of the spectrum, with overall success rates in the 25 25-35% % range and PB success rates scarcely above 30%. TankBind's learned binding-site attention makes its performance achieve nearly 40% on PB dataset, yet it still suffers under the rigorous clash and contact checks imposed by PB toolkit. The DiffDDck family marks turning point: vanilla DiffDock climbs to 45% overall but only 38% PB success rate, whereas pocket-aware variant breaches 50% overall and 45% PB success rate by conditioning on pre-identified cavities. DynamicBind and DifIBinnFR further
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4
3.5
3
2.5
2
1.5
1
0.5
0
TankBind
DiffDock
DiffDock- Pocket
DynamicBind
DiffBindFR
SurfDock
PackDock
FelxPose
DynaPhArM
Figure 5: Speed comparison between DynaPhArM and other baselines.
refine pocket flexibility modeling and non-cquilibrium binding pathways, respectively achieving 48 52% overall and 43-50% PB success rate. Surface- gureeddggdddd methods (SurfDock, PackDock) average 45% PB success rate by incorporating receptor surface complementarity, while FlexPose's hybrid sampling and filtering tactics push above 50% overall but still fall short under PB strict physical and geometric filters. DynaPhArM emerges at the 52% overall and 50% PB success rate), validating the power of combining generative diffusion with rigorous physics-informer penalties. The main reasons are in its cuffusiio-basedd generative core tightly coupled with differentiable geometry and physics constraints. The traditional rigid docking only jumps between a few discrete conformations, making easy to fall into the trap of just getting stuck in the pocket atomic collision. The diffusion process is continuous and smooth random walk a high-dimensional coordinate space, with each small step iteration allowing the system to explore feasible surrounding areas and correct minor collisions or geometric deviations layer by layer. During each reverse- reverse-diffusion denoising step, the model explores continuous manifold of drug poses, guided not only by statistical priors learned from known complexes but also by softly enforced vdW, hydrogen-borte bond, and geometric consistency losses. DynaPhArM naturally avoids steric clashes and spurious contacts, steering the generative trajectory toward low-energy, physically plausible basins. As a result, it attains high reconstruction fidelity, precisely recapitulating native drug coordinates. This synergy between generative flexibility and physics-constraine regularization ensures DynaPhArM's poses consistently pass PB rigorous physical and geometric sanity checks.
M Limitations
Despite the promising results demonstrated by our proposed method, several limitations remain that warrant further investigation:
M.1 Dependency accurate structural inputs
Our model requires high-quality target protein structural inputs to effectively capture spatial and physical interactions. In real-world applications where target structures predicted noisy, the model's performance may degrade. Incorporating uncertainty-awan structural encodings or learning from sequence-only inputs could be potential extensions.
M.2
Computational overhead of diffusion module
The diffusion denoising process introduces non-trivial computational complexity, especially during training. Although it enhances flexibility and robustness. this trade-off may limit scalability in thgu-throughput screening scenarios. Future work may explore more efficient generative backbones or lightweight denoising strategics.
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100%
90%
80%
60%
50%
40%
30%
20%
10%
0%
Gidde
Rosettadrig
AutoDock
Tankfind
DifDDok
DiffDokk PonDock-Poeker Pocker
DynanicBind
DifBindFR
SurlDock
PackBock
FelsPose
DynaPhArM
PB Success Rate
mn Overall Success Rate
Overall Rate
Figure 6: Performance of different methods in reconstructing complex structures within the Pose- Busters test set, evaluated by overall and PB success rate.
M.3 Assumption of homogeneous task importance
While the adaptive weighting strategy dynamically balances learning signals, it assumes that all tasks are cqually valuable in the normalized loss space. In practice, certain objectives (c.g., physics goometry-guided constraints) might be more critical for downstream performance. Incorporating task-priority priors or uncertainty-aware weighting schemes may offer finer control.
N Experiment setting
The optimization of the model's parameters performed using the Adam algorithm, implemented in the PyTorch library. The optimizer is applied to the learnable parameters of several distinct architectural components, including the side-chain feature projector, the drug feature projector, the physics-based interaction module, the denoiser network within the diffusion module, and the -quuivaana graph transformer decoder. Adam computes individual adaptive learning rates for each parameter by utilizing estimates of the first and second moments of the gradients, which is particularly advantageous for multifaceted model architecture such as the one employed, which integrates diverse modules requiring potentially different learning dynamics. The training process initiated with learning rate of 10-4, while the 31, 82, and hyperparameters of the Adam optimizer are maintained at their default PyTTrch values of 0.9, 0.999, and 10-8, respectively.
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Table 8: Key hyperparameters used in the proposed model, covering embedding dimensions, interac- tion modules, diffusion and decoder configuration, physical constraints, and inference setup.
Name
Value
Description
D_E
128
Embedding dimension for backbone, side-chain, and drug features Key/Query/Varn Value dimension Output dimension of the physics-based interaction module, input to diffusion
D K INTERACTION D_ PRIME_INTERAATIION
128
256
MLP HAP_HIDDEN LINTERATCN
512
Hidden dimension for MLP in the
interaction module Number of attention heads
NLATTN HEADS WEADS_INTRAACE INTERACTION
_ TRAASSTTMEESTESS TTMATTSSSSIISSSSIIISIO
4
DIFFUSION
1000
Total timesteps for the diffusion process during training
BENODE DIFFUSION
512
Hidden dimension for the denoiser model
LAYERRS D HIDDEN LRODDENATTTN_AO
6
Number of decoder layers Hidden dimension for attention in
128
decoder
RBF DECODER D_ MESSAGE_DDECODEER DECODER D_MLP_HIDDIE BHINN_PHH_WW M_DECODER
32
Number of RBF kernels in decoder
128
Message dimension in decoder
256
Hidden dim. for MLP in message generation
D MLP HIDDEN PSI DECODER
64
Hidden dim. for MLP in coordinate
update Learning rate Batch size
LEARNING RATE BATCH AATCH_SIZE NUM EPOCHS
le-4
64
50
Number epochs
REFINE SHINE_START_T INFERENCE
200
Start timestep for denoising
refinement
NUM_DENOISING SERDOISINGSSTEPSS....
50
Steps in inference denoising loop Minimum distance for RBF Maximum distance for RBF Max donor donor-acceptor distance (H-bond)
min_dist dist a dist max
0.0
20.0
3.2
a dist min
2.5
Min donor-acceptor distance (H-bond)
SIZE_X X SIZE_ SIZE
25
Grid size in each spatial direction
NUM WUM_MODES
3
Number of binding modes to generate
beta_start beta_end
le-4
Start of noise schedule
0.02
End of noise schedule
dropout_rate
0.1
Dropout rate
HMSD_THRESHON
2.0 Á
Threshold for success (RMSD)
angle_min sigle_min_deg angle_max_dee
120
Minimum bond angle (H-bond)
180
Maximum bond angle (H-bond)
mulipprocesinggnuu__ooffo
64
Number of worker processes for parallel tasks
multiprocessing.chunk size
10
Chunk size for multiprocessing pool operations
drug wwwpuppprrooonchaagggee model
gasteiger
Charge model used for ligand
preparation
dataset_split.ed hit identity
iintitecd_hi__ddetttty
0.9
Sequence identity threshold for
CD-HIT clustering
sanaset_sppit.validatinn..s
0.2
Proportion data for the validation
set
dataset_splitrrandon seed
42
Random seed for data splitting Number of layers in the backbone encoder Max degree for spherical harmonics
4
backbone, encoderr emcoder_paramss_ max sh
2
34


Reviews:
[{"review_id": "eKkZvOTjis", "reviewer": "Reviewer_wTUH", "summary": "This paper introduces DynaPhArM, a SE(3)-equivariant Transformer-based framework for modeling target–drug complexes with explicit consideration of protein conformational flexibility. By combining a cooperative scalar–vector representation, a diffusion-based dynamic embedding module, and multi-task physical–geometric constraints, DynaPhArM aims to generate physically realistic and chemically plausible 3D structures of protein–ligand complexes. Experiments across multiple benchmarks demonstrate that DynaPhArM achieves strong results compared to several classical and diffusion-based baselines.", "questions": "1. Could the authors clarify how DynaPhArM would perform compared to Re-Dock?\n2. How sensitive is DynaPhArM to potential errors in the AutoDock priors, and what strategies might mitigate their impact?", "limitations": "The authors provide a discussion of the limitations of their work, including the reliance on high-quality structural inputs, the computational cost of the diffusion module, and the equal-task-weight assumption in the multi-task loss. These points are described in Appendix L, with suggestions for future research directions. I appreciate this candid reflection, which demonstrates the authors' awareness of practical deployment challenges.", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n\n1. The cooperative scalar–vector encoding scheme enables tightly coupled geometric and semantic representations than standard SE(3) transformers.\n2. Incorporating a physics-constrained multi-task loss with seven biophysically inspired regularizations provides a strong inductive bias toward realistic molecular structures.\n3. The experimental evaluation is thorough, including diverse datasets and ablation studies, demonstrating consistently good performance in RMSD and binding affinity prediction.\n\n**Weaknesses**\n\n1. The paper does not include comparisons with recent baseline methods, such as Re-Dock [1], which are highly relevant benchmarks.\n2. The approach relies on pretrained codebooks (FoldToken4) and AutoDock-generated interaction priors, which might introduce bias or performance bottlenecks if these priors are imperfect.\n3. The reproducibility could be improved by releasing more detailed hyperparameters details.\n\n[1] Re-Dock: Towards Flexible and Realistic Molecular Docking with Diffusion Bridge, ICML 2024", "was_revised": true, "final_justification": "see above", "rebuttal": "**Dear Reviewer wTUH:**\n\nThank you for your thorough evaluation and insightful feedback. Our response to your suggestions and questions is as follows:\n\n---\n# Response to W1 and Q1: Comparison to Re-Dock\nWe agree that **Re-Dock** represents a significant advancement in flexible docking and a fair comparison would be highly valuable to the community.\n\nHowever, the omission of a direct comparison with Re-Dock was **not an oversight**, but rather due to **three objective limitations** that made a scientifically rigorous comparison infeasible at the time of our study.\n### 1. Unavailability of Code\nAt the time of our research, **Re-Dock’s source code, pre-trained models and data were not publicly available**, which prevented us from **re-training their model on our specific data splits** and **running inference with their model on our benchmark datasets**.\n### 2. Discrepancies in Datasets\nA valid comparison requires that models are **evaluated on identical test sets** and ideally **trained on comparable data**. \n#### Training Data Differences\n- **Re-Dock** was trained on the **entire PDBbind v2020 dataset** using a standard **time-based split**.\n- **DynaPhArM** was trained on a **curated subset** of **high-quality protein-drug pairs** derived from **PDBbind** and **DrugBank**.\n#### Evaluation Benchmark Differences\n- **Re-docking / Apo-docking Task**:\n  - Re-Dock evaluated on a **custom set** of apo crystal structures and **ESMFold-predicted structures** forming a unique “Apo Flexible Docking” benchmark.\n  - Our evaluation included **protein-drug pairs**, which Re-Dock did not report on.\n- **Cross-docking Task**:\n  - Re-Dock created a **custom-curated cross-docking benchmark**, **not publicly available**.\n  - Our cross-docking evaluations were performed on **public benchmarks**, such as **CDK2**, **EGFR** and **DUDE27-HoloEns**.\n\n> We believe that **quoting only the metrics from their paper would be methodologically unfair**, since differences in data preprocessing, dataset composition or evaluation details could lead to **unfair conclusions**.\n### 3. Divergences in Scopes\n- Re-Dock frames its primary contribution as solving the specific task of the apo-to-holo transition, which is a well-defined but relatively narrow subset of the overall flexible docking problem. It assumes the starting point is always a known and ligand-free structure and the goal is to predict the single transformation to a final bound state.\n- Our model is not limited to the apo-to-holo case. It is designed to be a general-purpose framework that learns from the entire universe of available structural data, whether it is apo or holo structure. It addresses the core challenge that proteins do not have one single bound state, but rather a diversity of bound conformations induced by a specific ligand. Our goal is to model this entire and ligand-modulated landscape.\n\nA direct comparison is not meaningful because the two models address problems of different scopes. Evaluating a general-purpose model and a specialist model on a single and narrow task is not a fair scientific comparison. However, On the PoseBusters benchmark, DynaPhArM surpasses Re-Dock on the more stringent and chemically meaningful criterion of RMSD < 2Å & PoseBusters-Valid by 10.1%, indicating the ability to generate physically plausible poses.\n\nIn conclusion, we fully acknowledge the importance of Re-Dock. However, due to the **lack of code availability**, **benchmark incompatibility** and **unfairness in problems to be solved**, such a comparison was **not feasible in an fair manner**. But we remain open and committed to future benchmarking efforts once Re-Dock becomes **accessible** to the research community.\n\n---\n# Response to W2: Robustness to Imperfect Priors\nYou've identified a fundamental challenge that we have alreday considered to our design. DynaPhArM is built upon a powerful and self-sufficient data-driven core, with external priors acting as supplementary and adaptive enhancements rather than as foundational core.\n### A Robust Data-Driven Engine\nThe primary strength of DynaPhArM lies in the SE(3)-equivariant Transformer and the physics-based interaction module, which is to learn the protein-drug complex interactions directly from inputs. It does not inherently depend on any pre-computed structural templates or interaction scores to function. This data-driven core is the skeleton of our model and the fundamental reason for our high performance.\n### The Role of Priors\nWe introduced priors like the codebook and interaction scores not as a necessity, but as supplements to boost the performance of our already capable core. We were aware from the outset that these supplements could be imperfect. Therefore, we designed a multi-layered system to mitigate potential risks:\n- Priors as Non-Dominant Guides: FoldToken4 provides a coarse-grained topological overview, while AutoDock offers an initial energy-based hypothesis. These are just two of several information streams. The model’s core is integrating these guides with the more detailed information from the drug and side-chain representations.\n- Inter-Correcting Information: Our model architecture' strength comes from the interconnection of many threads, not from a single one. If one thread (e.g., the prior) is weak, the model has been trained to rely more on the other threads, such as the precise local chemical environments and learned geometric relationships. The final prediction is a result of a powerful data-driven consensus, not from a single prior.\n- Ablation Studies: Our ablation experiments (Appendix, Table 7) validate this design, which show that while removing these priors leads to a performance decrease, the model's functionality remains strong, confirming their role as beneficial enhancers rather than essential components.\n\n---\n# Response to W3: Detailed Hyperparameters\nThank you for your valuable feedback regarding reproducibility. We wholeheartedly agree that comprehensive documentation of hyperparameters is crucial.\n\nWe would like to clarify that we have already provided a detailed list of 30 core hyperparameters in Appendix, Table 6. This initial list covers the most critical parameters that govern the model's architecture, the training loop and the core algorithm.\n\nRecognizing that readers might be interested in an more granular level of configuration, we are happy to provide an additional 20 hyperparameters below, which details auxiliary settings related to data preprocessing, the configurations used for AutoDock Vina and physical loss.\n|Name|Value|Description|\n|---|---|---|\n|`multiprocessing.num_workers`|64|Number of worker processes for parallel tasks|\n|`multiprocessing.chunk_size`|10|Chunk size for multiprocessing pool operations|\n|`drug_preparation.charge_model`|`gasteiger`|Charge model used for ligand preparation|\n|`dataset_split.cd_hit_identity`|0.9|Sequence identity threshold for CD-HIT clustering|\n|`dataset_split.validation_set_ratio`|0.2|Proportion of data for the validation set|\n|`dataset_split.random_seed`|42|Random seed for data splitting|\n|`backbone_encoder_params.num_layers`|4|Number of layers in the backbone encoder|\n|`backbone_encoder_params.l_max_sh`|2|Max degree for spherical harmonics|\n|`sidechain_encoder_params.num_layers`|4|Number of layers in the sidechain encoder|\n|`drug_encoder_params.num_layers`|4|Number of layers in the drug encoder|\n|`decoder_params.num_heads`|4|Number of attention heads in decoder|\n|`training.weight_decay`|1e-5|Weight decay for regularization|\n|`training.validate_every_n_epochs`|1|Validation frequency|\n|`vina_settings.exhaustiveness`|16|Exhaustiveness of Vina search|\n|`vina_settings.energy_range`|3.0|Energy range for modes|\n|`default_bond_length`|1.5|Default bond length|\n|`default_bond_angle_deg`|109.5|Default bond angle|\n|`default_vdw_radius`|1.7|Default VdW radius|\n|`pi_pi_distance_cutoff`|6.0|Max distance between ring centroids|\n|`message_mlp.hidden_dims`|[128,128]|The hidden layer dimensions for the message-passing|\n\n---\n# Response to Q2: Sensitivity to Priors\nThe primary mechanism for robustness against faulty AutoDock priors is the design of our physics-based interaction module. The LJ interaction matrix $S_{ij}^{xy}$ is not a rigid constraint but a soft and additive bias.\n\nThe primary driver of the attention score is the query-key dot product, which captures complex interaction patterns directly from the training data. A strong and data-driven signal from this term can override an incorrect signal from the LJ prior. And $\\gamma_{i}$ is not a fixed hyperparameter but a learnable scalar. During training, its value is optimized via backpropagation to minimize the final prediction loss. If following the LJ prior leads to worse predictions, the gradient will push $\\gamma_{i}$ towards 0. This allows the model to autonomously learn to down-weigh the physical prior on a case-by-case basis.\n\nAnd we have conducted a sensitivity analysis to quantify this effect. To measure the degradation in model performance, we added Gaussian noise with an increasing standard deviation (Noise Level) to the pre-computed LJ matrix.\n\n| Noise Level | Overall RMSD (Å) ↓ | Side-chain RMSD (Å) ↓ | Ligand Success Rate (<2Å) ↑ |\n|---|---|---|---|\n|0.0|2.01|0.29|61.60%|\n|1.0|2.07|0.38|58.10%|\n|2.0|2.10|0.49|54.20%|\n|5.0|2.21|0.55|53.17%|\n|No Prior|2.11|0.59|52.91%|\n- At low noise levels, performance changed very little, as the model's learned data-driven patterns and the adaptive $\\gamma_i$ effectively compensated for minor inaccuracies.\n- At very high noise levels, the prior became actively misleading. The performance degraded, but it did not collapse entirely. The performance plateaued at a level comparable to that of the model trained without any physical prior, demonstrating that the model could learn to effectively ignore a completely useless prior.\n\nIn conclusion, the model is not overly sensitive to errors in the AutoDock-generated LJ potential and can effectively mitigate its impact."}, {"review_id": "rmkQfdjbIo", "reviewer": "Reviewer_ddKX", "summary": "This paper introduces DynaPhArM, an SE(3)-equivariant Transformer model designed for flexible protein-ligand docking. The method aims to capture the dynamic adaptations of a target protein upon binding to different drugs, often referred to as induced fit. Key contributions include a cooperative scalar-vector representation module, a physics-constrained interaction module that incorporates Lennard-Jones potentials as an attention bias, and a diffusion denoising process to model conformational flexibility. The model is trained end-to-end with a multi-task loss function that enforces both structural accuracy (compared to crystal structures) and physical plausibility. The authors demonstrate that DynaPhArM achieves state-of-the-art performance on several benchmarks for complex structure reconstruction, cross-docking, and binding affinity prediction.", "questions": "I have a few key questions and suggestions for the authors. A clear response could significantly strengthen the paper and potentially raise my evaluation score.\n\n1. Clarification of the Cooperative Scalar-Vector Representation: The description of this module in Section 3.1 (lines 114-131) is quite dense and lacks formal equations. Could the authors please provide a more structured description, perhaps with key formulas (similar to those in Section 3.2) ? Specifically, how are the directional messages $h_{ij}$, attention weights $\\alpha_{ij}$, and cross-modal message hinteract formally defined and integrated? This would greatly improve the reproducibility and clarity of this core component.\n\n2. Reframing the \"Dynamic\" Nature of the Model: I appreciate the goal of modeling induced fit, but the term \"dynamic\" may be an overstatement. The model learns from static snapshots and uses static force field rules.  A more precise explanation of how the model generalizes from a set of static structures to predict adaptations for novel ligands would be very insightful. The core question is: is the model truly simulating a process, or is it performing pattern recognition to predict a likely end-state conformation?\n\n3. Elucidation of the Diffusion Process and Flexibility: On line 173, you state the diffusion process starts from the initial joint embedding e_f \"Instead of sampling from a Gaussian prior.\" This is confusing. The forward process of a DDPM typically adds Gaussian noise to reach a standard normal distribution $N(0, I)$. The reverse process then learns to denoise from this distribution. Please clarify:\n\n(a) What is the exact nature of the noise distribution at step T? If not N(0, I), what is it and why?\n\n(b) How does this specific diffusion process better \"reflect conformational flexibility\" compared to a standard DDPM? The flexibility learned here appears to be a statistical interpolation between different static states in the training data. Could you elaborate on why this should be considered a robust representation of physical flexibility, especially when compared to methods that use, for example, MD simulation data or normal mode analysis?\n\n4. Providing More Training Dataset Statistics: The performance of a data-driven model is critically dependent on its training data. Could you please provide more detailed statistics about the curated training set of 21,762 complexes? Key information would include:\n\n- The distribution of the number of unique ligands per protein target.\n\n- The number of protein targets that have, for example, >5, >10, or >20 different co-crystal structures in the dataset.\n\n- A breakdown of the protein families represented.\n\nThis information is crucial for the community to understand the scope and potential biases of the training data and to fairly assess the model's ability to generalize to targets with sparse structural information. A positive response with these details would significantly increase my confidence in the model's claimed ability to capture drug-specific adaptations.", "limitations": "Yes, the authors have included a dedicated limitations section in Appendix L, which is commendable. They discuss dependency on input structure quality, the computational overhead of the diffusion module, and assumptions about task importance. The discussion is transparent and constructive. No further suggestions on this point.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n1. Novel and Comprehensive Architecture: The proposed architecture is sophisticated and well-motivated. Integrating an SE(3)-equivariant framework, a diffusion model for flexibility, and physics-based priors into a single end-to-end model is a non-trivial and powerful approach for flexible docking.\n\n2. Strong Empirical Results: The model demonstrates impressive performance across a wide range of tasks and challenging datasets. Achieving top results in both structure prediction (low RMSD) and downstream binding affinity prediction (high PCC) suggests that the generated conformations are not only geometrically accurate but also biochemically meaningful.\n\n3. Emphasis on Physical Plausibility: The inclusion of a detailed physics and geometry-guided loss function is a significant strength. This addresses a common pitfall of deep learning models, ensuring that the generated structures adhere to fundamental chemical principles, which is critical for real-world drug design applications.\n\n**Weaknesses**\n1. Clarity of Model Description: The description of key model components, particularly the \"Cooperative scalar-vector representation\" (Section 3.1), lacks clarity. The text describes a complex update mechanism without accompanying formulas in the main text, making it difficult for readers to fully grasp the implementation details.\n\n2. Potentially Overstated Claims on \"Dynamics\": The paper claims to model \"dynamic alterations\" and \"evolving dynamics.\" However, the \"dynamic\" information seems to be primarily derived from static structural data (PDB) and static physics priors (Lennard-Jones potentials from AutoDock). This is fundamentally different from simulating a physical trajectory (e.g., via MD). The term \"dynamic\" could be misleading and warrants more precise framing.\n\n3. Ambiguity in the Diffusion Process and Flexibility Claims: The description of the diffusion process is confusing. The authors state their process does not sample from a Gaussian prior (line 173) but later use DDPM, which traditionally involves Gaussian noise. This needs clarification. Furthermore, the claim that the generated \"conformational flexibility\" is a reflection of dynamics is questionable, as it is learned from a collection of static snapshots rather than true temporal data, and the generated latents are 'pseudo-flexibility'.\n\n4. Insufficient Detail on the Training Dataset: As a data-driven method, the composition of the training set is paramount. The paper provides only the total number of complexes (21,762) but lacks crucial statistical details. For the model to genuinely learn \"drug-specific adaptations,\" the dataset should contain a sufficient number of targets with multiple, diverse ligand-bound structures. The lack of this information makes it hard to assess whether the model's capabilities stem from a truly diverse dataset or from memorizing patterns in a few well-represented protein families, e.g., kinases.", "was_revised": true, "final_justification": "Most of my questions and concerns have been addressed during the rebuttal period. Therefore, I decided to raise my score to 4.", "rebuttal": "**Dear Reviewer ddKX:**\n\nWe thank you for your thorough evaluation and insightful feedback. Our response to your suggestions and questions is as follows:\n\n---\n# Response to W1 and Q1: Clarification of the Cooperative Scalar-Vector Representation\nThank you for this critical feedback regarding the clarity of the model description in Section 3.1. We agree completely that the absence of accompanying formulas in the main text makes the mechanism difficult to fully understand.\n\nTo address this, we will revise Section 3.1 in the final manuscript. Here, we would like to provide the clear explanation.\n\nOur cooperative mechanism enhances standard message passing by ensuring a bidirectional coupling between scalar $h\\in\\mathbb{R}$ and vector $v\\in\\mathbb{R}^3$ features at each node i. For each layer of the encoder, the update proceeds in three main steps:\n### Step 1: Gated Message Aggregation\nWe first compute an aggregated message $m_{i}$ for each node i from its neighbors $j\\in\\mathcal{N}(i)$. The directional message $h_{ij}$ is defined by concatenating the scalar features of the interacting nodes $(h_i,h_j)$ and a learned encoding of the edge's geometric features (derived from the relative vector $v_j-v_i$):\n\n$h_{ij} = \\phi_m(h_i, h_j, \\text{SH}(v_j - v_i))$, where $\\phi_{m}$ is a MLP and $\\mathrm{SH}(\\cdot)$ is the Spherical Harmonic expansion.\n\nThe attention weights $\\alpha_{ij}$ are then computed from these messages using a learnable attention network $\\phi_{a}$ followed by a softmax over the neighborhood: $\\alpha_{ij} = \\text{Softmax}j(\\phi_a(h{ij}))$. \n\nThese are then used to compute the final aggregated message $m_{i}$ for node i: $m_i = \\sum_{j \\in \\mathcal{N}(i)} \\alpha_{ij} \\cdot h_{ij}$.\n### Step 2: Independent Scalar and Vector Updates\nThe aggregated message $m_{i}$ is used to update the scalar and vector features, yielding intermediate representations $h_i^{\\prime}$ and $v_i^{\\prime}$: $h_i^{\\prime}=\\mathrm{MLP}_h(h_i,m_i)\\quad,\\quad v_i^{\\prime}=v_i+\\mathrm{MLP}_v(m_i)$.\n### Step 3: Cooperative Bidirectional Feedback\nThis final step defines and integrates the cross-modal message $h_{\\mathrm{interact,}i}$ to create a coupling between the scalar and vector channels. The cross-modal message $h_{\\mathrm{interact,}i}$ is defined as the inner product of the updated vector features and a transformation of the updated scalar features: \n\n$h_{\\text{interact}, i} = \\text{MLP}_{\\text{interact}}(h'_i) \\cdot v'_i$\n\nThis message is then integrated as a feedback signal to update both channels simultaneously. Each channel is also residually boosted by the squared norm of the other, enabling true bidirectional information flow.\n\n---\n# Response to W2 and Q2: Reframing \"Dynamic\"\nYou correctly pointed out that our use of the term \"dynamic\" requires a more precise definition, as our method is fundamentally different from one that simulates a physical trajectory like MD. Your characterization of our model as \"performing pattern recognition to predict a likely end-state conformation\" is a more precise description of our core methodology. \n### 1. Biological Dynamics vs. Physical Dynamics\nPhysical Dynamics involves simulating the time-evolution of a system at the atomic level. It models the literal and femtosecond-by-femtosecond process of binding. DynaPhArM does not do this.\n\nOur work focuses on modeling **Biological Dynamics**. We define this as the conformational adaptability of a protein in response to a ligand, encompassing crucial phenomena like induced fit, conformational selection or allosteric regulation. These events occur over longer timescales (microseconds to milliseconds) and result in the protein settling into a stable and ligand-specific conformation.\n### 2. Learning Dynamics from Static Snapshots\nThe \"dynamic\" information in our model is not derived from simulating a trajectory but from learning the underlying patterns within a massive set of experimental end-states (PDB). Each structure is an experimental snapshot of a successful induced fit event. Collectively, the different structures of the same protein bound to different ligands form a static protein's biological plasticity.\nOur diffusion model learns the entire probability distribution of experimentally-observed end-state conformations. The basins in the conformations are the clusters of observed PDB structures, and the pathways between them are the geometrically plausible transitions implicitly learned by the diffusion model.\n### 3. Generalization\nWhen presented with a novel ligand, our SE(3)-equivariant encoders analyze its unique chemical and geometric features. The model then uses the vast patterns learned from the entire training set to infer the most probable outcome. It essentially asks: \"Based on the thousands of induced-fit events I have seen, what is the most likely conformational adaptation this specific protein will undergo to optimally accommodate the features of this specific new ligand?\" It generalizes by recognizing similarities and differences, allowing it to predict a specific end-state conformation without ever simulating the process of getting there.\n### 4. A More Precise Framing of \"Dynamic\"\nTherefore, we concede that using \"dynamic\" without the above context can be misleading. In our framework, \"dynamic\" refers to the model's **Adaptability**. It describes the model's ability to dynamically generate a specific and adapted protein conformation that is conditional on the unique input ligand. We will revise the language in our manuscript to more clearly articulate this important distinction.\n\n---\n# Response to W3 and Q3: Clarification of Diffusion\nWe apologize for the confusing sentence in line 173. You are absolutely correct that our model employs a standard conditional DDPM and we will correct the text to describe it accurately. \n\n### 1. What is the exact nature of the noise distribution at step T?\nThe noise distribution at the final timestep T is a standard normal distribution $\\mathcal{N}(0,I)$ as is standard in DDPMs. Our forward process is defined by adding Gaussian noise to the clean embedding $e_0=e^f$. Our implementation does not deviate from this DDPM principle. The confusing sentence in line 173 was a misguided attempt to describe the inference process. During inference, we start with a pure noise vector $e_T\\sim\\mathcal{N}(0,I)$ and perform the reverse process. This denoising is **conditioned** on the input protein and ligand (information encoded in $e^f$). The process is not starting from $e^f$, but rather it is guided by the information in $e^f$ to denoise a random vector towards a refined embedding.\n### 2. How does this specific diffusion process better \"reflect conformational flexibility\"?\nOur process is a standard conditional DDPM. Your characterization of the learned flexibility as a \"statistical interpolation between different static states\" is a technically accurate description. While your description is accurate, we must emphasize that this \"statistical flexibility\" is not a simplified approximation of MD's \"physical flexibility.\" Rather, it represents a fundamentally different and intentionally distinct approach aimed at modeling biological adaptability, which is the discrete and functional outcomes of ligand binding—rather than the continuous, time-resolved trajectory of the binding process itself.\n- MD (Physical Dynamics): It is powerful for studying the process but is often computationally limited to short timescales and may struggle to sample large-scale conformational changes.\n- DynaPhArM (Biological Flexibility): The PDB itself is a vast database of biological flexibility. It contains hundreds of different stable conformations of the same protein after binding to hundreds of different ligands. These snapshots are direct evidence of biological flexibility. DynaPhArM is explicitly designed to learn the rules of this biological flexibility. This is more than just a simple interpolation; it is a learned model of the biological conformational landscape. By training on tens of thousands of static snapshots, our model bypasses the intractable sampling problem of simulating the process. \n\nThis \"statistical\" or \"pseudo-flexibility\" is a core strength. It allows us to model the large-scale conformational changes that are critical for drug discovery and inaccessible to MD.\n\n---\n# Response to W4 and Q4: Training Dataset Statistics\nWe agree that providing detailed statistics is essential for assessing the model's ability. We have performed a detailed analysis of our full learnable dataset. The results summarized in the table below, confirm that the dataset is sufficiently large and diverse to support the learning of generalized principles of protein-ligand interaction. We will include this table and a discussion of these statistics in our final manuscript.\n\n|Category|Metric|Value|\n|---|---|---|\n|Overall Dataset Size|Total Complexes|21,762|\n||Unique Protein Targets|3,673|\n|Ligand Diversity|Mean Unique Ligands per Target|6.57|\n||Median Unique Ligands per Target|3.0|\n||Targets with > 5 Unique Ligands|917|\n||Targets with > 10 Unique Ligands|444|\n||Targets with > 20 Unique Ligands|200 |\n|Structural Diversity|Targets with > 5 Co-crystal Structures|609|\n||Targets with > 10 Co-crystal Structures|318|\n||Targets with > 20 Co-crystal Structures|148|\n|Protein Family Diversity|HYDROLASE|16.6%|\n||TRANSFERASE|16.0%|\n||HYDROLASE/INHIBITOR|10.3%|\n||TRANSFERASE/INHIBITOR|10.1%|\n||TRANSCRIPTION|3.6%|\n\n- Sufficient Data for Drug-Specific Adaptations: The data clearly shows that a significant portion of our dataset consists of proteins with multiple and diverse ligands. With 917 targets having more than five unique ligands, the model has a strong foundation to learn the principles of induced fit.\n- Broad Target and Family Coverage: The presence of over 3,600 unique protein targets distributed across a wide range of families ensures the model must learn generalizable rules of molecular recognition rather than memorizing family-specific patterns."}, {"review_id": "eETaFAWm8C", "reviewer": "Reviewer_6u6X", "summary": "The paper introduces DynaPhArM, a physical constrained diffusion model for accurately modeling target-drug complexes at the atomic level, addressing the limitations of traditional rigid transformation methods that fail to capture dynamic conformational changes. DynaPhArM proposes a cooperative scalar-vector representation, drug-specific embeddings, and a diffusion process to model evolving target-drug interactions, while integrating physical constraints within a multi-task learning framework to ensure geometric and energetic plausibility. Experimental results demonstrate state-of-the-art performance in complex structure reconstruction.", "questions": "See Weakness", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strength**\n\n1. The method is well motivated.\n\n2. The paper is well structured, and each module is provided with sufficient motivation and detailed explanations.\n\n3. The experiments are comprehensive.\n\n4. Open-source code is provided to facilitate the reproduction of the paper's results.\n\n**Weakness**\n\n1. In the interaction module, the magnitude of $\\gamma_i$ may cause the gradient to be dominated by the physical matrix, leading the model to overfit priors and ignore novel interaction patterns. How do DynaPhArM ensures that the learned $\\gamma_i$ is the optimal result?\n\n2. DynaPhArM relies on a physical-constrained interaction matrix calculated via LJ potential, which may affect the generalizability. For example, when encountering new binding modes not previously modeled by the model which is used to calculate the LJ potential, DynaPhArM might fail to accurately describe interactions, causing attention to deviate from true binding sites.\n\n3. Compared to methods like DynamicBind, DynaPhArM does not introduce conformational entropy terms or diversity rewards in the loss function, potentially biasing generated structures toward common modes. How is the diversity issue addressed is DynaPhArM?\n\n4. In the cooperative scalar-vector representation algorithm, what is the setting of the spherical harmonic expansion order $L$ (Appendix D - Algorithm 2 - line 19), and how does this parameter setting impact the model?\n\n5. I suggest that authors can provide specific metrics such as FLOPs and model parameter counts to better present the model complexity.", "was_revised": true, "final_justification": "The authors have addressed most of my concerns. I maintain my positive score.", "rebuttal": "**Dear Reviewer 6u6X:**\n\nWe thank you for your thorough evaluation and insightful feedback. Our response to your suggestions and questions is as follows:\n\n---\n# Response to W1: Mechanism for Physical Priors\nYou are correct that an uncontrolled $\\gamma_{i}$ could lead to overfitting and discovering novel patterns. However, our model's architecture is specifically designed to prevent them. Its core mechanism ensures that $\\gamma_{i}$ is not an uncontrolled variable, but rather a learnable parameter that balances physics-based guidance with dominant and data-driven patterns.\n### 1. Safeguards Against Overfitting and the Suppression of Novel Patterns\n- Primacy of the Data-Driven Term: The core of our physics-base dattention is an additive combination $\\text{Attention Score}\\propto Q_iK_i^\\top+\\gamma_iS_{ij}^{xy}$. The data-driven term $Q_iK_i^\\top$ is the primary engine for learning. Our powerful SE(3)-equivariant encoders are trained to capture all complex patterns from the ground-truth data. If a novel interaction pattern (e.g., a halogen bond, a cation-π interaction) is present in the data, the encoders will produce distinct embeddings for atoms, which results in a signal in $Q_iK_i^\\top$, which can override conflicting guidance from the LJ prior, ensuring the model's attention is not blinded.\n- Supervision from the Physical Loss: Beyond matching the ground truth, the final generated coordinates are also evaluated by the physical loss. If a novel pattern corresponds to a perfect hydrogen bond, the term will provide a reward for forming this geometry, which provides a direct gradient signal that incentivizes the model to learn these patterns, even if they are not captured by the LJ potential. The self-regulating nature of the learnable $\\gamma_i$ supervised by $\\mathcal{L}_{phy-geo}$, ensures that the influence of the LJ prior is down-weighted when novel patterns are present.\n### 2. The Mechanism for Ensuring an Optimal $\\gamma_i$\nThe optimality of $\\gamma_i$ is ensured because it is a learnable parameter optimized end-to-end to minimize the total loss. The optimal $\\gamma_i$ is defined as the value that maximally contributes to the model's goal: producing a structure that is simultaneously accurate with respect to the ground truth structure loss and physically plausible loss. The gradient descent process naturally drives $\\gamma_i$ towards this optimum. Any value of $\\gamma_i$ that leads to a suboptimal outcome is self-corrected. If $\\gamma_i$ is too large or small,  which will result in a high loss. The gradient from this high total loss will flow back and adjust $\\gamma_i$. \n### 3. Experimental Evidence\nWe conducted an experiment where we removed the physics-based interaction module, which is equivalent to forcing $\\gamma_i$=0.\n|Model|Overall RMSD↓|Side-chain RMSD↓|Ligand RMSD↓|Overall RMSD <2Å ↑|sc-RMSD <2Å ↑|L-RMSD <2Å ↑|\n|---|---|---|---|---|---|---|\n|DynaPhArM|2.01|0.29|2.17|65.30%|70.50%|61.60%|\n|w/o physics-based module|2.11|0.59|2.70|60.87%|57.45%|52.91%|\n- As shown, the degradation in performance is not catastrophic, which proves that $\\ gamma_i $does not play a dominant role in the gradient of the model. The prior is a beneficial guide, but the model is not critically dependent on it.\n---\n# Response to W2: Generalization to Novel Binding Modes\nThe concern that the LJ potential might bias the attention mechanism away from novel binding modes is valid, and our architecture is designed with a multi-layered strategy to specifically address this.\n### 1. LJ Prior Is Not a Definitive Guide\nWe do not employ the LJ prior as a specific interaction model. Instead, its primary function is to act as a foundational physical regularizer. We make two key simplifications: (1) we use a heavy-atom model, ignoring all hydrogen atoms, and (2) we employ a generalized parameter set rather than a specific molecular force field. These choices are intentional. The prior's most significant contribution is the strong repulsive term $r^{-12}$, which provides a universal gradient against steric clashes. We delegate the responsibility of discovering and modeling these sophisticated patterns to the data-driven components of our model.\n### 2. The Encoder as the Discovery Engine\nThe true engine for identifying all interaction patterns is our SE(3)-equivariant encoder. If a novel binding mode is present in the training data, especially one involving interactions that our simplified LJ prior cannot capture, the encoder is incentivized by the loss function to learn a unique feature representation for that pattern, which is encoded in the Q and K vectors, becomes the primary signal for the attention mechanism. The LJ term acts only as an auxiliary bias on top of this data-driven signal.\n### 3. The Diffusion Process as a Safeguard for Generalization\nDynaPhArM learns the conditional probability distribution $p(\\mathrm{structure}\\mid\\text{protein, ligand})$, which is shaped by all binding modes observed in the training data. The LJ prior helps to shape this landscape by penalizing physically impossible regions (i.e., assigning them near-zero probability), but the locations of the high-probability regions (the valid binding modes) are determined by the training data itself.\n\nBecause the model learns a full distribution, it inherently captures the diversity of interactions present in the data, including novel ones. The inference process is guided towards high-probability regions, not just regions that have low LJ energy. This ensures that even if the LJ prior is uninformative for a novel binding mode, the model can still generate the correct structure.\n\n---\n# Response to W3: Addressing Conformational Diversity without Explicit Rewards\nYour question highlights a key design choice in modern generative models: whether to enforce diversity explicitly through the loss function or implicitly through the model's architecture and sampling procedure.\n\nUpon careful review of the DynamicBind, we respectfully note that its core loss function (Equation 15 in their paper) also appears not to contain an explicit conformational entropy term or diversity reward. DynamicBind explicitly states this in their inference procedure: \"... For each pair, we perform 40 samplings...\" This confirms that they also rely on multiple stochastic trajectories to generate a diverse pool of candidate structures.\n- Explicit Diversity: Involves adding a specific term to the loss function to directly reward the model for generating a diverse set of outputs.\n- Implicit Diversity: Involves using a generative model that learns the underlying probability distribution of the data. Diversity is then achieved naturally by sampling from this learned distribution.\n\nDynaPhArM is designed around the implicit diversity paradigm.\n### 1. The Fundamental Goal of DDPMs\nThe training objective of a DDPM is not to learn a deterministic map to the most common (lowest energy) conformation. Instead, its goal is to learn the conditional probability distribution $p(\\mathrm{structure}\\mid\\text{protein, ligand})$. If the training data contains multiple distinct binding conformations, the DDPM is inherently trained to be able to reconstruct all of them from noise.\n### 2. Diversity is a Natural Consequence\nThe diversity of generated structures is a direct and natural consequence of the stochastic nature of the DDPM's reverse sampling process. Each denoising step introduces a small, random component, meaning that no two full sampling trajectories are identical.\nFor a single protein-ligand input, running the inference process multiple times will yield a different conformation each time. This naturally produces a conformational ensemble that reflects the diversity, without the need for an external diversity-promoting term in the loss function.\n\nIn conclusion, DynaPhArM addresses the diversity issue implicitly but fundamentally like other state-of-the-art generative models such as DynamicBind.\n\n---\n# Response to W4: Pherical Harmonic Expansion Order\nThe spherical harmonic expansion order L is a hyperparameter that defines the resolution of the angular information. Our analysis below reveals that L=2 offers a compelling alternative with a much better trade-off between performance and computational efficiency, achieving over 97% of the peak success rate with only ~50% of the training cost. \n\n|Expansion Order|Overall RMSD (Å) ↓|Side-chain RMSD (Å) ↓|Ligand Success Rate (<2Å) ↑|Relative Training Time|\n|---|---|---|---|---|\n|1|2.31|0.45|55.8%|0.7x|\n|2 (Our Choice)|2.01|0.29|61.60%|1.0x|\n|5|1.98|0.25|63.29%|1.9x|\n|8|2.09|0.42|57.97%|2.8x|\n- Performance at L=1 is lower, confirming that simple and dipole-like features are insufficient for this complex task. A leap in performance is observed at L=2, where quadrupole-like features proves critical for modeling anisotropic properties like planarity and bond angle distributions, establishing a strong performance-to-cost baseline. The model achieves its peak performance at L=5, suggesting that these higher-resolution harmonics are beneficial for capturing details, though this comes at the cost of nearly doubled training time (1.9x). However, L=8 leads to a degradation in performance which combined with a nearly 3x increase in computational cost.\n---\n# Response to W5: Model Complexity\nWe agree that providing specific metrics is essential for a quantitative presentation of our model's complexity. We have analyzed our model and will add these details to the final version of our manuscript.\n\nOur model has a total of 45.6 million trainable parameters. We achieve state-of-the-art performance with a model that is an order of magnitude smaller, highlighting the effectiveness of our novel architectural components in achieving high performance without resorting to a massive parameter count.\n\nIn terms of computational cost, a single forward pass on a typical medium-sized protein-ligand complex requires approximately 35.8 GFLOPs. This workload is very manageable for modern GPUs."}, {"review_id": "75YHMH3qWR", "reviewer": "Reviewer_hzse", "summary": "This paper presents DynaPhArM, an SE(3)-Equivariant Transformer framework that dynamically models target-drug interactions with physics-based constraints. By integrating a cooperative scalar-vector encoding, a discretization module, physics-aware cross-attention, and a diffusion process, the model captures atomic-level flexibility and conformational dynamics in protein–ligand binding. Empirical evaluations demonstrate state-of-the-art performance in complex reconstruction, cross-docking, and binding affinity prediction.", "questions": "1. What do the variables $L_b$, $L_s$, and $d_e$ in line 154 represent? \n2. How much computational overhead is introduced by the Lennard-Jones potential term? Is there profiling or ablation study on its effect?\n3. Why does the paper not include a comparison with AlphaFold 3 on the PoseBusters benchmark, given AlphaFold 3 is a strong baseline?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 4, "originality": 3, "strengths_and_weaknesses": "**Strengths** \n1. The model integrates physical constraints and structural knowledge, with clearly motivated module design.\n2. The paper is well-organized, and the appendices are comprehensive.\n3. It significantly enhances the flexible modeling of protein–drug complexes and achieves state-of-the-art results across multiple downstream tasks.\n\n**Weaknesses**\n1. The discussion in the introduction regarding the pros and cons of Transformers and GNNs lacks clear connection to the paper’s motivation.\n2. Figure 5's annotation is confusing, reducing clarity of the visual results. For example, in line 726, it is unclear what the 40% refers to, and whether the PoseBusters (PB) success rate overlaps with the overall success rate.\n3. The detailed dataset descriptions in Section 4.1 could be moved to the appendix to make space for more experimental results, such as the ablation studies currently in Appendix I.\n\n*Typo*\n\nLine 719: “Te” → “The”.", "was_revised": true, "final_justification": "The authors have addressed most of my concerns satisfactorily.\nI maintain my positive score.", "rebuttal": "**Dear Reviewer hzse:**\n\nWe thank you for your thorough evaluation and insightful feedback. Our response to your suggestions and questions is as follows:\n\n---\n# Response to W1: Discussing Transformers and GNNs in the Introduction\nThe discussion of Transformers and GNNs is central to our introduction as it frames the technical gap that DynaPhArM was designed to address. Our introduction is built upon the following logical progression:\n### 1. The Core Problem in the Field\nAs we state in the first two paragraphs of our introduction, the primary challenge in modern molecular docking is accurately modeling protein and ligand flexibility. It requires a model to operate effectively at two distinct scales simultaneously:\n\n- Global Scale: Capturing large-scale and long-range conformational changes that can reshape the binding site.\n- Local Scale: Modeling the fine-grained and geometrically-precise rearrangements of sidechains and the ligand within the binding pocket that determine the final and accurate binding pose.\n\n### 2. The State-of-the-Art Solutions and Trade-off\nHaving established this multi-scale problem, our introduction then surveys the two dominant architectures being applied to solve it. Our discussion is intended to show that the current state-of-the-art presents a fundamental trade-off, with each paradigm excelling at one scale at the expense of the other:\n\n- Transformers (Paragraph 3): We present Transformers as the natural architectural choice for the global scale. Their self-attention mechanism is powerful at capturing the long-range dependencies necessary for modeling large-scale dynamics. However, we note their weakness in handling the local scale and fine-grained geometric details of the binding site.\n- GNNs (Paragraph 4): We then present GNNs as the canonical solution for the local scale. The message-passing formulation is well-suited for local chemical environments and interactions. However, we note their weaknesses at the global scale, difficulty in capturing long-range effects and a lack of SE(3)-equivariance for handling global rotations and translations.\n\n### 3. DynaPhArM as the Motivated Solution\nThis established trade-off is the direct motivation for DynaPhArM. Our discussion of GNNs and Transformers serves to directly motivate our specific design choices, which represent a synthesis of the strengths of both of them:\n\nWe chose an SE(3)-Transformer as our framework to inherit its superior global, long-range modeling capabilities and native handling of 3D geometry.\n\nWe then explicitly address the Transformer's weakness at the local scale by introducing novel mechanisms, such as the cooperative scalar-vector representation and the physics-based interaction module, that are designed to infuse the model with the strong local-reasoning characteristic of GNNs.\n\nIn summary, the GNNs and Transformers discussion is the essential context that frames our central motivation: to create a unified architecture that resolves the \"local vs. global\" trade-off for flexible docking. \n\n---\n# Response to W2: Clarity of Figure 5\nWe agree that the annotations and the relationship between the presented metrics should be explained more clearly.\n### 1. Clarification of the Two Metrics\nThe two metrics are designed to evaluate performance from geometric accuracy and physico-chemical validity.\n- Overall Success Rate: A metric of pure geometric accuracy. We define it as the percentage of predicted poses for which the overall RMSD to the crystal structure is less than 2.0 Å. \n- PB Success Rate: A stricter metric that evaluates both geometric accuracy and physico-chemical realism. For a pose to be considered a PB Success, it must be geometrically accurate (Overall RMSD < 2.0 Å) and pass all the chemical and physical validity checks imposed by the PoseBusters toolkit.\n\nTherefore, the PB Success Rate is a strict subset of the Overall Success Rate.\n### 2. Clarification of Percentage Values\nThe phrase \"performance to nearly 40%\" in line 726 refers specifically to the PB Success Rate for the TankBind method.\n\nTo be precise, this sentence means: \"For the TankBind model, when evaluated on the PoseBusters test set, nearly 40% of the predicted complex structures had a RMSD of less than 2.0 Å  and passed the rationality check. \"\n### 3. Planned Revisions for the Final Manuscript\nWe will make the following revisions in the final version of the paper:\nRevise Figure 5's Legend: We will update the legend to be more self-explanatory: Overall Success Rate (RMSD < 2.0 Å), PB Success Rate (RMSD < 2.0 Å & Passes Rationality Checks).\n\nEnhance Figure 5's Caption: We will add a sentence to the figure caption (e.g., \"The PB Success Rate is a subset of the Overall Success Rate, requiring poses to be both geometrically accurate and physically valid according to the PoseBusters toolkit.\").\n\nClarify the Main Text: We will revise the text in line 726 to ensure the interpretation of these metrics is unambiguous.\n\n---\n# Response to W3: Restructuring the Paper\n\nThank you for this helpful suggestion on improving the structure of our paper. We agree that the ablation studies which provide critical evidence for our model's key components would be more impactful if presented in the main text.The detailed descriptions of the benchmark datasets can be summarized in the main paper with the full details deferred to the appendix.\n\n---\n# Response to Q1: Clarification of the Notation\nThe variables $L_b$, $L_s$, $d_e$ are used to define the dimensions of the input feature embedding tensors for the different components of the protein-ligand complex. \n- $L_b$ represents the number of nodes in the protein backbone. Each node in the backbone graph corresponds to a single residue. $L_b$ is the sequence length of the protein target.\n- $L_s$ represents the number of nodes in the protein side-chain. In our atom-level graph for the side-chain, each node corresponds to a single heavy atom.\n- $d_e$ represents the dimensionality of the node feature embeddings. It is a hyperparameter that defines the length of the feature vector used to represent each node, whether it is a residue in the backbone or an atom in the side-chains or the drug.\n\n---\n# Response to Q2: Overhead and Efficacy of the LJ Potential\nWe have carefully considered both the computational cost and the performance of the LJ potential.\n\n### 1. Computational Overhead\n- Offline Pre-computation: The LJ interaction matrices are pre-computed offline before any model training begins. This process took approximately 1.1 hours on a single NVIDIA RTX 4090 GPU. We consider this a manageable one-time cost for generating a valuable physical prior that can be reused for all subsequent experiments.\n- Online Training/Inference: During the model's forward pass, the overhead from the LJ is practically negligible. The only additional operations are loading the pre-computed matrix from disk (an I/O operation) and performing a single element-wise addition to the attention scores. Our profiling indicates that including the LJ increases the runtime of the attention block by less than 1%.\n\n### 2. Ablation Study\nYes, we have performed a specific ablation study to quantify theLJ potential, the results of which are presented in Table 7 of our Appendix. We trained a variant of DynaPhArM where the \"physics-based interaction module\" was replaced with removing the LJ prior.\n\n|Model|Overall RMSD↓|Side-chain RMSD↓|Ligand RMSD↓|Overall RMSD <2Å ↑|sc-RMSD <2Å ↑|L-RMSD <2Å ↑|\n|---|---|---|---|---|---|---|\n|DynaPhArM|2.01|0.29|2.17|65.30%|70.50%|61.60%|\n|w/o physics-based module|2.11|0.59|2.70|60.87%|57.45%|52.91%|\n\nThis ablation study provides quantitative evidence that the LJ potential is not just a minor addition but a critical component that contributes to the model's accuracy by providing an effective physical inductive bias.\n\nIn summary, the LJ potential term is a cost-effective design choice, introducing negligible computational overhead during runtime while providing an improvement in model performance.\n\n---\n# Response to Q3: Comparison with AlphaFold 3\nWe acknowledge that AF3 has demonstrated state-of-the-art performance on benchmarks like PoseBusters.\n\nHowever, our decision not to include a head-to-head comparison reflects the fact that DynaPhArM was not designed to compete with AF3 on raw accuracy, but rather to address a different challenge in the drug discovery.\n### 1. The Performance and Computational Cost\nAF3 is a resource-intensive model, requiring high-end GPUs, which makes it challenging for many research groups to run locally for large-scale tasks like high-throughput virtual screening. DynaPhArM is to create a highly efficient and lightweight alternative, which makes rapid cycles feasible for a broader scientific community, which is a problem AF3 is not optimized to solve.\n### 2. A Specialist Tool for a Specific Problem\nThis efficiency is achieved because we are building a specialist tool, not a generalist one. AF3 is a phenomenal achievement designed to tackle the entire challenges of structural biology predicting interactions between proteins, DNA, RNA, and ligands. DynaPhArM is focused on one specific problem: the modeling of drug-target adaptability.\n### 3. A Different Value Proposition\nUltimately, this leads to a different value proposition centered on cost-effectiveness. For many real-world tasks in drug development, achieving robust results with extreme speed is more valuable than achieving top accuracy at a high computational cost. Our method provides an optimal balance for this specific case.\n\nIn summary, while we openly acknowledge AlphaFold 3 as the current leader in raw predictive accuracy, our paper's contribution lies elsewhere. We present DynaPhArM as a complementary tool that fills a crucial gap, specifically tailored to the demands of structure-based drug discovery. We believe its value should be judged on these merits, rather than on a single performance metric."}]

Author rebuttal:

Meta-review: This paper introduces DynaPhArM, a novel SE(3)-equivariant Transformer framework for flexible protein-ligand docking that integrates a diffusion model and physics-based constraints. The initial reviews were unanimously borderline, praising the sophisticated architecture and strong empirical results but raising valid concerns about the clarity of certain components, the framing of the term "dynamics," the lack of dataset statistics, and missing comparisons to recent baselines. The authors provided an exceptionally thorough and convincing rebuttal that systematically addressed nearly all of these points. They supplied missing formulas, provided a detailed breakdown of their training data, clarified the diffusion process, and offered sound justifications for the absence of comparisons to models like Re-Dock and AlphaFold 3. This led to a very positive discussion, with one reviewer raising their score and two others explicitly stating their concerns were resolved and maintaining their support. While one reviewer remained unresponsive, the overall consensus after the rebuttal period is that the paper presents a significant, well-motivated, and technically sound contribution to computer-aided drug design. The initial concerns have been effectively mitigated, and the work's strengths in modeling conformational adaptability with physical plausibility are clear. Therefore, I recommend acceptance.
Decision: Accept (poster)