Boosting Protein Graph Representations through Static-Dynamic Fusion
Authors: Pengkang Guo
Bruno Correia
Pierre Vandergheynst
Daniel Probst
Venue: ICML 2025 poster (2025)
Keywords: Graph Neural Networks
Protein Modeling
Molecular Dynamics
Heterogeneous Graph
Primary area: deep_learning->graph_neural_networks

Abstract: Machine learning for protein modeling faces significant challenges due to proteins' inherently dynamic nature, yet most graph-based machine learning methods rely solely on static structural information. Recently, the growing availability of molecular dynamics trajectories provides new opportunities for understanding the dynamic behavior of proteins; however, computational methods for utilizing this dynamic information remain limited. We propose a novel graph representation that integrates both static structural information and dynamic correlations from molecular dynamics trajectories, enabling more comprehensive modeling of proteins. By applying relational graph neural networks (RGNNs) to process this heterogeneous representation, we demonstrate significant improvements over structure-based approaches across three distinct tasks: atomic adaptability prediction, binding site detection, and binding affinity prediction. Our results validate that combining static and dynamic information provides complementary signals for understanding protein-ligand interactions, offering new possibilities for drug design and structural biology applications.

Boosting Protein Graph Representations through Static-Dynamic Fusion
Pengkang Guo Bruno Correial
Pierre Vandergheynst'
Daniel Probst
Abstract
sche et al., 2024; Siebenmorgen et al., 2024a; Liu al., 2024). Consequently, various approaches are being devel- oped to train predictive and generative models capable of producing molecular dynamics trajectories or sample spe- cific conformations (López-Correa et al., 2023; Jing et al., 2024; Lewis et al., 2024). So far, the potential of these increasingly large trajectory datasets enhance property predictions in proteins and protein-ligant complexes, such as binding site identification and affinity prediction, remains largely unexplored (Dhakal et al., 2022).
Machine learning for protein modeling faces sig- nificant challenges due to proteins' inherently dynamic nature, yet most graph-based machine learning methods rely solely on static structural information. Recently, the growing availability of molecular dynamics trajectories provides new op- portunities for understanding the dynamic behav- ior of proteins; however, computational methods for utilizing this dynamic information remain lim- ited. We propose novel graph representation that integrates both static structural information and dynamic correlations from molecular dynamics trajectories, enabling more comprehensive model- ing of proteins. By applying relational graph neu- networks (RGNNs) to process this heteroge- neous representation, we demonstrate significant improvements over structure- based approaches across three distinct tasks: atomic adaptability prediction, binding site detection, and binding affinity prediction. Our results validate that com- bining static and dynamic information provides complementary signals for understanding protein- ligand interactions, offering new possibilities for drug design and structural biology applications.
Despite these advances, representing and exploiting molec- ular dynamics trajectories of proteins for machine learning remains challenging due to the diverse and complex nature of protein structures. One effective alternative focus on higher-order representation of protein dynamics through correlation patterns derived from molecular motion. These dynamic correlations are essential to protein function, and the resulting correlation matrices have long been used to analyze protein dynamics (Agarwal et al., 2002; Lange & Grubmüller, 2008).
In this work, we propose combining molecular struc- ture and simulated molecular trajectories through residue- based correlation matrices and relational graph neural net- works (Schlichtkrull et al., 2017). We show that this ap- proach enables the exploitation of the rapidly expanding collection of readily available protein dynamics trajecto- ries for protein and protein- property prediction. In summary:
1. Introduction
With the recent surge and successes of deep learning meth- ods in protein structure prediction, attention is rapidly turn- ing towards the prediction of the temporal behavior of these highly dynamic macromolecules. Combined with quantita- tive and qualitative advances in molecular dynamics simu- lations (Joshi & Deshmukh, 2021: Zeng et al., 2021; Ma- jewski et al., 2023; Nam & Wolf-Watz, 2023), this attention is resulting in the increased availability and accessibility of simulated molecular dynamics trajectories (Vander Meer-
We propose novel heterogeneous graph representa- tion that integrates both static structural information and dynamic correlations from molecular trajectories, enabling more comprehensive modeling of protein properties.
We introduce the first application of relational graph neural networks to directly process molccular dynam- ies trajectories, demonstrating clear benefiss over graph neural networks (GNNs) based on structure alone.
'École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland 'Wageningen University & research, Wagenin- gen, The Netherlands. Correspondence to: Pengkang Guo Epengkang.guo@ccff.cc guo@ceff.ch>.
We validate our approach across three distinct tasks: atomic adaptability prediction, binding site detection, and binding affinity prediction, showing consistent ben- efits of combining static and dynamic information.
Proceedings of the 4rnd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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Boosting Protein Graph Representations through Static-Dynamic Fusion
2. Related Work
2.1. Dynamic Correlations Protein Analysis
Dynamic correlations can be derived through various ap- proaches, including methods like the Gaussian Network Model that use coarse-grained representations and harmonic approximation (Bahar al., 1997), well as from molecu- lar dynamics trajectories. The latter approach has been ex- tensively applied in protein analysis, particularly for under- standing allosteric mechanisms and signal propagation (Mc- Clendon et al., 2009; Long Brüschweiler, 2011; I; Wang al., 2020), investigating tRNA-protein complex interac- tions (Sethi al., 2009), and identifying catalytically im- portant regions for enzyme engineering (Bunzel al., 2021; Gao et al., 2024).
Distance matrix from static molecular structure
Correlation matrix from molecular dynamics trajectory
Dionnee (A)
Conshsiion
However, they have not been used as a representation of trajectories when training predictive models on large data sets but mainly as a means to investigate the propagation of structural changes single, or class of proteins through methods such dynamical network analysis (Melo al., 2020; Calvó-Tusell et al., 2022).
2.2. Machine Learning for Protein Structure and Dynamics
Machine learning for protein structure and dynamics has primarily focused graph-based methods, though other paradigms are also emerging. Graph neural networks have been widely applied to predict properties and functions of proteins as well as properties of protein-liget ligand or protein- protein interactions based on structure (Gligorijević al., 2021a; Li al., 2021b; Réau et al., 2023). More recently, they have been used enhance and accelerate molecular dynamics simulations (Wang et al., 2022; Yue al., 2024).
Combine graphs
Heterogeneous graph
Relational GNN
Chiang et al. (2022) explored incorporating dynamic infor- mation into protein graphs by using normal mode analysis to generate correlation edges, combining this with ID and 2D persistence diagrams of a--arbons for molecular function classification using graph convolutional networks (GCN) (Defferrard et al., 2017; Kipf & Welling, 2017).
Figure 1. Fusion of static structure and molecular dynamics information. The left side shows the transformation of protein structure (PDB ID 5GMU) into distance-based matrix, while the right side presents the correlation matrix derived from molecular dynamics trajectories, which shows motion correlations between different regions. The correlation edges create direct connections between dynamically coupled regions that may be spatially distant (shown in red), enabling efficient information flow across pro- tein structure. The fusion of these structural and dynamic features creates a heterogeneous graph representation, which serves as in- put relational graph neural networks.
Relational graph neural networks have also shown promise in small molecular graph generation (Zou et al., 2023), and protein representation learning, integrating sequential and spatial distance in proteins (Zhang et al., 2022).
Beyond graph-based approaches, Sun et al. (2023) intro- duced Dynamical Surface Representation, which uses im- plicit neural networks to model protein dynamics through continuous surface representations, enabling scalable mod- cling of large protein conformational changes.
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Boosting Protein Graph Representations through Static-Dynamic Fusion
3. Methodology
tures meaningful atomic interactions (Bouysset & Fiorucei, 2021), while the 10 Á threshold is commonly adopted for residue-level contacts (Gligorijević et al., 2021b).
3.1. Graph Construction Framework
We represent a protein complex as a tuple (V, Ed, Ec), where V represents the set of nodes, Ed represents distance- based edges, and E. represents correlation-based edges derived from molecular dynamics trajectories.
3.1.3. DYNAMIC CORRELATION EDGE CONSTRUCTION
To capture dynamic behaviors, we analyze molecular dy- namics trajectories to construct correlation- based edges Ee. Before computing correlations, all trajectory frames are aligned the initial structure through rigid-body superpo- sition optimized to minimize the root-mean-squee devi- ation (RMSD) between equivalent atomic positions. The alignment eliminates global translations and rotations while preserving internal conformational changes.
We present novel approach for incorporating both static structural and dynamic motion information into protein graph representations. Our method consists of two key com- ponents: (1) a heterogeneous graph construction framework that combines spatial proximity with dynamic correlations from molecular dynamics simulations, and (2) the appli- cation of relational neural networks to effectively process the heterogeneous graphs enriched by both structural and dynamic information.
Unlike distance-based representations that primarily capture local structural relationships, correlation- edges can identify dynamically coupled regions regardless of spatial proximity, creating direct pathways between motion-related but spatially distant parts of the protein (as shown in Fig- ure 1). For each pair of nodes, we compute their motion correlation across simulation frames:
As illustrated in Figure 1, our approach derives two comple- mentary edge types from protein data: distance edges based on static structure, and correlation edges from molecular dy- namics trajectories. These correlation edges provide direct links between dynamically coupled regions of the protein, enabling more efficient long-range information flow than in the original graph structure. The mechanism is akin to graph rewiring, which is known to mitigate overssquahhin in GNNs (Topping et al., 2021) (see Appendix A.6 for fur- ther analysis).
T Arf
Ar Ar
Cij = T
(2)
Ar
where Art represents the displacement vector of node i at frame t, and T is the total number of frames. The correlation edges are then defined as:
3.1.1. NODE DEFINITION AND FEATURES
Nodes are defined based on the specific requirements of each task:
E. (2,, 04) | |Cabl Te
(3)
For atomic-level predictions (e.g., atomic property predic- tion), each node represents a non-hydrogen atom, capturing detailed molecular interactions at the atomic scale.
where To is the correlation threshold (0.6 for atomic-level and 0.3 for residue-level graphs). These thresholds are chosen maintain similar graph sparsity, thereby achieving fairer comparison when either Correlation Distance Graph is used.
For residue-level tasks (c.g.. binding site detection), each node represents residue, where the coordinates of its Ca atom are used to determine the residue's spatial position.
1.1.4. COMBINED GRAPH
Each node Ui E V is associated with feature vector h, E Rd consisting of the one-hot encoding of the atom/residue type and the atom charge (for atomic-level graphs).
The final graph representation integrates both distance- based and correlation- based edges, yielding a heterogeneous graph that captures both static structural information and dynamic behavioral patterns. This combined representation enables the model to utilize local spatial relationships and potential long-range dynamic interactions simultaneously.
3.1.2. DISTANCE-BASED EDGE CONSTRUCTION
The distance-bass based edges E, capture spatial proximity in the static structure:
3.2. Relational Graph Neural Network Architecture
E. = (1))0y) d(v,, u3) < Td
(1)
The heterogeneous nature of our Combined Graph, con- taining both distance-based and correlation -base edges, requires a neural network architecture capable of process- ing different types of relationships. We therefore employ two established relational neural networks: the Relational Graph Convolutional Network (RGCN) (Schlichtkrull et al.,
where d(v;, v.)) represents the Euclidean distance between nodes, and Ta is a distance threshold (4.5 Å for atomic-level and 10 A for residue-level graphs). These thresholds are widely used in protein modeling: the 4.5 À threshold cap-
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Boosting Protein Graph Representations through Static-Dynamic Fusion
2018) and the Relational Graph Attention Network (RGAT) (Busbridge et al., 2019). These architectures particu- larly suited for our approach they handle heterogeneous edges by learning different weight matrices for different edge types.
To validate the generalizability of our approach, we also evaluate three additional architectures representing different paradigms: EGNN (Satorras et al., 2021) as representative equivariant GNN, GPS (Rampášek et al., 2022) as pop- ular graph transformer, and SS-GNN (Zhang et al., 2023) as a domain-specitfe model for binding affinity prediction. We create relational variants (R-EGNN, R-GPS, and R- SS-GNN, respectively) as follows: for EGNN, we process distance and correlation graphs with separate models and merge their outputs; for GPS, we replace its local message passing layer with RGCN; for SS-GNN, we similarly re- place the GNN component with RGCN while maintaining the original hyperparameters and featurization.
The RGCN extends the traditional Graph Convolutional Network by introducing relation-specifie transformations. For each layer I, the message passing operation defined as:
h (1+1)
Σ
w + w h
(
PERJEEN (1)
(4)
where (i) denotes neighbors of node connected by
edges of type r, ( is the relation-specific transformation matrix, and w 0 is the self-connection weight matrix. In our case, R represents the set of edge types (distance and correlation). This formulation allows the network to learn distinct transformations for distance-based and correlation- based relationships, enabling it to capture the unique char- acteristics of each edge type.
4. Experiments
4.1. Dataset
We evaluate approach using the MISATO dataset (Siebenmorgen et al., 2024b), which contains 19,443 protein-ligand complexes derived from PDBbind (Su et al., 2018; Liu et al., 2017; Wang et al., 2005). Each complex un- dergoes semi-empirical quantum mechanical refinement and ns molecular dynamics simulation using the Amber20 software package. The dataset also provides key physico- chemical properties, forming high-quality benchmark for machine learning tasks.
The RGAT extends this formulation by incorporating attention mechanism. This formulation allows the net- work to learn distinct transformations for distance-based and correlation-basee relationships, enabling it to capture the unique characteristies of each edge type. For each layer l the cateetiion-baed message passing operation defined
To ensure robust evaluation and prevent information leak- age through structural similarities, the dataset is split into training (80%), validation (10%), and test (10%) sets using protein sequence clustering via BlastP, ensuring that pro- teins with high sequence similarity are assigned the same split (details in Appendix A.3).
h
1111
Σ Σ PER (EN.(0)
(c) of W + n. (5)
The attention coefficients oi are computed using query and key kernels for each relation type
4.2. Experimental Setup
As discussed in Section 3.2, we use RGCN, RGAT, R- EGNN, R-GPS, and R-SS-GNN validate our approach. We evaluate three tasks: (1) atom adaptability prediction, (2) binding site detection, and (3) binding affinity predic- tion. For each task, we evaluate three graph representations: Distance Graph based on the static structure, Correlation Graph derived from the molecular dynamics trajectory, and Combined Graph that integrates both sources. To ensure a fair comparison, we maintain identical input node features and model architectures across all graph types for all tasks, with edge definitions being the only variable, allowing us to validate the role of dynamic information.
(r) q.
w("xx x; (())
and k
w (r)
k(r)
(6)
These kernels are used to compute attention logits:
+ = Le + +k))))
The final attention coefficients are obtained as:
expla!?) ENER (xp(((()))
(8)
4.3. Results and Discussion
This attention mechanism enables the model to automati- cally determine the relative importance of different relation- ships, potentially providing insights into the contributions of structural and dynamic information in protein modeling.
We evaluate our approach on three distinct prediction tasks: atomic adaptability, binding site identification, and binding affinity prediction. For each task, we analyze how differ-
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Boosting Protein Graph Representations through Static-Dynamic Fusion
graph representations (Distance, Correlation, and Com-
achieving strong performance across all metries. Notably, R-EGNN shows a different pattern where the Correlation Graph alone achieves the best performance, while the Com- bined Graph performs similarly to the Distance Graph. We attribute this to limitations in our preliminary R-EGNN im- plementation, which may not optimally fuse information from different relation types. We leave the exploration of improved fusion mechanisms for equivariant architectures to future work.
bined) affect model performance using the various architec- tures.
4.3.1. ATOMIC ADAPTABILITY PREDICTION
Atomic adaptability quantifies the conformational plasticity of atoms within a protein structure, where higher values indicate greater flexibility and lower values indicate rigidity (see Appendix A.4). This property helps identify key re- gions of motion, making it crucial for understanding protein dynamics and molecular design. We formulate adaptability prediction as node-level regression task, where each atom is annotated with an adaptability score from the MISATO dataset (see Figure 2).
These performance improvements align with the physical nature of atomic adaptability. While spatial proximity (cap- tured by the Distance Graph) provides important structural constraints, atomic adaptability is inherently a dynamical property that highly depends on atomic fluctuations and conformational changes, which cannot be fully captured by spatial proximity alone. The Correlation Graph, leveraging dynamical information derived from molecular dynamics trajectories, better captures elements tied to motion and complements the structural information. When combined, these two edge types enable the model to learn from both spatial constraints and dynamic coupling patterns, resulting in the Combined Graph's superior performance.
The consistent improvement across multiple architectures suggests that the performance gains primarily stem from the richer graph structure rather than specific architectural choices. This robustness validates our approach of incorpo- rating dynamic information through correlation edges as an effective strategy for enhancing protein graph representa- tions in dynamical property prediction.
Figure 2. Atomic Adaptability Prediction. Visualization of per- atom adaptability in a protein structure (PDB ID 5C11). Left: ground-truth (target) adaptability values shown as blue spheres. Right: predicted adaptability values shown pink spheres. Sphere size indicates the magnitude of adaptability, with larger spheres corresponding to more flexible (higher adaptability) regions.
4.3.2. BINDING SITE DETECTION
Binding site detection aims to identify key residues in pro- teins that directly interact with ligands, specifically those residues within 10 Á from the ligand, following PDBbind. This task is essential for understanding protein functionality and facilitating early- drug design. We formulate this as a binary node classification problem at the residue level, where each node represents residue and is classified as either binding site non-binding site (see Figure 3).
Table presents the performance comparison across dif- ferent graph representations using four architectures. The Correlation Graph, which captures dynamic motion patterns derived from molecular dynamicss trajectories. consistently outperforms the Distance Graph across all metrics and archi- tectures. Using RGCN, we observe improvements in both error metrics (MAE reduces from 0.2658 to 0.2311) and correlation coefficients (Pearson R increases from 0.5259 to 0.6426). Similar comprehensive improvements are observed with RGAT, R-EGNN, and R-GPS, suggesting the value of dynamic information for atomic adaptability prediction.
Table 2 presents the classification performance across dif- ferent graph representations using four architectures. The Combined Graph consistently achieves the best performance across all metries for all architectures. For RGCN, the F1 score increases from 0.2428 (Distance Graph) and 0.2578 (Correlation Graph) to 0.2834, representing improvements of 16.7% and 9.9% respectively. Similar patterns emerge with RGAT, where the Fl score improves from 0.2089 (Dis- tance Graph) and 0.2294 (Correlation Graph) to 0.2574. R-EGNN and R-GPS show the same pattern of Combined Graph achieving the best results, with R-EGNN achieving notably higher performance, reaching an Fl score of 0.4142 with the Combined Graph.
When both types of information are integrated in the Combined Graph, we observe further significant improve- ments across all metries: the Pearson correlation coefficient reaches 0.7326 (RGCN) and 0.7153 (RGAT), representing improvements of 39.3% and 50.7% respectively over the Distance Graph baseline (0.5259 using RGCN and 0.4746 using RGAT). Similar improvements are observed across other metrics, as evidenced by the reduction in MAE from 0.2658 to 0.1981 (RGCN) and 0.2766 to 0.2074 (RGAT). R-GPS follows the same pattern, with the Combined Graph
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Boosting Protein Graph Representations through Static-Dynamic Fusion
Table Atomic Adaptability Prediction. Node-level regression task predicting atomic adaptability values using data from MISATO
dataset. Results show mean = standard deviation over 5 runs (J indicates lower is better. 1 indicates higher is better). Notably, the Correlation Graph alone achieves better performance than the Distance Graph on metrics, suggesting the importance of dynamic information for this task.
MODEL
GRAPH TYPE
MAE (L)
RMSE (4)
PEARSON R (1)
SPEARMAN (t)
DISTANCE
0.2658 0.0061
0.4274 = 0.0008
0,5259 + 0.0015
0.5543 + 0.0017
RGCN
CORRELATION
0.2311
0.0014
0.3846 = 0.0011
0.6426 + 0.0026
0.6990 + 0.0019
COMBINED
0.0020 0.1981
0.3417 = 0.0008
0.7326 + 0.0014
0.7922 0.0010
DISTANCE
0.2766 0.0038
0.4419 = 0.0018
0.4746 + 0.0066
0.4762 + 0.0085
RGAT
CORRELATION
0.2443
0.0013
0.3976 = 0.0013
0.6106 + 0.0037
0.6521 0.0068
COMBINED
0.2074 + 0.0030
0.3511 + 0.0018
0.7153 + 0.0033
0.7699 + 0.0024
DISTANCE
0.2305 0.0047
0.3807 = 0.0007
0.6530 + 0.0012
0.6914 + 0.0015
R-EGNN
CORRELATION
0.2028 + 0.0055
0.3387 + 0.0006
0.7398 + 0.0016
0.7710 + 0.0033
COMBINED
0.2321 + 0.0053
0.3809 = 0.0016
0.6532 + 0.0018
0.6917 + 0.0012
DISTANCE
0.2552 + 0.0098
0.4232 - 0.0015
0.5420 + 0.0091
0.5704 + 0.0136
R-GPS
CORRELATION
0.2293 = 0.0028
0.3806 0.0009
0.6543 + 0.0020
0.7066 + 0.0017
COMBINED
0.1921 0.0009
0.3434 = 0.0017
0.7361 + 0.0018
0.7961 + 0.0013
Table 2. Binding Site Detection. Node-level binary classification task identifying binding site residues (those within 10 A from the ligand) using data from the MISATO dataset. Results show mean standard deviation over runs (t indicates higher is better). The Combined Graph demonstrates superior performance across all metrics and architectures.
MODEL
GRAPH TYPE
Acc (1)
PRECISION (t)
RECALL (1)
Fl SCORE (1)
DISTANCE
0.7112 + 0.0092
0.1678 + 0.0024
0.4464 + 0.0164
0,2428 + 0.0027
RGCN
CORRELATION
0.7282 + 0.0069
0.1808 - 0.0022
0.4552 i 0.0102
0.2578 1 0.0012
COMBINED
0.7433 0.0067
0.2005
0.0030
0.4889 1 0.0111
0.2834 1 0.0023
DISTANCE
0.6602 1 0.0120
0.1475 + 0.0032
0.4439 1: 0.0234
0.2089 1: 0.0040
RGAT
CORRELATION
0.6938
0.0111
0.1664
0.0031
0.4441 1 0.0182
0.2294 1 0.0030
COMBINED
0.7226
0.0067
0.1861 + 0.0029
0.4750 + 0.0137
0.0032 0.2574
DISTANCE
0.8038 0.0131
0.2749 0.0110
0.5368 + 0.0359
0.3617 + 0.0049
R-EGNN
CORRELATION
0.7628
0.0136
0,2181 = 0.0043
0.4929 + 0.0356
0.3012 0.0037
COMBINED
0.8387 + 0.0149
0.3353 + 0.0191
0.5498 + 0.0414
0,4142 + 0.0043
DISTANCE
0.7574 0.0055
0.2065 + 0.0023
0.4675 + 0.0131
0.2856 0.0023
R-GPS
CORRELATION
0.7480 + 0.0051
0.2051 + 0.0021
0.4935 + 0.0093
0,2890 + 0.0008
COMBINED
0.7567 + 0.0060
0.2274 = 0.0029
0.5594 + 0.0142
0.3228 + 0.0022
Compared to atomic adaptability, which relies more directly on dynamic information, binding site identification depends heavily on static structural features such as protein surfaces and binding pockets. The varying performance patterns between Distance and Correlation graphs across different ar- chitectures reflect the balanced importance of both static and dynamic features in this context, with some architectures better suited for leveraging specific types of information. When combined, the model can utilize both spatial proxim- ity and motion patterns, leading to more accurate binding site identification.
approach of incorporating both types of information into protein graph representations, offering new possibilities for studying complex protein-ligamt interactions.
4.3.3. BINDING AFFINITY PREDICTION
Binding affinity prediction represents critical task in drug design and virtual screening, as it quantifies the interaction strength between proteins and ligands. We formulate this as graph-level regression task, where each graph represents a protein pocket and its ligand, with experimentally measured binding affinities as targets. Following previous work (Li et al., 2021a), we evaluate our approach the PDBbind 2020 benchmark (details in Appendix A.3).
The consistent improvement across various architectures demonstrates that these improvements result from the com- plementary nature of static and dynamic features rather than specific architectural choices. These results validate our
Table 3 presents the regression performance across different graph representations using five architectures. The Com-
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Boosting Protein Graph Representations through Static-Dynamic Fusion
Table Binding Affinity Prediction. Graph-level regression task predicting protein-ligand binding affinity values using MISATO and PDBbind datasets. Results show mean + standard deviation over 5 runs (6 indicates lower is better, t indicates higher is better). The Combined Graph consistently yields improvements across all metrics and architectures, demonstrating complementary value static and dynamic information for binding affinity prediction.
MODEL
GRAPH TYPE
MAR (4)
RMSE (4)
PEARSON R (1)
SPEARMAN R (1)
DISTANCE
1,3046 + 0.0267
1.6633 + 0.0336
0.6596 + 0.0156
0,6352 + 0.0234
RGCN
CORRELATION
1.3572 + 0.0792
1.6974 1 0. 0.0827
0,6360 +: 0.0428
0.6185 + 0.0440
COMBINED
1.2439 = 0.0256
1.5798 t 0.0447
0.6983 + 0.0193
0.6773 + 0.0208
DISTANCE
1.3028 1.02261
1,6427 1: 0.0459
0.6694 1 0.0222
0.6417 + 0.0225
RGAT
CORRELATION
1.3249 - 1..034
1.6623 1 0.0335
0.6643 1: 0.0212
0.6481 + 0.0254
COMBINED
1.2596 = 0.0290
1.6012 + 0.0411
0.6931 0.0157
0.6752 = 0.0157
DISTANCE
1.2900 = 0.0484
1.6614 + 0.0635
0.6721 +: 0.0265
0.6502 + 0.0265
R-EGNN
CORRELATION
1.4097 + 0.0334
1.7888 + 0.0585
0.5987 0.0248
0.5720 + 0.0199
COMBINED
1.2632 = 0.0463
1.6176 + 0.0394
0.6876 + 0.0178
0.6773 = 0.0206
DISTANCE
1.2444 + 0.0183
1.5832 + 0.0336
0.7026 0.0104
0.6814 + 0.0130
R-GPS
CORRELATION
1,2800 = 0.0418
1.6216 + 0.0561
0.6862 0.0155
0.6735 + 0.0168
COMBINED
1.2127 = 0.0365
1.5326 + 0.0521
0.7197 +
0.7080 - 0.0266
DISTANCE
1.2378 + 0.0338
1,4306 + 0.0491
0.7638 + 0.0205
0.7454 + 0.0256
R-SS-GNN
CORRELATION
1.2278 1 0.0330
1.5345 1 0.0397
0.7229 1 0.0181
0.7015 + 0.0254
COMBINED
1.0874 1 0.0430
1.3658 1 0.0504
0.7873 1 0.0187
0.7792 1 0.0221
Table Effect Trajectory Alignment Atomic Adaptability Prediction. Comparison of atomic adaptability prediction results using aligned versus unaligned molecular dynamics trajectories. Results show mean +: standard deviation over 5 runs (1 indicates lower is better, t indicates higher better). Trajectory alignment, performed by minimizing RMSD between frames, consistently enhances performance across all metrics for both Correlation and Combined graphs, highlighting the importance of isolating intrinsic conformational dynamics from global rigid-body motions.
MODEL.
GRAPH TYPE
MAE (4)
RMSE (4)
PEARSON R (t)
SPEARMAN (f)
UNALIGNED CORRELATION
0.2591 = 0,0050
0.4198 + 0.0010
0.5493 1 0.0024
0.5682 + 0,0014
ALIGNED CORRELATION
0.2311 = 0.0014
0.3846
0.0011
0.6426 1 0.0026
0.6990 1 0.0019
RGCN
UNALIGNED COMBINED
0.2192 0.0030
0.3703 1 0.0017
0.6762 + 0.0026
0.7016 1 0.0032
ALIGNED COMBINED
0.1981 = 0.0020
0.3417 0.0008
0.7326 = 0.0014
0.7922 + 0.0010
UNALIGNED CORRELATION
0.2653 0.0024
0.4350 1 0.0020
0.5001 + 0.0076
0.5194 + 0.0073
ALIGNED CORRELATION
0.2443 = 0.0013
0.3976 0.0013
0.6106 + 0.0037
0.6521 +: 0.0068
RGAT
UNALIGNED COMBINED
0.2274 0.0017
0.3759
0.0018
0.6633 + 0.0037
0.6914 + 0.0037
ALIGNED COMBINED
0.2074 = 0.0030
0.3511 0.0018
0.7153 # 0.0033
0.7699 + 0.0024
bined Graph consistently achieves the best performance across all metrics and architectures, demonstrating the value of fusing both types of information. Using RGCN, the Com- bined Graph reaches a Pearson correlation of 0.6983 and reduces MAE to 1. 1.2439, improving upon both the Distance Graph (0.6596, 1.3046) and Correlation Graph (0.6360, 1.3572). Similar patterns emerge with RGAT, where the Combined Graph achieves Pearson correlation of 0.6931 and MAE of 1. 1.2596, outperforming both single-information approaches (Distance Graph: 0.6694, 1.3028; Correlation Graph: 0.6643, 1.3249). R-EGNN, R-GPS, and R-SS-GNN show the same pattern of Combined Graph achieving the best results.
binding affinity, which requires both structural and dynamic information for accurate prediction. While static distance in- formation captures essential geometric constraints, it cannot reflect potential conformational adjustments and long-range interactions during binding. Similarly, dynamic correlations alone. though capturing important motion patterns, can- not fully characterize the binding pocket geometry, leaving room for additional improvements. The integration of both information types enables the model to simultaneously con- sider geometric constraints and dynamic interaction patterns, achieving better performance across both error metrics and correlation coefficients and demonstrating the value of this combined approach.
These results reflect the complex nature of protein-ligand
The consistent improvement pattern across multiple archi-
7

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Boosting Protein Graph Representations through Static-Dynamic Fusion
5. Conclusion
This work addresses key limitation in current protein graph representations: their exclusive reliance on static structural information without incorporating crucial information about protein dynamics. We propose novel heterogeneous graph representation that integrates static structural information and dynamic correlations from molecular simulation tra- jectories, and apply relational graph neural networks to process these enriched representations. Our systematic eval- uation across diverse architectures examines three distinet tasks: atomic adaptability prediction, binding site detection, and binding affinity prediction. The experimental results show that while Distance and Correlation graphs exhibit dif- ferent performance patterns across architectures and tasks, the Combined Graph consistently achieves superior perfor- mance across all tasks, metrics, and architectures. These results demonstrate that static and dynamic information provide complementary signals for understanding protein behavior. Our approach opens new possibilities for protein modeling and design by effectively capturing both static structural constraints and dynamic correlations in a unified framework.
Figure 3. Binding Site Prediction. Visualization of binding site detection task using protein structure (PDB ID 3M67). Left: Ground truth binding site residues (shown in red) and the bound ligand (yellow). Right: Predicted binding site residues using the Combined Graph, showing reasonable agreement with the true binding regions for this example. This case illustrates how the model aims to identify residues within 10 Åfrom the ligand. The ligand is shown only for reference and is not provided to the model.
Future directions include exploring advanced architectures like graph transformers to enhance heterogeneous infor- mation processing, and investigating additional correlation measures such mutual information enrich dynamic feature representation. As broader direction, integration with emerging generative models for molecular dynamics could further expand the applicability of our approach by trajectory generation, especially when molecular dynamics trajectories are not readily available. These developments will further strengthen our approach's 's capability in protein modeling, advancing applications in drug design and struc- tural biology.
tectures validates that these performance gains arise from the complementary nature of static and dynamic features rather than specific architectural choices. These results show that the fusion of both static and dynamic information en- hances the accuracy of binding affinity prediction, offering valuable insights for drug design and molecular screening applications.
4.3.4. EFFECT OF TRAJECTORY ALIGNMENT
To validate the impact of trajectory alignment our correlation-bass based representations, compare model per- formance using aligned versus unaligned trajectories on the atomic adaptability prediction task, as it most directly reflects the quality of our dynamic information capture. Ta- ble 4 shows that the aligned Correlation Graph consistently outperforms its unaligned counterpart across all metrics. Us- ing RGCN, alignment improves Pearson correlation from 0.5493 to 0.6426 and reduces MAE from 0.2591 to 0.2311. The Aligned Combined Graph, which integrates aligned cor- relations with distance information, also shows substantial performance improvements, with RGCN achieving a Pear- son correlation of 0.7326 (ys 0.6762 unaligned) and MAE of 0.1981 (vs 0.2192 unaligned). Similar comprehensive improvements are observed with RGAT for both Correla- tion and Combined graphs, where alignment consistently enhances performance across all metrics. These compre- hensive improvements across both architectures and graph types demonstrate that removing global figidbody motions effectively isolates meaningful conformational dynamics, leading to more accurate predictions.
8

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Boosting Protein Graph Representations through Static-Dynamic Fusion
Acknowledgements
tional residue identification. Cell Reports Physical Sci- ence, 3(7):100975, July 2022. ISSN 2666-3864. doi:
We thank the reviewers for their constructive feedback that helped improve the quality of this work. This research was conducted at the Laboratory of Signal Processing and the Laboratory of Protein Design& & Immunoengineeringg at École Polytechnique Fédérale de Lausanne, and Wagenin- gen University & Research. B.C. acknowledges support from the Swiss National Science Foundation.
10.1016ff.xrr.20221109999
Defferrard, M., Bresson, X., and Vandergheynst, P. Con- volutional neural networks on graphs with fast localized spectral filtering, 2017.
Dhakal, A., McKay, C., Tanner, J.J., and Cheng. J. Artificial intelligence in the prediction of protein-ligand interac- tions: Recent advances and future directions. Briefings in Bioinformatics, 23(1 (5(1):bba4476, January 2022. ISSN 1477-4054, doi: 10. 10.1099/bib/bbbb47..
Impact Statement
This paper presents work whose goal advance the field of Machine Learning, specifically protein modeling. Our approach for integrating static and dynamic protein infor- mation could contribute to drug discovery and protein en- gineering applications. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
Gao, C.-Y., Yang, G.-Y., Ding, X.-W., Xu, J.-H., Cheng, X., Zheng, G.- and Chen, Q. Engineering of Halide Methyltransferase BxHMT through Dynamic Cross- Correlation Network Analysis. Angewandte Chemie In- ternational Edition, 63(25):e022401335, 2024. ISSN 1521-3773. doi: 10. 10.1002/amie.222441333.
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Boosting Protein Graph Representations through Static-Dynamic Fusion
A. Appendix
A.I. Trajectory Alignment
During preprocessing, we aligned all molecular dynamics trajectories to their initial frames using PyTraj's align function (Roe & Cheatham III, 2013). The alignment eliminates global translations and rotations, ensuring that Ar; captures meaningful conformational changes rather than rigid-body motions. By focusing intrinsic protein dynamics, this preprocessing step improves the quality of our correlation-based edges and leads to more informative graph representations.
A.2. Implementation Details and Hyperparameters
We implemented our models using PyTorch Geometric. Each model consists of GNN layers followed by two-layer MLP for prediction. We trained models using the Adam optimizer with learning rate of le-4 and batch size of 32. Training epochs were task-specific: 50 for atomic adaptability prediction, 200 for binding site detection, and 500 for binding affinity prediction.
For model architecture optimization, we explored different hidden dimensions for each model-task-graph type combination, with detailed results presented in Tables 5, 6 and 7. The dimension ranges were selected based on architectural differences and memory constraints. For example, in atomic adaptability prediction using RGCN, we explored hidden dimensions {26, 32, 53, 64), while for RGAT we tested {17, 20, 24) due its higher memory requirements. For R-EGNN and R-GPS, tested hidden dimensions (32, 64) across all tasks. For R-SS-GNN, we followed the original SS-GNN hyperparameters and set the hidden dimension to 108.
Table 5. Detailed Results for Atomic Adaptability Prediction with Different Hidden Dimensions. Supplementary results to Table 1, showing the performance different hidden dimensions for cach model and graph type combination. Values represent individual runs (L indicates lower is better, 1 indicates higher is better).
MODEL
GRAPH TYPE
HIDDEN DIM
MAE (L)
RMSE (L)
PEARSON R (t)
SPEARMAN R (1)
26
0.2636
0.4347
0.5008
0.5292
32
0.2726
0.4361
0.4960
0.5216
DISTANCE
53
0.2670
0.4423
0.5134
0.5409
64
0.2687
0.4412
0.5160
0.5454
26
0.2359
0.3965
0.6130
0.6790
32
0.2397
0.3951
0.6170
0.6817
CORRELATION
RGCN
53
0.2316
0.3884
0.6336
0.6909
64
0.2321
0.3874
0.6359
0.6967
21
0.2074
0.3530
0.7115
0.7753
26
0.2077
0.3548
0.7073
0.7732
32
0.2078
0.3549
0.7084
0.7778
COMBINED
44
0.2039
0.3481
0.7206
0.7824
53
0.2016
0.3475
0.7214
0.7854
64
0.2034
0.3433
0.7301
0.7910
20
0.2768
0.4406
0.4790
0,4811
DISTANCE
24
0.2763
0.4426
0.4715
0.4750
0.2461
0.3976
0.6104
0,6496
RGAT
CORRELATION
24
0.2465
0.3984
0.6084
0.6504
17
0.2085
0.3536
0.7098
0.7555
COMBINED
20
0.2067
0.3538
0.7096
0.7578
24
0.2161
0.3557
0.7088
0.7615
A.3. Dataset Details
For atomic adaptability and binding site detection tasks, we used the data splitting in the MISATO dataset splits, with 13,597 samples for training. 1,582 for validation, and 1,593 for test. These splits were created using sequence-basee based clustering with BlastP (similarity threshold of 30%) to prevent information leakage through structural similarities. The dataset contains molecular dynamics trajectories generated using the Amber20 software package with simulation length of 10ns.
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Boosting Protein Graph Representations through Static-Dynamic Fusion
Table 6. Detailed Results for Binding Affinity Prediction with Different Hidden Dimensions. Supplementary results to Table 3,
showing performance different hidden dimensions each model and graph type combination. Values represent individual runs (4
indicates lower is better, 1 indicates higher is better).
MODEL
GRAPH TYPE
HIDDEN DIM
RMSE (U)
MAE (L)
PEARSON R (t)
SPEARMAN R (1)
32
1.7036
1.3441
0.6444
0.6147
DISTANCE
64
1.6377
1.2750
0.6740
0.6486
32
1.7497
1.4077
0.6204
0.5965
CORRELATION
RGCN
64
1.5761
1.2053
0.7025
0.6921
25
1.6186
1.2465
0.6772
0.6666
32
1.6454
1.3366
0.6650
0,6570
COMBINED
51
1.6150
1.2999
0.6821
0.6678
64
1.5996
1.2243
0.6860
0.6718
32
1.7134
1.3655
0.6330
0.6141
DISTANCE
1.6194
1.2626
0.6875
0.6478
32
1.6456
1.3295
0.6803
0.6651
CORRELATION
RGAT
64
1.6670
1.3527
0.6555
0.6150
26
1.7224
1.3993
0.6237
0.5948
32
1.7016
1.3542
0.6389
0.6196
COMBINED
55
1.6411
1.3309
0.6704
0.6563
64
1.5685
1.2378
0.7075
0.6855
Table 7. Detailed Results for Binding Site Detection with Different Hidden Dimensions. Supplementary results to Table 2, showing the performance of different hidden dimensions for each model graph type combination. Values represent mean standard deviation over 5 runs (t indicates higher is better).
MODEL
GRAPH TYPE
HIDDEN DIM
ACC (f)
PRECISION (t)
RECALL (f)
F1 SCORE (*)
32
0.7112 0.0092
0.1678 1 0.0024
0.4464 + 0.0164
0.2428 1 0.0027
DISTANCE
64
0.7217 +: 0.0136
0.1694 1 0.0031
0.4270 1 0.0223
0.2412 1 0.0018
32
0.7282 0.0069
0.1808 + 0.0022
0.4552 + 0.0102
0.2578 + 0.0012
CORRELATION
RGCN
64
0.7206 + 0.0033
0.1784 + 0.0007
0.4652 = 0.0079
0.2569 = 0.0014
26
0.7433 0.0067
0.2005 + 0.0030
0.4889 + 0.0111
0.2834 = 0.0023
32
0.7527 + 0.0054
0.2042 + 0.0037
0.4748 = 0.0125
0.2847 = 0.0044
COMBINED
53
0.7649 + 0.0100
0.2083 0.0029
0.4477 = 0.0244
0.2829 0,0033
0.7640 0.0063
0.2086 0.0025
0.4531 = 0.0133
0.2846 0.0018
32
0.6447 +: 0.0232
0.1453 1 0.0034
0.4607 + 0.0327
0.2084
0,0036
DISTANCE
0.6602 0.0120
0.1475 0.0032
0.4439 + 0.0234
0.2089 0.0040
32
0.6938 0.0111
0.1664 + 0.0031
0.4441 + 0.0182
0.2294 0.0030
CORRELATION
RGAT
0.6955 0.0122
0.1653 0.0036
0.4379 = 0.0169
0.2279 0.0031
27
0.7226 + 0.0067
0.1861 + 0.0029
0.4750 = 0.0137
0.2574 0,0032
0.7291 = 0.0148
0.1882 0.0072
0.4637 = 0.0218
0.2564 0.0075
COMBINED
40
0.7367 0.0055
0.1916 + 0.0018
0.4563
= 0.0133
0.2594 = 0.0037
48
0.7387 + 0.0103
0.1884 + 0.0077
0.4360 + 0.0033
0.2516 + 0.0071
13

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Boosting Protein Graph Representations through Static-Dynamic Fusion
For binding affinity prediction, following previous work (Li al., 2021a), we used the PDBbind 2020 refined set for training and validation, and evaluated the core set. The refined set consists of 5,316 protein-ligand complexes specifically selected for high-quality binding data and crystal structures through comprehensive filtering process (Liu al., 2017). This dataset construction ensures reliable binding affinity values derived from carefully curated experimental measurements.
A.4. Atomic adaptability
Atomic adaptability (%x) for each atom x is calculated the mean distance from its initial position across all simulation frames after alignment:
Nirmes
1
7/2
||rift ri,
(9)
Ntrames
where Tef,, is the initial position of atom and ri,x is its position in frame i. This measure quantifies each atom's mobility throughout the simulation, providing insight into conformational flexibility at atomic resolution.
While atomic adaptability can be directly computed from molecular dynamics trajectories, predicting it from graph representations provides a valuable benchmark for evaluating how effectively different graph structures capture dynamic information. The Correlation Graph represents a compressed encoding of the full trajectory information, so the ability to accurately predict adaptability demonstrates that this encoding successfully preserves essential dynamic features. This task also maintains continuity with the established MISATO benchmark, facilitating direct comparison with current and future approaches.
A.5. Architecture Performance Analysis
We analyzed the performance of invariant (RGCN, RGAT) and equivariant (R-EGNN) graph neural networks across our three tasks and graph types. R-GPS and R-SS-GNN excluded from this comparison they represent different paradigms (graph transformer and domain-specifie model, respectively). Table 8 summarizes the best-performing architecture for each scenario.
Table Best-performing GNN for each task and graph type combination
Task
Distance Graph Correlation Graph
Combined Graph
Atomic Adaptability Prediction Binding Site Detection
R-EGNN R-EGNN
R-EGNN
RGCN
R-EGNN
R-EGNN
Binding Affinity Prediction
R-EGNN
RGAT
RGCN
Several patterns emerge from this analysis. R-EGNN generally outperforms invariant models across most scenarios, which expected as equivariant architectures preserve rotational and translational symmetries crucial for protein modeling. R-EGNN consistently performs best on Distance Graphs across all tasks, which aligns with the fact that EGNN explicitly uses coordinates and distances in its message passing process, making them well-suited for distance-based representations. Binding site detection shows the most consistent benefit from equivariant architectures across all graph types, likely due to the more regular graph structure (all nodes represent C'a atoms, although belonging to different amino acids), making 3D spatial relationships particularly important.
Interestingly, for Combined Graphs, invariant models (RGCN) outperform R-EGNN in two tasks. This suggests that our current implementation of relational EGNN may not optimally integrate information from different edge types, indicating opportunities for improved fusion mechanisms for equivariant architectures future work.
A.6. Theoretical Analysis
To understand why our Combined Graph approach consistently improves performance, we conducted additional theoretical analyses.
14

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Boosting Protein Graph Representations through Static-Dynamic Fusion
1. GRAPH PROPERTIES
We analyzed graph properties of Distance and Combined graphs using randomly selected subsets of 50 proteins each atomic and residue levels. Table shows that adding correlation edges significantly reduces both graph diameter and average shortest path length at both levels, suggesting that correlation edges create critical shorteuts between dynamically coupled regions.
Table 9. Graph properties of Distance and Combined graphs
Graph Level Metric
Distance
Combined
Atomic
Diameter
24.4
21.3
Atomic
Avg. Shortest Path
9.7
8.9
Residue
Diameter
10.1
6.7
Residue
Avg. Shortest Path
4.3
3.2
A.6.2. GRAPH CURVATURE ANALYSIS
We analyzed Ollivier-Ried curvature of Distance and Combined graphs using an example protein (PDB-ID 215J). Figure shows that Combined graphs exhibit more positively curved edges, indicating reduced over-squashing and improved long-range information propagation in graph neural networks (Topping et al., 2021).
A.7. Code Availability
Implementation will be protein-statie-ddyaniie ftw.ammiiiiiiiingi........
made
available
https://github. com com/PKGuo
15

---

Boosting Protein Graph Representations through Static-Dynamic Fusion
Distance
0.4
Ollivie- Ricci curvalure Kon
0.0
Combined
-02
-04
2.0
Distance
Density
Combined
1.0
0.0
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
Ollivier-Ricci curvature kon
Figure Ollivier-Ried curvature analysis comparing Distance and Combined graphs for protein PDB-ID 215J. The color scale represents curvature values, with red indicating positive curvature and blue indicating negative curvature. The density plot shows the distribution of curvature values, showing Combined graphs have more positively curved edges.
16


Reviews:
[{"review_id": "JHDUVcC5VK", "reviewer": "Reviewer_n6c2", "summary": "The paper introduces a novel graph representation technique that integrates both static structural information and dynamic correlations from molecular dynamics (MD) trajectories for enhanced protein property prediction. This technique combines relational graph neural networks (RGNNs) with a dual approach:Distance-Based Graph: Captures spatial proximity using Euclidean distances between nodes.\nCorrelation-Based Graph: Derives motion correlations from MD trajectories, highlighting dynamically coupled regions that may be spatially distant. The Combined Graph integrates these two sources of information, allowing the model to leverage both structural constraints and dynamic interactions.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Essential References Not Discussed**\n\n> Dynamical surface representation methods, like [1]. [1] Sun, D., Huang, H., Li, Y., Gong, X., & Ye, Q. (2023). DSR: dynamical surface representation as implicit neural networks for protein. Advances in Neural Information Processing Systems, 36, 13873-13886.\n\nThank you for pointing out this relevant reference. We will include this citation in our revised manuscript and discuss how our approach relates to dynamical surface representation methods.\n\n**Weakness 1:** \n> The approach may be computationally intensive due to the incorporation of MD trajectories and complex graph processing.\n\nThe computational cost of our approach can be divided into three steps:\n\n1. **Generating molecular dynamics simulations.** Our approach utilizes the ever-growing availability of MD data rather than generating new simulations. For example, the recently funded EU Horizon project (Grant agreement ID: 101094651) aims at creating a Molecular Dynamics Data Bank similar to the existing protein data bank (PDB).\n\n2. **Data processing and preprocessing.** Various publicly available Python packages exist for analyzing MD trajectories, such as PyTraj which we used in our implementation. While computing correlation matrices requires significant computational resources, this is a one-time preprocessing step. We efficiently parallelized this computation across 50 jobs on Intel Xeon Platinum processors (36 cores each), completing all correlation matrices for the dataset in approximately 30 minutes. Once computed, these matrices are stored and reused without additional overhead.\n\n3. **Model training.** In our experiments, training with the Combined Graph requires only 15-30% more time compared to using the Distance Graph alone, which we consider an acceptable trade-off given the significant performance improvements observed across all tasks.\n\nWe argue that our integration of molecular dynamics information through correlation graphs is computationally efficient compared to methods that might incorporate entire molecular dynamics trajectories. By essentially compressing the complex dynamical behavior into correlation edges, we achieve a balance between capturing essential dynamic information and maintaining computational tractability.\n\n**Weakness 2:** \n> How to build the dataset, or how to get the dynamic information? In your setting, It seems that you get the complex and dynamics by Amber20 software package? it seems that the dynamics are obtained by software simulation instead of real wet-lab experiments, how to evaluate the correctness of the dataset?\n\nWhile the structures of the complexes have been experimentally determined through X-ray crystallography, the dynamics data was indeed collected through simulations. The main reason being that there are no wet-lab experiments that yield time-resolved atomic positions. Note there are methods such as NMR spectroscopy that can provide some information on dynamics, but the availability of these data is highly limited as the respective experiments are challenging. \n\nThe molecular dynamics data generated by MISATO follow the current state-of-the-art and have been extensively validated on experimental data (https://www.nature.com/articles/s43588-024-00627-2). This validation process ensures that the simulated dynamics reasonably approximate real protein behavior, providing confidence in the reliability of our approach.\n\n**Question 1:** \n> Line 124-125, why the threshold is set to 0.6 and 0.3?\n\nThese thresholds are indeed hyperparameters, and there's no theoretical method to determine their optimal values directly. For the distance thresholds (4.5Å for atomic-level and 10Å for residue-level), we adopted widely established values from the literature as stated in line 145, left column: \"These thresholds are widely used in protein modeling: the 4.5Å threshold captures meaningful atomic interactions (Bouysset & Fiorucci, 2021), while the 10Å threshold is commonly adopted for residue-level contacts (Gligorijevic et al., 2021b)\".\n\nAs we mention in the paper at line 127, right column: \"These thresholds are chosen to maintain similar graph sparsity, thereby achieving a fairer comparison when either Correlation or Distance Graph is used.\"\n\nSpecifically, we conducted an analysis on a subset of proteins to determine correlation thresholds that would yield graphs with comparable sparsity (similar average node degree and edge count) to the distance-based graphs. This approach ensures that any performance differences between Distance and Correlation graphs stem from the fundamental information encoded by different edge construction methods (spatial proximity versus dynamic correlation), rather than from differences in graph density.", "claims_and_evidence": "Yes. The authors claim that their approach provides superior performance across three tasks: Atomic Adaptability Prediction, Binding Site Detection and Binding Affinity Prediction.", "methods_and_evaluation_criteria": "Yes. The authors utilize Relational Graph Convolutional Networks (RGCN) and Relational Graph Attention Networks (RGAT) as baseline models. Experimental results are presented with statistical significance over multiple runs.", "theoretical_claims": "No. This is not a theoretical paper.", "experimental_designs_or_analyses": "Yes. The datasets are split using sequence clustering to prevent information leakage. Comprehensive ablation studies are conducted to demonstrate the benefit of combining static and dynamic graphs.", "relation_to_broader_scientific_literature": "The paper builds upon recent advancements in protein representation learning, graph neural networks, and MD simulations. It effectively combines concepts from static graph-based methods (e.g., structure-based GNNs) and dynamic analysis (e.g., dynamical network analysis, mutual information).", "essential_references_not_discussed": "dynamical surface representation methods, like [1].\n[1] Sun, D., Huang, H., Li, Y., Gong, X., & Ye, Q. (2023). DSR: dynamical surface representation as implicit neural networks for protein. Advances in Neural Information Processing Systems, 36, 13873-13886.", "other_strengths_and_weaknesses": "Strengths:\n1. Innovative Graph Representation: The combination of static and dynamic features offers a more comprehensive view of protein behavior.\n2. Robustness of Results: The improvements are consistent across different architectures and evaluation metrics.\n\nWeaknesses:\n1. The approach may be computationally intensive due to the incorporation of MD trajectories and complex graph processing.\n2. How to build the dataset, or how to get the dynamic information? In your setting, It seems that you get the complex and dynamics by Amber20 software package? it seems that the dynamics are obtained by software simulation instead of real wet-lab experiments, how to evaluate the correctness of the dataset?", "other_comments_or_suggestions": "None.", "questions_for_authors": "1. Line 124-125, why the threshold is set to 0.6 and 0.3? \n2.See weakness.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "DoAlMrWt4h", "reviewer": "Reviewer_Au2g", "summary": "The authors propose to integrate structural and dynamic distance-based features into relational graph neural networks to predict local and global properties of 3D protein biomolecules. The authors' experiments are comprehensive and informative, and this work outlines a notable gap in the literature on protein representation learning. Nonetheless, the depth of the authors' methodological contributions is quite limited, which makes this work still seem preliminary.\n\n## Update after rebuttal:\nThe authors have addressed my main concern regarding the novelty and impact of this work. As such, I am comfortable with my current score of \"Accept\".", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**To Weakness 1:**\n\nWe appreciate the reviewer's feedback. While our approach appears straightforward, its significance lies in bridging the gap between static structural information and dynamic behavior in protein representation.\n\nTo address concerns about experimental depth and generalizability, we've conducted additional experiments:\n\n- **Domain-specific architectures**: We evaluated our approach on SS-GNN (Zhang et al., 2023, https://doi.org/10.1021/acsomega.3c00085), a specialized model for binding affinity prediction. We maintained all hyperparameters and featurization exactly as reported by the original authors, only replacing the GNN component with RGCN. The results show consistent improvements when using our Combined Graph approach [Results: https://anonymous.4open.science/r/rebuttal_2025_1-16F1/ss-gnn_binding_affinity_dist5.0_corr0.70.png.png https://anonymous.4open.science/r/rebuttal_2025_1-16F1/ss-gnn_binding_affinity_dist8.0_corr0.60.png.png]\n\n- **Equivariant architectures**: As mentioned in our response to Weakness 2, we've also tested our approach with a relational EGNN variant.\n\nOur primary contribution is demonstrating that integrating static and dynamic information provides consistent benefits across different tasks and architectures. The intentional simplicity of our approach facilitates easy integration with various models and establishes an effective baseline for future research in protein dynamics modeling - particularly important as molecular dynamics data becomes increasingly available.\n\n**To Weakness 2:**\n\nWe thank the reviewer for this comment. We originally focused on topological information (without explicit coordinates) to isolate the impact of our core contribution - the integration of dynamic correlation information. This simpler setup allowed us to directly evaluate the benefit of our graph representation approach. However, we agree that equivariant GNNs are important for protein representation learning.\n\nTo address this concern, we've now implemented a simple relational variant of EGNN (Satorras et al., 2021) and conducted additional experiments across two tasks. These experiments show that our approach generalizes beyond invariant GNNs and delivers benefits when applied to equivariant architectures as well:\n\n1. **Binding Site Detection**: Our combined graph approach shows substantial improvements over the distance-only baseline across all metrics (+14.49% in F1 score, +23.78% in AUCPR). The correlation graph alone underperforms the distance graph, but when combined, we see consistent improvements, suggesting effective integration of both information types. [Results: https://anonymous.4open.science/r/rebuttal_2025_1-16F1/relational-egnn_binding_site_detection.png.png]\n\n2. **Atomic Adaptability Prediction**: For this inherently dynamic property, the correlation graph alone shows remarkable improvements over the distance baseline (+11.97% average improvement across all metrics). Interestingly, the combined graph performs similarly to the distance graph rather than outperforming both individual graphs. We attribute this to limitations in our preliminary relational EGNN implementation, which may not optimally fuse information from different relation types. Nevertheless, these results still validate that dynamic information captured in the correlation graph provides valuable signal for predicting motion-related properties. [Results: https://anonymous.4open.science/r/rebuttal_2025_1-16F1/relational-egnn_atomic_adaptability.png.png]\n\n3. **Binding Affinity Prediction**: Experiments are still ongoing.\n\nThese experiments demonstrate that our approach extends beyond simple invariant GNNs to more sophisticated equivariant architectures. While our simple relational EGNN implementation shows mixed results for combining information types, the experiments consistently confirm the value of dynamic information for protein property prediction. With further architectural refinements, we believe the complementary nature of static and dynamic information can be more effectively leveraged in equivariant networks.\n\n**To Weakness 3:**\n\nLigands are only included in the binding affinity prediction task (not in atomic adaptability prediction or binding site detection). In protein-ligand complexes, both protein and ligand atoms are treated consistently - they are part of the same correlation and distance matrices, to which thresholds are applied to construct the adjacency matrix. The only distinction is a binary attribute specifying whether each atom belongs to the ligand or protein. We can add these details to an updated version of the manuscript.\n\n**To Question 1:**\n\nPlease see our response to Weakness 3.\n\n**To Other Comments Or Suggestions:**\n\nWe thank the reviewer for these valuable suggestions. As mentioned in our response to Weakness 2, we have implemented a relational variant of EGNN, and we agree that further exploration of relational transformers would be valuable future work.", "claims_and_evidence": "The claims made by the authors are clear and convincing thanks to their repeat experiments.", "methods_and_evaluation_criteria": "The authors' evaluation criteria are clear and well-founded.", "theoretical_claims": "The authors do not make any notable theoretical claims.", "experimental_designs_or_analyses": "The validity of the authors' experimental designs is sound.", "relation_to_broader_scientific_literature": "The authors adequately establish their work in the existing body of protein representation learning literature.", "essential_references_not_discussed": "No essential references were omitted as best as I can tell.", "other_strengths_and_weaknesses": "**Strengths:**\n\n- The authors point out an important gap in the protein representation learning literature.\n- The authors conduct several key experiments to demonstrate the utility of including dynamic (i.e., molecular dynamics-derived) information for protein representation learning.\n- The authors' experiments, including their metrics and dataset splits, are standardized and easily interpretable.\n\n**Points for improvement:**\n\n- The authors' proposed methodological advances (i.e., adding dynamics-based edges into existing *invariant* relational graph neural network models) are somewhat limited in my view. The dynamics-driven insight is important, but the authors' experiments lack a depth of characterization of how far the benefits of such dynamics information extend beyond simple relational graph neural networks. More specifically, the paper currently reads as if the authors directly took the MISATO dataset, performed a simple integration of its features into existing relational graph neural networks, and then ran a bunch of experiments (which are important nonetheless). For a workshop paper, this would offer outstanding value for readers, though as a full conference submission, I believe more experimental depth is needed to provide readers (and the research community broadly speaking) with lasting value through this work.\n- Similar to the first point above, the authors only study *invariant* graph neural networks, though it has been shown for many years now that certain types of *equivariant* graph neural networks can deliver notable performance benefits for protein representation learning [1].\n- Some of the authors' (biomolecular) graph construction details are omitted, such as how ligands (i.e., small molecules) are integrated into the authors' static-dynamic graph construction processes.\n\n**References:**\n\n[1] Jamasb, A. R., Morehead, A., Joshi, C. K., Zhang, Z., Didi, K., Mathis, S. V., ... & Blundell, T. L. Evaluating Representation Learning on the Protein Structure Universe. In The Twelfth International Conference on Learning Representations.", "other_comments_or_suggestions": "I'd highly suggest the authors include experiments with more than relatively simple relational graph neural network architectures such as RGCN and RGAT. Instead, the authors may consider also experimenting with relational graph transformers such as those of [1]. More importantly in my view, however, the authors should consider relational variants of *equivariant* graph neural networks such as those of [2], since proteins can inherently be seen as 3D point clouds with node and edge features.\n\n**References:**\n\n[1] Diao, C., & Loynd, R. (2022). Relational attention: Generalizing transformers for graph-structured tasks. arXiv preprint arXiv:2210.05062.\n\n[2] Satorras, V. G., Hoogeboom, E., & Welling, M. (2021, July). E (n) equivariant graph neural networks. In International conference on machine learning (pp. 9323-9332). PMLR.", "questions_for_authors": "- How do the authors construct their input graphs for protein-ligand binding affinity prediction? Do they omit the ligands in such graphs, or do they extend their static-dynamic graph construction algorithm to ligand molecules in this setting? If the latter is the case, what are the details of this topology construction?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KVJwkMPiOQ", "reviewer": "Reviewer_RJR2", "summary": "This manuscript proposes a simple relational heterogeneous GNN model to represent both structural information and molecular dynamics correlations of proteins. It validates the effectiveness of approach in multiple protein graph representation related tasks simultaneously.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**To Weakness 1:**\n\nWe acknowledge the reviewer's concern about technical novelty. Our straightforward framework bridges static structures and dynamic correlations from molecular dynamics—a growing need as such data becomes increasingly available. The intentional simplicity of our approach is actually advantageous as it:  \n1) ensures broad applicability across different architectures,  \n2) facilitates easy adoption, and  \n3) establishes a clear baseline for future work in this emerging area.\n\nOur primary contribution is demonstrating that integrating these complementary information sources provides consistent benefits across different tasks and architectures. As detailed in our response to Reviewer 2, we've conducted additional experiments with both domain-specific (SS-GNN) and equivariant architectures (EGNN), showing that our approach generalizes beyond simple GNNs.\n\nWith AlphaFold having largely solved static structure prediction, the frontier has shifted toward sampling dynamical conformational ensembles and generating molecular trajectories. The EU Horizon project (ID: 101094651) aimed at creating a Molecular Dynamics Data Bank further emphasizes the timeliness of our contribution. Our framework provides a simple yet effective approach to leverage this emerging data, establishing a strong baseline for future research in protein dynamics modeling.\n\n**To Weakness 2:**\n\nWe appreciate the reviewer's concern about baseline comparisons. As detailed in our response to Reviewer 2, we have extended our evaluation with additional architectures beyond RGCN and RGAT:\n\n1) We implemented a relational variant of EGNN.  \n2) We adapted SS-GNN, a domain-specific model for binding affinity prediction.\n\nThese experiments demonstrate that our approach offers consistent benefits across different architectural complexity levels and maintains its advantages when integrated with domain-specific models.\n\n**To Question 1:**\n\nThank you for this question. We would like to clarify that these models address fundamentally different tasks than our approach:\n\n- **Different problem domains:** AlphaFold is designed for protein structure prediction from sequence, while our work focuses on utilizing existing structural and dynamic information to predict protein-related properties. Similarly, protein language models (PLMs) like ESM primarily operate on sequence data, not on integrating dynamics.\n\n- **Complementary research directions:** Our approach is complementary rather than competitive to powerful models like AlphaFold and protein language models (PLMs). As AlphaFold excels in static structure prediction, research is shifting toward dynamic conformations and trajectories, where our framework can provide valuable insights. Integrating PLM embeddings into node features also represents an intriguing avenue for capturing sequence, structural, and dynamic relationships simultaneously.\n\nWe believe our work effectively addresses the challenge of integrating molecular dynamics with structural data, laying a foundation for future models that bridge these currently separate areas.\n\n**To Question 2:**\n\nThank you for this question. Our approach of combining structural and dynamic information has solid theoretical foundations:\n\n- **Graph-theoretic properties:** We conducted network analysis on our Distance and Combined graphs, revealing significant improvements in key graph properties. For atomic-level graphs, the network diameter decreased from 24.44 to 21.32, and the average shortest path length reduced from 9.7 to 8.9 when correlation edges were added. For residue-level graphs, these improvements were even more dramatic, with diameter decreasing from 10.12 to 6.68 and average shortest path length from 4.3 to 3.2. These quantitative metrics demonstrate that correlation edges create critical shortcuts in the graph.\n\n- **Physics-driven graph rewiring:** Our approach can be viewed as a physics-driven graph rewiring method. Such rewiring is known to mitigate over-squashing in GNNs [1]. The correlation edges, derived from actual physical motion relationships, create direct pathways between dynamically coupled but spatially distant regions.\n\n- **Graph curvature analysis:** We analyzed the Ollivier-Ricci curvature of both Distance and Combined graphs. The combined graphs show general increases in positively curved edges (red in the visualization), indicating improved information flow properties. Positive curvature regions are associated with better message passing efficiency in graph neural networks. An example (PDB-ID 2I5J) is here: [https://anonymous.4open.science/r/rebuttal_2025_1-16F1/figure_ricci.png]\n\nThese analyses provide theoretical support for why our combined graph approach enhances performance, especially in tasks involving long-range protein interactions.\n\n**References:**  \n[1] Attali, H., Buscaldi, D., & Pernelle, N. (2024). *Rewiring techniques to mitigate oversquashing and oversmoothing in GNNs: A survey.", "claims_and_evidence": "I think the claims made by the manuscript have been well verified. There are no obvious flaws to be found.", "methods_and_evaluation_criteria": "This paper presents a simpler relational graph neural network model that addresses protein-related applications. Its technical contribution may be limited in terms of the GNN research field. It is of application value from the field of protein prediction applications.", "theoretical_claims": "This paper makes no new explicit theoretical claims.", "experimental_designs_or_analyses": "I believe that the experimental work in this paper is worthy of recognition for its validation of the model on multiple protein-related tasks. The downside is that it may lack a current hotspot approach for comparing each task. Since I don't know much about these tasks, I can't give specific examples, but I believe this should be present.", "relation_to_broader_scientific_literature": "From the GNN research area, with which I am more familiar, the model may have only a limited application contribution.\n\nIn terms of bioinformatics mothodology research, this manuscript proposes that there is some value in simultaneously combining protein structural information and molecular dynamics correlations to construct graph structures.\n\nIn terms of protein-related application tasks, the current model may be from in better results. For example, AlphaFold, or LLM, so its contribution deserves further discussion.", "essential_references_not_discussed": "I think it is clear that this paper is missing some key baseline model discussions. Using only RGCN and RGAT as baseline is clearly insufficient.", "other_strengths_and_weaknesses": "Strengths\n- This paper is original for the intersection of deep learning and the biomedical field. Its a cross-field study with practical contributions.\n- The writing in this manuscript is clear and no reading difficulties were found.\n\nWeaks\n- As mentioned earlier, technological innovation is limited\n- As mentioned earlier, there are limitations to the baseline approaches used.", "other_comments_or_suggestions": "N/A", "questions_for_authors": "- Do the authors have compared current advanced models like AlphaFold or LLM, and analyzed the contributions this manuscript can make?\n\n- This paper may lack a theoretical discussion of the methodology. This article may lack a theoretical exposition of the methodology, which may also potentially strengthen the validation of the article. So is there any theoretical support for combining protein structure information with molecular motion correlations?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper proposes to study protein representation learning by leveraging both their static structure and dynamic correlation information form MD trajectories. Experimental results on three different tasks including atomic adaptability prediction, binding site detection, and binding affinity prediction prove the effectiveness of the proposed approach over competitive baselines. 

All reviewers agree the novelty of leveraging the dynamic information from MD trajectories for protein understanding. The evaluations are comprehensive and compelling. Therefore, the AC votes for acceptance.
Decision: Accept (poster)