Boosting Protein Graph Representations through Static-Dynamic Fusion

To Weakness 1:

We 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:

1. ensures broad applicability across different architectures,
2. facilitates easy adoption, and
3. establishes a clear baseline for future work in this emerging area.

Our 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.

With 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.

To Weakness 2:

We 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:

1. We implemented a relational variant of EGNN.
2. We adapted SS-GNN, a domain-specific model for binding affinity prediction.

These experiments demonstrate that our approach offers consistent benefits across different architectural complexity levels and maintains its advantages when integrated with domain-specific models.

To Question 1:

Thank you for this question. We would like to clarify that these models address fundamentally different tasks than our approach:

• 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.

• 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.

We 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.

To Question 2:

Thank you for this question. Our approach of combining structural and dynamic information has solid theoretical foundations:

• 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.

• 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.

• 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]

These analyses provide theoretical support for why our combined graph approach enhances performance, especially in tasks involving long-range protein interactions.

References:
[1] Attali, H., Buscaldi, D., & Pernelle, N. (2024). *Rewiring techniques to mitigate oversquashing and oversmoothing in GNNs: A survey.

To Weakness 1:

We 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.

To address concerns about experimental depth and generalizability, we've conducted additional experiments:

• 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]

• Equivariant architectures: As mentioned in our response to Weakness 2, we've also tested our approach with a relational EGNN variant.

Our 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.

To Weakness 2:

We 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.

To 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:

1. 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]

2. 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]

3. Binding Affinity Prediction: Experiments are still ongoing.

These 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.

To Weakness 3:

Ligands 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.

To Question 1:

Please see our response to Weakness 3.

To Other Comments Or Suggestions:

We 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.

Essential References Not Discussed

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.

Thank 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.

Weakness 1:

The approach may be computationally intensive due to the incorporation of MD trajectories and complex graph processing.

The computational cost of our approach can be divided into three steps:

1. 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).

2. 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.

3. 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.

We 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.

Weakness 2:

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?

While 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.

The 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.

Question 1:

Line 124-125, why the threshold is set to 0.6 and 0.3?

These 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)".

As 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."

Specifically, 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.