Enhancing Graph Contrastive Learning for Protein Graphs from Perspective of Invariance

Method: The paper’s primary contributions—Functional Community Invariance (FCI) and 3D Protein Structure Invariance (3-PSI)—directly address known gaps in protein contrastive learning. Most existing approaches use 2D topology manipulations that may disrupt functionally critical residues or rely on overly simplistic 3D perturbations that distort key structural motifs. By incorporating community preservation (via spectral constraints and side-chain similarity) and 3D backbone constraints (via dihedral angles or secondary structure rotations), the paper’s techniques remain biologically plausible. This stronger biological grounding is exactly what protein graph methods need to capture higher fidelity embeddings.

Benchmark Datasets: The authors run experiments on four major tasks: fold classification, enzyme reaction classification, gene ontology (GO) prediction, and enzyme commission (EC) number prediction. These are widely used benchmarks in structure-based protein modeling research. For fold classification, they even subdivide it (family, superfamily, fold), which is aligned with SCOP classification and demonstrates how well the method distinguishes proteins at varying levels of structural/sequence similarity. GO and EC tasks capture functional annotation challenges, which are biologically relevant real-world scenarios.

Potential Improvements: One area that might strengthen the paper is a scalability discussion—e.g., how the computational overhead of generating more sophisticated 3D augmentations compares with simpler random approaches when moving to large datasets. Another is comparing or combining these graph-based methods with large-scale protein language models. However, the existing baselines and metrics remain representative of graph-based contrastive learning and typical protein structure tasks.

The paper’s main theoretical arguments center on characterizing how individual edge perturbations affect the graph spectrum. Specifically: Theorem 4.1 (Bounds of Spectral Changes) Claim: When a single edge is flipped (added or removed), the change in the eigenvalues of the normalized Laplacian can be upper-bounded and lower-bounded by expressions involving the spectral embeddings (the eigenvectors) of the unperturbed graph. Assessment: This result aligns with known techniques in spectral graph theory, where the Davis–Kahan or Weyl inequalities often provide bounds on eigenvalue/eigenvector perturbations. The text’s statement that spectral changes are related to the l_2 distance between the two node eigenvector embeddings also matches typical graph-spectral intuitions: if two nodes lie “far apart” in the spectral embedding, flipping edges between them tends to yield a larger spectral impact. No immediate inconsistencies stand out; the proof outline (in references to standard matrix perturbation results) appears coherent and consistent with existing spectral bounding approaches.

Lemma 4.2 (Weighted Graphs) Claim: The absolute spectral change when dropping an edge of weight  can be upper-bounded by the product of $\lvert w_{ij}\rvert$ and terms involving eigenvectors/eigenvalues. Assessment: This follows a similar logic to Theorem 4.1 but accounts for weighted adjacency. The bound’s proportionality to $\lvert w_{ij}\rvert$ is intuitively correct—heavier edges should create more significant perturbations when flipped. This is reminiscent of standard matrix perturbation arguments. The statement seems plausible, and no obvious red flags arise in the bounding steps as described. The full formal proofs are outlined briefly in the text (and presumably with additional detail in an appendix). From the information provided and familiarity with spectral graph theory, these claims appear mathematically consistent and do not contradict well-known eigenvalue/eigenvector perturbation theories. The derivations rely on expansions of the difference between Laplacian eigenvalues and standard bounding approaches (e.g., norm-based inequalities). While the paper does not reproduce the entire step-by-step derivation in the main body (likely for brevity), the reasoning is logically sound on inspection.

1. Benchmark Tasks and Datasets: The authors evaluate on four widely used tasks in protein representation learning (fold classification, enzyme reaction classification, GO term prediction, and EC number prediction), each with recognized standard datasets.

2. Comparisons with Baselines: Baseline Variety: The authors compare with multiple 2D topology-based GCL approaches (GraphCL, GCS, etc.) and 3D structure-based augmentations (random coordinate perturbation, homology modeling tools). Hyperparameters: The paper mentions the range of augmentation strengths (e.g., the proportion of edges changed in 2D, or number of dihedral/secondary structure rotations in 3D). They present ablation curves that show how these hyperparameters affect performance. This is helpful to confirm that gains are robust to different augmentation intensities.

3. Ablation Studies: FCI vs. 3-PSI vs. Combined: The experiments systematically compare using Functional Community Invariance (FCI) alone, 3D Protein Structure Invariance (3-PSI) alone, or combining them. Observing that the combined approach generally yields the best performance supports the synergy claim. Sensitivity to Augmentation Strength: Varying the fraction of edges dropped/added (2D) or the number of secondary-structure rotations/dihedral perturbations (3D) is a direct test of how robust the method is to over- or under-augmentation. This analysis appears well-motivated and thorough.

4. Robustness Checks: Structural Perturbation at Test Time: The authors apply random rotations to subsets of residues at test time, mimicking protein conformation changes or partial misalignments. They track performance as the proportion of rotated residues increases. This design is a realistic measure of robustness, given that experimental structural data can be noisy.

5. Qualitative Analyses: Functional Community Preservation: They measure the fraction of intact protein pockets under each augmentation method. This is a direct reflection of how well the augmentation strategy avoids disrupting crucial functional sites.

6. Potential Limitations or Omissions

   1. Comparison to Protein Language Models: The authors do not evaluate the proposed method in conjunction with or against large-scale pretrained language models (like ESM or ProtT5). While not necessarily invalidating the experiment design, it’s a potential extension.
   2. Scalability: They do not provide time or memory complexity analyses for 3D augmentations, though that would be helpful for large-scale applications.

1. Protein Representation Learning • Over the past few years, protein representation learning has emerged as a critical area at the intersection of machine learning, structural bioinformatics, and computational biology. Classic approaches include: • Sequence-based methods (e.g., language-model–type architectures such as ESM, ProtT5, and ProtBERT), focusing on large-scale protein sequence corpora. These methods often capture powerful evolutionary context but may overlook critical 3D structural cues. • Structure-based methods (e.g., GNNs like GVP, GearNet, and IEConv), which treat proteins as graphs of residues to incorporate geometric constraints. These approaches have proven effective in tasks such as fold classification, function prediction, and protein–protein interaction studies.

2. Graph Contrastive Learning (GCL) • In the broader machine learning literature, contrastive learning has become a standard technique for self-supervised representation learning on images, text, and graphs. Recent advances on graphs (e.g., GraphCL, GCS, Auto-GCL, and CI-GCL) demonstrate how data augmentations can push GNNs toward more generalizable embeddings. However, these methods often rely on simplistic graph transformations (like random edge dropping or adding) and rarely leverage specific biological or domain constraints.

3. Biologically Grounded Augmentations • In protein research, random manipulations of graph structures can cause the loss of essential structural or functional information (e.g., removing edges around catalytic sites). The idea of building biology-aware augmentations partly echoes earlier efforts in structure-based drug design and protein–ligand modeling, where physically plausible perturbations are used to sample conformational states. • This paper’s Functional Community Invariance (FCI) connects with the notion of residue interaction networks and community detection (common in network analyses of protein structures), ensuring that biologically relevant clusters (pockets, communities, etc.) remain intact. Prior literature on “residue co-evolution” and “community detection in protein structures” has highlighted the importance of pockets and functional domains for accurate protein functional interpretation.

1. Rives A, Meier J, Sercu T, Goyal S, Lin Z, Liu J, Guo D, Ott M, Zitnick CL, Ma J, Fergus R. Biological structure and function emerge from scaling unsupervised learning to 250 million protein sequences. Proceedings of the National Academy of Sciences. 2021 Apr 13;118(15):e2016239118.
2. Jumper J, Evans R, Pritzel A, Green T, Figurnov M, Ronneberger O, Tunyasuvunakool K, Bates R, Žídek A, Potapenko A, Bridgland A. Highly accurate protein structure prediction with AlphaFold. nature. 2021 Aug;596(7873):583-9.
3. Batzner S, Musaelian A, Sun L, Geiger M, Mailoa JP, Kornbluth M, Molinari N, Smidt TE, Kozinsky B. E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nature communications. 2022 May 4;13(1):2453.

The design of the augmentation techniques make sense, as they are rooted in biological principles to ensure that the augmentations are meaningful and realistic. However, the authors did not describe the GNN encoder used in detail, simply pointing to the work of Fan et al. (2023). The model was also trained on an end-to-end fashion for each classification task, which means the learnt representation would change for each downstream task. I have two concerns/suggestions: 1) To fully demonstrate the effectiveness of the proposed augmentation techniques, the authors could use the benchmark models (eg. ProNet, CDConv, GraphCL, GearNet, etc.) and compare performance before and after the augmentation methods are used. 2) The model is trained with equal weight to classification loss and CL loss (λ=1). There is no ablation study on how different λ impact model performance. 3) To demonstrate robustness of the learnt representation, a probable way is to train the GCL model using the proposed augmentation methods and use the learnt representation on downstream tasks. Regarding evaluation, the proposed metrics (accuracy and F-1 score) is suitable for classification tasks.

Yes, the equations and theorems in the main text are correct. One question, L_FCL is defined but L_(3-PSI) is not clearly defined.

The authors used 4 datasets for classification tasks only. The model performance and ablation studies on these datasets are valid. However, since the protein structure and functionality is preserved, it is interesting to investigate the model performance on dataset such as ligand binding affinity (eg. PDBbind).

The manuscript points out one important limitation in the literature, that the graph augmentation is solely based on topological features, ignoring the intrinsic biological properties of proteins. As one of the most important large molecules to study, how GNN models can be tailored to effectively learn protein representation is an important problem. The proposed augmentation techniques are carefully designed following biological principles and should have broader impact to future work.

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The proposed methods and evaluation criteria make sense for the problem except for the selection of the random rotation angle θ in Section 4.2 (line 246). There appears to be no theoretical justification for the choice of the random rotation angle, which requires further clarification.

I have verified the accuracy of the claim stated in lines 90–96: "To generate augmented graphs while preserving the 3D-related information of proteins, 3-PSI employs two distinct coordinate perturbation strategies: (1) rotations of backbone dihedral angles and (2) rotations of secondary structures (α-helices and β-sheets), ensuring that peptide planes and secondary structures remain intact during graph augmentation." It has been well-established that dihedral angles, α-helices, and β-sheets significantly influence a protein's structure and, consequently, its function. However, it is worth noting that other factors may also have a substantial impact on protein structure and function, which this paper has not considered.

I have carefully examined the experimental designs and analyses. Overall, the experiments in this paper are highly convincing. However, when comparing 2D topology-based methods, the selected baseline methods are all graph contrastive learning approaches that do not specifically account for the topological structure of protein graphs. Intuitively, these methods may significantly impact the original protein structure. If there are 2D topology-based methods designed specifically for protein graph topology, it would be beneficial to use them as baselines for comparison.

1. This paper extends spectral graph contrastive learning by incorporating functional community constraints, building on prior work like GraphCL, GCS, and CI-GCL.
2. This paper bridges the gap between 2D and 3D protein graph learning, incorporating structural constraints often overlooked in self-supervised learning.
3. This paper improves generative augmentation techniques, refining methods used in homology modeling tools (e.g., SWISS-MODEL, MODELLER) by introducing rotation-aware 3D augmentation.

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The proposed methods are appropriate for the problem. The authors evaluate on standard protein-related benchmarks with comprehensive comparison across various baselines, including protein-specific methods, 2D topology-based GCL, and 3D structure-based GCL methods. However:

1. Since protein structures are assumed to be known in advance before model training, their annotations are easily obtainable. Alternatively, structure retrieval approaches like Foldseek [r1] could be used to find similar structures with known function annotations. This should be considered as a baseline in the comparison.

2. The evaluation would benefit from comparison with state-of-the-art structure learning models [r2,r3,r4,r5] and equivariant graph neural networks [r6] as encoders for protein-specific baselines.

3. The paper lacks complexity analysis, making it unclear whether 3-PSIAlpha + FCI could be easily adopted into mainstream transformer-based foundation models.

[r1] Kempen et al. Fast and accurate protein structure search with Foldseek. Nature biotechnology 2024.

[r2] Zhou et al. Uni-mol: A universal 3d molecular representation learning framework. ICLR 2023.

[r3] Huang et al. Protein 3D Graph Structure Learning for Robust Structure-Based Protein Property Prediction. AAAI 2024.

[r4] Lin et al. Evolutionary-scale prediction of atomic-level protein structure with a language model. Science 2023.

[r5] Wang et al. S‐PLM: Structure‐Aware Protein Language Model via Contrastive Learning Between Sequence and Structure. Advanced Science 2025.

[r6] Liao et al. EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations. ICLR 2024.

The derivation of the Functional Community Invariance approach is sound, establishing clear connections between spectral constraints and community preservation. The authors effectively develop theoretical links between graph spectra and community structures, providing solid motivation for their approach.

The experimental setup is comprehensive. The authors:

1. Compare against multiple baseline approaches.

2. Perform ablation studies to validate each key component.

3. Analyze augmentation strength effects, evaluate robustness against structural perturbations.

4. Provide qualitative analyses through visualization and functional community preservation.

The performance improvements are modest but consistent across tasks and evaluation settings. The robustness analysis is particularly valuable, showing that their approach maintains better performance under structural perturbations.

This paper builds upon both graph contrastive learning and protein-specific approaches. However, the comparison with equivariant graph neural networks and protein foundation models could be more extensive. Recent works like ESM-2 [r1], EquiformerV2 [r2], and other models have shown strong performance on protein-related tasks but are not thoroughly compared against.

[r1] Lin et al. Evolutionary-scale prediction of atomic-level protein structure with a language model. Science 2023.

[r2] Liao et al. EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations. ICLR 2024.

[r1] Kempen et al. Fast and accurate protein structure search with Foldseek. Nature biotechnology 2024.

[r2] Zhou et al. Uni-mol: A universal 3d molecular representation learning framework. ICLR 2023.

[r3] Huang et al. Protein 3D Graph Structure Learning for Robust Structure-Based Protein Property Prediction. AAAI 2024.

[r4] Lin et al. Evolutionary-scale prediction of atomic-level protein structure with a language model. Science 2023.

[r5] Wang et al. S‐PLM: Structure‐Aware Protein Language Model via Contrastive Learning Between Sequence and Structure. Advanced Science 2025.

[r6] Liao et al. EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations. ICLR 2024.