Multi-Scale Representation Learning on Proteins

• Robustly predicting candidate-protein properties can guide searches through the vast design space of proteins, while understanding protein function matters for studying disease mechanisms.Source: §1 · p. 1
• Prior methods typically focus on sequence, three-dimensional structure, or surface alone, although protein representations need to capture their complex nature.Similar sequences can fold into different conformations, and protein-ligand interactions are controlled by surface contacts.Source: §1 · pp. 1–2
• HOLOPROT connects surface and structure graphs with explicit edges, allowing each level to integrate the encoding from the level below.Information from the surface can inform residue encodings with geometric and chemical properties arising from residue-neighborhood interactions.Source: §1 · p. 2
• Molecular superpixels segment protein surfaces into higher-level motifs, improving construction memory efficiency with little to no performance degradation across evaluated tasks.Source: §1 · p. 2
• The paper evaluates HOLOPROT on protein-ligand binding-affinity regression and enzyme-catalyzed reaction classification.Source: §1 · p. 2

Sequence-based methods

• Sequence-based methods use one-dimensional CNNs or pretrained language models for fold, function, and binding-affinity tasks, but ignore proteins’ full spatial complexity.Source: §2 · pp. 2–3

Structure-based methods

• Structure-based methods use 3D CNNs or graph neural networks for tasks including affinity, enzyme, interface, and structure-quality prediction.Other approaches combine sequence encoding with tertiary-structure graph convolution or adapt filters to primary, secondary, and tertiary structure.Source: §2 · p. 3

Surface-based methods

• Surface-based geodesic convolutions learn chemical and geometric fingerprint vectors and improve performance on binding-pocket and protein-interface prediction.Source: §2 · p. 3

Protein Motif Detection

• Existing motif tools detect evolutionary motifs but do not fully segment the surface; prior surface methods may omit physiological properties, be computationally expensive, or target particular tasks.HOLOPROT’s molecular superpixels instead use both geometric and chemical features for task-independent, computationally efficient segmentation.Source: §2 · p. 3

3 Multi-Scale Protein Representation

• The surface graph captures coarser protein details, while the structure graph captures finer details; directed links connect surface nodes to residue nodes sharing their residue identifier.Typically, 20–40 surface nodes map to one structure node.Source: §3 · p. 3
• The structure graph represents residues as nodes and links residues whose Cα atoms fall within a distance threshold, implicitly capturing structural levels in each node’s neighborhood.Source: §3 · p. 3

3.1 Multi-Scale Encoder

• The multi-scale encoder uses one message-passing neural network per graph layer, tying representations together through connections between scales.Source: §3.1 · p. 4

3.1.1 Surface Message Passing Network

• The surface network takes surface-node and edge features as input, propagates messages for K iterations, and outputs a representation for each surface node.Source: §3.1.1 · p. 4

3.1.2 Structure Message Passing Network

• For each structure node, an MLP combines its initial features with the mean encoding of surface nodes sharing its residue identifier before structure message passing computes node representations.Source: §3.1.2 · p. 4

3.2 Task Specific Training

• The protein graph representation aggregates structure-node representations and is used for downstream tasks; the encoder is evaluated on affinity regression and enzyme-reaction classification.Source: §3.1.2 · p. 4, §3.2 · p. 4

3.2.1 Protein-Ligand Binding Affinity

• For binding-affinity prediction, HOLOPROT’s protein graph representation is concatenated with a message-passing ligand graph representation and passed to an MLP.The model is trained with mean squared error.Source: §3.2.1 · p. 4

3.2.2 Enzyme-Catalyzed Reaction Classification

• For enzyme-catalyzed reaction classification, the protein graph representation is passed to an MLP to obtain prediction logits, and training uses cross-entropy loss.Source: §3.2.2 · p. 5

4 Superpixels on Molecular Surfaces

• Molecular superpixels are surface segments that capture higher-level fingerprint features and motifs, including hydrophobic binding sites.They are introduced to improve computational and memory efficiency for large protein-surface meshes.Source: §4 · p. 5
• ERS segmentation maximizes random-walk entropy rate to favor compact, homogeneous clusters and adds a balancing term that encourages similar cluster sizes.The method is selected to meet the desired molecular-superpixel properties after other segmentation tools are described as producing irregular, non-compact regions.Source: §4 · p. 5
• The surface graph incorporates geometric and chemical features through non-negative edge similarities, which define transition probabilities for a random walk over surface vertices.The transition probability is the edge similarity divided by the total similarity of edges incident to the starting vertex.Source: §4 · p. 5
• The ERS objective combines entropy rate and a balancing function; both terms are monotone and submodular, enabling efficient optimization with submodular-optimization techniques.The optimization is constrained to edge subsets with at least k connected components.Source: §4 · p. 6
• Each molecular superpixel is represented by mean, standard deviation, maximum, and minimum surface-feature values, while graph edges use Wasserstein distances between neighboring superpixels.The superpixel graph is denoted GM = (VM, EM).Source: §4 · p. 6
• HIV-1 protease superpixels are spatially compact and overlap hydrophobic patches while capturing coherent areas across surface features.Figure 2 shows the example; further examples are in Appendix C.2.Source: §4 · p. 6

5 Evaluation

• HOLOPROT evaluates binding-affinity regression and enzyme reaction-classification as representative tasks reflecting protein engineering’s multi-objective and multi-task demands.Affinity prediction uses PDBBIND 2019 and ligand-scaffold or 30% and 60% sequence-identity splits; classification predicts all four EC-number levels.Source: §5 · p. 6, §5.1 · p. 6, §5.2 · p. 8

5.1 Protein-Ligand Binding Affinity Prediction

• HOLOPROT outperforms all methods on scaffold and identity 60% affinity splits, and most baselines on identity 30%, with lower metric variability.The molecular-superpixel version performs similarly, with no or little performance loss.Source: §5.1 · p. 7, Table 1 · p. 7

5.2 Enzyme-Catalyzed Reaction Classification

• HOLOPROT does not surpass the top enzyme-classification method, but achieves equivalent or better results than other methods with a fraction of their parameters.Molecular superpixels produce a small increase in overall classification performance.Source: §5.2 · p. 8, Table 2 · p. 8

5.3 Ablation Studies

• HOLOPROT with and without molecular superpixels improves over structure-only and surface-only representations, while surface-only performs poorly for enzyme reaction classification.Table 3 also shows no improvement from applying an MPN within a molecular superpixel over using summary features.Source: §5.3 · pp. 8–9, Table 3 · p. 9

5.4 Limitations

• HOLOPROT depends on existing protein structures and generated surface manifolds, and requires precomputed surface meshes that add preprocessing before deployment.The paper notes that structure prediction, cryo-electron microscopy, homology modeling, or on-the-fly surface computation could partly address these constraints.Source: §5.4 · p. 9

6 Conclusion

• HOLOPROT integrates finer and coarser protein details by connecting sequence and structure with the surface.Molecular superpixels capture higher-level surface fingerprint motifs and improve memory efficiency without reducing overall performance.Source: §6 · p. 9
• The paper validates HOLOPROT on protein-ligand binding affinity and enzyme-catalyzed reaction class prediction, reporting consistent performance across tasks and dataset splits.It partly outperforms current state-of-the-art methods and is significantly more parameter-efficient.Source: §6 · p. 9

A Message Passing Network

• The Weisfeiler-Lehmann network message-passing step uses node features, edge features, and neighboring nodes to update node representations.The passage defines τ as a nonlinear function, L as the total number of message-passing steps, and initializes h_v^(0) from f_v.Source: A Message Passing Network · p. 14

B.1 Ablation Studies

• Table 4 is intended to compare HOLOPROT components and molecular-superpixel feature summarization on PDBBind identity 60% and scaffold splits, but HOLOPROT-with-superpixels-and-MPN values were still pending.The table caption identifies the architectural choices under evaluation; no comparative outcomes are supplied here.Source: §B.1 · p. 14, Table 4 · p. 14

C.1 Computing Molecular Surfaces

• MSMS constructs triangulated molecular surfaces from a reduced surface; meshes were downsampled to roughly 2600 faces to balance detail and preprocessing memory use.Meshes used hydrogen density 3.0 and a water probe radius of 1.5, with geometric and chemical features computed on the mesh.Source: §C.1 · pp. 14–15

C.2 Examples of Molecular Superpixels

• With k = 20, molecular superpixels are spatially compact and overlap with single-feature surface regions while capturing coherent areas across features.Examples include a hepatitis C virus helicase inhibitor complex with 867 residues and an aspartic proteinase complex with 330 residues.Source: Figure 3 · p. 15, §C.2 · p. 15

D Experimental Details

• The implementation uses PyTorch, PyTorch Geometric, RDKit, and W&B; an example molecular-superpixel visualization depicts a 330-residue protein complex.Figure 4 shows superpixels and hydropathy, shape-index, and free-electron surface features for Endothia aspartic proteinase.Source: D Experimental Details · p. 15, Figure 4 · p. 15

D.1.1 Surface Layer

• Surface-graph nodes carry four geometric and chemical features, while edges encode triangulation geometry, edge-length ratios, node distance, and the angle between node normals.The node features are shape index, free electrons and proton donors, hydropathy, and Poisson–Boltzmann electrostatics.Source: §D.1.1 · p. 16

D.1.2 Structure Layer

• The structure graph uses amino-acid residues as nodes and connects residues within a distance threshold, with residue descriptors and inter-residue angle and Cα distance as features.Node descriptors include residue name, secondary structure, solvent-accessible surface, and hydrophobicity; DSSP computes secondary structure.Source: §D.1.2 · p. 16

D.1.3 Ligand Molecules

• Ligands are represented as graphs whose listed edge features encode bond type, conjugation, and ring membership.Bond type distinguishes single, double, triple, and aromatic bonds.Source: §D.1.3 · p. 16

D.2 Datasets

• Binding-affinity evaluation uses the refined 2019 PDBBind subset with scaffold, identity 60%, and identity 30% splits.The identity splits constrain test-set sequence identity relative to training, while the scaffold split places molecules with rare or unseen Bemis–Murcko scaffolds in the test set.Source: §D.2 · p. 16
• Enzyme-catalyzed reaction classification uses the PDB files and splits provided by Hermosilla et al. [2021].The dataset construction details are referred to Hermosilla et al. [2021, § C].Source: §D.2 · p. 17

D.3 Network Architectures

• Affinity tuning sweeps surface and structure hidden dimensions and MLP dimensions, while classification tuning is limited to learning rates and hidden-layer activations.Classification tuning was restricted because of time constraints.Source: §D.3 · p. 17
• All HOLOPROT models use Adam and clip gradients to a maximum norm of 10.0.Source: §D.3 · p. 17

D.3.1 Protein-Ligand Binding Affinity

• The full-surface affinity model has 1.44M parameters, while its molecular-superpixel counterpart has 1.76M, with different structure-layer dimensions and message-passing steps.Both use a 300-dimensional ligand MPN with 4 steps; the affinity MLP has one hidden layer, sized 512 for full surface and 256 for superpixels.Source: §D.3.1 · p. 17

D.3.2 Enzyme-Catalyzed Reaction Classification

• Both classification models have roughly 0.64M parameters; a 5.2M-parameter model without hyperparameter search reaches 79.2% accuracy, a small overall improvement.The standard models use LeakyReLU and dropout at each message-passing step and in the classification MLP.Source: §D.3.2 · p. 17

D.3.3 Baselines

• Affinity baselines use concatenated protein and ligand representations as MLP input, with ligand embeddings generally restricted to dimension 300 where possible.Townshend et al. [2020] results are reported values; other baselines use repository code, with task-specific adaptations and tuning.Source: §D.3.3 · p. 17
• Öztürk et al. [2018] uses five-fold cross-validation after combining the training and validation sets, with the best model using 32 filters and ligand and protein sequence filter sizes of 4 and 8.The model typically stops early around epoch 80 during 100-epoch training.Source: §D.3.3 · p. 17
• The Bepler and Berger, Rao, Gainza, and Hermosilla baselines use pretrained or repository implementations, with ligand encoders and hyperparameter sweeps varying by model.The passages describe a bidirectional LSTM for Bepler and Berger [2019], a Transformer for Rao et al. [2019], graph ligand representations for Gainza et al. [2020] and Hermosilla et al. [2021], and memory or time constraints on some sweeps.Source: §D.3.3 · p. 18

D.4 Computing Infrastructure

• HOLOPROT models run within 16 hours for 200 epochs and within 8 hours for 100 epochs; Rao et al. [2019] and Hermosilla et al. [2021] baselines take about 40 hours for 300 epochs.For the enzyme-catalyzed reaction classification dataset, HOLOPROT training is stopped after 24 hours on an NVIDIA 1080Ti GPU, typically at 100–110 epochs with batch size 10.Source: §D.4 · p. 18