TopEC

Summary¶

TopEC is a 3D graph neural network (GNN) framework that predicts 4-digit Enzyme Commission (EC) numbers by processing localized 3D structural descriptors centered on active-site regions rather than global protein folds or sequence homology.[1] Trained explicitly without fold bias on over 800 EC classes, TopEC avoids the widespread failure mode where global-fold similarity or sequence homology misdirects functional annotation for enzymes sharing convergent catalytic geometry within non-homologous scaffolds.[1] On benchmarks stripped of sequence and fold overlap (AF703+PDB300), TopEC achieves an $F_1$-score of $0.72$, outperforming 2D GNNs, global-fold classifiers, and sequence-alignment algorithms on novel enzyme folds.[1]

Architecture & Localized 3D Active-Site Descriptor¶

TopEC abandons whole-protein sequence/structure embeddings in favor of localized 3D atomic subgraphs extracted around known or predicted catalytic/binding pockets.[1]

             ┌─────────────────────────────────────────────────────────────┐
             │       Full 3D Structural Model (PDB / AlphaFold2)           │
             └──────────────────────────────┬──────────────────────────────┘
                                            │
                                            ▼
             ┌─────────────────────────────────────────────────────────────┐
             │ Localized Active-Site Extractor (Radius r = 10 - 15 Å)     │
             │ - Center on catalytic centroid / ligand / pocket prediction │
             │ - Extract atomic coordinates (x, y, z) & Amber ff19SB types │
             └──────────────────────────────┬──────────────────────────────┘
                                            │
                                            ▼
             ┌─────────────────────────────────────────────────────────────┐
             │ 3D Graph Construction (Nodes = Atoms, Edges = Geometry)     │
             │ - Node features: Atom type, formal charge, SASA, H-bond cap │
             │ - Edge features: Interatomic distances r_ij & angles θ_ijk  │
             └──────────────────────────────┬──────────────────────────────┘
                                            │
                                            ▼
             ┌─────────────────────────────────────────────────────────────┐
             │ Directional 3D GNN Message Passing (DimeNet++ / SchNet)    │
             │ - Spherical Fourier-Bessel basis functions: e_ij, a_ijk     │
             │ - Directional message updates: m_ij = f(m_ki, e_ij, a_ijk)  │
             └──────────────────────────────┬──────────────────────────────┘
                                            │
                                            ▼
             ┌─────────────────────────────────────────────────────────────┐
             │ Hierarchical EC Classifier (Multi-Label Sigmoid Output)     │
             │ - EC 1-7 (Main class) -> 4-digit specific EC annotation     │
             └─────────────────────────────────────────────────────────────┘

Subgraph Extraction & Node Construction¶

Centroid Selection: The descriptor centers a spherical bounding volume of radius $r = 10\text{--}15$ Å around the catalytic centroid (derived from Catalytic Site Atlas [CSA] ground truth, bound ligand coordinates, or pocket prediction tools like POCKET-PRO/FPocket).[1]
Node Features: Each node represents a heavy atom (or $C_\alpha$ residue in reduced modes) containing a 28-dimensional feature vector:[1]
Amber ff19SB force-field atom types and elemental identity.[1]
Solvent Accessible Surface Area (SASA).[1]
Formal charge, partial charge, and hydrogen-bonding donor/acceptor capacity.[1]
Edge Construction & Geometric Encodings: Edges connect all atom pairs within cutoff distance $d_{\text{cutoff}} = 5.0$ Å.[1] Geometric relations are represented using 3D directional message passing:
Distances ($r_{ij}$): Expanded via Radial Bessel Basis functions.[1]
Angles ($\theta_{ijk}$): Expanded via Spherical Fourier-Bessel basis functions (DimeNet++ backbone), embedding 3D spatial orientation into message passing updates:[1] $$e_{ij} = \text{RBF}(r_{ij}), \quad a_{ijk} = \text{SBF}(r_{ij}, \theta_{ijk})$$

Message-Passing Mechanism¶

TopEC executes $L=4$ directional message-passing layers where atom representations $h_i$ and directional edge representations $m_{ij}$ update iteratively:[1] $$m_{ij}^{(l+1)} = \sigma \left( W_{\text{msg}} h_i^{(l)} + \sum_{k \in \mathcal{N}(i) \setminus {j}} f_{\text{angle}}(a_{kib}) \cdot m_{ki}^{(l)} \right)$$ Global pooling aggregates localized subgraphs into a unified active-site embedding vector, which is classified across $\sim 800$ EC output nodes via multi-label sigmoid heads.[1]

Zero-Fold-Bias Evaluation Benchmark Methodology¶

Standard enzyme annotation benchmarks suffer from fold bias leakage: models memorize global tertiary topologies that happen to co-occur with specific functions in training sets, failing when encountering novel folds or convergent evolution.[1] TopEC evaluated functional performance using a rigorous dual-clustering split:[1]

Sequence Identity Split: MMseqs2 clustering at $30\%$ sequence identity threshold.[1]
Structural Topology Split: Foldseek structural alignment clustering to isolate distinct protein folds.[1] Test sets (AF703 and PDB300) contained zero sequence or structural fold overlap with training enzymes.[1]

Empirical Benchmark Results¶

Model Architecture	Input Granularity	Sequence Split $F_1$	Fold-Unbiased Split $F_1$	Performance Loss on Novel Folds
TopEC (3D DimeNet++)	Localized 3D Active-Site Subgraph	0.78	0.72	-7.7% (Robust)
CLEAN (Contrastive LLM)	Full Sequence Embedding	0.84	0.61	-27.4% (Severe Drop)
DeepEC	1D CNN Sequence Classifier	0.68	0.50	-26.5% (Severe Drop)
DeepFRI	2D Contact Map GNN	0.52	0.25	-51.9% (Failure)
EnzyNet	3D Volumetric Grid CNN	0.44	0.20	-54.5% (Failure)

TopEC demonstrated near-complete invariance to global fold shifts, retaining $92.3\%$ of its predictive power on novel structural folds, whereas sequence- and contact-based models suffered performance drops of $27\%\text{--}55\%$.[1]

Evaluation Across Specialist Benchmark Sets¶

Price Dataset (Challenging & Misannotated Enzymes, $N=149$): On experimentally characterized enzymes with low sequence identity to canonical database entries, TopEC correctly annotated $68.5\%$ of 4-digit EC numbers, outperforming BLAST ($31.2\%$) and DeepEC ($42.1\%$).[1]
ProSPECCTs Benchmark (Binding Site Properties DS1--DS7): TopEC maintained $> 0.70$ $F_1$-score across varying pocket volumes, structural resolution degradation (up to $2.5$ Å coordinate noise), and side-chain rotamer flexibility.[1]
Catalytic Site Atlas (CSA) Ground Truth: When pocket centroids were shifted up to $4.0$ Å away from exact CSA catalytic centers, TopEC maintained an $F_1$-score $> 0.65$, demonstrating high robustness to binding site localization uncertainty.[1]

Interpretability via GNNExplainer & Biophysical Sensitivity¶

Using GNNExplainer, TopEC identifies atomic feature subgraphs that drive catalytic classification:[1]

                     ┌─────────────────────────────────────────────────────────┐
                     │          TopEC GNNExplainer Attribution Map            │
                     └────────────────────────────┬────────────────────────────┘
                                                  │
                       ┌──────────────────────────┴──────────────────────────┐
                       ▼                                                     ▼
        ┌──────────────────────────────┐                      ┌──────────────────────────────┐
        │ Catalytic Side-Chains        │                      │ Backbone C-alpha Atoms       │
        │ - High Attribution Weights   │                      │ - Low Attribution Weights    │
        │ - Alanine mutation drops     │                      │ - Coordinate perturbation    │
        │   median AUPR by >20%        │                      │   up to 0.75 Å tolerated     │
        └──────────────────────────────┘                      └──────────────────────────────┘

Side-Chain Alanine Mutagenesis: Computational alanine scanning of top GNNExplainer-identified residues caused a median AUPR drop of $> 20\%$, confirming that the network attends directly to functional catalytic groups (e.g., Ser-His-Asp triads in hydrolases) rather than inert structural backbone atoms.[1]
Coordinate Perturbation Threshold: Gaussian noise up to $0.75$ Å applied to atomic coordinates resulted in $< 3\%$ change in predicted EC probabilities, while perturbations $> 1.5$ Å disrupted angle-dependent Fourier-Bessel representations, confirming fine-grained geometric sensitivity.[1]

Software Availability & Integration¶

Source Code & Pre-trained Models: Available at github.com/IBG4-CBCLab/TopEC.[1]
Datasets: Training subgraphs, PDB300/AF703 splits, and evaluation scripts are deposited on Dataverse at doi.org/10.25838/d5p-66.[1]

Citations¶

[1] van der Weg, K., Merdivan, E., Piraud, M., Gohlke, H. (2025). TopEC: prediction of Enzyme Commission classes by 3D graph neural networks and localized 3D protein descriptor. Nature Communications, 16, 2646. Supports: TopEC 3D DimeNet++ architecture; localized active-site descriptor ($r=10\text{--}15$ Å); fold-unbiased evaluation protocol; $F_1=0.72$ benchmark on AF703/PDB300; performance comparisons against CLEAN, DeepEC, DeepFRI, EnzyNet; Price, ProSPECCTs, and CSA benchmark results; GNNExplainer alanine mutagenesis and perturbation sensitivity. Location: Abstract; Results ("Localized 3D active-site descriptor", "Zero-fold-bias evaluation benchmark", "Performance on novel structural folds", "Evaluation on Price and ProSPECCTs datasets", "GNNExplainer feature attribution"); Figures 1--6; Supplementary Notes 1--5.