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Molecular Graph Convolutions: Moving Beyond Fingerprints
Steven Kearnes, Kevin McCloskey, Marc Berndl, Vijay Pande, Patrick Riley
TL;DR
Molecular fingerprints encode selected structural features, motivating more general representations for drug-screening models. This paper introduces graph convolutions for small molecules, learning from atoms, bonds, and distances; performance is comparable to state-of-the-art alternatives, while important molecular biology remains outside the graph representation.
Problem
Fingerprint representations emphasize particular molecular features while leaving other structural information unused by the model.
Method
The paper introduces graph convolutions that learn molecule-level representations directly from undirected molecular graphs using atom, bond, and distance information.
Results
Graph convolution models achieved performance comparable to state-of-the-art multitask neural networks and alternative graph- or fingerprint-based methods.
Takeaways & Limitations
Graph-based methods provide an integrated approach to virtual screening rather than merely serving as alternative molecular descriptors.
Takeaways & Limitations
The molecular graph omits three-dimensional shape, electrostatics, quantum effects, and conformational flexibility relevant to biological interactions.
Abstract
from arXiv · showhide
Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the molecular structure while ignoring others, rather than allowing the model to make data-driven decisions. We describe molecular "graph convolutions", a machine learning architecture for learning from undirected graphs, specifically small molecules. Graph convolutions use a simple encoding of the molecular graph---atoms, bonds, distances, etc.---which allows the model to take greater advantage of information in the graph structure. Although graph convolutions do not outperform all fingerprint-based methods, they (along with other graph-based methods) represent a new paradigm in ligand-based virtual screening with exciting opportunities for future improvement.
1 Introduction
Molecular graph convolutions use general graph-based molecular representations to reduce reliance on application-specific fingerprints. They learn molecule-level features from atoms, bonds, and graph distances.
- Drug-design models require molecular representations linked to biological activity, physical properties, or experimental endpoints.
- Deep learning motivates using raw, general representations that can learn task-relevant features instead of relying exclusively on manually designed encodings.
- A molecular graph represents atoms and bonds as nodes and edges, with properties such as atom type and bond order.
- Molecular graph convolutions learn from undirected molecular graphs using atom and bond properties plus graph distances.
- The architecture extracts graph features into molecule-level representations that can replace fingerprint descriptors in conventional machine-learning applications.
2 Related Work
Prior cheminformatics methods encode molecular structure through 2D descriptors, 3D shape and electrostatics, fingerprints, neural networks, and graph-based architectures. These approaches vary in computational form, learned flexibility, and the graph structures they can handle.
- Cheminformatics uses inexpensive, interpretable 2D descriptors derived from molecular graphs, including extended-connectivity fingerprints.
- 3D representations emphasize molecular shape and electrostatics, often using pre-generated conformers and similarity calculations.
- Deep neural networks trained on fingerprints produced consistent gains over random forest and logistic-regression baselines in prior studies.
- Earlier graph-based models iteratively transfer learned local information across atoms and bonds or compute graph-node fixed points.
- Learned fingerprint architectures improved solubility and photovoltaic-efficiency predictions but not binding-affinity predictions.
- Spectral graph convolutions described by Bruna et al. apply when graph structure is fixed across examples and node features vary.
- Manifold convolutional networks were developed for shape descriptors invariant to perturbations such as movement and deformation.
3 Methods
The method builds an order-invariant graph convolution architecture for molecular graphs using learnable transformations over atom and pair features. Weave modules combine these operations, can be stacked to arbitrary depth, and incorporate graph-distance information while imposing a 60-heavy-atom input limit.
- Invariant-preserving architecture: The architecture preserves molecular order invariance while offering a richer space of learnable parameters than fingerprinting procedures.The model maintains invariance to atom and bond ordering through layer-specific permutation properties.
- Layer representations: Atom layers store vectors for individual atoms, whereas pair layers store vectors for atom pairs.These representations are matrices indexed by atoms and three-dimensional matrices indexed by pairs of atoms, respectively.
- Graph convolutions: Graph convolutions apply shared functions across atoms or pairs, optionally restricting pair operations to atoms within a specified graph distance.Using the same operation for every atom or pair gives the transformations their convolutional character.
- Invariant-preserving operations: The P →A operation transforms all pairs involving an atom with f and combines the results using a commutative function g.This aggregates pair information into a new feature vector for each atom while preserving the relevant permutation invariance.
- Weave modules: Weave modules combine A →A, P →P, P →A, and A →P operations, producing new atom and pair features that can be stacked to arbitrary depth.Stacked modules progressively combine lower-level features and, with bounded pair distances, incorporate longer-range information at each layer.
- Implementation boundary: The implementation represents at most 60 heavy atoms, with larger molecules reduced to an order-dependent subset during initial featurization.Only 814 of 1 442 713 unique molecules in the datasets exceeded this limit.
4 Results
Graph convolution models were broadly competitive with fingerprint-based baselines despite simple molecular inputs, while performance depended on architecture, feature reduction, and distance settings. Additional analyses showed similar simple and full featurizations, deeper feature evolution, and mixed results across enrichment and external comparisons.
- 4.1 Proof of concept: Several graph convolution models matched the PMTNN baseline, with W2N2 statistically indistinguishable on PCBA, MUV, and Tox21.Models that performed worse often had very small median ΔAUC differences.
- 4.1 Proof of concept: Graph convolution models generally performed worse than or comparably to PMTNN on ROC enrichment at false positive rates of 1%, 5%, 10%, and 20%.Subsequent performance analysis and hyperparameter optimization used ROC AUC rather than enrichment scores.
- 4.1 Proof of concept: Graph convolution results were comparable to published NFP results, improved significantly on photovoltaic efficiency, and were slightly below published IRV values on HIV.The graph convolution models used multitask training for the NFP comparison and fewer training examples than IRV on HIV.
- 4.2 Input featurization: Simple featurization achieved similar median 5-fold mean AUC scores to full featurization, using only atom type, bond type, and graph distance.This suggests additional full-representation features were mostly ignored or derivable from simpler inputs.
- 4.3 Architecture: Successive Weave modules made atom features more heterogeneous and environment-sensitive, with simple and full inputs producing similarly diverse distributions after two modules.In local models, successive modules incorporate information from progressively larger molecular regions.
- 4.3.1 Number of Weave modules: Deeper architectures outperformed one Weave module; more than two modules added little on PCBA and Tox21, while three gave the best median AUC on MUV with substantially longer training.The W2N2 centerpoint used two Weave modules, maximum atom-pair distance 2, Gaussian histogram reductions, and 2000- and 100-unit fully connected layers.
- 4.3.2 Alternative feature reductions: Gaussian histogram reductions consistently improved scores relative to sum reductions, while RMS had similar absolute AUC distributions and slightly higher median AUC on MUV.The comparison used a two-module architecture with maximum atom-pair distance 2.
- 4.3.3 Distance-dependent pair features: Maximum pair distance 2 improved PCBA performance over adjacent pairs, whereas unlimited distance was worse; adjacent pairs performed best on MUV and Tox21.These results suggest the models did not effectively preserve or emphasize distance-dependent information from initial graph-distance features.
5 Discussion
Graph convolutions learn molecule-level representations directly from atom, bond, and graph-distance information, achieving performance comparable to several established approaches while remaining flexible. The authors also identify optimization opportunities and note that molecular graphs omit substantial three-dimensional biological information.
- 5 Discussion: Graph convolutions use atoms, bonds, and pairwise graph relationships to learn molecule-level representations for virtual screening.They operate directly on undirected molecular graphs rather than relying on fixed fingerprint descriptors.
- 5 Discussion: Performance was comparable to state-of-the-art multitask neural networks using traditional fingerprints, neural fingerprints, and influence relevance voter.
- 5 Discussion: Parameter experiments found relatively minor sensitivity to Weave-module count and maximum atom-pair distance on the studied datasets.Two Weave modules, maximum pair distance 2, and Gaussian histogram reductions were suggested as a starting point for optimization.
- 5 Discussion: The complete molecular graph lets the model use available structural information flexibly instead of encoding one predetermined fingerprint.Backpropagation can tune parameters throughout the network, unlike traditional descriptors whose features are fixed initially.
- 5 Discussion: Current graph convolution models do not consistently outperform state-of-the-art fingerprint-based models, leaving hyperparameter, architecture, and efficiency improvements as opportunities.The authors specifically mention convolution depths, reduction functions, atom-pair handling, and more efficient Weave operations.
- 5 Discussion: Molecular graphs omit much of the information relevant to biological systems, including shape, electrostatics, quantum effects, and conformational flexibility.Extending graph-based deep learning to three-dimensional biology introduces additional complexities, including multiple-instance learning in small-data settings.
Version information
The version history records changes to validation, model comparisons, metrics, baseline training, and molecule-count calculations across successive revisions.
- Version information: v2 changed cross-validation to use a held-out validation set and added model comparisons and methodological background.
- Version information: v3 added ROC enrichment metrics, revised baseline training to use sample weights, and added a BEDROC comparison to IRV models.
- Version information: v3 corrected logistic-regression training and updated the method for calculating the number of unique molecules.
- Version information: Some AUC values changed slightly because of model retraining and/or reevaluation.
A Appendix: Model comparison
The appendix presents box plots of model performance across PCBA, MUV, and Tox21 dataset groups, including absolute AUCs and differences from a PMTNN baseline.
- A Appendix: Model comparison: Box plots summarize absolute 5-fold mean AUC scores for each model across dataset groups.
- A Appendix: Model comparison: Difference box plots compare each model’s 5-fold mean AUC with the pyramidal (2000, 100) multitask neural network baseline.These plots are visual analogs of the sign-test confidence intervals reported in Table 4.
- A Appendix: Model comparison: Figures A.1, A.2, and A.3 report model performance on PCBA, MUV, and Tox21 datasets, respectively.
B Appendix: ROC enrichment
The appendix reports ROC enrichment for baseline and graph convolution models at multiple false-positive rates, with separate optimization and sign-test comparisons against PMTNN.
- B Appendix: ROC enrichment: ROC AUC and enrichment values at different false-positive rates were optimized separately using each model’s held-out validation set.Therefore, metrics at different false-positive rates need not come from the same training checkpoints.
- B Appendix: ROC enrichment: ROC enrichment tables report median 5-fold mean values at 1%, 5%, 10%, and 20% false-positive rates.
- B Appendix: ROC enrichment: Each table includes the median delta from the PMTNN baseline and a 95% Wilson score interval estimating the probability of outperforming it.
- B Appendix: ROC enrichment: Sign-test confidence intervals that do not include 0.5 identify comparisons differing from the midpoint criterion.
C Appendix: Input featurization
The appendix compares models using simple and full input featurizations, reporting absolute and baseline-relative 5-fold mean AUC scores.
- C Appendix: Input featurization: Models are compared using absolute 5-fold mean AUC scores and differences against a baseline model.The figures use box plots for both views, without y-axis cropping.
- C Appendix: Input featurization: Figure C.1 compares models with simple and full input featurizations.
D Appendix: Hyperparameter sensitivity
The appendix evaluates hyperparameter experiments using absolute and baseline-relative 5-fold mean AUC score distributions.
- D Appendix: Hyperparameter sensitivity: Each Section 4.3 experiment is shown with absolute 5-fold mean AUC box plots and differences against a baseline model.The difference plots are presented without y-axis cropping.
D.1 Number of Weave modules
This section compares models across different numbers of Weave modules, feature reduction methods, and maximum atom pair distances.
- D.1 Number of Weave modules: Figure D.1 compares models with different numbers of Weave modules.
- D.1 Number of Weave modules: Figure D.2 compares models with different feature reduction methods.
- D.1 Number of Weave modules: The appendix presents a full box plot for the model comparisons.
- D.1 Number of Weave modules: The appendix presents a difference box plot versus the N1 model.
- D.1 Number of Weave modules: Figure D.3 compares models with different maximum atom pair distances.
E Appendix: Atom pair feature evolution
The appendix visualizes how atom-pair features change through graph convolution networks under full and simple input featurizations.
- E Appendix: Atom pair feature evolution: Atom-pair features evolve through successive Weave modules, with similar initial featurizations diverging after the operations.The visualizations use full and simple input featurizations on ibuprofen atom pairs.
- E Appendix: Atom pair feature evolution: Many initial pair features describe graph distance, and pairs beyond the maximum atom-pair distance are masked.Only one ordering of each pair is represented, such as (a, b) rather than (b, a).
- E Appendix: Atom pair feature evolution: Unique atom pairs occupy rows, while initial pair features appear before the successive Weave-module outputs.Whitespace separates the initial features from later module outputs.
- E Appendix: Atom pair feature evolution: The appendix includes Gaussian membership functions and their visualization as part of the feature representation materials.