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Atomic Convolutional Networks for Predicting Protein-Ligand Binding Affinity
Joseph Gomes, Bharath Ramsundar, Evan N. Feinberg, Vijay S. Pande
TL;DR
Drug discovery needs accurate, efficient ways to predict protein-ligand affinity across an enormous chemical space, but existing approaches rely on hand-designed physical or cheminformatics features. This paper introduces end-to-end Atomic Convolutional Neural Networks that learn interactions from 3-D atomic coordinates and achieve competitive or better performance than established structure-based methods, while reaching sub-1 kcal/mol test errors on evaluated datasets.
Problem
Drug discovery must screen vast numbers of small molecules while balancing prediction speed, cost, and accuracy.
Method
Atomic Convolutional Neural Networks learn 3-D atomic features end-to-end and predict binding free energy by modeling energies of protein-ligand complexes and their components.
Results
ACNN models perform comparably or better than GRID-RF and other evaluated methods, with test errors below 1 kcal/mol on core-set models and maximum mean unsigned errors below 1 kcal/mol on refined-set tests.
Takeaways & Limitations
The fully differentiable, learned representation provides a data-driven physics-based foundation for future structure-based bioactivity prediction improvements.
Takeaways & Limitations
ACNN performance degrades on larger, lower-quality PDBBind data because raw-coordinate representations are sensitive to noise in crystal structures and binding measurements.
Abstract
from arXiv · showhide
Empirical scoring functions based on either molecular force fields or cheminformatics descriptors are widely used, in conjunction with molecular docking, during the early stages of drug discovery to predict potency and binding affinity of a drug-like molecule to a given target. These models require expert-level knowledge of physical chemistry and biology to be encoded as hand-tuned parameters or features rather than allowing the underlying model to select features in a data-driven procedure. Here, we develop a general 3-dimensional spatial convolution operation for learning atomic-level chemical interactions directly from atomic coordinates and demonstrate its application to structure-based bioactivity prediction. The atomic convolutional neural network is trained to predict the experimentally determined binding affinity of a protein-ligand complex by direct calculation of the energy associated with the complex, protein, and ligand given the crystal structure of the binding pose. Non-covalent interactions present in the complex that are absent in the protein-ligand sub-structures are identified and the model learns the interaction strength associated with these features. We test our model by predicting the binding free energy of a subset of protein-ligand complexes found in the PDBBind dataset and compare with state-of-the-art cheminformatics and machine learning-based approaches. We find that all methods achieve experimental accuracy and that atomic convolutional networks either outperform or perform competitively with the cheminformatics based methods. Unlike all previous protein-ligand prediction systems, atomic convolutional networks are end-to-end and fully-differentiable. They represent a new data-driven, physics-based deep learning model paradigm that offers a strong foundation for future improvements in structure-based bioactivity prediction.
Introduction
Drug discovery must screen an enormous chemical space while balancing speed, cost, and accuracy. ACNNs address limitations of hand-curated molecular representations by learning chemically relevant features directly from molecular structure and experimental data.
- Introduction: Drug discovery faces a trade-off between screening speed, cost, and accuracy across a chemical space estimated at over 10^60 compounds.Testing the entire synthetically accessible small-molecule space is computationally intractable.
- Introduction: Traditional machine-learning models require molecules to be represented with hand-curated, fixed-length feature vectors.These models have been used extensively in virtual screening and cheminformatics.
- Introduction: Previous protein-ligand models used hand-curated features or voxel-based convolutional networks for binder classification.These approaches did not directly provide the same end-to-end prediction framework introduced here.
- Introduction: ACNNs optimize molecular featurization and the neural network simultaneously, enabling data-driven learning of hierarchical chemical features from local three-dimensional structure.The architecture applies convolutional operations directly to atomic coordinates.
- Introduction: The paper applies ACNNs to predict binding free energy from non-covalent interactions using experimental data and reports a fully differentiable, size-extensive energy function.The evaluation uses protein-ligand complexes from the PDBBind dataset.
Atomic Convolutional Neural Networks
The ACNN converts neighbor-listed atomic coordinates and types into learned radial interaction features, then aggregates per-atom energies into a molecular energy. Radial pooling reduces dimensionality, limits overfitting, and makes representations invariant to neighbor-list ordering.
- Distance matrix and neighbor list construction: Neighbor listing converts Cartesian coordinates into a distance matrix and atomic-number matrix while reducing construction complexity from O(N^2) to O(NM).The neighbor list uses a 12 Å cutoff and typically retains 12 nearest neighbors.
- Atom type convolution: Atom type convolution applies a 1x1 filter to neighbor distances and creates separate feature channels for each atomic number.Its output has shape (N,M,Nat) and can be viewed as atom-type-specific copies of the distance matrix.
- Radial pooling layer: Radial pooling reduces parameters and overfitting while producing representations invariant to neighbor-list atom-index permutations.The operation abstracts the convolution output through feature binning.
- Radial pooling layer: Radial pooling downsamples atom-type convolution outputs through non-overlapping (1xM x1) receptive fields with Nr learned radial filters.The pooled output has shape (N,Nat,Nr), with a fixed 12 Å interaction cutoff.
- Radial pooling layer: Radial pooling features represent summed pairwise interactions between a central atom and neighboring atoms grouped by atom type.Examples include H-H, H-C, and H-N interactions.
- Atomistic fully connected network: The network maps each atom’s pooled features to an atomic energy and sums these energies to obtain a permutation-invariant molecular energy.Shared fully connected weights allow generalization to larger systems when atom types and radial filters remain fixed.
Application of atomic convolution networks to predicting protein-ligand binding affinity
The model uses an energy-based architecture with weight-sharing replicas for the complex, protein, and ligand, incorporating a thermodynamic cycle into end-to-end training.
- Architecture: The architecture produces an energy that is size-extensive and differentiable with respect to atomic positions.
- Architecture: Three weight-sharing replica networks separately process the complex, protein, and ligand to predict the complex energy difference.The replicas correspond to the complex, protein, and ligand components.
- Thermodynamic training: The thermodynamic cycle is integrated as a subcomponent of the complete network while training it end-to-end to predict ΔG.This design respects the underlying adsorption thermodynamics.
- Optimization: ACNN models are trained with stochastic gradient descent using batch size 24, the ADAM optimizer, and 100 epochs.
Baseline Comparison
The study benchmarks ACNNs against structure-based GRID models, ligand-based graph convolutional and ECFP models, and PDBBind evaluation protocols using multiple train/test splits and affinity metrics.
- Structure-based baselines: GRID combines ligand and protein structural information, including binding-pocket interactions and individual protein and ligand features.
- Structure-based baselines: GRID features support both random forest and fully connected neural network regressors, forming the GRID-RF and GRID-NN baselines.
- Ligand-based baselines: GCNN provides a ligand-based baseline by representing molecules as undirected graphs whose vertices and edges encode atoms and bonds.A graph convolutional layer applies the same learnable function to every atom.
- Ligand-based baselines: ECFP decomposes molecules into non-hydrogen-atom segments and extends them through bonds into larger substructures with corresponding identifiers.
- Dataset: PDBBind 2015 contains core, refined, and full subsets with 195, 3,706, and 14,260 structures, respectively.The study uses the core and refined subsets to train and benchmark ACNNs.
- Evaluation: Four 80/20 train/test split strategies are evaluated: random, stratified, scaffold, and temporal, using a fixed random seed.
- Evaluation: Performance is evaluated with squared Pearson correlation R2 for logKi and mean unsigned error for binding free energy.
Discussion and Results
On PDBBind core and refined sets, ACNN models generally matched or exceeded structure-based baselines and achieved sub-1 kcal/mol test error, while overfitting and noisy structural data limited broader scaling and extrapolation.
- ACNN models show comparable or better performance than GRID-RF across all PDBBind core splits in Pearson R2 and mean absolute error.
- Ligand-based baselines generally generalized less well than structure-based models on core sets, although GCNN performed best on the scaffold-split core test set.
- Less than 1 kcal/mol test mean absolute error was achieved across all ACNN core models, despite training on fewer than 160 datapoints.The authors identify this threshold as previously cited chemical accuracy for rapid computational drug design.
- Large core-set train–test gaps indicate overfitting, while larger full PDBBind datasets introduce structural noise that destabilizes training and performance.The authors suggest more data, stronger regularization, and higher-quality or refined structures as remedies.
- On refined datasets, ACNN models had comparable Pearson R2 and nearly identical mean absolute error to GRID models, with dropout improving train–test generalizability.The maximum ACNN test mean unsigned error across refined-set splits was less than 1 kcal/mol.
- ACNN performance is expected to worsen when extrapolating to substantially different atom types, interaction types, ligand scaffolds, or protein binding pockets.The authors note that retraining with relatively few data points may improve prediction on systems outside the original training set.
Author contributions statement
The authors report distinct contributions to algorithm development, featurization, experimental planning, data analysis, interpretation, and manuscript preparation.
- J.G. and B.R. developed the atomic convolution algorithm, while E.N.F. and B.R. developed the grid featurizer algorithm.
- J.G., B.R., and E.N.F. planned the experiments, and J.G. collected and analyzed the experimental data.
- J.G., B.R., and E.N.F. interpreted the data and wrote the manuscript, with V.S.P. advising and editing it.
- All authors approved the final revision of the manuscript.
Supplementary Information
The supplementary figures compare experimental and predicted logKi for ACNN and GRID-RF across core and refined PDBBind training and test splits. Each figure includes random, stratified, scaffold, and temporal evaluations.
- Figure 3 compares experimental and predicted logKi for ACNN on the PDBBind core training set across four split types.
- Figure 4 compares experimental and predicted logKi for ACNN on the PDBBind core test set across four split types.
- Figures 5 and 6 show GRID-RF comparisons on the PDBBind core training and test sets, respectively, using the same four split types.
- Figures 7 and 8 show ACNN comparisons on the PDBBind refined training and test sets, respectively, across random, stratified, scaffold, and temporal splits.
- Figures 9 and 10 show GRID-RF comparisons on the PDBBind refined training and test sets, respectively, across the same four split types.