Molecular geometry prediction using a deep generative graph neural network

Elman Mansimov; Omar Mahmood; Seokho Kang; Kyunghyun Cho

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Molecular geometry prediction using a deep generative graph neural network

Elman Mansimov, Omar Mahmood, Seokho Kang, Kyunghyun Cho

arXiv:1904.00314v2Mar 31, 2019cs.LGphysics.comp-phstat.ML

TL;DR

Molecular conformation generation is important, but conventional force-field energies may not match molecular energies observed in nature. The paper learns an energy function with a conditional deep generative graph neural network, which on three datasets produces diverse conformations generally closer to references and faster than conventional methods, while enabling a QM9 hybrid strategy.

Problem
Conformation generation requires valid molecular geometries, but conventional methods rely on hand-designed force-field energies that are often poorly correlated with molecular energy observed in nature.
Method
A conditional deep generative graph neural network learns an energy function from data by generating molecular conformations likely to be energetically favorable and experimentally observed.
Results
Across three small-molecule datasets, the method generates conformations generally closer to reference conformations, with lower RMSD variance, preserved geometric diversity, and faster computation than force-field methods.
Takeaways & Limitations
The model can serve both as a standalone conformation generator and as an initialization for MMFF, combining the strengths of learned generation and force-field minimization on QM9.
Takeaways & Limitations
Performance is weaker on larger COD and CSD molecules, where architecture capacity and inconsistent reference environments may degrade results; force-field refinement also increases RMSD there.

Abstract

from arXiv · show

A molecule's geometry, also known as conformation, is one of a molecule's most important properties, determining the reactions it participates in, the bonds it forms, and the interactions it has with other molecules. Conventional conformation generation methods minimize hand-designed molecular force field energy functions that are often not well correlated with the true energy function of a molecule observed in nature. They generate geometrically diverse sets of conformations, some of which are very similar to the lowest-energy conformations and others of which are very different. In this paper, we propose a conditional deep generative graph neural network that learns an energy function by directly learning to generate molecular conformations that are energetically favorable and more likely to be observed experimentally in data-driven manner. On three large-scale datasets containing small molecules, we show that our method generates a set of conformations that on average is far more likely to be close to the corresponding reference conformations than are those obtained from conventional force field methods. Our method maintains geometrical diversity by generating conformations that are not too similar to each other, and is also computationally faster. We also show that our method can be used to provide initial coordinates for conventional force field methods. On one of the evaluated datasets we show that this combination allows us to combine the best of both methods, yielding generated conformations that are on average close to reference conformations with some very similar to reference conformations.

Introduction

Conformation generation matters for molecular properties and several applications, but conventional force-field energies only crudely approximate nature’s molecular energy. The paper proposes learning this function directly from data and reports favorable accuracy, diversity, speed, and a dataset-specific hybrid strategy.

Motivation: Molecular conformation generation predicts valid three-dimensional atomic coordinates relevant to chemical and physical properties and applications such as 3-D QSAR and virtual screening.Experimental determination can be time-consuming and costly.
Existing approach: Conventional methods minimize hand-designed force-field energy functions whose minima approximate, but may poorly represent, molecular energy observed in nature.These methods commonly generate geometrically diverse conformations, including some near lowest-energy configurations.
Proposed method: The proposed deep generative graph neural network learns an energy function end-to-end by generating energetically favorable conformations more likely to be observed experimentally.The method learns from data rather than relying solely on a hand-designed energy function.
Evaluation: Across three small-molecule databases, the model’s conformations are on average more likely to be close to reference conformations than those from conventional force-field methods.The comparison uses RMSD between generated and reference conformations.
Results: The model has lower RMSD variance, preserves geometric diversity, and is computationally faster than force-field methods.These findings concern average closeness, diversity, and computational cost rather than a uniformly better best conformation.
Hybrid strategy: For QM9, initializing force-field minimization with model-generated conformations combines the methods’ strengths, while the model’s best conformation is generally farther from reference than the force-field best.The hybrid strategy is presented as a dataset-specific result.

Conformation Generation

The paper represents molecules as complete graphs and treats conformation generation as finding or sampling plausible local energy minima. Conventional pipelines construct semi-automated force fields, generate diverse starting conformations, and repeatedly optimize them.

Molecular representation: A molecule is modeled as an undirected complete graph whose vertices are atoms and whose edges represent pairwise atomic interactions.Node and edge features encode atom and pairwise-interaction information.
Conformations: Each conformation assigns a three-dimensional coordinate vector to every atom, and multiple plausible conformations can arise from different local minima and environmental conditions.The formulation therefore concerns a set of conformations rather than a single configuration.
Sampling: Conformation generation can alternatively sample conformations from a Gibbs distribution defined by the molecular energy function.The number of generated conformations is denoted by S.
Pipeline: The computational problem separates into constructing an efficient energy function and then optimizing or sampling from it to generate conformations.This decomposition covers both minimization and sampling-based generation.
Energy function construction: Conventional energy functions are semi-automatically designed to encode chemical properties, with parameters estimated computationally or experimentally; UFF and MMFF are examples.These force fields provide established baselines for molecular geometry generation.
Energy minimization: Repeated minimization from different initial conformations exploits energy-function non-convexity to collect multiple local-minimum conformations.Each run may reach a distinct local minimum.
Initialization: Distance geometry methods such as DG or ETKDG generate constraint-satisfying initial conformations before iterative algorithms such as L-BFGS minimize the energy.The initial coordinates satisfy lower and upper bounds on interatomic distances.

Deep Generative Model for Molecular Geometry

The paper learns a data-driven energy function with a conditional variational graph autoencoder, modeling molecular conformations likely to be experimentally observed. Its architecture uses graph message passing, latent variables, alignment-aware likelihoods, and prior regularization.

Learning the Energy Function: The model learns an energy function from molecule–reference-conformation pairs by maximizing the data likelihood.Here, “energy” denotes an objective reflecting the likelihood of a conformation given a molecular graph.
Latent Generative Model: A conditional variational graph autoencoder captures the multimodal conformation distribution while allowing efficient sampling through latent variables Z.The marginal likelihood is optimized through a stochastic lower bound because it is generally intractable.
Graph Representation: Message passing updates node and edge representations across layers, with shared aggregation and gated-recurrent parameters.The MPNN operates directly on molecular graphs and is invariant to graph isomorphism.
Distribution Parameterization: The prior, likelihood, and approximate posterior are parameterized with related MPNNs, while the likelihood additionally conditions on latent variables and outputs 3-D atom-coordinate distributions.The posterior uses the reference conformation’s distance matrix for amortized inference.
Geometric Invariance: Rotation and translation are handled by aligning reference conformations to predictions before computing likelihoods, encouraging high probability for easily aligned conformations.This makes the objective compatible with RMSD-style geometric comparison.
Prior Regularization: An unconditional factorized Normal prior regularizes the model because the posterior–prior KL divergence is unchanged by jointly shifting both distributions.Without this regularization, the posterior and prior means could diverge during optimization.

Experimental Setup

The experiments evaluate one model per dataset against ETKDG-initialized force-field baselines on three chemically diverse molecular databases. Inference compares direct generative sampling with using generated conformations to initialize MMFF optimization, and quality is assessed by RMSD.

Datasets: The study uses three databases—QM9, COD, and CSD—to examine the approach across datasets with distinct molecular properties.COD and CSD include crystallographic data, while QM9 references are obtained under a consistent DFT environment.
Datasets: QM9 contains 133,015 molecules with up to 9 heavy atoms, paired with DFT-optimized reference conformations.The dataset includes separate 5,000-molecule validation and test sets.
Datasets: COD contains 66,663 filtered molecules with at most 50 heavy atoms, and its reference conformations come from varied experimental or DFT environments.Separate 3,000-molecule validation and test sets are held out.
Datasets: CSD contains 236,985 filtered organic and metal-organic crystallographic structures, with separate 3,000-molecule validation and test sets.Its structures were observed experimentally and span many atom types.
Baselines: Baselines minimize UFF or MMFF force fields from ETKDG-generated initial conformations using RDKit default hyperparameters.The comparison controls for implementation and environmental effects through common default settings.
Training: The proposed approach trains one conditional variational graph autoencoder per dataset and uses dropout, Adam, and fixed batch-based training settings.Networks use 50 hidden units per message-passing layer and dataset-specific depths.
Inference: Direct CVGAE samples can either be used as generated conformations or passed to MMFF as trainable initializations instead of DG or ETKDG.The two inference modes are CVGAE and CVGAE+MMFF.
Evaluation: Evaluation uses RMSD between generated and reference conformations because DFT energy calculations are often impractical for larger molecules.This follows prior work rather than directly evaluating molecular energies.

Results

Across three small-molecule datasets, CVGAE reliably generates conformations with lower RMSD variability than force-field baselines while preserving diversity and improving computational efficiency. Its predictions are generally competitive on median RMSD, though force-field methods can achieve better best-case RMSD for larger molecules.

Generation success: CVGAE always generated the specified 100 conformations for test molecules, whereas UFF and MMFF failed on some molecules.Results were reported on molecules for which all evaluated methods generated at least one conformation.
RMSD results: CVGAE achieved significantly lower RMSD standard deviation than ETKDG + Force Field across all three datasets, while median mean RMSD was roughly similar across methods.The evaluation sampled 100 conformations per test molecule and reported median mean, standard deviation, and best RMSD.
Conformation diversity: CVGAE did not collapse to extremely similar conformations, although its samples were less diverse than ETKDG + MMFF on all datasets.Diversity was measured using the mean and standard deviation of pairwise RMSD among generated conformations.
Computational efficiency: CVGAE was 2× more efficient than ETKDG + UFF/MMFF on QM9, while CVGAE + MMFF was slightly slower on that dataset.Efficiency was measured by generating one conformation for one molecule at a time on an Intel(R) Xeon(R) E5-2650 v4 CPU.
RMSD by molecular size: Across molecule sizes, CVGAE had lower or similar median RMSD and lower standard deviation, whereas ETKDG + MMFF often had lower best RMSD for larger COD/CSD molecules.For molecules with at most 12 atoms, CVGAE and CVGAE + MMFF had slightly higher best-RMSD standard deviation; for larger molecules, it was lower.

Analysis and Future Work

CVGAE performs better on QM9 than on COD and CSD, while dataset environment inconsistency and molecular size constrain performance. Figures analyze RMSD by molecule size and illustrate cases where neural-network and force-field methods differ, including mixed outcomes after MMFF refinement.

Limitations: CVGAE performs better than ETKDG + MMFF on QM9 than on COD and CSD.For larger molecules, limited message passing and hidden units may produce conservative conformations; larger architectures are proposed as future work.
Limitations: Inconsistent environments for COD and CSD reference conformations may degrade performance, particularly for larger molecules.The paper recommends evaluating larger molecules with reference conformations obtained under identical environments and conditioning the model on environment.
Results: CVGAE has lower RMSD variance, so relatively few samples are needed before obtaining a conformation with good RMSD.The method is also faster than force-field methods and uses fewer computational resources after training.
Figure analysis: Figures 3 and 4 plot mean and standard deviation of best and median RMSDs against heavy-atom count for COD/CSD and QM9.Molecules are grouped by heavy-atom count, while groups containing fewer than 1% of the mean number of molecules are omitted.
Figure analysis: Figure 5 compares extreme RMSD differences between CVGAE and ETKDG + MMFF, while Figure 6 shows the largest RMSD changes after applying MMFF to CVGAE conformations.The figures organize reference, predicted, and force-field-refined conformations in rows to expose cases favoring either approach.
Future work: Initializing force-field optimization with CVGAE conformations is promising on QM9 but increases RMSD on COD and CSD.The paper suggests investigating this dataset-dependent behavior and exploring joint training of CVGAE with a force-field method.