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Quantitative toxicity prediction using topology based multi-task deep neural networks

Kedi Wu, Guo-Wei Wei

arXiv:1712.04339v1q-bio.QM

TL;DR

Quantitative toxicity analysis matters for human health and environmental protection, but molecular representations must preserve relevant chemical information while remaining useful for small molecules. The paper introduces ESPH-derived descriptors, supplements them with physical descriptors, and combines them with machine-learning and multitask models; the reported methods establish state-of-the-art quantitative toxicity predictions.

  • Problem

    Experimental quantitative toxicity measurements are valuable but typically time-consuming, costly, and ethically concerning, motivating computer-aided prediction.

  • Method

    The paper constructs element-specific topological descriptors from ESPH, develops physical descriptors, and integrates them with DNN, RF, GBDT, and multitask learning.

  • Results

    ESTDs combined with physical descriptors and an MT-DNN architecture establish state-of-the-art predictions for quantitative toxicity.

  • Takeaways & Limitations

    The proposed topological learning methods provide a competitive representation for relatively small drug-like molecules and support quantitative toxicity prediction.

  • Takeaways & Limitations

    Primitive persistent homology had limited power in protein classification because it oversimplified biological information.

Abstract

from arXiv · show

The understanding of toxicity is of paramount importance to human health and environmental protection. Quantitative toxicity analysis has become a new standard in the field. This work introduces element specific persistent homology (ESPH), an algebraic topology approach, for quantitative toxicity prediction. ESPH retains crucial chemical information during the topological abstraction of geometric complexity and provides a representation of small molecules that cannot be obtained by any other method. To investigate the representability and predictive power of ESPH for small molecules, ancillary descriptors have also been developed based on physical models. Topological and physical descriptors are paired with advanced machine learning algorithms, such as deep neural network (DNN), random forest (RF) and gradient boosting decision tree (GBDT), to facilitate their applications to quantitative toxicity predictions. A topology based multi-task strategy is proposed to take the advantage of the availability of large data sets while dealing with small data sets. Four benchmark toxicity data sets that involve quantitative measurements are used to validate the proposed approaches. Extensive numerical studies indicate that the proposed topological learning methods are able to outperform the state-of-the-art methods in the literature for quantitative toxicity analysis. Our online server for computing element-specific topological descriptors (ESTDs) is available at http://weilab.math.msu.edu/TopTox/

1 Introduction

Quantitative toxicity prediction requires representations that balance molecular detail with computational tractability. This work evaluates element-specific topological and physical descriptors with machine-learning models, including a multitask strategy for small-data settings.

  • Methods: Multitask learning is motivated by sparse QSAR data because related toxicity tasks can share generalized feature representations.The paper specifically connects correlated quantitative toxicity endpoints with the viability of a topology-based multitask strategy.
  • Motivation: Molecular geometry can be prohibitively expensive to represent, whereas traditional topological methods may discard too much geometric information.Persistent homology is presented as a compromise because it captures topology across spatial scales while retaining geometric information in topological invariants.
  • Research gap: ESPH had not been validated for small-molecule characterization, whose diverse element types, compositions, and stereochemical structures make properties sensitive to molecular differences.The work therefore examines ESPH representability and predictive power for small molecular diversity and variability.
  • Contribution: Element-specific topological descriptors are introduced via ESPH to represent small molecules for quantitative toxicity analysis and prediction.The descriptors are designed to retain chemical information during topological simplification while addressing molecular diversity and structural variability.
  • Methods: The study pairs topological and microscopic-model physical descriptors with MT-DNN, ST-DNN, RF, and GBDT to assess quantitative toxicity prediction.Physical descriptors serve both as ancillary descriptors and as competitive descriptors for evaluating the proposed topological methods.
  • Results: The proposed topological learning provides a competitive description of relatively small drug-like molecules for quantitative toxicity analysis.The authors report that inherent correlations among toxicity endpoints make the topology-based multitask approach viable.

2 Methods and algorithms

The methods combine element-specific topological and auxiliary physical descriptors with machine-learning models for quantitative toxicity prediction. Persistent homology summarizes molecular structure through simplicial complexes, homology groups, Betti numbers, filtrations, and persistence barcodes, while ESTDs preserve element-specific information.

  • Descriptor and learning framework: The study pairs element-specific topological descriptors and auxiliary physical-model descriptors with random forest, gradient boosting, and deep neural-network algorithms.The workflow also considers single-task and multi-task learning, emphasizing multi-task deep convolutional neural networks for quantitative toxicity endpoints.
  • Filtration and persistence: Filtration varies a nested sequence of simplicial complexes, allowing persistent homology to track which homology classes remain alive across scales.The resulting birth, death, and persistence values are recorded in barcodes and provide chemical or biological information used by the method.
  • Element-specific descriptors: ESTDs construct topological features from molecular point clouds using element-specific selections and distance-based Vietoris–Rips complexes.The approach is intended to retain chemical information lost when all atoms are treated uniformly and to support structure–function analysis with machine learning.
  • Interpretation and scope: Persistent-homology descriptors are systematic and comprehensive but should not be interpreted as direct chemical-bond or physical-relationship models.The filtration radius is not a chemical bond, and topological connectivity differs from classical chemical and physical bond theories.

2.2 Auxiliary molecular descriptors

The study constructs auxiliary molecular descriptors from physical models, emphasizing element-specific statistics that complement topological descriptors. The resulting feature vector is designed for ensemble and deep-learning models.

  • 2.2 Auxiliary molecular descriptors: Physical descriptors are based on atomic charges, solvent-excluded surface areas, and electrostatic solvation free energies computed from optimized molecular structures.The workflow optimizes 3D structures, assigns charges, computes surfaces, and estimates electrostatic solvation free energies.
  • 2.2 Auxiliary molecular descriptors: Element-specific descriptors avoid dependence on atomic positions or atom counts, supporting scalable application across molecule types.The construction derives atomic properties by element type and aggregates them into statistics suitable for machine learning.
  • 2.2 Auxiliary molecular descriptors: 330 molecular descriptors combine element-specific and all-atom statistics over charge, surface area, and electrostatic solvation free energy.Element-level descriptors cover 10 element types, three descriptor types, and signed and absolute-value statistics; all-atom descriptors add 30 features.
  • 2.2 Auxiliary molecular descriptors: The auxiliary descriptors form an independent set that can be combined with ESTDs into a full descriptor representation.The descriptors are organized as a one-dimensional feature vector suitable for ensemble methods and DNNs.

2.3 Descriptor selection

Because descriptor construction produces many features, the study ranks descriptors by feature importance and evaluates models under multiple selection thresholds.

  • 2.3 Descriptor selection: Descriptor ranking addresses overfitting concerns arising from the large number of constructed descriptors.The selection protocol ranks all descriptors before training separate models for test-set evaluation.
  • 2.3 Descriptor selection: Feature importance is defined using Gini importance from a GBDT baseline, weighted by the number of trees in the forest.Separate models are trained after descriptor selection to examine predictive performance.
  • 2.3 Descriptor selection: Four feature-importance thresholds are evaluated: 2.5e-4, 5e-4, 7.5e-4, and 1e-4.The study reports detailed performance analyses for these threshold settings in a later section.

2.4 Topological learning algorithms

The study integrates topological descriptors with ensemble and deep neural-network algorithms, including single-task and multi-task architectures. Multi-task learning jointly models toxicity endpoints to exploit shared information and support smaller datasets.

  • 2.4 Topological learning algorithms: Topology-based learning combines topological features with ensemble methods and deep neural networks.Random forest and gradient boosting decision trees serve as ensemble baselines, while DNNs provide single-task and multi-task models.
  • 2.4.3 Multi-task learning: Multi-task learning can benefit small datasets with incomplete statistical distributions by using relatively large datasets with more complete distributions.The stated motivation is to learn multiple tasks simultaneously while sharing information across endpoints.
  • 2.4.3 Multi-task learning: The multi-task objective minimizes losses for all tasks simultaneously and adds L2 weight regularization to reduce overfitting.The regression loss is described using mean squared error, with β controlling the regularization penalty.
  • 2.4.3 Multi-task learning: MT-DNN jointly learns different toxicity endpoints and can potentially improve overall performance across multiple prediction models.The architecture contains multiple predictor outputs and is intended to exploit commonalities and differences among tasks.
  • 2.4.4 Network parameters and training: The networks use four deep layers with 1000 neurons per layer and an ADAM learning rate of 0.0001.The authors report that adding dropout or L2 decay did not necessarily increase accuracy and therefore omitted both techniques.

2.5 Evaluation criteria

The evaluation uses correlation-based statistics, error metrics, and prediction coverage to assess quantitative toxicity models.

  • 2.5 Evaluation criteria: Test-set performance is assessed using the squared correlation coefficient between experimental and predicted toxicities with zero-intercept regression.The regression is constrained to Y = kX, and the metric is distinguished from the corresponding training-set coefficient.
  • 2.5 Evaluation criteria: The study additionally reports root mean square error and mean absolute error for prediction performance.These metrics complement the correlation-based criteria.
  • 2.5 Evaluation criteria: Prediction coverage measures the fraction of chemicals predicted by each method.Coverage is included as an additional method-level evaluation criterion.

3 Results

The study evaluates topology-based and physical descriptors with neural and ensemble models across four quantitative toxicity datasets, comparing them with TEST methods. MT-DNN and descriptor consensus models achieve strong predictive results, with coverage generally exceeding TEST models.

  • 3.1 An overview of data sets: The four datasets range from hundreds to thousands of molecules, and LD50 excludes some arsenic-containing molecules because of force-field failure.These dataset differences affect coverage and robustness comparisons.
  • 3.2 Fathead minnow LC50 test set: R2 0.789 and RMSE 0.677 log(mol/L) are achieved by the all-descriptor consensus on the fathead minnow LC50 set.This is the best reported result for that dataset.
  • 3.2 Fathead minnow LC50 test set: MT-DNN using only ESTDs outperforms TEST consensus on the fathead minnow LC50 set, while adding physical descriptors or combining all descriptors also improves predictions.
  • 3.3 Daphnia magna LC50 test set: R2 improves from around 0.5 to 0.788, 0.705, and 0.726 for MT-DNN models using ESTDs, physical descriptors, and all descriptors on the Daphnia magna LC50 set.The ESTD model produces the strongest reported result among these descriptor configurations.
  • 3.3 Daphnia magna LC50 test set: R2 0.802 and RMSE 0.438 log(mol/L) are obtained by the all-descriptor consensus on the Daphnia magna LC50 set.

4 Discussion

The discussion examines descriptor redundancy, multitask learning, element-specific network choices, and model consensus. MT-DNN remains robust to descriptor selection, while consensus performs best on larger datasets and worse on the smallest dataset.

  • 4.1 Descriptor redundancy and overfitting: Increasing descriptors from 222 to 1030 does not increase RMSE or substantially change R2, indicating limited overfitting in MT-DNN.The analysis uses four descriptor subsets for the LC50 set.
  • 4.1 Descriptor redundancy and overfitting: MT-DNN can exploit related toxicity tasks and improves performance especially on small datasets.The authors associate its alternative training procedure with reduced overfitting on individual datasets.
  • 4.2 Predictive power of ESTDs: ESTDs alone outperform TEST consensus on LC50 and LC50-DM, while ESTD consensus exceeds TEST on LD50; IGC50 remains slightly below TEST consensus.
  • 4.3 Alternative element-specific networks: Alternative element-specific networks produce slightly better results on LC50, IGC50, and LD50, but lower accuracy on LC50-DM while still exceeding TEST consensus.
  • 4.4 Consensus models: Consensus improves accuracy on reasonably large datasets, whereas MT-DNN performs better on the small LC50-DM set.The authors attribute the small-set difference to overfitting from many descriptors in other algorithms.

5 Conclusion

The paper addresses the need for quantitative toxicity prediction by introducing ESTDs from element-specific persistent homology and combining them with physical descriptors and machine learning. Across four benchmark datasets, the resulting topological learning methods achieve competitive or state-of-the-art predictions with broad molecular coverage.

  • 5 Conclusion: ESTDs are introduced as a new descriptor class for characterizing and predicting quantitative toxicity in small molecules.
  • 5 Conclusion: The approach combines element-specific persistent homology, physical descriptors, DNNs, RF, and GBDT for quantitative toxicity prediction.
  • 5 Conclusion: The benchmark evaluation uses fathead minnow LC50, Daphnia magna LC50, Tetrahymena pyriformis IGC50, and oral rat LD50 datasets.
  • 5 Conclusion: ESTDs with physical descriptors and MT-DNN establish state-of-the-art predictions across four quantitative toxicity datasets.The study compares these methods with TEST and ensemble algorithms.
  • 5 Conclusion: ESTDs are easy to generate and provide almost 100% molecular coverage, while physical descriptors depend on physical models and force fields.The authors present this as supporting broader practical applicability of the topological descriptors.

Availability

The authors provide online and supplementary resources for computing ESTDs and auxiliary molecular descriptors.

  • Availability: Software for computing ESTDs and auxiliary molecular descriptors is available online, with source code provided in the Supplementary materials.

Supplementary materials

The supplementary materials report descriptor-performance results for MT-DNN and ESTDs across multiple algorithmic settings and feature-importance thresholds.

  • Descriptor performances at different feature-importance thresholds are detailed in Supplementary Tables S1–S4.
  • MT-DNN results are presented in Supplementary Tables S1–S4.
  • ESTD results using different algorithms are listed in Supplementary Tables S5–S12.

Funding information

The work received partial support from NSF grants and the MSU Center for Mathematical Molecular Biosciences Initiative.

  • The work was supported in part by NSF Grant IIS-1302285.
  • The work was supported in part by NSF Grant DMS-1721024.
  • The work was also supported in part by the MSU Center for Mathematical Molecular Biosciences Initiative.
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