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TopologyNet: Topology based deep convolutional neural networks for biomolecular property predictions

Zixuan Cang, Guo-Wei Wei

arXiv:1704.00063v1q-bio.QM

TL;DR

Deep learning on 3D biomolecular structures is hindered by entangled geometric and biological complexity and by small, noisy training sets. The paper introduces ESPH-based multichannel representations and TopologyNet, including multitask learning, and reports improved predictions across binding-affinity and mutation-impact tasks.

  • Problem

    3D biomolecular prediction lacks competitive deep-learning methods because geometric complexity, biological information, and limited noisy training data are difficult to handle together.

  • Method

    ESPH converts 3D structures into one-dimensional topological invariants with element-specific multichannel representations, which are processed by CNN and multitask topological networks.

  • Results

    TopologyNet architectures outperform other state-of-the-art methods for protein–ligand binding affinities and globular and membrane protein mutation-impact predictions.

  • Takeaways & Limitations

    ESPH-based topological representations support biomolecular structure–function prediction across binding and mutation-impact applications.

Abstract

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Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the entangled geometric complexity and biological complexity. We introduce topology, i.e., element specific persistent homology (ESPH), to untangle geometric complexity and biological complexity. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains crucial biological information via a multichannel image representation. It is able to reveal hidden structure-function relationships in biomolecules. We further integrate ESPH and convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the limitations to deep learning arising from small and noisy training sets, we present a multitask topological convolutional neural network (MT-TCNN). We demonstrate that the present TopologyNet architectures outperform other state-of-the-art methods in the predictions of protein-ligand binding affinities, globular protein mutation impacts, and membrane protein mutation impacts.

I Introduction

3D biomolecular structure–function prediction is difficult because geometric detail and biological information are entangled. The paper proposes element specific persistent homology and neural networks to separate these complexities while retaining biological information.

  • Motivation: Physics-based models provide physical insights into biomolecular structure–function relationships but rely on detailed modeling frameworks.The cited approaches include quantum, molecular, continuum, multiscale, statistical, and thermodynamic models.
  • Learning framework: Deep learning can extract nonlinear representations from large datasets, and multitask learning can transfer information across related tasks.
  • Research gap: Direct CNN application to 3D biomolecules is costly for long-range interactions, motivating a robust multitask approach for binding and mutation-impact prediction.
  • Motivation: Geometric models can contain excessive structural detail and become computationally intractable.
  • Persistent homology: Persistent homology captures multiscale geometric information through topological invariants that track structures across filtration scales.Barcodes visualize homology generators surviving over different filtration scales.
  • Research gap: Existing persistent homology can oversimplify biological information, limiting the competitiveness of persistent-homology-based machine learning for protein classification.
  • Contribution: ESPH separates geometric and biological complexity, while TopologyNet combines its topological representation with CNNs for biomolecular structure–function prediction.The representation reduces 3D data through topological invariants and retains biological information through element-specific multichannel features.

II Methods

The paper constructs multichannel and multitask topological deep-learning architectures for predicting protein–ligand binding affinities and mutation-induced stability changes.

  • Deep-learning architectures: Persistent-homology outputs are combined with convolutional neural networks to build multichannel and multitask models for binding and mutation-impact prediction.

II.A Persistent homology

Persistent homology builds topological descriptions of biomolecular structures by tracking connectivity and homology across systematically varied spatial scales.

  • Simplicial homology: Simplicial homology uses simplicial complexes of vertices, edges, triangles, and higher-dimensional components to compute topological invariants.
  • Filtration: Persistent homology applies a filtration that creates nested subcomplexes as a scale parameter changes, enabling Betti numbers to be computed across scales.For biomolecules, the filtration can use the growing radius around atoms at their initial coordinates.

II.B Topological representation of biomolecules

The paper converts persistent barcodes into element-specific, one-dimensional multichannel representations that encode topology and chemical context for neural-network input.

  • Topological fingerprints: Topological fingerprints use one-dimensional persistent barcodes to characterize three-dimensional biomolecular structures.The paper illustrates fingerprints for a wild-type protein and its W60A mutant.
  • Element-specific fingerprints: Element-specific topological fingerprints add biological detail beyond all-heavy-atom representations for binding and mutation analyses.They capture information associated with atom types and interactions such as hydrophobic effects.
  • Feature parameterization: B(α, C, D) labels atom selection, simplicial-complex type, and homology dimension, while barcode birth, death, and persistence encode structural features.The filtration interval is divided into n equal subintervals to characterize these quantities.
  • Feature construction: The representation vectors count barcode births, deaths, and intervals within filtration subintervals; Betti-0 features use death positions because births are uniformly zero.
  • Image-like representation: Each filtration subinterval becomes a pixel in a one-dimensional image, while channels encode element type, mutation status, topological dimension, and event type.This multichannel arrangement allows chemical and topological information to enter convolutional neural networks together.

II.C Multichannel topological convolutional neural network (MT-TCNN)

MT-TCNN converts multichannel topological representations into learned features with 1D convolutional networks and uses multitask training to share information across mutation-impact prediction tasks.

  • Architecture: The network standardizes multichannel topological images before applying 1D convolutional and fully connected layers for feature extraction and regression.The convolutional layers extract higher-level features from the image-like topological inputs.
  • Convolution operation: A 1D convolution layer maps an n × m tensor of topological pixels and channels to an Nf × nf tensor through sliding filters and tensor contraction.The filtration dimension supplies the sequence direction, while the representation vectors supply the channels.
  • Regularization: Dropout randomly removes hidden-unit outputs during training to reduce overfitting in networks with many convolutional and fully connected layers.Bagging additionally averages separately trained models to reduce generalization error.
  • Multitask learning: MT-TCNN shares and transforms topological information while simultaneously predicting globular and membrane protein mutation impacts.Its multitask objective combines task losses, a similarity penalty for shared layers, and regularization.

III.A Deep learning prediction of protein-ligand binding affinities

The paper applies topology-based deep learning to protein-ligand binding-affinity prediction, representing complexes with element-specific topological features and evaluating the approach against existing scoring functions.

  • Background: Protein-ligand binding-affinity predictors include physics-based, empirical, and knowledge-based scoring functions.Physics-based approaches use quantum-mechanical or hybrid quantum-mechanical/molecular-mechanical models, while empirical methods require selected data and parametrization.
  • Binding model: The method models binding free energy through an energy cycle whose main contributors are intermolecular interactions and solvation effects.The representation distinguishes protein and ligand atom affiliations when defining opposition distances.
  • Topological representation: Five sets of element-specific topological feature vectors and their differences produce 72 channels for each protein-ligand complex.Zero-dimensional topological features describe intramolecular interactions between the protein and ligand.
  • Evaluation: The PDBBind 2007 core set contains 195 protein-ligand complexes for testing, while the refined set excluding the core set supplies training data.The reported training-set description specifies 1105 protein-ligand complexes.
  • Results: TNet-BP outperforms all other scoring functions reported by Li et al. in the comparison summarized in Table 2.The method is evaluated on the PDBBind 2007 data set.

III.B Deep learning prediction of protein folding free energy changes upon mutation

The study applies topology-based neural networks to predict mutation-induced protein folding free-energy changes, using folded-state structural information and complementary sequence and evolutionary features. TNet-MP-2 extends the topology-only model with these additional features.

  • Modeling protein folding free-energy changes: Mutation impact prediction uses folded mutant and wild-type structures because unfolded states are highly dynamic and costly to sample.The model characterizes atomic interactions, geometric effects, and hydrophobic effects from the folded states.
  • Topological representation: The protein-folding free-energy application represents mutation-related topological changes with a 45-channel 1D image-like representation.The representation includes differences between wild-type and mutant-related sets, illustrated with persistent-homology barcodes.
  • Datasets and evaluation: The S2648 dataset contains 2648 mutation instances from 131 proteins, while S350 is used as a held-out prediction set.Thermodynamic data are obtained from the ProTherm database.
  • Topology-based predictors: TNet-MP-1 uses only topological information, whereas TNet-MP-2 additionally incorporates evolutionary and sequence information.The added features are merged into the convolutional network’s fully connected layer.
  • Evaluation: Table 4 compares Pearson correlation coefficients and RMSEs in kcal/mol for S350 prediction and 5-fold cross-validation on S2648.The table includes results for TNet-MP-1, TNet-MP-2, and other methods, with notes concerning reported and online-server values.

III.C Multitask deep learning prediction of membrane protein mutation impacts

The paper uses multitask learning to address the small membrane-protein mutation dataset by sharing information with the larger globular-protein stability task. The resulting membrane-protein predictor is reported as the best available method in this comparison, although its performance remains unsatisfactory.

  • Motivation: Membrane-protein mutation datasets contain only about 200–300 examples, limiting data-driven prediction methods.The multitask strategy uses larger globular-protein mutation data to improve prediction for the smaller membrane-protein task.
  • Multitask architecture: The multitask architecture combines membrane-protein mutation prediction with globular-protein stability-change prediction as an auxiliary task.The architecture shares information between tasks through a hierarchical neural network.
  • Evaluation: The membrane-protein evaluation uses 223 mutation instances from seven protein families in 5-fold cross-validation.This dataset is designated M223.
  • Results: Pearson correlation improves 8.3%, from 0.48 to 0.52, for membrane-protein mutation prediction.The paper states that these TopologyNet results are the best reported for this problem, though not satisfactory.
  • Results: Table 5 compares Pearson correlation coefficients and RMSEs for the M223 membrane-protein mutation dataset.Comparison values are drawn largely from prior work, while TNet-MMP-1 and TNet-MMP-2 provide the present results.

IV Discussion

The discussion examines why convolutional filters are useful across filtration scales and how different topological dimensions contribute to prediction. It also summarizes the method’s broader applicability and comparisons with tree-based models.

  • Convolution across filtration scales: Replacing convolutional layers with locally connected layers significantly degrades performance, supporting shared filters across distance scales.The degradation occurs for protein-ligand binding affinity and S350 mutation-impact prediction.
  • Topological dimensions: Dimension 0 inputs represent pairwise atomic interactions, while the contribution of higher-dimensional inputs is tested separately.These comparisons are made for S350 mutation prediction and protein-ligand binding affinity prediction.
  • Topological dimensions: Combining dimension 0 with higher-dimensional Betti features improves performance to Pearson correlation 0.74 (RMSE 1.08) and 0.83 (RMSE 1.37).The results indicate that both feature sets contribute and neither is redundant.
  • Comparison with tree ensembles: Neural-network and gradient-boosted-tree methods can exhibit different error characteristics across samples.The discussion links this difference to their distinct ways of learning the underlying function.
  • Broader applicability: The approach combines element-specific persistent homology, CNN feature extraction, handcrafted features, and tunable multitask branching.The authors state that the method can extend to other biomolecular structure-prediction applications.
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