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A topological approach for protein classification

Zixuan Cang, Lin Mu, Kedi Wu, Kristopher Opron, Kelin Xia, Guo-Wei Wei

arXiv:1510.00953v1q-bio.BM

TL;DR

Predicting protein function and dynamics from sequence or structure remains a fundamental challenge, while proteins with different conformations can share sequences and similar physical properties. The MTF-SVM classifier builds feature vectors solely from protein topological fingerprints generated during filtration and classifies them with an SVM. For protein-superfamily classification, using 1,357 samples across 55 classification tasks, 5-fold cross-validation yielded 82% average classification accuracy.

  • Problem

    Predicting protein function and dynamics from sequence or structure remains a fundamental challenge, while proteins with different conformations can share sequences and similar physical properties.

    Source: I Introduction · p. 5

  • Method

    The MTF-SVM classifier builds feature vectors solely from protein topological fingerprints generated during filtration and classifies them with an SVM.

    Source: I Introduction · p. 7, IV Discussion and Conclusion · p. 22

  • Results

    For protein-superfamily classification, using 1,357 samples across 55 classification tasks, 5-fold cross-validation yielded 82% average classification accuracy.

    Source: IV Discussion and Conclusion · p. 23

  • Takeaways & Limitations

    The study concludes that topology provides an independent and valuable option for large-scale protein classification.

    Source: IV Discussion and Conclusion · p. 23

    The evaluated method uses only topological information; the authors identify combining it with sequence and physical features as a possible improvement.

    Source: IV Discussion and Conclusion · p. 23

Abstract

from arXiv · show

Protein function and dynamics are closely related to its sequence and structure. However prediction of protein function and dynamics from its sequence and structure is still a fundamental challenge in molecular biology. Protein classification, which is typically done through measuring the similarity be- tween proteins based on protein sequence or physical information, serves as a crucial step toward the understanding of protein function and dynamics. Persistent homology is a new branch of algebraic topology that has found its success in the topological data analysis in a variety of disciplines, including molecular biology. The present work explores the potential of using persistent homology as an indepen- dent tool for protein classification. To this end, we propose a molecular topological fingerprint based support vector machine (MTF-SVM) classifier. Specifically, we construct machine learning feature vectors solely from protein topological fingerprints, which are topological invariants generated during the filtration process. To validate the present MTF-SVM approach, we consider four types of problems. First, we study protein-drug binding by using the M2 channel protein of influenza A virus. We achieve 96% accuracy in discriminating drug bound and unbound M2 channels. Additionally, we examine the use of MTF-SVM for the classification of hemoglobin molecules in their relaxed and taut forms and obtain about 80% accuracy. The identification of all alpha, all beta, and alpha-beta protein domains is carried out in our next study using 900 proteins. We have found a 85% success in this identifica- tion. Finally, we apply the present technique to 55 classification tasks of protein superfamilies over 1357 samples. An average accuracy of 82% is attained. The present study establishes computational topology as an independent and effective alternative for protein classification.

I Introduction

Protein structure and function are linked, but predicting function from sequence or structure remains a major challenge. This work explores persistent-homology fingerprints as an independent basis for protein classification.

I Introduction

  • Protein structure and function are closely related, yet predicting function from sequence or structure remains a major challenge.Protein similarity is commonly measured using sequence or physical information.Source: I Introduction · p. 5
  • Existing approaches use sequence, physical, geometrical, or structural similarity, but topological information has been little used to study protein structure-function relationships.Geometric methods may be computationally expensive, while traditional topology can discard too much geometric and physical information.Source: I Introduction · pp. 5–6
  • Different conformations can share a sequence and similar physical properties while minor structural differences correspond to different functions.Hemoglobin’s taut and relaxed forms and open and closed ion channels illustrate this issue.Source: I Introduction · p. 6
  • Persistent homology varies a filtration parameter to represent topological features across scales while retaining geometric or quantitative information in its invariants.Its representations include barcodes and persistence diagrams.Source: I Introduction · pp. 6–7
  • The study constructs molecular topological fingerprint feature vectors for SVM classification across protein conformations, local secondary structures, and families or superfamilies.The paper positions the approach for applications including protein binding analysis and ion-channel study.Source: I Introduction · pp. 7–8

II Materials and Methods

The methods review persistent homology and machine learning, then describe topological feature construction. Persistent homology tracks topological attributes across a filtration, illustrated here with a Vietoris–Rips complex and barcode representations.

II.A Persistent homology

  • A filtration is a nested sequence of subcomplexes, and Betti numbers describe homology through counts of components, tunnels, and cavities.The method section reviews simplices, simplicial complexes, chains, boundaries, and homology.Source: II.A Persistent homology · pp. 8–9
  • Persistent homology generates topological attributes for each complex in a filtration, with long-lived features treated as more likely to capture significant properties.The text notes that a suitable persistence threshold can filter topological noise.Source: II.A Persistent homology · p. 9
  • The Vietoris–Rips complex adds an edge between points closer than cutoff distance d, then forms higher-dimensional simplices; Figure 1 illustrates its growth on M2 channel α-carbon atoms.The work uses this complex for its intuitive nature and the moderate size of the studied systems.Source: II.A Persistent homology · p. 10, Figure 1 · p. 10

II Materials and Methods

Basic theory

The section introduces SVM classification as a maximum-margin separation problem and describes the optimization, kernel, and dual formulations used to support classification.

Basic theory

  • SVM separates labeled samples by finding a maximum-margin hyperplane in feature space.For two classes, the separating hyperplane is written as w^T x + b = 0.Source: Basic theory · p. 11
  • The soft-margin formulation permits misclassification through slack variables and penalizes them with coefficient C.The feature vector is x_i, the label y_i is either 1 or −1, and C is the penalty coefficient.Source: Basic theory · p. 11
  • For linearly inseparable data, a kernel represents dot products in a higher-dimensional feature space without explicitly computing the mapping.The study uses a Gaussian kernel and 5-fold cross-validation to optimize training parameters for large-sample problems.Source: Basic theory · p. 12
  • The constrained optimization problem is transformed into a Lagrange dual problem, which is solved with sequential minimal optimization.The dual formulation uses Lagrange multipliers and Karush-Kuhn-Tucker conditions.Source: Basic theory · p. 12

Receiver operating characteristic (ROC)

The section explains ROC curves as a way to assess binary classifiers across decision thresholds, using true-positive and false-positive rates.

Receiver operating characteristic (ROC)

II.C Topological feature selection and construction

The method converts persistent topological invariants from protein-structure filtrations into feature vectors for SVM classification, using selected Betti 0, 1, and 2 bar properties.

II.C Topological feature selection and construction

  • Protein MTF features encode persistence of topological invariants during filtration and are assembled into SVM feature vectors.The selected features include both long- and short-lasting Betti 0, Betti 1, and Betti 2 intervals.Source: II.C Topological feature selection and… · p. 13
  • The listed support-vector features use bar lengths and locations measured in angstroms for protein data.The feature list is presented in Table 1.Source: II.C Topological feature selection and… · p. 13, Table 1 · p. 13
  • Betti 0 features summarize connectivity and compactness through bar onset and length, including the onset of one or two connected components.The averaged Betti 0 bar length is not correlated with atom number.Source: II.C Topological feature selection and… · p. 14
  • Betti 1 features characterize loops through their formation point, persistence, onset, midpoint location, and average bar value.For alpha-carbon protein point clouds, a Betti 1 bar longer than 1.5 is treated as important.Source: II.C Topological feature selection and… · p. 14
  • Short Betti 1 bars around filtration value 5 Å provide a feature for estimating alpha-helix portion, while another feature indicates beta-sheet portion.A bar is short if its length is below 0.5 Å and around 5 Å if its midpoint is within 0.6 Å of 5 Å.Source: II.C Topological feature selection and… · p. 14
  • Betti 2 features track cavity births and deaths, and each feature is linearly scaled to [0, 1].The specified Betti 2 feature is the smallest onset value of a bar ending after a given value.Source: II.C Topological feature selection and… · p. 14

III Results

The results section evaluates MTF-SVM across four protein classification settings, with different validation and parameter-selection procedures for smaller and larger datasets.

III Results

  • The evaluation covers M2 channel drug binding, hemoglobin conformations, three protein-domain classes, and protein-family classification.The family task uses benchmark set PCB00019 from the Protein Classification Benchmark Collection.Source: III Results · p. 15
  • Brute-force cross-validation with default parameters is used for the relatively small M2 and hemoglobin cases.Source: III Results · p. 15
  • For the domain and family cases, cross-validation grid search optimizes SVM parameters; the family case also uses varied penalty parameters for unbalanced data and ROC analysis.Source: III Results · p. 15
  • M2 structures come from NMR, hemoglobin structures from X-ray crystallography, and the latter two test sets are mostly X-ray structures.Where database samples have NMR alternatives, the second structure is selected.Source: III Results · p. 15
  • JavaPlex computes MTFs and LIBSVM implements the support vector machine.Source: III Results · p. 15

III.A Protein-drug binding analysis

The MTF-SVM distinguishes M2 channels with and without rimantadine using topological changes associated with binding-induced geometric variation. The reported class accuracies are 93.91% for unbound channels and 98.31% for bound channels.

III.A Protein-drug binding analysis

  • Binding-induced geometric variation is recorded as changes in topological invariants in the molecular topological fingerprints used for classification.The inhibitor itself was not included in the filtration.Source: III.A Protein-drug binding analysis · p. 15, Figure 3 · p. 16
  • The test distinguishes M2 channels with and without rimantadine, an inhibitor that binds the channel pore and blocks proton permeation.The structures were 2LJC with inhibitor and 2LJB without inhibitor.Source: III.A Protein-drug binding analysis · pp. 15–16
  • Using 10 instances from each class for training and the rest for testing in brute-force cross-validation, average accuracy for unbound form was 93.91% and accuracy for bound form was 98.31%.Source: III.A Protein-drug binding analysis · p. 17

III.B Discrimination of hemoglobin molecules in relaxed and taut forms

The MTF-SVM classifies relaxed and taut hemoglobin forms, which differ in oxygen affinity and have slightly different structures. Across the test set, average accuracy was 84.50%.

III.B Discrimination of hemoglobin molecules in relaxed and taut forms

  • The test used 9 relaxed-form and 10 taut-form hemoglobin structures, with brute-force cross-validation because the sample count was small.Each test set contained one instance from each class.Source: III.B Discrimination of hemoglobin… · pp. 17–18
  • Relaxed hemoglobin has high oxygen-binding affinity, whereas taut hemoglobin has low affinity that helps release oxygen to tissues.The two forms are structurally slightly different.Source: III.B Discrimination of hemoglobin… · p. 17
  • In this test case, brute-force cross-validation with the same default parameters as the last case held out one instance from each class per test set, yielding 84.50% average prediction accuracy.Average accuracy was 77.16% for the R form and 91.11% for the T form; ROC analysis was not applied because the test set was small.Source: III.B Discrimination of hemoglobin… · p. 18

III.C The classification of all alpha, all beta, and mixed alpha and beta protein domains

Using geometric data without sequence information, the MTF-SVM classifies all-alpha, all-beta, and mixed alpha-beta protein domains. Its overall accuracy on 900 structures was 84.93%.

III.C The classification of all alpha, all beta, and mixed alpha and beta protein domains

  • The classification used geometric data to generate molecular topological fingerprints without sequence information.The examples were drawn from the SCOPe database.Source: III.C The classification of all alpha,… · p. 19
  • 84.93% overall accuracy was achieved across 900 domains classified as all-alpha, mixed alpha-beta, or all-beta.Class accuracies were 90.67% for all alpha, 78.77% for mixed alpha and beta, and 83.31% for all beta.Source: III.C The classification of all alpha,… · p. 19
  • The study used 300 structures per class, with 60 from each class reserved for testing and five-fold cross-validation.Training parameters were optimized using five-fold cross-validation within each training process.Source: III.C The classification of all alpha,… · p. 19

III.D Classification of protein superfamilies

The method was evaluated on 55 protein-superfamily classification tasks involving 1,357 samples, using alpha-carbon structure information. Average AUC was 0.8954, with a standard deviation of 0.09.

III.D Classification of protein superfamilies

IV Discussion and Conclusion

The study presents persistent-homology fingerprints as a multiscale structural basis for MTF-SVM protein classification and evaluates the approach across several tasks. It concludes that topology is an independent option, while combining it with sequence and physical features remains future work.

  • The study uses α-carbon coarse-graining because all-atom detail obscures useful structural information and increases spatial complexity and computational time.The authors note that an all-atom model may be preferable for some physical descriptions.Source: IV Discussion and Conclusion · p. 22
  • The fingerprints retain both long-lived global features and short-lived local traits because protein interactions span multiple characteristic length scales.Source: IV Discussion and Conclusion · p. 22
  • The other tests report 96% accuracy for drug-bound versus unbound M2 channels, 80% for hemoglobin forms, and 85% for three protein-domain classes.The domain study used 900 proteins.Source: IV Discussion and Conclusion · pp. 22–23
  • MTF-SVM builds feature vectors from molecular topological fingerprints and uses an SVM; persistent homology records invariant births and deaths as a filtration grows.Source: IV Discussion and Conclusion · pp. 21–22
  • 82% average classification accuracy was found across 55 protein-superfamily tasks involving 1357 samples, using 5-fold cross-validation.Source: IV Discussion and Conclusion · p. 23
  • The study uses only topological information; combining it with sequence and physical features is identified as future work beyond the present scope.Source: IV Discussion and Conclusion · p. 23
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