CoChat
Sign Up
Cited by 93Topological and Geometric Data AnalysisMachine Learning in BioinformaticsProtein Structure and Dynamics

A topological approach for protein classification

Open access
Cang, Zixuan, Mu, Lin, Wu, Kedi, Opron, Kristopher, Xia, Kelin, Wei, Guo-Wei·2015·Computational and Mathematical Biophysics
DOI 10.1515/mlbmb-2015-0009
Open this paper in CoChat — free accountOpen PDF

Abstract

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 between 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 independent 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 fromprotein topological fingerprints,which are topological invariants generated during the filtration process. To validate the presentMTF-SVMapproach, 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. Secondly, we examine the use of MTF-SVM for the classification of hemoglobin molecules in their relaxed and taut forms and obtain about 80% accuracy. Thirdly, the identification of all alpha, all beta, and alpha-beta protein domains is carried out using 900 proteins.We have found a 85% success in this identification. Finally, we apply the present technique to 55 classification tasks of protein superfamilies over 1357 samples and 246 tasks over 11944 samples. Average accuracies of 82% and 73% are attained. The present study establishes computational topology as an independent and effective alternative for protein classification.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper introduces a molecular topological fingerprint (MTF) based support vector machine (MTF-SVM) classifier that uses persistent homology features from protein structures for protein classification. Across four test problems, it reports accuracies ranging from about 73% to 98% depending on the task.

Key findings

  • For influenza A M2 channel drug binding, MTF-SVM distinguished drug-bound and unbound channels with average accuracy 93.91% for unbound and 98.31% for bound; the abstract summarizes this as 96% accuracy.
  • For hemoglobin relaxed (R) and taut (T) forms, average testing accuracy was 84.50%, with 77.16% for R form and 91.11% for T form; the abstract reports about 80% accuracy.
  • For classifying all-alpha, all-beta, and alpha-beta protein domains using 900 proteins, overall accuracy was 84.93%: 90.67% for all-alpha, 78.77% for mixed alpha-beta, and 83.31% for all-beta.
  • For protein superfamily classification, PCB00019 (1357 samples, 55 tasks) gave average positive/negative accuracies of 82.29% and 80.94%, with average AUC 0.8954 (SD 0.09); PCB00020 (11944 samples, 246 tasks) gave 72.32% and 73.18%, with average AUC 0.7813 (SD 0.2).

Methods

  • Persistent homology was computed on protein structural point clouds using Vietoris-Rips complexes and JavaPlex, with results represented as barcodes; 13 topological features were selected from Betti 0, Betti 1, and Betti 2 bars, then linearly scaled to [0, 1].
  • Classification used C-support vector classification (C-SVC) with a Gaussian kernel and LIBSVM; small cases used default parameters and brute-force cross validation, while larger cases used grid search with cross validation, and the superfamily tasks used different positive/negative penalty parameters to address unbalanced data.
  • Data included M2 channel NMR snapshots (15 per class; PDB 2LJC with inhibitor, 2LJB without), hemoglobin structures (9 R-form, 10 T-form), 900 SCOPe domains (300 per class), and Protein Classification Benchmark Collection sets PCB00019 and PCB00020.

Limitations

  • The paper states that only topological information was employed, and suggests combining topological features with sequence and physical features in future work.
  • The paper states that PCB00020 performance was relatively poor partly because the problem set is tougher and partly because some sample differences lie in sequence information not contained in the model.
  • The paper states that automated feature selection was not performed due to the moderate system size; it also notes that all-atom models contain too much detail and that a coarse-grained alpha-carbon model was used throughout.
  • Evident from the text: the first two test cases had small sample sizes, and ROC/AUC analysis was not applied there because the testing sets were small.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1515/mlbmb-2015-0009

Cites

108 of 108 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 3 cited sources checked · 0 supported · 0 flagged

  • Findingown data
    § 3.3 The classification of all alpha, all beta, and mixed alpha and beta protein domains

    The accuracy for mixed alpha helix and beta sheet domains is 78.77%.

    “the accuracy for mixed alpha helix and beta sheet domains is 78.77%”
    Quote in the paperNot a substantial claim
    • Rests on an assumption: Alpha helices form short Betti 1 bars around filtration value 5Å.
  • Findingown data
    § 3.3 The classification of all alpha, all beta, and mixed alpha and beta protein domains

    The overall accuracy for classification of all alpha, all beta, and mixed alpha and beta protein domains is 84.93%.

    “The overall accuracy is 84.93%.”
    Quote in the paperSubstantial claim
  • Findingown data
    § 3.4 Classification of protein superfamilies

    The average accuracy for the positive testing set in PCB00019 is 82.29%.

    “The average accuracy for the positive testing set and the negative testing set in PCB00019 are 82.29% and 80.94%, respectively.”
    Quote in the paperNot a substantial claim
  • Findingown data
    § A topological approach for protein classification

    The MTF-SVM approach achieved about 80% accuracy in classifying hemoglobin molecules in their relaxed and taut forms.

    “Secondly, we examine the use of MTF-SVM for the classification of hemoglobin molecules in their relaxed and taut forms and obtain about 80% accuracy.”
    Quote in the paperSubstantial claim
  • Findingown data
    § A topological approach for protein classification

    The MTF-SVM approach attained an average accuracy of 73% over 246 classification tasks of protein superfamilies over 11944 samples.

    “we apply the present technique to 55 classification tasks of protein superfamilies over 1357 samples and 246 tasks over 11944 samples. Average accuracies of 82% and 73% are attained.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim. 15
  • May combine two claims. 4
  • The quote only partly states this claim. 1

  • Classified as probably not a substantial claim.

    Study design and conductreasoning
    § 3.4 Classification of protein superfamilies

    The criteria for cross validation was chosen to be the recall value.

    “The criteria for cross validation is chosen to be the recall value which is defined as (true positive)/(true positive + false negative) to overcome the extremely unbalanced nature of the data set.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given
    § 3.4 Classification of protein superfamilies

    For each task in superfamily classification, 5-fold cross validation on the training set was performed to search for reasonable parameters.

    “For each task, we perform 5 fold cross validation on the training set to search for reasonable parameters.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given
    § 3.4 Classification of protein superfamilies

    The relatively poor performance in PCB00020 is because problem set PCB00020 is tougher.

    “On the one hand, this is because that problem set PCB00020 is tougher.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductown data
    § 3.2 Discrimination of hemoglobin molecules in relaxed and taut forms

    A brute-force cross validation was performed for the hemoglobin classification.

    “a brute-force cross validation is performed with the same default parameters as in last case.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data
    § 4 Discussion and Conclusion

    The proposed method does an excellent job in analyzing drug binding of M2 channels, with a 96% prediction accuracy recorded.

    “It is found that the proposed method does an excellent job in analyzing drug binding of M2 channels. A 96% prediction accuracy is recorded.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given
    § 2.2.0.1 Basic theory

    A 5-fold cross validation was applied to search for optimized training parameters for problems with large amount of samples.

    “In this work, The Gaussian kernel is used and a 5-fold cross validation was applied to search for optimized training parameters for problems with large amount of samples.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Study design and conductown data
    § 3.3 The classification of all alpha, all beta, and mixed alpha and beta protein domains

    A 5-fold cross-validation was performed to test accuracy in the protein domain classification.

    “A 5-fold cross-validation is performed to test accuracy.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationreasoning
    § 4 Discussion and Conclusion

    Using a coarse-grained model with α-carbon atoms reveals more information of the entire structure of the protein and dramatically reduces spatial complex and computational time.

    “Using a coarse-grained model with α -carbon atoms reveals more information of the entire structure of the protein and dramatically reduces spatial complex and computational time.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: A protein structure can be represented as point cloud in three dimension for atoms or graph with edges corresponding to different types of chemical bonds.

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationnone given
    § 4 Discussion and Conclusion

    At the all-atom scale, different proteins have some common features due to the structures of amino acids.

    “Essentially, at the all-atom scale, different proteins have some common features due to the structures of amino acids.”
    Quote in the paperNot a substantial claim
    • Rests on an assumption: A protein structure can be represented as point cloud in three dimension for atoms or graph with edges corresponding to different types of chemical bonds.

  • May combine two claims.

    Interpretationown data
    § A topological approach for protein classification

    The present study establishes computational topology as an independent and effective alternative for protein classification.

    “The present study establishes computational topology as an independent and effective alternative for protein classification.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Topological information has been hardly employed in studying the protein structure-function relationship.
    • Rests on an assumption: Same proteins can have different conformations with different properties or functions, and minor structural differences can lead to dramatically different functions.

  • May combine two claims.

    Interpretationown data
    § 4 Discussion and Conclusion

    The extensive test study establishes topology as an independent and valuable option for large scale protein classification.

    “The extensive test study establishes topology as an independent and valuable option for large scale protein classification.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given
    § 3.3 The classification of all alpha, all beta, and mixed alpha and beta protein domains

    In each training process for protein domain classification, a 5-fold cross validation on the training set only was carried out to optimize training parameters.

    “In each training process, a 5-fold cross validation on the training set only is carried out to optimize training parameters.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given
    § 1 Introduction

    Persistent homology is able to bridge traditional geometry and topology.

    “Persistent homology, a new branch of applied topology, is able to bridge traditional geometry and topology.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Study design and conductreasoning
    § 3.4 Classification of protein superfamilies

    Different values for penalty parameters were used to prevent unbalanced training results in superfamily classification.

    “To prevent unbalanced training results, different values for penalty parameters are used.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Study design and conductreasoning
    § 3.4 Classification of protein superfamilies

    The ratio between positive penalty parameter and negative penalty parameter was set to equal the ratio between number of negative instances and number of positive instances in the training set.

    “Specifically, the ratio between positive penalty parameter and negative penalty parameter is set to equal the ratio between number of negative instances and number of positive instances in the training set.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 2.3 Topological feature selection and construction

    A strong correlation between accumulation bar length of Betti 1 and total energy has been reported.

    “A strong correlation between accumulation bar length of Betti 1 and total energy has been reported [108].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [108] [108] K. L. Xia and G. W. Wei. Persistent homology analysis of protein structure, flexibility and folding. International Journal for Numerical Methods in Biomedical Engineerings , 30:814-844, 2014. -

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). The quote only partly states this claim.

    Study design and conductown data
    § 3.1 Protein-drug binding analysis

    A brute-force cross validation was performed for the M2 channel classification.

    “A brute-force cross validation is performed.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given
    § 3.4 Classification of protein superfamilies

    The thresholds used to determine ROC curve were set to a list of decision values corresponding to each instance in the testing set from the model.

    “The thresholds used to determine ROC curve are set to be a list of decision values corresponding to each instance in the testing set from the model.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § 3.4 Classification of protein superfamilies

    The relatively poor performance in PCB00020 may be due to some information about differences between samples lying in sequence which is not contained in the model.

    “On the other hand, this may due to the fact that some information about differences between samples lies in sequence which is not contained in our model.”
    Quote in the paperNot a substantial claim
19 of 19

  • The paper relies on this without support.

    Topological information has been hardly employed in studying the protein structure-function relationship.

    “In contrast, topological information has been hardly employed in studying the protein structurefunction relationship.”

  • The paper relies on this without support.

    Same proteins can have different conformations with different properties or functions, and minor structural differences can lead to dramatically different functions.

    “The data-driven analysis of the protein structure-function relationship is compromised by the fact that same protein may have different conformations which possess different properties or deliver different functions.”
    “However, their minor structural differences might lead to dramatically different functions.”

  • The paper relies on this without support.

    Alpha helices form short Betti 1 bars around filtration value 5Å.

    “For each four α -carbons on a alpha helix, they are likely to form a short Betti 1 bar around filtration value 5Å.”

  • The paper relies on this without support.

    The average value of Betti 1 bars correlates to the average loop size.

    “The average value of Betti 1 bars correlates to the average loop size.”

  • The paper relies on this without support.

    The total length of Betti 0 bars describes how compactly the points are located.

    “Geometrically, the total length of Betti 0 bars describes how compactly the points are located.”

  • The paper relies on this without support.

    The persistence of the longest Betti 1 bar reflects the size of the geometrically dominating loop.

    “The persistence of the longest Betti 1 bar reflects the size of the geometrically dominating loop.”

  • The paper relies on this without support.

    For protein analysis, both global features and local traits are important.

    “For protein analysis, both global features and local traits are important.”

  • The paper relies on this without support.

    A protein structure can be represented as point cloud in three dimension for atoms or graph with edges corresponding to different types of chemical bonds.

    “A protein structure can be represented as point cloud in three dimension for atoms or graph with edges corresponding to different types of chemical bonds.”
8 of 8

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Primitive persistent homology has limited power in protein classification due to its oversimplification of biological information.

    “However, it was found that primitive persistent homology has a limited power in protein classification due to its oversimplification of biological information.”

    From Quantitative Toxicity Prediction Using Topology Based Multitask Deep Neural Networks (2018) · cites this paper as [25]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Definition of an m-face uses the wrong number of vertices

    Minor

    The paper defines a simplex of dimension k using k + 1 vertices, but defines an m-face using only m vertices. An m-dimensional face would require m + 1 vertices under its own simplex definition.

  • Feature 9 gives inconsistent ranges for bars around 5 Å

    Minor

    The table specifies [4.5, 5.5] Å, while the prose defines "around 5Å" by a midpoint distance of less than 0.6 Å, corresponding to a range from 4.4 to 5.6 Å.

  • The stated Gaussian kernel grows rather than decays with distance

    Minor

    With γ > 0, the displayed exponential increases as the distance between inputs increases, contrary to the paper's description of the kernel as decaying.

3 of 3

Cites

Flagged first, then by citations

Research works printed but not linked: 9

  1. [10][10] S. Biasotti, L. De Floriani, B. Falcidieno, P. Frosini, D. Giorgi, C. Landi, L. Papaleo, and M. Spagnuolo. Describing shapes by geometrical-topological properties of real functions. ACM Computing Surveys , 40(4):12, 2008. -
  2. [26][26] D. Chen, Z. Chen, and G. W. Wei. Quantum dynamics in continuum for proton transport II: Variational solvent-solute interface. International Journal for Numerical Methods in Biomedical Engineering , 28:25 - 51, 2012. -
  3. [40][40] T. K. Dey, F. Fan, and Y. Wang. Computing topological persistence for simplicial maps. In Proc. 30th Annu. Sympos. Comput. Geom. (SoCG) , pages 345-354, 2014. -
  4. [64][64] T. Kaczynski, K. Mischaikow, and M. Mrozek. Computational Homology , volume 157 of Applied Mathematical Sciences . Springer-Verlag, New York, 2004. -
  5. [90][90] V. Robins. Towards computing homology from finite approximations. In Topology Proceedings , volume 24, pages 503-532, 1999. -
  6. [93][93] G. Singh, F. Memoli, T. Ishkhanov, G. Sapiro, G. Carlsson, and D. L. Ringach. Topological analysis of population activity in visual cortex. Journal of Vision , 8(8), 2008. -
  7. [101][101] B. Wang and G. W. Wei. Objective-oriented Persistent Homology. ArXiv e-prints , Dec. 2014. -
  8. [105][105] W. Wu, A. Srivastava, J. Laborde, and J. F. Zhang. An eflcient multiple protein structure comparison method and its application to structure clustering and outlier detection. IEEE, BIBM , pages 69-73, 2013. -
  9. [114][114] Q. Zheng, S. Y. Yang, and G. W. Wei. Molecular surface generation using PDE transform. International Journal for Numerical Methods in Biomedical Engineering , 28:291-316, 2012. -

Cited by

Sorted by citations

Related

Authors
Cang, Z., Mu, L., Wu, K., Opron, K., Xia, K., & Wei, G.-W.
Affiliations
  • Michigan State University (US)
  • Oak Ridge National Laboratory (US)
  • The Ohio State University (US)
ORCID
Venue
Computational and Mathematical Biophysics
Publisher
Walter de Gruyter GmbH
Published
2015-11-30
Volume
3
Issue
1
ISSN
2544-7297 (ISSN-L)
DOI
10.1515/mlbmb-2015-0009
OpenAlex
W2481594651
Cited by
93
References
107
Citations by year
2026: 2 · 2025: 10 · 2024: 16 · 2023: 12 · 2022: 5 · 2021: 14 · 2020: 17 · 2019: 6 · 2018: 8 · 2017: 3
FWCI
3.77
Type
journal article
Language
en
Open access
Licence
Locations
  • Computational and Mathematical Biophysics (publishedVersion, cc-by-nc-nd)
  • arXiv (Cornell University) (submittedVersion)
  • OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • DR-NTU (Nanyang Technological University) (submittedVersion, cc-by-nc-nd)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (1160352, 1302285)
  • National Institutes of Health (R01GM)
  • National Institute of General Medical Sciences (R01GM090208)
Topics
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Machine Learning in Bioinformatics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
Keywords
protein classification, persistent homology, topological data analysis, support vector machine, drug-protein binding, protein domain identification, protein superfamilies, protein function prediction

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-10.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-10.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review