Using persistent homology and dynamical distances to analyze protein binding
Open accessAbstract
Persistent homology captures the evolution of topological features of a model as a parameter changes. The most commonly used summary statistics of persistent homology are the barcode and the persistence diagram. Another summary statistic, the persistence landscape, was recently introduced by Bubenik. It is a functional summary, so it is easy to calculate sample means and variances, and it is straightforward to construct various test statistics. Implementing a permutation test we detect conformational changes between closed and open forms of the maltose-binding protein, a large biomolecule consisting of 370 amino acid residues. Furthermore, persistence landscapes can be applied to machine learning methods. A hyperplane from a support vector machine shows the clear separation between the closed and open proteins conformations. Moreover, because our approach captures dynamical properties of the protein our results may help in identifying residues susceptible to ligand binding; we show that the majority of active site residues and allosteric pathway residues are located in the vicinity of the most persistent loop in the corresponding filtered Vietoris-Rips complex. This finding was not observed in the classical anisotropic network model.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
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?
Persistent homology is able to bridge geometry and topology, leading to a new efficient approach for the simplification of biological structural complexity.
“Persistent homology22–25—a new branch of algebraic topology—is able to bridge geometry and topology, leading to a new efficient approach for the simplification of biological structural complexity26–31; however, it neglects critical chemical/biological information when it is directly applied to complex biomolecular structures.”
From A topology-based network tree for the prediction of protein–protein binding affinity changes following mutation (2020) · cites this paper as [31]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Topological Persistence and Simplification
Edelsbrunner, Letscher, & Zomorodian (2002) · Discrete & Computational Geometry · doi:10.1007/s00454-002-2885-2 · Cited by 1,779 · see citing works
Maltose/Maltodextrin System of Escherichia coli : Transport, Metabolism, and Regulation
Boos, W., & Shuman, H. A. (1998) · Microbiology and Molecular Biology Reviews · doi:10.1128/mmbr.62.1.204-229.1998 · Cited by 638 · see citing works
Sharff, A., Rodseth, L. E., Spurlino, J. C., & Quiocho, F. A. (1992) · Biochemistry · doi:10.1021/bi00159a003 · Cited by 477 · see citing works
Role of bacterial cell surface structures in Escherichia coli biofilm formation
Houdt, R. V., & Michiels, C. W. (2005) · Research in Microbiology · doi:10.1016/j.resmic.2005.02.005 · Cited by 445 · see citing works
Compressibility-structure relationship of globular proteins
Gekko, K., & Hasegawa, Y. (1986) · Biochemistry · doi:10.1021/bi00369a034 · Cited by 433 · see citing works
Large sample theory of intrinsic and extrinsic sample means on manifolds
Bhattacharya, R. N., & Patrangenaru, V. (2003) · The Annals of Statistics · doi:10.1214/aos/1046294456 · Cited by 402 · see citing works
Tobi, D., & Bahar, İ. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0507603102 · Cited by 380 · see citing works
Anisotropic network model: systematic evaluation and a new web interface
Eyal, E., Yang, L., & Bahar, İ. (2006) · Bioinformatics · doi:10.1093/bioinformatics/btl448 · Cited by 324 · see citing works
Confidence sets for persistence diagrams
Fasy, B. T., Lecci, F., Rinaldo, A., Wasserman, L., Balakrishnan, S., & Singh, A. (2014) · The Annals of Statistics · doi:10.1214/14-aos1252 · Cited by 251 · see citing works
Probability measures on the space of persistence diagrams
Mileyko, Y., Mukherjee, S., & Harer, J. (2011) · Inverse Problems · doi:10.1088/0266-5611/27/12/124007 · Cited by 249 · see citing works
Hudault, S. (2001) · Gut · doi:10.1136/gut.49.1.47 · Cited by 225 · see citing works
Fréchet Means for Distributions of Persistence Diagrams
Turner, K., Mileyko, Y., Mukherjee, S., & Harer, J. (2014) · Discrete & Computational Geometry · doi:10.1007/s00454-014-9604-7 · Cited by 207 · see citing works
Marvin, J. S., Corcoran, E., Hattangadi, N. A., Zhang, J. V., Gere, S. A., & Hellinga, H. W. (1997) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.94.9.4366 · Cited by 186 · see citing works
A barcode shape descriptor for curve point cloud data
Collins, A., Zomorodian, A., Carlsson, G., & Guibas, L. J. (2004) · Computers & Graphics · doi:10.1016/j.cag.2004.08.015 · Cited by 132 · see citing works
Categorification of Persistent Homology
Bubenik, P., & Scott, J. A. (2014) · Discrete & Computational Geometry · doi:10.1007/s00454-014-9573-x · Cited by 97 · see citing works
Self-citationMultidimensional persistence in biomolecular data
Xia, K., & Wei, G. (2015) · Journal of Computational Chemistry · doi:10.1002/jcc.23953 · Cited by 74 · see citing works
Rizk, S. S., Paduch, M., Heithaus, J. H., Duguid, E. M., Sandstrom, A., & Kossiakoff, A. A. (2011) · Nature Structural & Molecular Biology · doi:10.1038/nsmb.2002 · Cited by 72 · see citing works
Duan, X. J., & Quiocho, F. A. (2001) · Biochemistry · doi:10.1021/bi015784n · Cited by 69 · see citing works
Persistent topology for cryo‐EM data analysis
Xia, K., & Wei, G. (2015) · International Journal for Numerical Methods in Biomedical Engineering · doi:10.1002/cnm.2719 · Cited by 36 · see citing works
Bandulasiri, A., Bhattacharya, R. N., & Patrangenaru, V. (2009) · Journal of Multivariate Analysis · doi:10.1016/j.jmva.2009.03.007 · Cited by 32 · see citing works
Approximating cycles in a shortest basis of the first homology group from point data
Dey, T. K., Sun, J. Z., & Wang, Y. (2011) · Inverse Problems · doi:10.1088/0266-5611/27/12/124004 · Cited by 27 · see citing works
Kobryn, A. E., Nikolić, D., Lyubimova, O., Gusarov, S., & Kovalenko, A. (2014) · The Journal of Physical Chemistry B · doi:10.1021/jp503981p · Cited by 8 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 9
- Chazal, F., B. T. Fasy, F. Lecci, A. Rinaldo and L. Wasserman (2014b): "Stochastic convergence of persistence landscapes and silhouettes," In: Proceedings of the Thirtieth Annual Symposium on Computational Geometry, SOCG'14, New York, NY, USA: ACM, 474-483.
- Dryden, I. L. and K. V. Mardia (1998): Statistical shape analysis, New York: John Wiley and Sons.
- Gameiro, M., Y. Hiraoka, S. Izumi, M. Kramar, K. Mischaikow and V. Nanda (2012): "Topological measurement of protein compressibility via persistence diagrams," In The Global COE Program, MI Preprint Series, volume 6, Math for Industry Education & Research Hub, Fukuoka, Japan: Kyushu University, MI Preprint Series, volume 6, 1-10.
- Hatcher, A. (2002): Algebraic topology, Cambridge: Cambridge University Press.
- Kovacev-Nikolic, V. (2012): Persistent homology in analysis of point-cloud data, Master's thesis, Department of Mathematical and Statistical Sciences, University of Alberta.
- Ledoux, M. and M. Talagrand (2002): Probability in Banach spaces: isoperimetry and processes, A Series of Modern Surveys in Mathematics Series, Springer, first reprint 2002 edition.
- McNaught, A. D. and A. Wilkinson (1997): IUPAC compendium of chemical terminology, 2nd ed., Oxford: Blackwell Scientific Publications.
- Nikolić, D. and V. Kovacev-Nikolic (2013): "Dynamical model of the maltose-binding protein," unpublished, 11 pages, Research Gate. DOI: 10.13140/2.1.3269.8883. · DOI
- Reininghause, J., S. Huber, U. Bauer and R. Kwitt (2015): "A stable multi-scale kernel for topological machine learning," In: Proc. 2015 IEEE Conf. Comp. Vision & Pat. Rec. (CVPR '15), Boston, MA, USA, 4741-4748.
Cited by
Sorted by citations
Wang, M., Cang, Z., & Wei, G.-W. (2020) · Nature Machine Intelligence · doi:10.1038/s42256-020-0149-6 · Cited by 202 · see citing works
- Authors
- Kovacev-Nikolic, V., Bubenik, P., Nikolić, D., & Heo, G.
- Affiliations
- University of Alberta (CA)
- Corresponding author
- Heo, Giseon
- ORCID
- Bubenik, Peter
- Venue
- Statistical Applications in Genetics and Molecular Biology
- Publisher
- Walter de Gruyter GmbH
- Published
- 2016-01-01
- Volume
- 15
- Issue
- 1
- Pages
- 19-38
- ISSN
- 1544-6115 (ISSN-L)
- 2194-6302
- OpenAlex
- W2408772186
- Cited by
- 116
- References
- 22
- Citations by year
- 2026: 7 · 2025: 15 · 2024: 7 · 2023: 12 · 2022: 17 · 2021: 20 · 2020: 19 · 2019: 9 · 2018: 3 · 2017: 4 · 2016: 3
- FWCI
- 5.83
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Statistical Applications in Genetics and Molecular Biology (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Compute Canada
- University of Alberta
- Natural Sciences and Engineering Research Council of Canada (293180)
- Air Force Office of Scientific Research (FA9550-)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Machine Learning in Bioinformatics
- Keywords
- persistent homology, persistence landscapes, protein binding, maltose-binding protein, protein conformational change, permutation tests, Vietoris-Rips complex, support vector machine, active site residues, allosteric pathways, ligand binding, anisotropic network model, topological data analysis
- MeSH terms
- Algorithms, Binding Sites, Models, Molecular, Protein Binding, Protein Conformation, Proteins, Models, Statistical, Catalytic Domain, Molecular Dynamics Simulation
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.
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
