IDEAS home Printed from https://ideas.repec.org/a/bpj/sagmbi/v13y2014i1p1-18n1.html
   My bibliography  Save this article

Modeling angles in proteins and circular genomes using multivariate angular distributions based on multiple nonnegative trigonometric sums

Author

Listed:
  • Fernández-Durán Juan José

    (School of Business and Department of Statistics, Instituto Tecnológico Autónomo de México, Río Hondo 1, Col. Progreso Tizapán, C.P. 01080, México D.F., México)

  • Gregorio-Domínguez MarÍa Mercedes

    (Department of Actuarial Science, Instituto Tecnológico Autónomo de México, Río Hondo 1, Col. Progreso Tizapán, C.P. 01080, México D.F., México)

Abstract

Fernández-Durán, J. J. (2004): “Circular distributions based on nonnegative trigonometric sums,” Biometrics, 60, 499–503, developed a family of univariate circular distributions based on nonnegative trigonometric sums. In this work, we extend this family of distributions to the multivariate case by using multiple nonnegative trigonometric sums to model the joint distribution of a vector of angular random variables. Practical examples of vectors of angular random variables include the wind direction at different monitoring stations, the directions taken by an animal on different occasions, the times at which a person performs different daily activities, and the dihedral angles of a protein molecule. We apply the proposed new family of multivariate distributions to three real data-sets: two for the study of protein structure and one for genomics. The first is related to the study of a bivariate vector of dihedral angles in proteins. In the second real data-set, we compare the fit of the proposed multivariate model with the bivariate generalized von Mises model of [Shieh, G. S., S. Zheng, R. A. Johnson, Y.-F. Chang, K. Shimizu, C.-C. Wang, and S.-L. Tang (2011): “Modeling and comparing the organization of circular genomes,” Bioinformatics, 27(7), 912–918.] in a problem related to orthologous genes in pairs of circular genomes. The third real data-set consists of observed values of three dihedral angles in γ-turns in a protein and serves as an example of trivariate angular data. In addition, a simulation algorithm is presented to generate realizations from the proposed multivariate angular distribution.

Suggested Citation

  • Fernández-Durán Juan José & Gregorio-Domínguez MarÍa Mercedes, 2014. "Modeling angles in proteins and circular genomes using multivariate angular distributions based on multiple nonnegative trigonometric sums," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 13(1), pages 1-18, February.
  • Handle: RePEc:bpj:sagmbi:v:13:y:2014:i:1:p:1-18:n:1
    DOI: 10.1515/sagmb-2012-0012
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/sagmb-2012-0012
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.1515/sagmb-2012-0012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hyun Joo & Archana G Chavan & Ryan Day & Kristin P Lennox & Paul Sukhanov & David B Dahl & Marina Vannucci & Jerry Tsai, 2011. "Near-Native Protein Loop Sampling Using Nonparametric Density Estimation Accommodating Sparcity," PLOS Computational Biology, Public Library of Science, vol. 7(10), pages 1-14, October.
    2. Hommola Kerstin & Gilks Walter R. & Mardia Kanti V., 2011. "Log-Linear Modelling of Protein Dipeptide Structure Reveals Interesting Patterns of Side-Chain-Backbone Interactions," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-27, January.
    3. Harshinder Singh, 2002. "Probabilistic model for two dependent circular variables," Biometrika, Biometrika Trust, vol. 89(3), pages 719-723, August.
    4. Thomas Hamelryck & John T Kent & Anders Krogh, 2006. "Sampling Realistic Protein Conformations Using Local Structural Bias," PLOS Computational Biology, Public Library of Science, vol. 2(9), pages 1-13, September.
    5. Daniel Ting & Guoli Wang & Maxim Shapovalov & Rajib Mitra & Michael I Jordan & Roland L Dunbrack Jr, 2010. "Neighbor-Dependent Ramachandran Probability Distributions of Amino Acids Developed from a Hierarchical Dirichlet Process Model," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-21, April.
    6. Lennox, Kristin P. & Dahl, David B. & Vannucci, Marina & Tsai, Jerry W., 2009. "Density Estimation for Protein Conformation Angles Using a Bivariate von Mises Distribution and Bayesian Nonparametrics," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 586-596.
    7. Kanti V. Mardia, 2013. "Statistical approaches to three key challenges in protein structural bioinformatics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(3), pages 487-514, May.
    8. Kanti V. Mardia & Charles C. Taylor & Ganesh K. Subramaniam, 2007. "Protein Bioinformatics and Mixtures of Bivariate von Mises Distributions for Angular Data," Biometrics, The International Biometric Society, vol. 63(2), pages 505-512, June.
    9. Grace Shieh & Richard Johnson, 2005. "Inferences based on a bivariate distribution with von Mises marginals," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 789-802, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    2. Saptarshi Chakraborty & Samuel W. K. Wong, 2023. "On the circular correlation coefficients for bivariate von Mises distributions on a torus," Statistical Papers, Springer, vol. 64(2), pages 643-675, April.
    3. Mohammad Arashi & Najmeh Nakhaei Rad & Andriette Bekker & Wolf-Dieter Schubert, 2021. "Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture," Mathematics, MDPI, vol. 9(21), pages 1-24, October.
    4. M. Jones & Arthur Pewsey & Shogo Kato, 2015. "On a class of circulas: copulas for circular distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(5), pages 843-862, October.
    5. Kanti Mardia, 2010. "Bayesian analysis for bivariate von Mises distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 515-528.
    6. Shogo Kato & Arthur Pewsey & M. C. Jones, 2022. "Tractable circula densities from Fourier series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 595-618, September.
    7. Marco Marzio & Stefania Fensore & Agnese Panzera & Charles C. Taylor, 2018. "Circular local likelihood," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 921-945, December.
    8. David B. Dahl & Ryan Day & Jerry W. Tsai, 2017. "Random Partition Distribution Indexed by Pairwise Information," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 721-732, April.
    9. Kanti V. Mardia, 2021. "Comments on: Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 59-63, March.
    10. Mardia, Kanti V. & Wiechers, Henrik & Eltzner, Benjamin & Huckemann, Stephan F., 2022. "Principal component analysis and clustering on manifolds," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    11. Bee, Marco & Benedetti, Roberto & Espa, Giuseppe, 2017. "Approximate maximum likelihood estimation of the Bingham distribution," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 84-96.
    12. Kim, Sungsu & SenGupta, Ashis & Arnold, Barry C., 2016. "A multivariate circular distribution with applications to the protein structure prediction problem," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 374-382.
    13. Dong, Aqi & Melnykov, Volodymyr, 2024. "Contaminated Kent mixture model for clustering non-spherical directional data with heavy tails or scatter," Statistics & Probability Letters, Elsevier, vol. 208(C).
    14. Yukari Shirota & Takako Hashimoto, 2017. "Visual Explanation of Deformation Theories in Shape Analysis," Gakushuin Economic Papers, Gakushuin University, Faculty of Economics, vol. 54(1), pages 1-12.
    15. Simon Byrne & Mark Girolami, 2013. "Geodesic Monte Carlo on Embedded Manifolds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 825-845, December.
    16. Armando D Solis, 2014. "Deriving High-Resolution Protein Backbone Structure Propensities from All Crystal Data Using the Information Maximization Device," PLOS ONE, Public Library of Science, vol. 9(6), pages 1-21, June.
    17. Saptarshi Chakraborty & Tian Lan & Yiider Tseng & Samuel W.K. Wong, 2022. "Bayesian analysis of coupled cellular and nuclear trajectories for cell migration," Biometrics, The International Biometric Society, vol. 78(3), pages 1209-1220, September.
    18. Kanti V. Mardia & Karthik Sriram & Charlotte M. Deane, 2018. "A statistical model for helices with applications," Biometrics, The International Biometric Society, vol. 74(3), pages 845-854, September.
    19. Jes Frellsen & Ida Moltke & Martin Thiim & Kanti V Mardia & Jesper Ferkinghoff-Borg & Thomas Hamelryck, 2009. "A Probabilistic Model of RNA Conformational Space," PLOS Computational Biology, Public Library of Science, vol. 5(6), pages 1-11, June.
    20. Abhishek Bhattacharya & David Dunson, 2012. "Strong consistency of nonparametric Bayes density estimation on compact metric spaces with applications to specific manifolds," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 687-714, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:sagmbi:v:13:y:2014:i:1:p:1-18:n:1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.