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

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  • 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
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    References listed on IDEAS

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    1. 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.
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    5. 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.
    6. 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.
    7. 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.
    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.
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