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Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture

Author

Listed:
  • Mohammad Arashi

    (Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 4897, Iran
    Department of Statistics, University of Pretoria, Pretoria 0002, South Africa)

  • Najmeh Nakhaei Rad

    (Department of Statistics, University of Pretoria, Pretoria 0002, South Africa
    DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), Johannesburg 2000, South Africa)

  • Andriette Bekker

    (Department of Statistics, University of Pretoria, Pretoria 0002, South Africa)

  • Wolf-Dieter Schubert

    (Department of Biochemistry, Genetics and Microbiology, University of Pretoria, Pretoria 0002, South Africa)

Abstract

Proteins are found in all living organisms and constitute a large group of macromolecules with many functions. Proteins achieve their operations by adopting distinct three-dimensional structures encoded within the sequence of the constituent amino acids in one or more polypeptides. New, more flexible distributions are proposed for the MCMC sampling method for predicting protein 3D structures by applying a Möbius transformation to the bivariate von Mises distribution. In addition to this, sine-skewed versions of the proposed models are introduced to meet the increasing demand for modelling asymmetric toroidal data. Interestingly, the marginals of the new models lead to new multimodal circular distributions. We analysed three big datasets consisting of bivariate information about protein domains to illustrate the efficiency and behaviour of the proposed models. These newly proposed models outperformed mixtures of well-known models for modelling toroidal data. A simulation study was carried out to find the best method for generating samples from the proposed models. Our results shed new light on proposal distributions in the MCMC sampling method for predicting the protein structure environment.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2749-:d:667993
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    References listed on IDEAS

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    1. Mullen, Katharine M. & Ardia, David & Gil, David L. & Windover, Donald & Cline, James, 2011. "DEoptim: An R Package for Global Optimization by Differential Evolution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i06).
    2. 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.
    3. 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.
    4. Harshinder Singh, 2002. "Probabilistic model for two dependent circular variables," Biometrika, Biometrika Trust, vol. 89(3), pages 719-723, August.
    5. Kato, Shogo & Jones, M. C., 2010. "A Family of Distributions on the Circle With Links to, and Applications Arising From, Möbius Transformation," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 249-262.
    6. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
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