Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture

Mohammad Arashi, Najmeh Nakhaei Rad, Andriette Bekker and Wolf-Dieter Schubert
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Mohammad Arashi: Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 4897, Iran
Najmeh Nakhaei Rad: Department of Statistics, University of Pretoria, Pretoria 0002, 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

Mathematics, 2021, vol. 9, issue 21, 1-24

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.

Keywords: bioinformatics; cosine model; mixture distributions; Möbius transformation; sine model; toroidal data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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