Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture

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 flexibl...

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Autores principales:	Mohammad Arashi, Najmeh Nakhaei Rad, Andriette Bekker, Wolf-Dieter Schubert
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	bioinformatics cosine model mixture distributions Möbius transformation sine model toroidal data Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/a7a4369d97304a3eafc03b53c3932133
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spelling	oai:doaj.org-article:a7a4369d97304a3eafc03b53c39321332021-11-11T18:17:48ZMöbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture10.3390/math92127492227-7390https://doaj.org/article/a7a4369d97304a3eafc03b53c39321332021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2749https://doaj.org/toc/2227-7390Proteins 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.Mohammad ArashiNajmeh Nakhaei RadAndriette BekkerWolf-Dieter SchubertMDPI AGarticlebioinformaticscosine modelmixture distributionsMöbius transformationsine modeltoroidal dataMathematicsQA1-939ENMathematics, Vol 9, Iss 2749, p 2749 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	bioinformatics cosine model mixture distributions Möbius transformation sine model toroidal data Mathematics QA1-939
spellingShingle	bioinformatics cosine model mixture distributions Möbius transformation sine model toroidal data Mathematics QA1-939 Mohammad Arashi Najmeh Nakhaei Rad Andriette Bekker Wolf-Dieter Schubert Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture
description	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.
format	article
author	Mohammad Arashi Najmeh Nakhaei Rad Andriette Bekker Wolf-Dieter Schubert
author_facet	Mohammad Arashi Najmeh Nakhaei Rad Andriette Bekker Wolf-Dieter Schubert
author_sort	Mohammad Arashi
title	Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture
title_short	Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture
title_full	Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture
title_fullStr	Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture
title_full_unstemmed	Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture
title_sort	möbius transformation-induced distributions provide better modelling for protein architecture
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/a7a4369d97304a3eafc03b53c3932133
work_keys_str_mv	AT mohammadarashi mobiustransformationinduceddistributionsprovidebettermodellingforproteinarchitecture AT najmehnakhaeirad mobiustransformationinduceddistributionsprovidebettermodellingforproteinarchitecture AT andriettebekker mobiustransformationinduceddistributionsprovidebettermodellingforproteinarchitecture AT wolfdieterschubert mobiustransformationinduceddistributionsprovidebettermodellingforproteinarchitecture
_version_	1718431903262965760

Möbius Transformation-Induced Distributions Provide Better Modelling for Protein Architecture

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