A mathematical model for the interaction of a virus with the plasma membrane of cell
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Remat (Bento Gonçalves) |
Texto Completo: | https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4149 |
Resumo: | Understanding the interactions of viruses with cell membranes is important for the proposal of vaccines and treatments for diseases caused by this type of contamination. An example of this is the case of the pandemic caused by the new Covid-19, which in 2020 placed was responsible for a third of the world under virus quarantine, causing huge economic losses and thousand of deaths across the planet. In this context, this research proposes to build a mathematical model for the interaction of a virus with the plasma membrane in a mammalian cell, which leads to a mathematical problem with boundary conditions. Using Green’s functions, the model was able to answer what is the general expression for potential electrostatic energy of this interaction in terms of Bessel functions and Wigner coefficients. It is reasonable to speculate, based on the results presented by the model, that a virus has to present an effective charge resulting in a solution with a pH value of about 7 to approach the cell membrane, while an electrically neutral virus should not have the ability to interact and enter membranes. The values ?for the interaction energy and the force between the membrane and the cluster offer the order of magnitude of the distances over which such interaction is effective. |
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A mathematical model for the interaction of a virus with the plasma membrane of cellUm modelo matemático para a interação de um vírus com a membrana plasmática da célulaFunções de GreenModelagemProblemas com Condições de ContornoGreen’s FunctionsModelingProblems with Boundary ConditionsUnderstanding the interactions of viruses with cell membranes is important for the proposal of vaccines and treatments for diseases caused by this type of contamination. An example of this is the case of the pandemic caused by the new Covid-19, which in 2020 placed was responsible for a third of the world under virus quarantine, causing huge economic losses and thousand of deaths across the planet. In this context, this research proposes to build a mathematical model for the interaction of a virus with the plasma membrane in a mammalian cell, which leads to a mathematical problem with boundary conditions. Using Green’s functions, the model was able to answer what is the general expression for potential electrostatic energy of this interaction in terms of Bessel functions and Wigner coefficients. It is reasonable to speculate, based on the results presented by the model, that a virus has to present an effective charge resulting in a solution with a pH value of about 7 to approach the cell membrane, while an electrically neutral virus should not have the ability to interact and enter membranes. The values ?for the interaction energy and the force between the membrane and the cluster offer the order of magnitude of the distances over which such interaction is effective.O entendimento das interações dos vírus com as membranas celulares é de fundamental importância para a proposta de vacinas e tratamentos de doenças causadas por esse tipo de contaminação. A exemplo disso, cita-se o caso da pandemia causada pelo novo coronavírus causador da Covid-19, que no ano de 2020 colocou um terço do mundo em situação de quarentena, causando milhares de mortes e prejuízos econômicos em todo o planeta. Nesse contexto, o presente estudo propõe-se a construir um modelo matemático para a interação de um vírus com a membrana plasmática da célula de um mamífero, que conduz a um problema matemático com condições de contorno. Fazendo uso das funções de Green, o modelo foi capaz de responder qual é a expressão geral para energia potencial eletrostática desta interação em termos das funções de Bessel e os coeficientes de Wigner. Pode-se especular, ancorado nos resultados apresentados pelo modelo, que um vírus tem que apresentar uma carga efetiva resultante em solução com pH da ordem de 7 para se aproximar da membrana celular, enquanto um vírus eletricamente neutro não deve apresentar a capacidade de interagir e adentrar em membranas. Os valores para a energia de interação e para a força entre a membrana e o aglomerado oferecem a ordem de grandeza das distâncias em que tal interação é efetiva.Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul2020-12-17info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArtigos; Avaliado pelos paresapplication/pdfhttps://periodicos.ifrs.edu.br/index.php/REMAT/article/view/414910.35819/remat2020v6i2id4149REMAT: Revista Eletrônica da Matemática; Vol. 6 No. 2 (2020); e4007REMAT: Revista Eletrônica da Matemática; Vol. 6 Núm. 2 (2020); e4007REMAT: Revista Eletrônica da Matemática; v. 6 n. 2 (2020); e40072447-2689reponame:Remat (Bento Gonçalves)instname:Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)instacron:IFRSporhttps://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4149/2832Copyright (c) 2020 REMAT: Revista Eletrônica da Matemáticahttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessMartins Gonçalves de Morais, Diogo2022-12-28T16:05:32Zoai:ojs2.periodicos.ifrs.edu.br:article/4149Revistahttp://periodicos.ifrs.edu.br/index.php/REMATPUBhttps://periodicos.ifrs.edu.br/index.php/REMAT/oai||greice.andreis@caxias.ifrs.edu.br2447-26892447-2689opendoar:2022-12-28T16:05:32Remat (Bento Gonçalves) - Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS)false |
dc.title.none.fl_str_mv |
A mathematical model for the interaction of a virus with the plasma membrane of cell Um modelo matemático para a interação de um vírus com a membrana plasmática da célula |
title |
A mathematical model for the interaction of a virus with the plasma membrane of cell |
spellingShingle |
A mathematical model for the interaction of a virus with the plasma membrane of cell Martins Gonçalves de Morais, Diogo Funções de Green Modelagem Problemas com Condições de Contorno Green’s Functions Modeling Problems with Boundary Conditions |
title_short |
A mathematical model for the interaction of a virus with the plasma membrane of cell |
title_full |
A mathematical model for the interaction of a virus with the plasma membrane of cell |
title_fullStr |
A mathematical model for the interaction of a virus with the plasma membrane of cell |
title_full_unstemmed |
A mathematical model for the interaction of a virus with the plasma membrane of cell |
title_sort |
A mathematical model for the interaction of a virus with the plasma membrane of cell |
author |
Martins Gonçalves de Morais, Diogo |
author_facet |
Martins Gonçalves de Morais, Diogo |
author_role |
author |
dc.contributor.author.fl_str_mv |
Martins Gonçalves de Morais, Diogo |
dc.subject.por.fl_str_mv |
Funções de Green Modelagem Problemas com Condições de Contorno Green’s Functions Modeling Problems with Boundary Conditions |
topic |
Funções de Green Modelagem Problemas com Condições de Contorno Green’s Functions Modeling Problems with Boundary Conditions |
description |
Understanding the interactions of viruses with cell membranes is important for the proposal of vaccines and treatments for diseases caused by this type of contamination. An example of this is the case of the pandemic caused by the new Covid-19, which in 2020 placed was responsible for a third of the world under virus quarantine, causing huge economic losses and thousand of deaths across the planet. In this context, this research proposes to build a mathematical model for the interaction of a virus with the plasma membrane in a mammalian cell, which leads to a mathematical problem with boundary conditions. Using Green’s functions, the model was able to answer what is the general expression for potential electrostatic energy of this interaction in terms of Bessel functions and Wigner coefficients. It is reasonable to speculate, based on the results presented by the model, that a virus has to present an effective charge resulting in a solution with a pH value of about 7 to approach the cell membrane, while an electrically neutral virus should not have the ability to interact and enter membranes. The values ?for the interaction energy and the force between the membrane and the cluster offer the order of magnitude of the distances over which such interaction is effective. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-17 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Artigos; Avaliado pelos pares |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4149 10.35819/remat2020v6i2id4149 |
url |
https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4149 |
identifier_str_mv |
10.35819/remat2020v6i2id4149 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/4149/2832 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2020 REMAT: Revista Eletrônica da Matemática https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2020 REMAT: Revista Eletrônica da Matemática https://creativecommons.org/licenses/by/4.0 |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul |
publisher.none.fl_str_mv |
Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul |
dc.source.none.fl_str_mv |
REMAT: Revista Eletrônica da Matemática; Vol. 6 No. 2 (2020); e4007 REMAT: Revista Eletrônica da Matemática; Vol. 6 Núm. 2 (2020); e4007 REMAT: Revista Eletrônica da Matemática; v. 6 n. 2 (2020); e4007 2447-2689 reponame:Remat (Bento Gonçalves) instname:Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) instacron:IFRS |
instname_str |
Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) |
instacron_str |
IFRS |
institution |
IFRS |
reponame_str |
Remat (Bento Gonçalves) |
collection |
Remat (Bento Gonçalves) |
repository.name.fl_str_mv |
Remat (Bento Gonçalves) - Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) |
repository.mail.fl_str_mv |
||greice.andreis@caxias.ifrs.edu.br |
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1798329705674309632 |