The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ Tregs

Detalhes bibliográficos
Autor(a) principal: Yusuf, Aliyu
Data de Publicação: 2020
Outros Autores: Figueiredo, Isabel, Afsar, Atefeh, Burroughs, Nigel, Pinto, Alberto, Oliveira, Bruno
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.22/19470
Resumo: We study the equilibria of an Ordinary Differencial Equation (ODE) system where CD4 + effector or helper T cells and Regulatory T cells (Tregs) are present. T cells trigger an immune response in the presence of their specific antigen. Regulatory T cells (Tregs) play a role in limiting auto-immune diseases due to their immune-suppressive ability. Here, we present explicit exact formulas that give the relationship between the concentration of T cells, the concentration of Tregs, and the antigenic stimulation of T cells, when the system is at equilibria, stable or unstable. We found a parameter region of bistability, limited by two thresholds of antigenic stimulation of T cells (hysteresis). Moreover, there are values of the slope parameter of the tuning for which an isola-center bifurcation appears, and, for some other values, there is a transcritical bifurcation. We also present time evolutions of the ODE system.
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spelling The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ TregsCD4+ T cellsCD4+ TregsBifurcationEigenvaluesODE modelWe study the equilibria of an Ordinary Differencial Equation (ODE) system where CD4 + effector or helper T cells and Regulatory T cells (Tregs) are present. T cells trigger an immune response in the presence of their specific antigen. Regulatory T cells (Tregs) play a role in limiting auto-immune diseases due to their immune-suppressive ability. Here, we present explicit exact formulas that give the relationship between the concentration of T cells, the concentration of Tregs, and the antigenic stimulation of T cells, when the system is at equilibria, stable or unstable. We found a parameter region of bistability, limited by two thresholds of antigenic stimulation of T cells (hysteresis). Moreover, there are values of the slope parameter of the tuning for which an isola-center bifurcation appears, and, for some other values, there is a transcritical bifurcation. We also present time evolutions of the ODE system.A.A.P., B.M.P.M.O., and A.A.Y. would like to thank the financial support by the ERDF—European Regional Development Fund through the Operational Program for Competitiveness and Internationalization—COMPETE 2020 Program within project “POCI-01-0145-FEDER-006961”, and by National Funds through the FCT—Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) as part of project UID/EEA/50014/2013, project “Dynamics, Optimization and Modelling”, with reference PTDC/MAT-NAN/6890/2014, project “Modelling, Dynamics and Games”—MDG—with the reference PTDC/MAT-APL/31753/2017, and project “NanoSTIMA—Macro-to-Nano Human Sensing: Towards Integrated Multimodal Health Monitoring and Analytics”/NORTE-01-0145-FEDER-000016, financed by the North Portugal Regional Operational Program (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement. A.A.P. is also thankful for the financial support received through the Special Visiting Researcher Program (Bolsa Pesquisador Visitante Especial—PVE) “Dynamics, Games and Applications”, with reference 401068/2014-5 (call: MEC/MCTI/CAPES/CNPQ/FAPS) at IMPA, Rio de Janeiro, Brasil. Acknowledgments The authors thank the anonymous referees of for their valuable comments. A.A.P., B.M.P.M.O., A.A.Y., and A.A. thank LIAAD-INESC TEC for all the support. Part of this research was done during visits by the authors to IMPA (Brazil) and University of Warwick (United Kingdom), and we thank them for their hospitality.MDPIRepositório Científico do Instituto Politécnico do PortoYusuf, AliyuFigueiredo, IsabelAfsar, AtefehBurroughs, NigelPinto, AlbertoOliveira, Bruno2022-01-13T17:16:14Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/19470eng10.3390/math8020293info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-13T13:13:47Zoai:recipp.ipp.pt:10400.22/19470Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:39:24.851162Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ Tregs
title The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ Tregs
spellingShingle The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ Tregs
Yusuf, Aliyu
CD4+ T cells
CD4+ Tregs
Bifurcation
Eigenvalues
ODE model
title_short The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ Tregs
title_full The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ Tregs
title_fullStr The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ Tregs
title_full_unstemmed The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ Tregs
title_sort The Effect of a Linear Tuning between the Antigenic Stimulations of CD4+ T Cells and CD4+ Tregs
author Yusuf, Aliyu
author_facet Yusuf, Aliyu
Figueiredo, Isabel
Afsar, Atefeh
Burroughs, Nigel
Pinto, Alberto
Oliveira, Bruno
author_role author
author2 Figueiredo, Isabel
Afsar, Atefeh
Burroughs, Nigel
Pinto, Alberto
Oliveira, Bruno
author2_role author
author
author
author
author
dc.contributor.none.fl_str_mv Repositório Científico do Instituto Politécnico do Porto
dc.contributor.author.fl_str_mv Yusuf, Aliyu
Figueiredo, Isabel
Afsar, Atefeh
Burroughs, Nigel
Pinto, Alberto
Oliveira, Bruno
dc.subject.por.fl_str_mv CD4+ T cells
CD4+ Tregs
Bifurcation
Eigenvalues
ODE model
topic CD4+ T cells
CD4+ Tregs
Bifurcation
Eigenvalues
ODE model
description We study the equilibria of an Ordinary Differencial Equation (ODE) system where CD4 + effector or helper T cells and Regulatory T cells (Tregs) are present. T cells trigger an immune response in the presence of their specific antigen. Regulatory T cells (Tregs) play a role in limiting auto-immune diseases due to their immune-suppressive ability. Here, we present explicit exact formulas that give the relationship between the concentration of T cells, the concentration of Tregs, and the antigenic stimulation of T cells, when the system is at equilibria, stable or unstable. We found a parameter region of bistability, limited by two thresholds of antigenic stimulation of T cells (hysteresis). Moreover, there are values of the slope parameter of the tuning for which an isola-center bifurcation appears, and, for some other values, there is a transcritical bifurcation. We also present time evolutions of the ODE system.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01T00:00:00Z
2022-01-13T17:16:14Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.22/19470
url http://hdl.handle.net/10400.22/19470
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.3390/math8020293
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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