Multistationarity in structured reaction networks

Autores
Dickenstein, Alicia Marcela; Pérez Millán, Mercedes Soledad; Shiu, Anne; Tang, Xiaoxian
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an effective question in real algebraic geometry, it is in general difficult to determine whether a given network can give rise to a multistationary system, and if so, to identify witnesses to multistationarity, that is, specific parameter values for which the system exhibits multiple steady states. Here we investigate both problems. First, we build on work of Conradi, Feliu, Mincheva, and Wiuf, who showed that for certain reaction networks whose steady states admit a positive parametrization, multistationarity is characterized by whether a certain “critical function” changes sign. Here, we allow for more general parametrizations, which make it much easier to determine the existence of a sign change. This is particularly simple when the steady-state equations are linearly equivalent to binomials; we give necessary conditions for this to happen, which hold for many networks studied in the literature. We also give a sufficient condition for multistationarity of networks whose steady-state equations can be replaced by equivalent triangular-form equations. Finally, we present methods for finding witnesses to multistationarity, which we show work well for certain structured reaction networks, including those common to biological signaling pathways. Our work relies on results from degree theory, on the existence of explicit rational parametrizations of the steady states, and on the specialization of Gröbner bases.
Fil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Pérez Millán, Mercedes Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires; Argentina
Fil: Shiu, Anne. Texas A&M University; Estados Unidos
Fil: Tang, Xiaoxian. Texas A&M University; Estados Unidos
Materia
REACTION NETWORK
MASS-ACTION KINETICS
MULTISTATIONARITY
PARAMETRIZATION
BINOMIAL IDEAL
BROUWER DEGREE
GRÖBNER BASIS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/135881
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/135881
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Multistationarity in structured reaction networksDickenstein, Alicia MarcelaPérez Millán, Mercedes SoledadShiu, AnneTang, XiaoxianREACTION NETWORKMASS-ACTION KINETICSMULTISTATIONARITYPARAMETRIZATIONBINOMIAL IDEALBROUWER DEGREEGRÖBNER BASIShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an effective question in real algebraic geometry, it is in general difficult to determine whether a given network can give rise to a multistationary system, and if so, to identify witnesses to multistationarity, that is, specific parameter values for which the system exhibits multiple steady states. Here we investigate both problems. First, we build on work of Conradi, Feliu, Mincheva, and Wiuf, who showed that for certain reaction networks whose steady states admit a positive parametrization, multistationarity is characterized by whether a certain “critical function” changes sign. Here, we allow for more general parametrizations, which make it much easier to determine the existence of a sign change. This is particularly simple when the steady-state equations are linearly equivalent to binomials; we give necessary conditions for this to happen, which hold for many networks studied in the literature. We also give a sufficient condition for multistationarity of networks whose steady-state equations can be replaced by equivalent triangular-form equations. Finally, we present methods for finding witnesses to multistationarity, which we show work well for certain structured reaction networks, including those common to biological signaling pathways. Our work relies on results from degree theory, on the existence of explicit rational parametrizations of the steady states, and on the specialization of Gröbner bases.Fil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Pérez Millán, Mercedes Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires; ArgentinaFil: Shiu, Anne. Texas A&M University; Estados UnidosFil: Tang, Xiaoxian. Texas A&M University; Estados UnidosSpringer2019-02-20info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/135881Dickenstein, Alicia Marcela; Pérez Millán, Mercedes Soledad; Shiu, Anne; Tang, Xiaoxian; Multistationarity in structured reaction networks; Springer; Bulletin Of Mathematical Biology; 81; 5; 20-2-2019; 1527-15810092-8240CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs11538-019-00572-6info:eu-repo/semantics/altIdentifier/doi/10.1007/s11538-019-00572-6info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1810.05574info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:40:26Zoai:ri.conicet.gov.ar:11336/135881instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:40:26.396CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Multistationarity in structured reaction networks
title Multistationarity in structured reaction networks
spellingShingle Multistationarity in structured reaction networks
Dickenstein, Alicia Marcela
REACTION NETWORK
MASS-ACTION KINETICS
MULTISTATIONARITY
PARAMETRIZATION
BINOMIAL IDEAL
BROUWER DEGREE
GRÖBNER BASIS
title_short Multistationarity in structured reaction networks
title_full Multistationarity in structured reaction networks
title_fullStr Multistationarity in structured reaction networks
title_full_unstemmed Multistationarity in structured reaction networks
title_sort Multistationarity in structured reaction networks
dc.creator.none.fl_str_mv Dickenstein, Alicia Marcela
Pérez Millán, Mercedes Soledad
Shiu, Anne
Tang, Xiaoxian
author Dickenstein, Alicia Marcela
author_facet Dickenstein, Alicia Marcela
Pérez Millán, Mercedes Soledad
Shiu, Anne
Tang, Xiaoxian
author_role author
author2 Pérez Millán, Mercedes Soledad
Shiu, Anne
Tang, Xiaoxian
author2_role author
author
author
dc.subject.none.fl_str_mv REACTION NETWORK
MASS-ACTION KINETICS
MULTISTATIONARITY
PARAMETRIZATION
BINOMIAL IDEAL
BROUWER DEGREE
GRÖBNER BASIS
topic REACTION NETWORK
MASS-ACTION KINETICS
MULTISTATIONARITY
PARAMETRIZATION
BINOMIAL IDEAL
BROUWER DEGREE
GRÖBNER BASIS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an effective question in real algebraic geometry, it is in general difficult to determine whether a given network can give rise to a multistationary system, and if so, to identify witnesses to multistationarity, that is, specific parameter values for which the system exhibits multiple steady states. Here we investigate both problems. First, we build on work of Conradi, Feliu, Mincheva, and Wiuf, who showed that for certain reaction networks whose steady states admit a positive parametrization, multistationarity is characterized by whether a certain “critical function” changes sign. Here, we allow for more general parametrizations, which make it much easier to determine the existence of a sign change. This is particularly simple when the steady-state equations are linearly equivalent to binomials; we give necessary conditions for this to happen, which hold for many networks studied in the literature. We also give a sufficient condition for multistationarity of networks whose steady-state equations can be replaced by equivalent triangular-form equations. Finally, we present methods for finding witnesses to multistationarity, which we show work well for certain structured reaction networks, including those common to biological signaling pathways. Our work relies on results from degree theory, on the existence of explicit rational parametrizations of the steady states, and on the specialization of Gröbner bases.
Fil: Dickenstein, Alicia Marcela. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Pérez Millán, Mercedes Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires; Argentina
Fil: Shiu, Anne. Texas A&M University; Estados Unidos
Fil: Tang, Xiaoxian. Texas A&M University; Estados Unidos
description Many dynamical systems arising in biology and other areas exhibit multistationarity (two or more positive steady states with the same conserved quantities). Although deciding multistationarity for a polynomial dynamical system is an effective question in real algebraic geometry, it is in general difficult to determine whether a given network can give rise to a multistationary system, and if so, to identify witnesses to multistationarity, that is, specific parameter values for which the system exhibits multiple steady states. Here we investigate both problems. First, we build on work of Conradi, Feliu, Mincheva, and Wiuf, who showed that for certain reaction networks whose steady states admit a positive parametrization, multistationarity is characterized by whether a certain “critical function” changes sign. Here, we allow for more general parametrizations, which make it much easier to determine the existence of a sign change. This is particularly simple when the steady-state equations are linearly equivalent to binomials; we give necessary conditions for this to happen, which hold for many networks studied in the literature. We also give a sufficient condition for multistationarity of networks whose steady-state equations can be replaced by equivalent triangular-form equations. Finally, we present methods for finding witnesses to multistationarity, which we show work well for certain structured reaction networks, including those common to biological signaling pathways. Our work relies on results from degree theory, on the existence of explicit rational parametrizations of the steady states, and on the specialization of Gröbner bases.
publishDate 2019
dc.date.none.fl_str_mv 2019-02-20
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/135881
Dickenstein, Alicia Marcela; Pérez Millán, Mercedes Soledad; Shiu, Anne; Tang, Xiaoxian; Multistationarity in structured reaction networks; Springer; Bulletin Of Mathematical Biology; 81; 5; 20-2-2019; 1527-1581
0092-8240
CONICET Digital
CONICET
url http://hdl.handle.net/11336/135881
identifier_str_mv Dickenstein, Alicia Marcela; Pérez Millán, Mercedes Soledad; Shiu, Anne; Tang, Xiaoxian; Multistationarity in structured reaction networks; Springer; Bulletin Of Mathematical Biology; 81; 5; 20-2-2019; 1527-1581
0092-8240
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs11538-019-00572-6
info:eu-repo/semantics/altIdentifier/doi/10.1007/s11538-019-00572-6
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1810.05574
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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