Chemical Reaction Systems with Toric Steady States

Autores
Pérez Millán, Mercedes Soledad; Dickenstein, Alicia Marcela; Shiu, Anne; Conradi, Carsten
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Mass-action chemical reaction systems are frequently used in computational biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly parameterized (due to noisy measurement data and a small number of data points and repetitions). Therefore, it is often difficult to establish the existence of (positive) steady states or to determine whether more complicated phenomena such as multistationarity exist. If, however, the steady state ideal of the system is a binomial ideal, then we show that these questions can be answered easily. The focus of this work is on systems with this property, and we say that such systems have toric steady states. Our main result gives sufficient conditions for a chemical reaction system to have toric steady states. Furthermore, we analyze the capacity of such a system to exhibit positive steady states and multistationarity. Examples of systems with toric steady states include weakly-reversible zero-deficiency chemical reaction systems. An important application of our work concerns the networks that describe the multisite phosphorylation of a protein by a kinase/phosphatase pair in a sequential and distributive mechanism.
Fil: Pérez Millán, Mercedes Soledad. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Dickenstein, Alicia Marcela. 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: Shiu, Anne. University of Duke; Estados Unidos
Fil: Conradi, Carsten. Max Planck Institut Dynamik komplexer technischer Systeme; Alemania
Materia
Chemical Reaction Network
Binomial Ideal
Steady State
Multistationarity
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:11336/19942
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Chemical Reaction Systems with Toric Steady StatesPérez Millán, Mercedes SoledadDickenstein, Alicia MarcelaShiu, AnneConradi, CarstenChemical Reaction NetworkBinomial IdealSteady StateMultistationarityhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Mass-action chemical reaction systems are frequently used in computational biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly parameterized (due to noisy measurement data and a small number of data points and repetitions). Therefore, it is often difficult to establish the existence of (positive) steady states or to determine whether more complicated phenomena such as multistationarity exist. If, however, the steady state ideal of the system is a binomial ideal, then we show that these questions can be answered easily. The focus of this work is on systems with this property, and we say that such systems have toric steady states. Our main result gives sufficient conditions for a chemical reaction system to have toric steady states. Furthermore, we analyze the capacity of such a system to exhibit positive steady states and multistationarity. Examples of systems with toric steady states include weakly-reversible zero-deficiency chemical reaction systems. An important application of our work concerns the networks that describe the multisite phosphorylation of a protein by a kinase/phosphatase pair in a sequential and distributive mechanism.Fil: Pérez Millán, Mercedes Soledad. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Dickenstein, Alicia Marcela. 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: Shiu, Anne. University of Duke; Estados UnidosFil: Conradi, Carsten. Max Planck Institut Dynamik komplexer technischer Systeme; AlemaniaSpringer2012-05info: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/11336/19942Pérez Millán, Mercedes Soledad; Dickenstein, Alicia Marcela; Shiu, Anne; Conradi, Carsten; Chemical Reaction Systems with Toric Steady States; Springer; Bulletin Of Mathematical Biology; 74; 5; 5-2012; 1027-10650092-82401522-9602CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s11538-011-9685-xinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs11538-011-9685-xinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1102.1590info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:31:04Zoai:ri.conicet.gov.ar:11336/19942instacron: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 10:31:04.737CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Chemical Reaction Systems with Toric Steady States
title Chemical Reaction Systems with Toric Steady States
spellingShingle Chemical Reaction Systems with Toric Steady States
Pérez Millán, Mercedes Soledad
Chemical Reaction Network
Binomial Ideal
Steady State
Multistationarity
title_short Chemical Reaction Systems with Toric Steady States
title_full Chemical Reaction Systems with Toric Steady States
title_fullStr Chemical Reaction Systems with Toric Steady States
title_full_unstemmed Chemical Reaction Systems with Toric Steady States
title_sort Chemical Reaction Systems with Toric Steady States
dc.creator.none.fl_str_mv Pérez Millán, Mercedes Soledad
Dickenstein, Alicia Marcela
Shiu, Anne
Conradi, Carsten
author Pérez Millán, Mercedes Soledad
author_facet Pérez Millán, Mercedes Soledad
Dickenstein, Alicia Marcela
Shiu, Anne
Conradi, Carsten
author_role author
author2 Dickenstein, Alicia Marcela
Shiu, Anne
Conradi, Carsten
author2_role author
author
author
dc.subject.none.fl_str_mv Chemical Reaction Network
Binomial Ideal
Steady State
Multistationarity
topic Chemical Reaction Network
Binomial Ideal
Steady State
Multistationarity
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Mass-action chemical reaction systems are frequently used in computational biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly parameterized (due to noisy measurement data and a small number of data points and repetitions). Therefore, it is often difficult to establish the existence of (positive) steady states or to determine whether more complicated phenomena such as multistationarity exist. If, however, the steady state ideal of the system is a binomial ideal, then we show that these questions can be answered easily. The focus of this work is on systems with this property, and we say that such systems have toric steady states. Our main result gives sufficient conditions for a chemical reaction system to have toric steady states. Furthermore, we analyze the capacity of such a system to exhibit positive steady states and multistationarity. Examples of systems with toric steady states include weakly-reversible zero-deficiency chemical reaction systems. An important application of our work concerns the networks that describe the multisite phosphorylation of a protein by a kinase/phosphatase pair in a sequential and distributive mechanism.
Fil: Pérez Millán, Mercedes Soledad. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Dickenstein, Alicia Marcela. 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: Shiu, Anne. University of Duke; Estados Unidos
Fil: Conradi, Carsten. Max Planck Institut Dynamik komplexer technischer Systeme; Alemania
description Mass-action chemical reaction systems are frequently used in computational biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly parameterized (due to noisy measurement data and a small number of data points and repetitions). Therefore, it is often difficult to establish the existence of (positive) steady states or to determine whether more complicated phenomena such as multistationarity exist. If, however, the steady state ideal of the system is a binomial ideal, then we show that these questions can be answered easily. The focus of this work is on systems with this property, and we say that such systems have toric steady states. Our main result gives sufficient conditions for a chemical reaction system to have toric steady states. Furthermore, we analyze the capacity of such a system to exhibit positive steady states and multistationarity. Examples of systems with toric steady states include weakly-reversible zero-deficiency chemical reaction systems. An important application of our work concerns the networks that describe the multisite phosphorylation of a protein by a kinase/phosphatase pair in a sequential and distributive mechanism.
publishDate 2012
dc.date.none.fl_str_mv 2012-05
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/11336/19942
Pérez Millán, Mercedes Soledad; Dickenstein, Alicia Marcela; Shiu, Anne; Conradi, Carsten; Chemical Reaction Systems with Toric Steady States; Springer; Bulletin Of Mathematical Biology; 74; 5; 5-2012; 1027-1065
0092-8240
1522-9602
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19942
identifier_str_mv Pérez Millán, Mercedes Soledad; Dickenstein, Alicia Marcela; Shiu, Anne; Conradi, Carsten; Chemical Reaction Systems with Toric Steady States; Springer; Bulletin Of Mathematical Biology; 74; 5; 5-2012; 1027-1065
0092-8240
1522-9602
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s11538-011-9685-x
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs11538-011-9685-x
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1102.1590
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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