Show simple item record Pérez Millán, Mercedes Soledad Dickenstein, Alicia Marcela Shiu, Anne Conradi, Carsten 2017-07-07T21:49:14Z 2012-05
dc.identifier.citation 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
dc.identifier.issn 0092-8240
dc.description.abstract 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.
dc.format application/pdf
dc.language.iso eng
dc.publisher Springer
dc.rights info:eu-repo/semantics/restrictedAccess
dc.subject Chemical reaction network
dc.subject Binomial ideal
dc.subject Steady state
dc.subject Multistationarity
dc.subject.classification Matemática Aplicada
dc.subject.classification Matemáticas
dc.subject.classification CIENCIAS NATURALES Y EXACTAS
dc.title Chemical Reaction Systems with Toric Steady States
dc.type info:eu-repo/semantics/article
dc.type info:ar-repo/semantics/artículo
dc.type info:eu-repo/semantics/publishedVersion 2017-07-07T14:43:48Z
dc.identifier.eissn 1522-9602
dc.journal.volume 74
dc.journal.number 5
dc.journal.pagination 1027-1065
dc.journal.pais Alemania
dc.journal.ciudad Berlin
dc.description.fil 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
dc.description.fil 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
dc.description.fil Fil: Shiu, Anne. University of Duke; Estados Unidos
dc.description.fil Fil: Conradi, Carsten. Max Planck Institut Dynamik komplexer technischer Systeme; Alemania
dc.journal.title Bulletin Of Mathematical Biology
dc.relation.alternativeid info:eu-repo/semantics/altIdentifier/doi/
dc.relation.alternativeid info:eu-repo/semantics/altIdentifier/url/
dc.relation.alternativeid info:eu-repo/semantics/altIdentifier/url/

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