Artículo

Pérez Millán, M.; Dickenstein, A.; Shiu, A.; Conradi, C. "Chemical Reaction Systems with Toric Steady States" (2012) Bulletin of Mathematical Biology. 74(5):1027-1065
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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. © 2011 Society for Mathematical Biology.

Registro:

Documento: Artículo
Título:Chemical Reaction Systems with Toric Steady States
Autor:Pérez Millán, M.; Dickenstein, A.; Shiu, A.; Conradi, C.
Filiación:Dto. de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, Buenos Aires C1428EGA, Argentina
IMAS/CONICET, Universidad de Buenos Aires, Buenos Aires, Argentina
Dept. of Mathematics, Duke University, Box 90320, Durham, NC 27708-0320, United States
Max-Planck-Institut Dynamik komplexer technischer Systeme, Sandtorstr. 1, 39106 Magdeburg, Germany
Palabras clave:Binomial ideal; Chemical reaction networks; Mass-action kinetics; Multisite phosphorylation; Multistationarity; phosphatase; phosphotransferase; algorithm; article; chemical model; chemistry; computer simulation; kinetics; phosphorylation; protein processing; standard; Algorithms; Computer Simulation; Kinetics; Models, Chemical; Phosphoric Monoester Hydrolases; Phosphorylation; Phosphotransferases; Protein Processing, Post-Translational
Año:2012
Volumen:74
Número:5
Página de inicio:1027
Página de fin:1065
DOI: http://dx.doi.org/10.1007/s11538-011-9685-x
Título revista:Bulletin of Mathematical Biology
Título revista abreviado:Bull. Math. Biol.
ISSN:00928240
CODEN:BMTBA
CAS:phosphatase, 9013-05-2; phosphotransferase, 9031-09-8, 9031-44-1; Phosphoric Monoester Hydrolases, 3.1.3.-; Phosphotransferases, 2.7.-
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00928240_v74_n5_p1027_PerezMillan

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Citas:

---------- APA ----------
Pérez Millán, M., Dickenstein, A., Shiu, A. & Conradi, C. (2012) . Chemical Reaction Systems with Toric Steady States. Bulletin of Mathematical Biology, 74(5), 1027-1065.
http://dx.doi.org/10.1007/s11538-011-9685-x
---------- CHICAGO ----------
Pérez Millán, M., Dickenstein, A., Shiu, A., Conradi, C. "Chemical Reaction Systems with Toric Steady States" . Bulletin of Mathematical Biology 74, no. 5 (2012) : 1027-1065.
http://dx.doi.org/10.1007/s11538-011-9685-x
---------- MLA ----------
Pérez Millán, M., Dickenstein, A., Shiu, A., Conradi, C. "Chemical Reaction Systems with Toric Steady States" . Bulletin of Mathematical Biology, vol. 74, no. 5, 2012, pp. 1027-1065.
http://dx.doi.org/10.1007/s11538-011-9685-x
---------- VANCOUVER ----------
Pérez Millán, M., Dickenstein, A., Shiu, A., Conradi, C. Chemical Reaction Systems with Toric Steady States. Bull. Math. Biol. 2012;74(5):1027-1065.
http://dx.doi.org/10.1007/s11538-011-9685-x