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  Chemical Reaction Systems with Toric Steady States

Pérez, M. M., Dickenstein, A., Shiu, A., & Conradi, C. (2012). Chemical Reaction Systems with Toric Steady States. Bulletin of Mathematical Biology, 74(5), 1027-1065. doi:10.1007/s11538-011-9685-x.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-8990-C Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0025-C058-C
Genre: Journal Article

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 Creators:
Pérez, M. M.1, Author
Dickenstein, A.1, 2, Author
Shiu, A.3, Author
Conradi, C.4, Author              
Affiliations:
1Dto. de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, C1428EGA, Buenos Aires, Argentina , ou_persistent22              
2IMAS/CONICET, Universidad de Buenos Aires, Buenos Aires, Argentina , ou_persistent22              
3Dept. of Mathematics, Duke University, Box 90320, Durham, NC, 27708-0320, USA , ou_persistent22              
4Analysis and Redesign of Biological Networks, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society, ou_1738139              

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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. © Springer, Part of Springer Science+Business Media [ accessed 2013 July 2nd]

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Language(s): eng - English
 Dates: 2012
 Publication Status: Published in print
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 Rev. Method: Peer
 Identifiers: eDoc: 573808
DOI: 10.1007/s11538-011-9685-x
Other: 46/12
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Title: Bulletin of Mathematical Biology
Source Genre: Journal
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Pages: - Volume / Issue: 74 (5) Sequence Number: - Start / End Page: 1027 - 1065 Identifier: -