Preclusion of switch behavior in networks with mass-action kinetics

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Preclusion of switch behavior in networks with mass-action kinetics. / Feliu, Elisenda; Wiuf, Carsten.

In: Applied Mathematics and Computation, Vol. 219, No. 4, 01.11.2012, p. 1449-1467.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Feliu, E & Wiuf, C 2012, 'Preclusion of switch behavior in networks with mass-action kinetics', Applied Mathematics and Computation, vol. 219, no. 4, pp. 1449-1467. https://doi.org/10.1016/j.amc.2012.07.048

APA

Feliu, E., & Wiuf, C. (2012). Preclusion of switch behavior in networks with mass-action kinetics. Applied Mathematics and Computation, 219(4), 1449-1467. https://doi.org/10.1016/j.amc.2012.07.048

Vancouver

Feliu E, Wiuf C. Preclusion of switch behavior in networks with mass-action kinetics. Applied Mathematics and Computation. 2012 Nov 1;219(4):1449-1467. https://doi.org/10.1016/j.amc.2012.07.048

Author

Feliu, Elisenda ; Wiuf, Carsten. / Preclusion of switch behavior in networks with mass-action kinetics. In: Applied Mathematics and Computation. 2012 ; Vol. 219, No. 4. pp. 1449-1467.

Bibtex

@article{bba73c6a2d08474aba441941eff2cb16,
title = "Preclusion of switch behavior in networks with mass-action kinetics",
abstract = "We study networks taken with mass-action kinetics and provide a Jacobian criterion that applies to an arbitrary network to preclude the existence of multiple positive steady states within any stoichiometric class for any choice of rate constants. We are concerned with the characterization of injective networks, that is, networks for which the species formation rate function is injective in the interior of the positive orthant within each stoichiometric class. We show that a network is injective if and only if the determinant of the Jacobian of a certain function does not vanish. The function consists of components of the species formation rate function and a maximal set of independent conservation laws. The determinant of the function is a polynomial in the species concentrations and the rate constants (linear in the latter) and its coefficients are fully determined. The criterion also precludes the existence of degenerate steady states. Further, we relate injectivity of a network to that of the network obtained by adding outflow, or degradation, reactions for all species.",
keywords = "Degenerate steady state, Injectivity, Jacobian criterion, Multiple steady states, Stoichiometric subspace",
author = "Elisenda Feliu and Carsten Wiuf",
year = "2012",
month = nov,
day = "1",
doi = "10.1016/j.amc.2012.07.048",
language = "English",
volume = "219",
pages = "1449--1467",
journal = "Applied Mathematics and Computation",
issn = "0096-3003",
publisher = "Elsevier",
number = "4",

}

RIS

TY - JOUR

T1 - Preclusion of switch behavior in networks with mass-action kinetics

AU - Feliu, Elisenda

AU - Wiuf, Carsten

PY - 2012/11/1

Y1 - 2012/11/1

N2 - We study networks taken with mass-action kinetics and provide a Jacobian criterion that applies to an arbitrary network to preclude the existence of multiple positive steady states within any stoichiometric class for any choice of rate constants. We are concerned with the characterization of injective networks, that is, networks for which the species formation rate function is injective in the interior of the positive orthant within each stoichiometric class. We show that a network is injective if and only if the determinant of the Jacobian of a certain function does not vanish. The function consists of components of the species formation rate function and a maximal set of independent conservation laws. The determinant of the function is a polynomial in the species concentrations and the rate constants (linear in the latter) and its coefficients are fully determined. The criterion also precludes the existence of degenerate steady states. Further, we relate injectivity of a network to that of the network obtained by adding outflow, or degradation, reactions for all species.

AB - We study networks taken with mass-action kinetics and provide a Jacobian criterion that applies to an arbitrary network to preclude the existence of multiple positive steady states within any stoichiometric class for any choice of rate constants. We are concerned with the characterization of injective networks, that is, networks for which the species formation rate function is injective in the interior of the positive orthant within each stoichiometric class. We show that a network is injective if and only if the determinant of the Jacobian of a certain function does not vanish. The function consists of components of the species formation rate function and a maximal set of independent conservation laws. The determinant of the function is a polynomial in the species concentrations and the rate constants (linear in the latter) and its coefficients are fully determined. The criterion also precludes the existence of degenerate steady states. Further, we relate injectivity of a network to that of the network obtained by adding outflow, or degradation, reactions for all species.

KW - Degenerate steady state

KW - Injectivity

KW - Jacobian criterion

KW - Multiple steady states

KW - Stoichiometric subspace

UR - http://www.scopus.com/inward/record.url?scp=84867575860&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2012.07.048

DO - 10.1016/j.amc.2012.07.048

M3 - Journal article

AN - SCOPUS:84867575860

VL - 219

SP - 1449

EP - 1467

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 4

ER -

ID: 200690607