NDLI: Simplifying the Jacobian Criterion for Precluding Multistationarity in Chemical Reaction Networks

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Shiu, Anne Joshi, Badal
Copyright Year	2012
Abstract	Chemical reaction networks taken with mass-action kinetics are dynamical systems that arise in chemical engineering and systems biology. In general, determining whether a chemical reaction network admits multiple steady states is difficult, as this requires determining existence of multiple positive solutions to a large system of polynomials with unknown coefficients. However, in certain cases, various easy criteria can be applied. One such test is the Jacobian criterion, due to Craciun and Feinberg, which gives sufficient conditions for ruling out the possibility of multiple steady states. A chemical reaction network is said to pass the Jacobian criterion if all terms in the determinant expansion of its parametrized Jacobian matrix have the same sign. In this article, we present a procedure which simplifies the application of the Jacobian criterion, and as a result, we identify a new class of networks for which multiple steady states is precluded: those in which all chemical species have total molecularity of at most two. The total molecularity of a species refers to the sum of all of its stoichiometric coefficients in the network. We illustrate our results by examining enzyme catalysis networks.
Starting Page	857
Ending Page	876
Page Count	20
File Format	PDF
ISSN	00361399
DOI	10.1137/110837206
e-ISSN	1095712X
Issue Number	3
Volume Number	72
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2012-06-07
Access Restriction	Subscribed
Subject Keyword	species-reaction graph Nonlinear equations and systems, general injectivity Roots of polynomial equations chemical reaction networks Jacobian criterion multiple steady states mass-action kinetics Fixed points, periodic points, fixed-point index theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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