Existence of Positive Steady States for Mass Conserving and Mass-Action Chemical Reaction Networks with a Single Terminal-Linkage Class

We establish that mass conserving single terminal-linkage networks of chemical reactions admit positive steady states regardless of network deficiency and the choice of reaction rate constants. This result holds for closed systems without material exchange across the boundary, as well as for open sy...

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Bibliographic Details
Published inarXiv.org
Main Authors Akle, Santiago, Dalal, Onkar, Fleming, Ronan M T, Saunders, Michael, Taheri, Nicole, Ye, Yinyu
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.10.2011
Subjects
Algorithms
Chemical reactions
Computational geometry
Convexity
Exchanging
Iterative methods
Networks
Open systems
Optimization
Organic chemistry
Rate constants
Reaction kinetics
Steady state
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Summary:We establish that mass conserving single terminal-linkage networks of chemical reactions admit positive steady states regardless of network deficiency and the choice of reaction rate constants. This result holds for closed systems without material exchange across the boundary, as well as for open systems with material exchange at rates that satisfy a simple sufficient and necessary condition. Our proof uses a fixed point of a novel convex optimization formulation to find the steady state behavior of chemical reaction networks that satisfy the law of mass-action kinetics. A fixed point iteration can be used to compute these steady states, and we show that it converges for weakly reversible homogeneous systems. We report the results of our algorithm on numerical experiments.
ISSN:2331-8422