Reference : Existence of Positive Steady States for Mass Conserving and Mass-Action Chemical Reac...
Scientific journals : Article
Life sciences : Multidisciplinary, general & others
Systems Biomedicine
Existence of Positive Steady States for Mass Conserving and Mass-Action Chemical Reaction Networks with a Single Terminal-Linkage Class
Fleming, Ronan MT mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Akle, Santiago []
Dalal, Onkar []
Saunders, Michael []
Taheri, Nicole []
Ye, Yinyu []
arXiv preprint arXiv:1105.2359
[en] 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.

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