Simpliﬁcation of Reaction Networks, Conﬂuence and Elementary Modes
AbstractReaction networks can be simpliﬁed by eliminating linear intermediate species in partial steadystates. Inthispaper,westudythequestionwhetherthisrewriteprocedureisconﬂuent,so that for any given reaction network with kinetic constraints, a unique normal form will be obtained independently of the elimination order. We ﬁrst show that conﬂuence fails for the elimination of intermediates even without kinetics, if “dependent reactions” introduced by the simpliﬁcation are not removed. This leads us to revising the simpliﬁcation algorithm into a variant of the double description method for computing elementary modes, so that it keeps track of kinetic information. Folklore results on elementary modes imply the conﬂuence of the revised simpliﬁcation algorithm with respect to the network structure, i.e., the structure of fully simpliﬁed networks is unique. We show, however, that the kinetic rates assigned to the reactions may not be unique, and provide a biological example where two different simpliﬁed networks can be obtained. Finally, we give a criterion on the structure of the initial network that is sufﬁcient to guarantee the conﬂuence of both the structure and the kinetic rates. View Full-Text
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Madelaine, G.; Tonello, E.; Lhoussaine, C.; Niehren, J. Simpliﬁcation of Reaction Networks, Conﬂuence and Elementary Modes. Computation 2017, 5, 14.
Madelaine G, Tonello E, Lhoussaine C, Niehren J. Simpliﬁcation of Reaction Networks, Conﬂuence and Elementary Modes. Computation. 2017; 5(1):14.Chicago/Turabian Style
Madelaine, Guillaume; Tonello, Elisa; Lhoussaine, Cédric; Niehren, Joachim. 2017. "Simpliﬁcation of Reaction Networks, Conﬂuence and Elementary Modes." Computation 5, no. 1: 14.
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