Reaction networks can be simpli?ed by eliminating linear intermediate species in partial steadystates. Inthispaper,westudythequestionwhetherthisrewriteprocedureiscon?uent,so that for any given reaction network with kinetic constraints, a unique normal form will be obtained independently of the elimination order. We ?rst show that con?uence fails for the elimination of intermediates even without kinetics, if “dependent reactions” introduced by the simpli?cation are not removed. This leads us to revising the simpli?cation 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 con?uence of the revised simpli?cation algorithm with respect to the network structure, i.e., the structure of fully simpli?ed 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 simpli?ed networks can be obtained. Finally, we give a criterion on the structure of the initial network that is suf?cient to guarantee the con?uence of both the structure and the kinetic rates.
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