We study the structural simplification of chemical reaction networks with partial steady state semantics assuming that the concentrations of some but not all species are constant. We present a simplification rule that can eliminate intermediate species that are in partial steady state, while preserving the dynamics of all other species. Our simplification rule can be applied to general reaction networks with some but few restrictions on the possible kinetic laws. We can also simplify reaction networks subject to conservation laws. We prove that our simplification rule is correct when applied to a module of a reaction network, as long as the partial steady state is assumed with respect to the complete network. Michaelis-Menten's simplification rule for enzymatic reactions falls out as a special case. We have implemented an algorithm that applies our simplification rules repeatedly and applied it to reaction networks from systems biology.

Reaction 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.