Abstract
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.
Highlights
Chemical reaction networks are widely used in systems biology for modeling the dynamics of biochemical molecular systems [1,2,3,4]
Chemical reaction networks can either be given a deterministic semantics in terms of ordinary differential equations (O DEs), which describes the evolution of the average concentrations of the species of the network over time, or a stochastic semantics in terms of continuous time Markov chains, which defines the evolution of molecule distributions of the different species over time
A general structural simplification algorithm for reaction networks with deterministic semantics was first presented by Radulescu et al They proposed yet another method [18] for simplifying reaction networks with kinetic expressions in partial steady states
Summary
Chemical reaction networks are widely used in systems biology for modeling the dynamics of biochemical molecular systems [1,2,3,4]. S which produces S with constant speed k4 , and the k5 P reaction P −−→ ∅ which degrades P with mass-action kinetics with rate constant k5 In this context, the concentration of P will saturate quickly under exact steady state assumptions for C, E, and . A general structural simplification algorithm for reaction networks with deterministic semantics was first presented by Radulescu et al They proposed yet another method [18] for simplifying reaction networks with kinetic expressions in partial steady states. Their method assumes the same linearity restriction considered in this paper, preserves exactly the deterministic semantics, but uses different algorithmic techniques.
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