Normalizing Chemical Reaction Networks by Confluent Structural Simplification

Abstract

Reaction networks can be simplified by eliminating linear intermediate species in partial steady states. In this paper, we study the question whether this rewrite procedure is confluent, so that for any given reaction network, a unique normal form will be obtained independently of the elimination order. We first contribute a counter example which shows that different normal forms of the same network may indeed have different structures. The problem is that different “dependent reactions” may be introduced in different elimination orders. We then propose a rewrite rule that eliminates such dependent reactions and prove that the extended rewrite system is confluent up to kinetic rates, i.e., all normal forms of the same network will have the same structure. However, their kinetic rates may still not be unique, even modulo the usual axioms of arithmetics. This might seem surprising given that the ODEs of these normal forms are equal modulo these axioms.