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Abstract

The Deficiency Zero Theorem (DZT) provides definitive results about the dynamical behavior of chemical reaction networks with deficiency zero. Thus far, the available DZTs only apply to classes of power-law kinetic systems with reactant determined interactions (i.e., the kinetic order vectors of the branching reactions of a reactant complex are identical). In this paper, we present the first DZT valid for a class of power-law systems with non-reactant-determined interactions (i.e., there are reactant complexes whose branching reactions have different kinetic order vectors). This class of power-law systems is characterized here by a decomposition into subnetworks with specific properties of their stoichiometric and reactant subspaces, as well as their kinetics. We illustrate our results to a power-law system of a pre-industrial carbon cycle model, from which we abstracted the properties of the above-mentioned decomposition. Specifically, our DZT is applied to a subnetwork of the carbon cycle system to describe the subnetwork's steady states. It is also shown that the qualitative dynamical properties of the subnetwork may be lifted to the entire network of pre-industrial carbon cycle.