Steady states of constrained reaction systems

Reaction systems, a mathematical formalism inspired by the mechanisms within a biological cell, focuses on an abstract set-based representation of chemical reactions via facilitation and inhibition. The simple yet elegant nature of reaction systems makes them ideal tools for analysing qualitatively the phenomena which typically are dealt with quantitatively. Steady states are one of the well studied and important subjects across various fields of science ranging from biology, to chemistry, to engineering and economics. Finding all steady states of an arbitrary reaction system has been shown to be an NP-complete problem. We study reaction systems with a small number of reactants and inhibitors and we propose an algorithm to list all steady states of such reaction systems. We also show that the complexity of such an algorithm is polynomial. This reduction in complexity opens a door to transform modelling with reaction systems from an abstract concept to a tool that can be used on real-life case studies.