Determining all extreme semi-positive conservation relations in chemical reaction systems: a test criterion for conservativity

An algorithm for deciding whether a chemical reaction system is conservative is given. As a prerequisite, the notions of semi-positive conservation relations and extreme semi-positive conservation relations are defined. All conservative reaction systems and, hence, all closed reaction systems involve the maximal possible number of linearly independent semi-positive conservation relations. This number is given by the difference of the number of reacting species and the rank of the stoichiometric matrix. Finally, it is shown that conservativity is a necessary and sufficient condition that for a given stoichiometric matrix, an atomic stoichiometry satisfying mass conservation for each atomic species can be found. The investigations presented are of importance for model design in chemical kinetics and for convenient application of the quasi-equilibrium approximation.