Stoichiometric Network Analysis: a Critical Review of its Algorithmic Strength

We survey the mathematical foundations of Clarke Stochiometric Network Analysis (SNA, for short). We show that SNA is heavily based on a special change of coordinates that we call Clarke's velocity function. Given a chemical reaction network Omega, the associated system of Clarke's coordinates (also called convex coordinates) allows one to compute a polyhedral definition for the set of steady states of Omega. The latter fact yields a reduction to linear programming of some algorithmic tasks that are related to the linear stability analysis of chemical reaction networks. We discuss the algorithmic potential of Clarke's theory, which is strongly limited by its dependence on a hard intractable problem, the problem of computing spanning sets of polyhedral cones. We discuss how the hardness of the latter problem reduces the algorithmic potential of SNA. We also show that SNA can be happily applied in some scenarios. To this end we study a problem that is related to the linear stability analysis of network models of biological homochirality. We show that SNA provides us with algorithmic tools that can be used to solve the aforementioned problem.