Maximizing output and recognizing autocatalysis in chemical reaction networks is NP-complete

Here we show that the output maximization problem in chemical reaction networks is NP-complete. This statement remains true even if all reactions are monomolecular or bi-molecular and if only a single molecular species is used as influx. As a corollary we show, furthermore, that the detection of autocatalytic species, i.e., types that can only be produced from the influx material when they are present in the initial reaction mixture, is an NP-complete computational problem.Hardness results on combinatorial problems and optimization problems are important to guide the development of computational tools for the analysis of metabolic networks in particular and chemical reaction networks in general. Our results indicate that efficient heuristics and approximate algorithms need to be employed for the analysis of large chemical networks since even conceptually simple flow problems are provably intractable.Networks of chemical reactions lie at the heart of "systems approaches" in chemistry and biology. After all, metabolic networks are merely collections of chemical reactions entrenched by enzymes that favor some possible reactions over physiologically undesirable side reactions. A detailed understanding of their aggregate properties thus is a prerequisite to efficiently manipulating them in technical applications such as metabolic engineering and at the same time form the basis for deeper explorations into their evolution. Due to the size of reaction networks of practical interest, efficient algorithms are required for their investigation.Chemical reaction networks cannot be modeled appropriately as graphs despite the many attempts in this direction [1]. Instead, they are canonically specified by their stoichiometric matrix S, augmented by information on catalysts. Equivalently, a collection of chemical reactions on a given set of compounds forms a directed (multi)-hypergraph [2]. As a consequence, most of computational problems associated with chemical reaction networks