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Background: A classical problem in metabolic design is to maximize theproduction of desired compound in a given chemical reaction network byappropriately directing the mass flow through the network. Computationally,this problem is addressed as a linear optimization problem over the "fluxcone". The prior construction of the flux cone is computationally expensive andno polynomial-time algorithms are known. Results: Here we show that the outputmaximization problem in chemical reaction networks is NP-complete. Thisstatement remains true even if all reactions are monomolecular or bimolecularand if only a single molecular species is used as influx. As a corollary weshow, furthermore, that the detection of autocatalytic species, i.e., typesthat can only be produced from the influx material when they are present in theinitial reaction mixture, is an NP-complete computational problem. Conclusions:Hardness results on combinatorial problems and optimization problems areimportant to guide the development of computational tools for the analysis ofmetabolic networks in particular and chemical reaction networks in general. Ourresults indicate that efficient heuristics and approximate algorithms need tobe employed for the analysis of large chemical networks since even conceptuallysimple flow problems are provably intractable.

Maximizing Output and Recognizing Autocatalysis in Chemical Reaction Networks is NP-Complete