NetRed, an algorithm to reduce genome-scale metabolic networks and facilitate the analysis of flux predictions

Flux balance analysis (FBA) of large, genome-scale stoichiometric models (GSMs) is a powerful and popular method to predict cell-wide metabolic activity. FBA typically generates a flux vector containing O(1,000) fluxes. The interpretation of such a flux vector is difficult, even for expert users, because of the large size and complex topology of the underlying metabolic network. This interpretation could be simplified by condensing the network to a reduced, yet fully representative version. Toward this goal we report NetRed, an algorithm that systematically reduces a stoichiometric matrix and a corresponding flux vector to a more easily interpretable form. The reduction offered by NetRed is transparent because it relies purely on matrix algebra and not on optimization. Uniquely, it involves zero information loss; therefore, the original unreduced network can be easily recovered from the reduced network. The inputs to NetRed are (i) a stoichiometric matrix, (ii) a flux vector with numerical flux values, and (iii) a list of "protected" metabolites recommended by the user to remain in the reduced network. NetRed outputs a reduced metabolic network containing a reduced number of metabolites, of which the protected metabolites are a subset. The algorithm also generates a corresponding reduced flux vector. Due to its simplified presentation and easier interpretability, the reduced network allows the user to quickly find fluxes through metabolites and reaction modes or pathways of interest. In this manuscript, we first demonstrate NetRed on a simple network consisting of glycolysis and the pentose phosphate pathway (PPP), wherein NetRed reduced the PPP to a single net reaction. We followed this with applications of NetRed to E. coli and yeast GSMs. NetRed reduced the size of an E. coli GSM by 20- to 30-fold and enabled a comprehensive comparison of aerobic and anaerobic metabolism. The application of NetRed to a yeast GSM allowed for easy mechanistic interpretation of a double-gene knockout that rerouted flux toward dihydroartemisinic acid. When applied to an E. coli strain engineered for enhanced valine production, NetRed allowed for a holistic interpretation of the metabolic rerouting resulting from multiple genetic interventions.