Enumerating Precursor Sets of Target Metabolites in a Metabolic Network

We present the first exact method based on the topology of a metabolic network to find minimal sets of metabolites (called precursors) sufficient to produce a set of target metabolites. In contrast with previous proposals, our model takes into account self-regenerating metabolites involved in cycles, which may be used to generate target metabolites from potential precursors. We analyse the complexity of the problem and we propose an algorithm to enumerate all minimal precursor sets for a set of target metabolites. The algorithm can be applied to identify a minimal medium necessary for a cell to ensure some metabolic functions. It can be used also to check inconsistencies caused by misannotations in a metabolic network. We present two illustrations of these applications.