Hardness and approximability of the inverse scope problem

Abstract

For a given metabolic network, we address the problem of determining the minimum cardinality set of substrate compounds necessary for synthesizing a set of target metabolites, called the inverse scope problem. We define three variants of the inverse scope problem whose solutions may indicate minimal nutritional requirements that must be met to ensure sustenance of an organism, with or without some side products. Here, we show that the inverse scope problems are NP-hard on general graphs and directed acyclic graphs (DAGs). Moreover, we show that the general inverse scope problem cannot be approximated within n 1/2∈-∈ε for any constant ε>∈0 unless P = NP. Our results have direct implications for identifying the biosynthetic capabilities of a given organism and for designing biochemical experiments. © 2008 Springer-Verlag Berlin Heidelberg.