Exploring the connectivity structure in metabolic networks: Going beyond graphs via discrete optimization

Complex biological networks are commonly represented as graphs, where nodes represent biological entities and edges interactions between such entities. An important topological property of such graphs is the connectivity between any pair of nodes, as well as, if connected, their underlying minimum distance, which overall restricts the global behavior of the system. Algorithms from graph theory are typically used to accomplish this connectivity analysis. In particular, connectivity analysis via graph theory has been extensively applied to metabolic networks. Metabolic networks involve the inter-conversions of low molecular weight compounds (metabolites), which are responsible for the generation of building blocks of complex macromolecules and cellular energy. In these networks, nodes usually represent metabolites and edges inter-conversions between metabolites, which are technically biochemical reactions. In this article we illustrate that graph theory is not an appropriate tool to fully capture the topological properties of metabolic networks. We present a novel methodology based on linear discrete optimization, which is applied to examine the connectivity of certain key metabolites in Escherichia Coli, a well-known bacteria in the biological world.