Robust Flux Balance Analysis of Metabolic Networks

Metabolic networks describe the set of biochemical reactions and regulatory interactions of metabolism that govern the phenotypical properties of a cell. Analysis of such networks is critical not only to promote biological knowledge, but also in drug discovery, where it can be used to identify and knockout the targeted pathways. Flux Balance Analysis (FBA) has been widely used to study metabolic networks. This powerful technique employs the reaction stoichiometries and reversibility constraints along with experimental measurements of phenotypical properties of the cell, e.g., biomass composition or ATP synthesis, to compute the fluxes of metabolites that are best manifested in the cell. Although FBA has been shown to satisfactorily capture cell behavior, its performance could be significantly improved if measurement uncertainty is introduced in the models. In this paper we propose Robust Flux Balance Analysis (RFBA) to determine optimal fluxes of metabolites for all phenotypical measurements in a given uncertainty set. We derive a least squares bi-criterion approximation of the uncertain problem and, using the S-procedure and tools from matrix analysis, we show that this is equivalent to a semidefinite program that can be solved optimally using available techniques. We illustrate our approach on synthetic metabolic networks and discuss the effect of regularization on the final solutions. Due to its convex nature, our approach can be applied to genome-scale networks.