Structural Sensitivity Analysis of Metabolic Networks

The knowledge about control and dynamics of biological systems is often limited or incomplete but, especially for cell metabolism, network structures are often well-characterized. A major challenge in systems biology, therefore, concerns the reverse-engineering of cellular control structures from the available knowledge on the controlled systems’ structures. Here, we propose a method to analyze the sensitivities in metabolic reaction networks that makes use only of the stoichiometry of the metabolic network and the assumption that the biological system is (and remains) in steady state. It is based on least-squares analysis of reaction flux adjustments to disturbances, for which we present an analytic solution. The method can be extended to include multivariate disturbances and, if a reference flux distribution as an operating point is available, to compute relative sensitivities. The resulting sensitivities are instrumental in predicting the regulation of the affected reactions. We demonstrate the utility of the method with the example of a medium-size network model for E. coli metabolism. In particular, we focus on the relation of structural network sensitivities to the variance of gene expression data resulting from external perturbations and from the action of cellular control circuits.