Robustness of Optimal Metabolic Performance by Optimal Gene Expression in Varying Environments

To understand the principles of the remarkable adaptivity of metabolic networks in dynamic environments, their underlying gene regulatory networks need to be characterised. Typically, little is known about the kinetics and topology of those gene networks in contrast to the metabolic networks that they regulate. Here, we present a theoretical approach based on metabolic control analysis to elucidate gene regulatory networks that can achieve a specific metabolic control task on the basis of information about the metabolic network alone. We focus on optimal gene networks that are capable of restoring the metabolic network to an optimal state upon an environmental perturbation. We show how the demand for optimal regulation of metabolism sets constraints on the input-output relationship of gene networks and leaves degrees of freedom for the gene network to meet other demands. We derive the theory to identify the constraints acting on the gene network to guarantee perfect adaptation of metabolic optimal behaviour by regulation of metabolic gene expression. We also show how gene network structures can be found that give rise to this optimal steering of metabolism using a linear programming approach, given gene network design criteria and a mathematical model of metabolism. Our approach is applicable to synthetic biology studies for rational engineering of metabolism.