Maintaining maximal metabolic flux by gene expression control

One of the marvels of biology is the phenotypic plasticity of microorganisms. It allows them to maintain high growth rates across conditions. Studies suggest that cells can express metabolic enzymes at tuned concentrations through adjustment of gene expression. The associated transcription factors are often regulated by intracellular metabolites. Here we study metabolite-mediated regulation of metabolic-gene expression that maximises metabolic fluxes across conditions. We developed an adaptive control theory, qORAC (for ‘Specific Flux (q) Optimization by Robust Adaptive Control’), and illustrate it with several examples of metabolic pathways. The key feature of the theory is that it does not require knowledge of the regulatory network, only of the metabolic part. We derive that maximal metabolic flux can be maintained in the face of varying N environmental parameters only if the number of transcription-factor binding metabolites is at least equal to N. The controlling circuits appear to require simple biochemical kinetics. We conclude that microorganisms likely can achieve maximal rates in metabolic pathways, in the face of environmental changes.Author summary: To attain high growth rates, microorganisms need to sustain high activities of metabolic reactions. Since the catalysing enzymes are in finite supply, cells need to carefully tune their concentrations. When conditions change, cells need to adjust those concentrations. How cells maintain high metabolism rates across conditions by way of gene regulatory mechanisms and whether they can maximise metabolic activity is far from clear. Here we present a general theory that solves this metabolic control problem, which we have called qORAC for specific flux (q) Optimisation by Robust Adaptive Control. It considers that external changes are sensed by internal “sensor” metabolites that bind to transcription factors in order to regulate enzyme-synthesis rates. We show that such a combined system of metabolism and its gene network can self-optimise its metabolic activity across conditions. We present the mathematical conditions for the required adaptive control for robust system-steering to optimal states across conditions. We provide explicit examples of such self-optimising coupled metabolism and gene network systems. We prove that a cell can be robust to changes in K parameters, e.g. external conditions, if at least K internal metabolite concentrations act transcription-factor binding sensors. We find that the optimal relation of the enzyme synthesis rates of self-optimising systems and the concentration of the sensor metabolites can generally be implemented by basic biochemistry. Our results indicate how cells are able to maintain maximal reaction rates, even in changing conditions.