Dynamic optimization identifies optimal programmes for pathway regulation in prokaryotes

To survive in fluctuating environmental conditions, microorganisms must be able to quickly react to environmental challenges by upregulating the expression of genes encoding metabolic pathways. Here we show that protein abundance and protein synthesis capacity are key factors that determine the optimal strategy for the activation of a metabolic pathway. If protein abundance relative to protein synthesis capacity increases, the strategies shift from the simultaneous activation of all enzymes to the sequential activation of groups of enzymes and finally to a sequential activation of individual enzymes along the pathway. In the case of pathways with large differences in protein abundance, even more complex pathway activation strategies with a delayed activation of low abundance enzymes and an accelerated activation of high abundance enzymes are optimal. We confirm the existence of these pathway activation strategies as well as their dependence on our proposed constraints for a large number of metabolic pathways in several hundred prokaryotes.