Fig. 4

Predicted optimal timing in a \({\text {SO}_4^{2-}}\) limited linear fed-batch process. A shows average volumetric productivities of pDNA production (g L\(^{-1}\) h\(^{-1}\)) as a function of the initial \({\text {SO}_4^{2-}}\) concentration in a linear fed-batch process. The full line represents different levels of increased pDNA production during starvation as percentages of pDNA production rate during biomass growth (\(\kappa _{\text {pDNA}}\)). The dotted line indicates the location of the optima for \(\kappa _{\text {pDNA}}\) between 100 and 500%. The second X-axis of A (top) illustrates the length of the sulfate starved process phase (\(t^*\)). For all modeled linear fed-batch processes, right of the gray dashed line, no \({\text {SO}_4^{2-}}\) limitation occurred. B and C show the process curves of metabolites of interest in the optimal process for \(\kappa _{\text {pDNA}}= {200}{\%}\). The gray dashed lines indicate the switching time point between the growth and production phases