Fig. 8

Breakthrough production length during starvation in linear fed-batch processes. If the pDNA production during starvation can be held longer than the breakthrough production length (\(t^*_\text {breakthrough}\), blue full line), the \({\text {SO}_4^{2-}}\) limited process outperforms a control (i.e., not starved) process. A visual explanation of \(t^*_\text {breakthrough}\) is given in Additional file 1: Fig. S4. The start of the starvation is defined by the optimal \(C_{\text {SO}_4^{2-}}(0)\) calculated in Fig. 4A (red dotted line). The maximum pDNA production length during starvation is equal to the total starvation length \(t^*\) (blue dashed line). The contour colors indicate the productivity of a \({\text {SO}_4^{2-}}\) limited process compared to the control in % (color bar on the right)