(Fig. 8a, d) causes a maximum cell number between 8 Â 10
6 cells mL
À1 and
15 Â 10
6 cells mL
À1 (Fig. 8b). The maximum antibody concentration lies in a
range between 75 mg L
À1 and 380 mg L
À1 (Fig. 8e). The simulated concentrations
for lactate and ammonium range between 12 mmol L
À1 to 35 mmol L
À1 and
2 mmol L
À1 to 11 mmol L
À1 (Fig. 8c, f). By simulation, the time course is also
determined, which is not the practice in typical experimental DoEs.
4.4 Evaluation of Planned Design
Out of the simulations, the maximal simulated values of X v , c Lac , c mAb , c Amm were
exported as responses to generate response surface plots (Design-Expert 9). The
simulated responses were treated in the same way as data from experiments. For this
purpose, no data transformation was applied, and after analysis of variance
(ANOVA, all hierarchical design mode, quadratic process order), an internal RSM
was set up with a maximal significance value of 0.05. As can be seen in Fig. 9,
different shapes of the response surface plots were determined, and their individual
optimum is different, e.g., X v is maximal for high initial glucose and glutamine,
while c mAb is high, regardless of the glutamine concentration. Such interaction could
hardly be predicted before and was only possible through the simulations. After
defining the RSM for each response, user-defined constraints for medium optimization were chosen (displayed in Fig. 9). The constraints were chosen to maximize X v
above a minimal X v of 10
7 cells mL
À1 . Furthermore, c mAb should be maximized. The
constraints for the metabolic waste products were defined based on the literature data
with respect to cell growth and product quality. High lactate concentrations were
shown to correlate with a reduced integral of viable cell density and a reduced
product titer at day 14 in pH-controlled shaking flask cultivation with added sodium
lactate [95]. Lactate concentration below 20 mmol L
À1 is considered to not harm cell
growth and productivity, whereby lactate concentration higher than 40 mmol L
À1
was shown to harm CHO cell growth [96]. Therefore, a maximal c Lac of 30 mmol L
À1
was defined as the upper constraint, and the lactate concentration was minimized
below this value to avoid potential lactate inhibition. The ammonium concentration
was defined to be minimized. This was motivated based on the following understanding of its impact on product quality, even if it was not measured. Andersen et al.
(1995) identified that the sialylation of a granulocyte colony-stimulating factor was
significantly reduced by ammonium concentrations over 2 mmol L
À1 [97]. Ha et al.
(2015) investigated the mRNA expression levels of 52 N-glycosylation-related
genes in recombinant CHO cells producing an Fc-fusion protein and observed a
decrease of the protein production and the viable cell density after an addition of
10 mmol L
À1 ammonium chloride. Simultaneously, the sialic acid content and the
acidic isoforms were reduced after 5 days of cultivation [98].
Digital Twins and Their Role in Model-Assisted Design of Experiments
51
6 cells mL
À1 and
15 Â 10
6 cells mL
À1 (Fig. 8b). The maximum antibody concentration lies in a
range between 75 mg L
À1 and 380 mg L
À1 (Fig. 8e). The simulated concentrations
for lactate and ammonium range between 12 mmol L
À1 to 35 mmol L
À1 and
2 mmol L
À1 to 11 mmol L
À1 (Fig. 8c, f). By simulation, the time course is also
determined, which is not the practice in typical experimental DoEs.
4.4 Evaluation of Planned Design
Out of the simulations, the maximal simulated values of X v , c Lac , c mAb , c Amm were
exported as responses to generate response surface plots (Design-Expert 9). The
simulated responses were treated in the same way as data from experiments. For this
purpose, no data transformation was applied, and after analysis of variance
(ANOVA, all hierarchical design mode, quadratic process order), an internal RSM
was set up with a maximal significance value of 0.05. As can be seen in Fig. 9,
different shapes of the response surface plots were determined, and their individual
optimum is different, e.g., X v is maximal for high initial glucose and glutamine,
while c mAb is high, regardless of the glutamine concentration. Such interaction could
hardly be predicted before and was only possible through the simulations. After
defining the RSM for each response, user-defined constraints for medium optimization were chosen (displayed in Fig. 9). The constraints were chosen to maximize X v
above a minimal X v of 10
7 cells mL
À1 . Furthermore, c mAb should be maximized. The
constraints for the metabolic waste products were defined based on the literature data
with respect to cell growth and product quality. High lactate concentrations were
shown to correlate with a reduced integral of viable cell density and a reduced
product titer at day 14 in pH-controlled shaking flask cultivation with added sodium
lactate [95]. Lactate concentration below 20 mmol L
À1 is considered to not harm cell
growth and productivity, whereby lactate concentration higher than 40 mmol L
À1
was shown to harm CHO cell growth [96]. Therefore, a maximal c Lac of 30 mmol L
À1
was defined as the upper constraint, and the lactate concentration was minimized
below this value to avoid potential lactate inhibition. The ammonium concentration
was defined to be minimized. This was motivated based on the following understanding of its impact on product quality, even if it was not measured. Andersen et al.
(1995) identified that the sialylation of a granulocyte colony-stimulating factor was
significantly reduced by ammonium concentrations over 2 mmol L
À1 [97]. Ha et al.
(2015) investigated the mRNA expression levels of 52 N-glycosylation-related
genes in recombinant CHO cells producing an Fc-fusion protein and observed a
decrease of the protein production and the viable cell density after an addition of
10 mmol L
À1 ammonium chloride. Simultaneously, the sialic acid content and the
acidic isoforms were reduced after 5 days of cultivation [98].
Digital Twins and Their Role in Model-Assisted Design of Experiments
51