Corynebacterium glutamicum - JUWEL - Forschungszentrum Jülich

4.2. First Case: Fermentation
The same standard deviations of the measured values were used to add normally
distributed noise with mean 0 to the data and re-estimate the parameters as shown in
the setup before.
4.2.2. Designed Experiments
A fed-batch experiment was planned, similar to the experiments used for the development
of the L-valine production process as mentioned in paragraph 3.4.1 on page 50. A
maximal duration of 48 hours was used and the feed of a solution of 3.9 M substrate
was described as periods of constant feed rates of six hours duration, with the first period
without feed. The sampling times were fixed to every 1.5 hours with a longer period
without sampling between 13.5 and 19.5 and between 37.5 and 43.5 hours. The initial
volume was set to be 1.7 L and with the designed feed and the samples of 25 mL, the
suspension volume was limited between 1.5 and 2.5 liter throughout the experiment in
a similar matter as mentioned in paragraph 3.4.1. The initial biomass concentration
was fixed at 0.25 g/L and the initial product concentration was kept fixed at 0.05 mM.
Throughout the experiment, the substrate concentration was bound between 0.01 and
277 mM, again in a similar matter as described in paragraph 3.4.1.
The designed experiment consists of the parameters describing the feedrate over time
and of the initial concentration of substrate. The initial substrate concentration was
bound between 55 and 222 mM. The feedrates were bound between 0 and 0.1 L/h.
The experiment was designed according to the 5 different design criteria which will be
discussed in the following paragraphs.
Box and Hill (BH)
The designed experiment according to the BH criterion is shown in figure 4.3, illustrated
by the expected concentrations according to the competing models.
The Box and Hill criterion consists of a part which has the difference in the expected
concentrations as its driving force and a part which is driven by the difference between
the variances of the expected concentrations (model variances). In the current designed
experiment, the model variances had by far the larger influence: only 3.4 · 10 −5 %ofthe
criterion was accounted for by the part which is driven by the differences in the expected
concentrations!
The BH criterion is calculated as a summation over all measured values. The criterion
for each state variable and each measured point is shown in figure 4.2.2. This figure
clearly shows, that the criterion is practically completely accounted for by only a few
substrate measurements. The criterion is especially high in a region where the expected
substrate concentrations, shown in figure 4.3(b), differ much and where especially the
concentration according to model Ferm2 gets high. The maximal contribution is found
at the point where the concentration decreases rapidly to very low values according to
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