Corynebacterium glutamicum - JUWEL - Forschungszentrum Jülich

2.5. Experimental Design
The squared brackets are added around the timing dependent covariance matrix of the
values from the first sample Σi,t(1) to the last of ns samples Σi,t(ns), to emphasize the
fact that these are [nv × nv] matrices taken from equation 2.67 and not just scalars.
Now, this matrix can simply be added to the corresponding covariance matrix Σi,m,
caused by measurement errors such as dilution inaccuracy or the accuracy of the used
analytic equipment
(2.70)
Σi = Σi,m + Σi,t
and used in the criterion formulated in equation 2.53 and 2.55.
Obviously, when the measurement variance would be determined from replication of
complete experiments, this part of the measurement error, caused by timing of the
sampling, would be included in the measurement variance. This would, however, not
be the case when the measurement variance would be determined solely based on the
accuracy of the analytical methods or repeated measurement from one sample.
Another adaptation of the simple criterion of 2.53 on page 27 comes from the idea
that, in dynamic experiments, besides the difference between the expected values, also
the difference between the expected shapes of the curves is likely to improve the discrimination
between models. To elucidate this idea, regard the curves in figure 2.3. The
fact that the two curves have clearly different shapes is expected to provide a better
discrimination than when both curves would stay horizontal, although this would result
in the same distance between measured points.
y
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25
20
15
10
5
0
0 5 10 15 20
time[h]
Figure 2.3.: Expected responses of two competing models (one with a solid line and
+ and the other as dashed line with ×) for a designed dynamic experiment. It is
hypothesized that the different shapes of the two curves around 10 hours makes a good
discrimination more likely than when both curves would have stayed on a constant
distance.
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