Corynebacterium glutamicum - JUWEL - Forschungszentrum Jülich

More documents

Recommendations

Info

4.2. First Case: Fermentation The reduced chi-squared values of the two competing models were calculated for each of the 100 fits. In each case, a proper low value was found for the ’true’ model structure, as should be expected. Even values below 1 were reached, indicating that the fitted model were closer to the measured values than expected, based on the measurement variance. The ratio between the χ 2 values for the ’false’ models and the ’true’ models are shown in box-plots in figure 4.8. Higher values indicate better performance of the discriminating design criterion. [−] 2 2 χ /χ Ferm2 Ferm1 120 100 80 60 40 20 0 BH BF CA HR ND criterion (a) Ratio between the reduced χ 2 of Ferm2 and Ferm1, fitted to data generated with Ferm1. [−] 2 2 χ /χ Ferm1 Ferm2 35 30 25 20 15 10 5 0 BH BF CA HR ND criterion (b) Ratio between the reduced χ 2 of Ferm1 and Ferm2, fitted to data generated with Ferm2. Figure 4.8.: Ratios between reduced χ 2 value of the ’false’ and the ’true’ models. The boxes have horizontal lines at the lower quartile, median and upper quartile. Points outside the quartiles are shown as +. Except for the BH criterion, the discriminating power of each of the criteria was better when Ferm1 was the ’true’ model. As could be expected from the concentrations in figure 4.5(b), the CA criterion did not perform very well in the current example. As mentioned before, the reached value of this criterion was too low according to the original paper. It was suggested, to perform an experiment to improve the parameter estimation in such a case instead. It was surprising that the CA- and the BF criterion supposed such strongly different experiments, although the differences between the two criteria seem small. The difference mainly consists of the way to deal with dependent- or independent measurements and a slightly smaller influence of the measurement variance in weighting the criterion. The partly large variances in the resulting ˜χ 2 values, as indicated by large boxes in figure 4.8, are mainly caused by the variance introduced by the different parameter values, which were used to generate data and not so much by the added noise. In the BF and CA criteria, large effects of the parameter inaccuracies result in reduced values of the design criterion through the weighting by the model variance, which might therefore explain smaller variances in the results using these criteria. 73
4. Simulative Comparison of Model Discriminating Design Criteria Although statistically, there is not yet a hard proof, it seems like the adjustments for use with dynamic experiments in the ND criterion gave a slight improvement compared to the HR criterion. Unfortunately, the results of this simulative case study do not yield one clear preferred criterion. The highest discriminating power was achieved using the ND criterion when Ferm1 was the ’true’ model and also the best average was achieved using this criterion. The smaller variation is on the other hand a positive characteristic of the BF criterion. The highest minimal discriminating power was achieved by the BH criterion. 4.3. Second Case: Catalytic Conversion The second case is a catalytic conversion. This case deals with a common and important question, whether a decrease in reaction rate over time could be caused by product inhibition or rather by deactivation of the catalyst. Again, only one substrate is converted to one product. The concentrations of substrate and product are the only measured state variables. 4.3.1. Prior Situation The initial situation consists of two subsequent batch experiments with different initial concentrations of substrate and catalyst. Three Michaelis-Menten type models were fitted to these data. The kinetic equations of these models are as follows: Model Cat1: rC =0 (4.5) −rS = rP = Km · vmax · CC · CS � 1+ CP KiP � + CS (4.6) Again, the used symbols are as explained in appendix A on page 133. Subscript C is used to indicate the catalyst. Model Cat2 is similar to Cat1, but with non-competitive instead of competitive product inhibition, so equation 4.6 is changed to: −rS = rP = vmax · CC · CS Km · +CS1 KiP , (4.7) CP + KiP but still, the amount of catalyst C does not change. In model Cat3, instead of a product inhibition, a first order degradation of the catalyst 74
Page 1 and 2:
Lebenswissenschaften Life Sciences
Page 4 and 5:
Forschungszentrum Jülich GmbH Inst
Page 6:
’Therefore, mathematical modeling
Page 9 and 10:
Contents 3.4. Application: L-Valine
Page 11 and 12:
Contents 4
Page 13 and 14:
1. Introduction need for improved m
Page 15 and 16:
2. Theory In a batch process, all s
Page 17 and 18:
2. Theory 1997; Goncalves et al., 2
Page 19 and 20:
2. Theory For batch fermentations,
Page 21 and 22:
2. Theory with Yps being the yield
Page 23 and 24:
2. Theory Inhibition Some catalytic
Page 25 and 26:
2. Theory The method of least squar
Page 27 and 28:
2. Theory evaluation can be made by
Page 29 and 30: 2. Theory We define the measured or
Page 31 and 32: 2. Theory build in the model. An ob
Page 33 and 34: 2. Theory nations, the researcher i
Page 35 and 36: 2. Theory W = J · Covθ · J T (2.
Page 37 and 38: 2. Theory arg max ξ � m� m�
Page 39 and 40: 2. Theory with all measured values
Page 41 and 42: 2. Theory which can be estimated us
Page 43 and 44: 2. Theory One option to account for
Page 45 and 46: 2. Theory θ 2 $θ 2 0 area ≅ det
Page 47 and 48: 2. Theory designed using a paramete
Page 49 and 50: 2. Theory proteome14 (Hermann et al
Page 51 and 52: 2. Theory 44
Page 53 and 54: 3. Dynamic Modeling Framework itera
Page 55 and 56: 3. Dynamic Modeling Framework 3.3.
Page 57 and 58: 3. Dynamic Modeling Framework 3.3.3
Page 59 and 60: 3. Dynamic Modeling Framework 52 du
Page 61 and 62: 3. Dynamic Modeling Framework the c
Page 63 and 64: 3. Dynamic Modeling Framework For d
Page 65 and 66: 3. Dynamic Modeling Framework subse
Page 67 and 68: 3. Dynamic Modeling Framework 60
Page 69 and 70: 4. Simulative Comparison of Model D
Page 79: 4. Simulative Comparison of Model D
Page 95 and 96: 5. L-Valine Production Process Deve
Page 131 and 132:
5. L-Valine Production Process Deve
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 140 and 141:
A. Nomenclature Table A.1.: Symbols
Page 142 and 143:
Table A.1.: Symbols and Abbreviatio
Page 144 and 145:
Table A.1.: Symbols and Abbreviatio
Page 146 and 147:
B. Ratio between OD600 and Dry Weig
Page 148 and 149:
C. The Influence of the Oxygen Supp
Page 150 and 151:
The measurements of amino acids and
Page 152 and 153:
kiv [mM] lac [mM] 15 10 5 0 0 10 20
Page 154 and 155:
OTR, CTR 0.06 0.04 0.02 0 0 10 20 3
Page 156 and 157:
DO properly at a low value in dynam
Page 158 and 159:
D. Dilution for Measurement of Amin
Page 160 and 161:
E. Models used in the First Model D
Page 162 and 163:
Model 1.6 Model 1.6 is similar to m
Page 164 and 165:
Table E.1: Model Parameters of the
Page 166 and 167:
Table E.2: Model Parameters of the
Page 168 and 169:
161
Page 170 and 171:
Model 2.2 Model 2.2 is similar to m
Page 172 and 173:
Table F.1.: Model Parameters of the
Page 174 and 175:
Table F.2.: Estimated Lag-Times of
Page 176 and 177:
Table F.3: Model Parameters of the
Page 178 and 179:
Table F.4.: Estimated Lag-Times of
Page 180 and 181:
G. Alternative Off-line Optimized P
Page 182 and 183:
G.2. Overall Yield of Product on Su
Page 184 and 185:
Summary Fast development of product
Page 186 and 187:
Zusammenfassung Es ist wichtig, die
Page 188 and 189:
Acknowledgements This thesis result
Page 190 and 191:
Bibliography K. Akashi, H. Shibai,
Page 192 and 193:
Bibliography A. Bodalo-Santoyo, J.L
Page 194 and 195:
Bibliography A.J. Cooper, J.Z. Gino
Page 196 and 197:
Bibliography A.G. Fredrickson, R.D.
Page 198 and 199:
Bibliography W.G. Hunter and A.M. R
Page 200 and 201:
Bibliography A.C. McHardy, A. Tauch
Page 202 and 203:
Bibliography E. Radmacher, A. Vaits
Page 204 and 205:
Bibliography K.J. Versyck, J.E. Cla
Page 206 and 207:
6FKULIWHQ GHV )RUVFKXQJV]HQWUXPV -
Page 208 and 209:
6FKULIWHQ GHV )RUVFKXQJV]HQWUXPV -
show all

Corynebacterium glutamicum - JUWEL - Forschungszentrum Jülich

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?