Corynebacterium glutamicum - JUWEL - Forschungszentrum Jülich

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[−] 2 2 χ /χ Cat2 Cat1 100 80 60 40 20 0 BH BF CA criterion HR ND (a) Ratio between the reduced χ 2 of model Cat2 and Cat1, fitted to data generated with Cat1. [−] 2 2 χ /χ Cat1 Cat2 40 35 30 25 20 15 10 5 0 BH BF CA criterion HR ND (c) Ratio between the reduced χ 2 of model Cat1 and Cat2, fitted to data generated with Cat2. [−] 2 2 χ /χ Cat1 Cat3 35 30 25 20 15 10 5 0 BH BF CA criterion HR ND (e) Ratio between the reduced χ 2 of model Cat1 and Cat3, fitted to data generated with Cat3. [−] 2 2 χ /χ Cat3 Cat1 4.3. Second Case: Catalytic Conversion 25 20 15 10 5 0 BH BF CA criterion HR ND (b) Ratio between the reduced χ 2 of model Cat3 and Cat1, fitted to data generated with Cat1. [−] 2 2 χ /χ Cat3 Cat2 70 60 50 40 30 20 10 0 BH BF CA criterion HR ND (d) Ratio between the reduced χ 2 of model Cat3 and Cat2, fitted to data generated with Cat2. [−] 2 2 χ /χ Cat2 Cat3 400 350 300 250 200 150 100 50 0 BH BF CA criterion HR ND (f) Ratio between the reduced χ 2 of model Cat2 and Cat3, fitted to data generated with Cat3. Figure 4.14.: 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 +. 83
4. Simulative Comparison of Model Discriminating Design Criteria χ 2 20 15 10 5 0 BH BF CA criterion HR ND Figure 4.15.: Reduced χ 2 of Cat1, fitted to data generated with Cat1 itself as the ’true’ model. Analogue to figure 4.14 The differences between the performances of the 4 other criteria are very small, as might also have been expected from the similar expected results. The discrimination between model Cat2 and Cat3 seems somewhat better using the BF criterion. On the other hand, this criterion performed slightly less good for discrimination between Cat1 and Cat3 when Cat3 was ’true’. The differences between the results using the HR criterion and the ND criterion are only caused by the added random white noise, since exactly the same experiments were used. 4.4. Discussion and Conclusion All model discriminating design criteria which are compared here are certainly useful and it is of course not the aim of this study to show useless criteria, but to compare their use in dynamic systems with potentially poor parameter estimates. The use of the CA criterion was problematic in the fermentation experiment. As discussed in paragraph 4.2.2 on page 67, it was suggested in the original paper to perform an experiment for improvement of the parameter estimation in such a case. This might not be that simple, since still a series of competing models are available. One obvious option would be to design the parameter estimation experiment based on the model with the best fit so far. However, other discriminating design criteria did suggest proper discriminating experiments and this seems to be just a good example of the potential risks and problems in using the CA criterion. The potentially large and fast changes in model variances in dynamic systems with poor parameter estimates seem to be the major cause of these problems. Note however, that the original CA criterion was especially developed for dynamic systems and it was shown to perform properly with a fermentation example with pa- 84
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Lebenswissenschaften Life Sciences
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Forschungszentrum Jülich GmbH Inst
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’Therefore, mathematical modeling
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Contents 3.4. Application: L-Valine
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Contents 4
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1. Introduction need for improved m
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2. Theory In a batch process, all s
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2. Theory 1997; Goncalves et al., 2
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2. Theory For batch fermentations,
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2. Theory with Yps being the yield
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2. Theory Inhibition Some catalytic
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2. Theory The method of least squar
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2. Theory evaluation can be made by
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2. Theory We define the measured or
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2. Theory build in the model. An ob
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2. Theory nations, the researcher i
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2. Theory W = J · Covθ · J T (2.
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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
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Page 49 and 50: 2. Theory proteome14 (Hermann et al
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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 89: 4. Simulative Comparison of Model D
Page 95 and 96: 5. L-Valine Production Process Deve
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A. Nomenclature Table A.1.: Symbols
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Table A.1.: Symbols and Abbreviatio
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Table A.1.: Symbols and Abbreviatio
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B. Ratio between OD600 and Dry Weig
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C. The Influence of the Oxygen Supp
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The measurements of amino acids and
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kiv [mM] lac [mM] 15 10 5 0 0 10 20
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OTR, CTR 0.06 0.04 0.02 0 0 10 20 3
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DO properly at a low value in dynam
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D. Dilution for Measurement of Amin
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E. Models used in the First Model D
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Model 1.6 Model 1.6 is similar to m
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Table E.1: Model Parameters of the
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Table E.2: Model Parameters of the
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161
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Model 2.2 Model 2.2 is similar to m
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Table F.1.: Model Parameters of the
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Table F.2.: Estimated Lag-Times of
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Table F.3: Model Parameters of the
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Table F.4.: Estimated Lag-Times of
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G. Alternative Off-line Optimized P
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G.2. Overall Yield of Product on Su
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Summary Fast development of product
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Zusammenfassung Es ist wichtig, die
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Acknowledgements This thesis result
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Bibliography K. Akashi, H. Shibai,
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Bibliography A. Bodalo-Santoyo, J.L
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Bibliography A.J. Cooper, J.Z. Gino
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Bibliography A.G. Fredrickson, R.D.
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Bibliography W.G. Hunter and A.M. R
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Bibliography A.C. McHardy, A. Tauch
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Bibliography E. Radmacher, A. Vaits
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Bibliography K.J. Versyck, J.E. Cla
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Corynebacterium glutamicum - JUWEL - Forschungszentrum Jülich

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