Corynebacterium glutamicum - JUWEL - Forschungszentrum Jülich

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2.3. A Model of a Fed-Batch Process with µmax being the maximal specific growth rate, KS the Monod-constant, analogous to the Michaelis-Menten constant and Yxs the yield of biomass production on substrate, which is the amount of biomass which is produced from one unit of substrate. The Monod equation is probably the most often used equation to describe biomass growth. Some alternative equations have also been proposed, amongst which the Blackman equation (Dabes et al., 1973), the equations by Konak (1974) and a logistic equation (used for instance in Bona and Moser (1997)). Maintenance Substrate is not only needed for biomass production, but also some energy is needed for the maintenance of the cells. This is usually added as an extra maintenance term in the equations, either as extra substrate uptake: or as biomass degradation: rs = − rx − mSCX Yxs CSCX rx = µmax − mSCX KS + CS (2.11) (2.12) with mS the maintenance coefficient. From a mechanistic point of view, the former can be expected to be more correct as long as substrate is available (Roels, 1983). Product Formation In fermentations, besides the biomass also another product is formed from the substrate. This production can be classified into three groups: directly associated to the energy generation of the organism, indirectly coupled to it and a group in which no clear coupling to the energy generation of the cell is apparent (Roels, 1983). Production of ethanol, acetic acid and many other products are directly associated to the energy generation. In these cases the substrate uptake rate can still be described as in equation 2.11 and the production rate can be given by: rp = rx · Ypx + mP CX. (2.13) where Ypx is the ratio between the production of product and biomass of the growth associated part of the production and mP is the specific production rate without growth (Luedeking and Piret, 1959). For instance the production of amino acids is regarded to be indirectly coupled to the energy metabolism. Here, a separate contribution of the product formation is added to the substrate conversion: − rs = rx + Yxs rp + mSCX Yps (2.14) 13
2. Theory with Yps being the yield of product on substrate and rp the rate of product formation, which can for instance be described by a Monod-type equation: CSCX rp = πmax KP + CS (2.15) where πmax is the maximal specific production rate and KP a bindings constant analogue to the Monod-constant KS in equation 2.9. For the third class, where there is no clear coupling between the energy generation and product formation, one general mechanistic model cannot be given. For instance secondary metabolites such as antibiotics have been categorized in this group. Multiple Substrates The prior model equations presume one rate-controlling substrate. This may hold for many cases, but an increasing amount of processes which are controlled by more than one substrate are being reported. Now let the overall specific growth rate µ be defined by rx = µCX (2.16) Several macroscopic descriptions of this overall specific growth rate, controlled by multiple substrates, have been reported, such as a multiplicative, additive and noninteractive approach (Neeleman et al., 2001; Roels, 1983). In the multiplicative case, the overall specific growth rate is calculated by multiplying the fractions of the maximal specific growth rate according to the different substrates, so for n substrates: n� µ = (2.17) µS,i i=1 where µS,i is the specific growth rate supported by substrate i. So for instance using two simple Monod type kinetics for both substrates S1 andS2, the overall specific growth rate according to the multiplicative approach would be 9,10 µ = µmax CS1 CS2 KS1 + CS1 KS2 + CS2 (2.18) One major drawback of this multiplicative approach is the fact that moderate limitation by several substrates leads to severe limitation of the overall growth rate, which is unlikely to be the real case. 9 Only one maximal specific growth rate µmax is used here. When separate maximal growth rates for both substrates are used, these would not be distinguishable mathematically. Furthermore, from a mechanistic point of view, one maximal rate and two processes which limit this is also well interpretable. 10 The mechanistic theory behind the Michaelis-Menten kinetics for enzyme reactions does not support this multiplication (Biselli, 1992) but for whole cell processes it has often been used successfully. 14
Page 1 and 2: Lebenswissenschaften Life Sciences
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Page 6: ’Therefore, mathematical modeling
Page 9 and 10: Contents 3.4. Application: L-Valine
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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: 2. Theory For batch fermentations,
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
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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
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4. Simulative Comparison of Model D
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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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