Chemostat Growth Kinetics

As a third example let us consider the growth kinetics in a chemostat used by Kalogerakis (1984) to evaluate sequential design procedures for model discrimination in dynamic systems. We consider the following four kinetic models for biomass growth and substrate utilization in the continuous baker s yeast fermentation. 

Model 1 (Monod kinetics with constant specific death rate) 

In the above ODEs, X] and x2 represent the biomass and substrate concentration in the chemostat, cF is the substrate concentration in the feed stream (g/L) and D is the dilution factor (h 1) defined as the feed flowrate over the volume of the liquid phase in the chemostat. It is assumed that both state variables, xt and x2 are observed. 

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More extensive discussions of the theoretical aspects of chemostat culture have been published elsewhere (e.g. Herbert et al, 1956 Pirt, 1975 Bailey Ollis, 1977). Many of the theoretical principles apphed to microbial chemostat cultures can be applied successfully to animal cell cultures, although there are a number of instances where the behaviour of animal cells has been reported to deviate from the models used to describe microbial growth kinetics (Tovey, 1980 Boraston et al, 1984 Miller et al., 1988). 

Harrison, P.J., Conway, H.L. and Dugdale, R.C. (1976) Marine diatoms grown in chemostats under silicate or ammonium limitation. I. Cellular chemical composition and steady-state growth kinetics of Skeletonema costatum. Marine Biology, 35, 177-186. 

In the last section, the concepts of enzymatic reactions are extended to microorganisms and biomass synthesis. Here micro-organism growth kinetics are used in modeling both batch reactors and CSTRs (chemostats). 

Furthermore, since most large-scale fermentations are carried out in batch mode, the kinetic parameters determined by the chemostat study should be able to predict the growth in a batch fermenter. However, due to the significantly different environments of batch and continuous fermenters, the kinetic model developed from the CSTF runs may fail to predict the growth behavior of a batch fermenter. Nevertheless, the verification of a kinetic model and the evaluation of kinetic parameters by running chemostat is the most reliable method because of its constant medium environment. 

Several special terms are used to describe traditional reaction engineering concepts. Examples include yield coefficients for the generally fermentation environment-dependent stoichiometric coefficients, metabolic network for reaction network, substrate for feed, metabolite for secreted bioreaction products, biomass for cells, broth for the fermenter medium, aeration rate for the rate of air addition, vvm for volumetric airflow rate per broth volume, OUR for 02 uptake rate per broth volume, and CER for C02 evolution rate per broth volume. For continuous fermentation, dilution rate stands for feed or effluent rate (equal at steady state), washout for a condition where the feed rate exceeds the cell growth rate, resulting in washout of cells from the reactor. Section 7 discusses a simple model of a CSTR reactor (called a chemostat) using empirical kinetics. 

So is the constant concentration of growth substrate that is added at flow rate D to the chemostat. S and B are the concentrations of growth substrate and bacteria in the chemostat, respectively. K is the Monod constant, which is formally identical to the Michaelis constant of enzyme kinetics, p is the maximal growth rate constant, and Y is the amount of bacterial cells produced from a given amount of substrate (yield). 

A., Bindley, N.D. (1996) Growth rate-dependent modulation of carbon flux through central metabolism and the kinetic consequences for glucose-limited chemostat cultures of Corynebacterium glutamicum. Appl. Environ. Microbiol 62(2), 429-436. 

Senn H, Lendenmann U, Snozzi M, Hamer G, Egli T (1994) The growth of Escherichia coli in glucose-limited chemostat cultures a re-examination of the kinetics. Biochim Biophys Acta 1201 424-436... 

Figure 5.37. Dependence of kinetic parameters and 2 the model of filamentous growth (see Equ. 5.110) on glucose concentration s in case of chemostat culture of Streptomyces hydroscopicus. (From Bergter, 1978.)...

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