Luedeking-Piret Model

Our presentation of methodologies for interpretation of kinetic data from a bioreactor operated in a batch mode would not be complete without a brief discussion of the Luedeking-Piret model. In a sense this model is related to... 

When only small quantities of product are required, scale-up of production via roller bottles in a laboratory robot assisted facility may be feasible, but this approach is susceptible to contamination. Moreover, ensuring uniform environmental conditions throughout a multitude of bottles is not a trivial task. Control of a small stirred tank bioreactor is more readily accomplished. The kinetics of product formation in animal cells can often be represented in terms of the Luedeking-Piret model (see Section 13.1.5). 

Luedeking and Piret<56) proposed that the formation of microbial products could be described by a two parameter model. This was based on their studies of lactic acid fermentation using Lactobacillus delbruekii in which the accumulation of the acid is not directly linked to the growth rate. The function used was ... 

Equation 31 shows the generic model for product synthesis formulated by Luedeking and Piret (1959). In this model, the product synthesis can be associated to growth (term apx), and also in a non-associated form ( 3). In many situations only one of the phenomena is observed - the synthesis is associated or non-associated - employing only one of the terms of Equation 31. Figure 8.5 illustrates the kinetics profiles for the three different possibilities of product synthesis described above. 

Some models utilize the concept of Luedeking and Piret (1959) for growth associated and/or non-growth associated production (Equations 65 to 67). However, in some circumstances, the best fit occurs when the specific death rate kj is considered, instead of the specific growth rate px (Equations 68, 70 and 71) (Linardos et al., 1991 Zeng, 1996a, 1996b). This statement follows the observation that antibody production increases when cells are under conditions of stress. 

A final point of importance here is the production of substances other than biomass, since microbial growth processes are used to produce a number of products such as alcohols, antibiotics, vitamins, and so on. A typical model is that of Luedeking and Piret [R. Luedeking and E.L. Piret, J. Biochem. Microbiol. Tech. Eng.. 1. 393 (1959)]. Here... 

Specific growth rate of the producing strain is also a relevant parameter for enzyme production by fermentation. Many enzymes are synthesized as growth-associated metabolites so that cell specific growth rate has a direct impact on enzyme specific rate of synthesis as shown by the non-structured model of Luedeking and Piret (1959) ... 

A model proposed by Luedeking and Piret combines both the terms in a kinetic equation containing two empirical parameters (a and j3) ... 

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