Luedeking-Piret equation

The specific rate of product formation is often given in terms of the Luedeking-Piret equation, which has two parameters a (growth) and P (nongrowth)... 

The kinetic aspects of product formation in continuous culture are usually dealt with using the simple, formal kinetic approach of the Luedeking-Piret equation (Equ. 5.122). A modified kinetic approach to microbial product formation uses the concept that Vp not only is proportional to the actual biomass concentration but also depends on a second carbon source S2 (Hegewald et al., 1978) ... 

In the previous discussion, extreme cases concerning the stage of product synthesis were considered, but actual production may occur in both exponential and stationary phases of growth. In order to account for this, the specific rate of product formation, qp, is then given by the Luedeking-Piret equation ... 

Luedeking-Piret equation for the rate with of product formation... 

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 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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