Kinetic Model Equations for Repression

Catabolite repression plays a central role in many industrial fermentations such as in yeast technology (diauxic growth) and secondary metabolite productions. Even though the exact nature of the biochemical mechanisms involved in these regulations is often unknown (see Demain et al., 1979), the following type of formal kinetic equation 

The influence of pH of a bioprocess can be dealt with in combination with inhibition kinetics. Andreyeva and Biryukov (1973) gave a number of different models for dealing with combined inhibition (see also Brown and Halsted, 1975). 

For example, using Equ. 5.88 a formal kinetic equation can be constructed wherein the ion concentration h is treated as if it were a substrate concentration. The value of the constant K is found by a method analogous to that in Fig. 5.29 using the concentration at the half-maximum value of fi from the two parts of the curve representing stimulation and inhibition K2 (Humphrey, 1977b, 1978). Thus, a mixed inhibition function is obtained 

Andreyeva and Biryukov also gave a numerical curve-fitting procedure 

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