[325, 470]

• promoted by increased presence of a nutrient Ni (Xji increases with increasing concentration of N¿) at least up to some threshold levels and may be discouraged at high concentrations of Ni (the so-called "substrate inhibition"),

• discouraged by increased presence of the nutrient Ar, (\ji decreases with increasing concentration of Ni, Xji < 1); or

• unaffected by variations in concentration of Ni (\ji = 1 for all values of Ni) (Table 2.2).

Production of a metabolite Pj is usually (i) unaffected by the presence of a target metabolite Pk {ipjkiPk) = 1] or may be discouraged as the product Pk accumulates in the culture [i.e., tpjk(Pk) decreases with increasing Pk ■ Accessibility of nutrients in the abiotic phase to cell mass is reduced with increasing biomass concentration in the culture (X) at high levels of the same and as a result, cellular metabolism (including synthesis of metabolite Pj) may be affected negatively as the biotic fraction of the culture is increased [i.e., v>(X) may decrease with increasing X, ip(X) < 1], The popular forms of Xji(N), ipjk(Pk) and i>(X) are provided in Table 2.2.

The second approach in relating the specific formation rate of metabolite Pj (ej) to concentrations of various nutrients, cell mass and target metabolites involves expressing £j as a function of the specific cell growth rate, viz., £j = Sj(ji). A popular relation that follows this approach is the Leudeking-Piret rate expression used to represent kinetics of synthesis of metabolite Pj, viz., ej^a^ + Pj, (2.21)

with Oij and 3j being constants characteristic of the particular metabolite Pr

2.5.4 Miscellaneous Remarks

It was mentioned at the beginning of section 2.5 that the cell mass-specific rates of cell growth, uptake of various nutrients, and synthesis of various metabolites are influenced by two additional culture parameters, viz., pH and temperature. Many of the parameters in the rate expressions discussed in Eqs. 2.17 - 2.21 and Tables 2.1 and 2.2 are functions of pH and temperature. These two culture parameters are tightly controlled in bioreactor operations in research laboratories and industrial bioprocesses. This is the reason why we do not dwell much on the effects of pH and temperature on culture dynamics. Before concluding this section, it is pertinent to relate the discussion in this section to the compact representation of bioreactor dynamics provided in Eqs. 2.1 and 2.2. When an unstructured representation is used for cellular metabolism, the state variables (x) would include concentrations of gaseous species such as O2 and CO2, concentrations of nutrients (including dissolved O2) and extracellular products of interest (including dissolved CO2), cell mass concentration, culture volume, and concentrations of intracellular metabolites of interest. If pH and temperature are not controlled, the state variables would also include these two additional variables. The inputs to the bioreactor (u and d) typically would include volumetric flow rates and composition of gas feed and liquid feed (for fed-batch and continuous operations). The outputs from the biopro-cess (y) typically would include all bioreactor variables that are monitored (including culture parameters that are measured on-line or off-line, composition of the effluent gas, and volumetric flow rates of effluent gas and culture withdrawal).

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