Biochemical Engineering Fundamentals Part 1 - Bailey J., Ollis D. 1989

Kinetics of substrate utilization, metabolite production, and biomass formation in cell cultures
Kinetics of balanced growth
Influence of other environmental parameters on cell growth kinetics

Under balanced growth conditions, a single parameter μ (or the population doubling time

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For this reason, the specific growth rate parameter μ is widely used to describe the Environmental Impact on population behavior. Let us first consider the Effect of Temperature; it is well known that living organisms can exist within a temperature range of approximately —5 to 95 °С. Prokaryotes are conventionally classified according to their growth temperature range. As shown in Table 7.2, each class of microorganisms is characterized by an optimal temperature at which the growth rate reaches its maximum, as well as upper and lower temperature limits beyond which the population is incapable of growth altogether.

The curves presented in Fig. 7.11 demonstrate a profound effect of temperature on the growth of E. coli. Note that in Arrhenius coordinates, classical Arrhenius behavior is observed only at low temperatures; as the temperature approaches the threshold where Bacteria begin to die, their growth rate drops sharply. The striking similarity between the temperature dependencies of cellular growth (Fig. 7.11) and enzymatic catalytic activity (Fig. 3.25) is immediately apparent. In this regard, it is hardly surprising that the dependence of the specific Cell Growth Rate on temperature can often be expressed by an equation of the type (3.73). Obviously, within the relatively low temperature range, the increase in metabolic activity with rising temperature is associated with the enhanced catalytic activity of its constituent Enzymes. When the temperature reaches the limit at which the Denaturation of the most thermally labile, vital cellular Proteins begins, The Cell dies. In several cases, this hypothesis has been confirmed by Genetic Methods; specifically, it has been shown that a single Gene mutation can drastically alter the maximum temperature a microorganism can withstand.

Table 7.2. Classification of microorganisms According to the dependence of their growth rate on temperature^a

^aStanier R. Y., Doudoroff M., Adelberg E. A., The Microbial World, 3rd ed., p. 316. Prentice-Hall, Inc., Englewood Cliffs, N. J., 1970.

Since protein conformation and activity are pH-dependent, we should expect pH to exert a significant influence on cell transport processes, reaction rates, and consequently, the cell growth rate. Typically, bacterial growth rates are maximal within the pH range of 6.5 to 7.5. As an example, Fig. 7.12 illustrates the pH dependence of the E. coli growth rate. However, there are exceptions to this rule. For instance, acidophilic bacteria grow at pH 2.0. Generally, a deviation of 1.5 to 2 pH units in either direction from the optimal value leads to an almost complete cessation of growth (Fig. 7.12). Yeasts grow best in the pH range of 4 to 5, while the optimum pH for mold growth is usually 5 to 7. Yeasts and Molds are characterized by a fairly broad growth range—approximately from pH 3.0 to pH 8.5. As the data in Fig. 7.12 show, as the temperature increases, the pH corresponding to the maximum cell growth rate generally increases as well.

FIG. 7.11. a — with increasing temperature, the growth rate of E. coli Cells increases up to a certain point, but at excessively high temperatures the cells die; b — the same dependence in Arrhenius coordinates. (Reproduced with permission of the publisher from: Stanier R. Y., Doudoroff M., Adelberg E. A., The Microbial World, 3rd ed., pp. 316, 317, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1970.)

FIG. 7.12. Effect of temperature and pH on the doubling time of E. coli. [Reproduced with permission from: Methods in Microbiology, Norris J. R., Ribbons D. W. (eds.), vol. 2, Academic Press, New York, 1970.]

The specific growth rate of microorganisms is also affected by the thermodynamic activity of the medium (which in turn depends on the solutes dissolved in it) and by hydrostatic pressure. The growth rate of aerobic organisms is evidently strongly dependent on the dissolved oxygen concentration. We will examine The Effect of oxygen uptake by cells on their growth kinetics when discussing bioreactor aeration in Chapter 8.