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

Kinetics of substrate utilization, metabolic product formation, and biomass generation in cell cultures
Kinetics of balanced growth
Effects of endogenous metabolism and maintenance metabolism on cell growth kinetics

The data for the A. aerogenes culture presented in Fig. 7.8 show that at low dilution rates, The Cell concentration drops noticeably. Similar behavior was observed for the fodder Yeast Torula utilis. This feature, which contradicts the Monod chemostat model, can be explained by accounting for the possibility of endogenous METABOLISM in the model. Endogenous metabolism refers to intracellular reactions that consume cellular components. To account for this effect, we add the term —k_ex to the Monod equation:

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FIG. 7.8. The decrease in cell mass concentration (A. aerogenes culture) in a glycerol medium within a continuous Reactor at decreasing dilution rates contradicts the Monod model. (Reprinted from: Herbert D., Continuous Culture of Microorganisms: Some Theoretical Aspects, in Continuous Culture of Microorganisms: A Symposium, p. 48, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1958.)

FIG. 7.9. Linear dependence of the specific Respiration rate of the A. aerogenes bacterium on the dilution rate in a continuous reactor, consistent with Equation (7.24). (Reprinted from: Herbert D., Continuous Culture of Microorganisms: Some Theoretical Aspects, in Continuous Culture of Microorganisms: A Symposium, p. 49, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1958.)

Note that the term —k_ex in Equation (7.22) can also be interpreted as the cell death rate.

The modified Monod model is also consistent with other experimental data. For example, if the respiration rate of an aerobic culture is proportional to the substrate utilization rate, i.e.,

it follows from Equations (7.8), (7.22), and (7.23) that the specific respiration rate is equal to

The experimental data presented in Fig. 7.9 are in good agreement with Equation (7.24).

The observed dependence of the yield coefficient Y on D also confirms the validity of Equation (7.22) for The rate of cell growth. If the substrate uptake rate is

where Y'_x/s is the "true" coefficient, then from Equations (7.22) and (7.25) and the definition of Y_x/s (recall that Y_x/s is the stoichiometric coefficient equal to The ratio of the total mass of formed Cells to the total mass of consumed substrate; therefore, under nutrient sterility conditions, -r_s = Dx/Y_x/s), it follows that

It has been shown experimentally that for A number of microorganisms, the dependence of Y_x/s on D is expressed precisely by this equation.

Another possibility, briefly discussed in the context of cell growth stoichiometry in Section 5.10.1, involves the simultaneous utilization of substrate both for cell growth and for other cellular Energy Requirements (maintenance metabolism). In this case, the substrate utilization rate is determined by the expression

where m is the specific rate of substrate consumption for maintenance metabolism. Assuming that r_x equals μx, we obtain

Thus, we have obtained the exact same functional dependence of Y_x/s on D as in the case of the endogenous metabolism model [Equation (7.26)].

As shown in Fig. 7.10, at high dilution rates, The behavior of a cell culture in a continuous reactor can deviate significantly from that predicted by the Monod chemostat model. Not only is there a substantial error in determining the cell concentration near the wash-out point, but the entire cell population can survive at dilution rates considerably exceeding the critical value predicted by theory. Furthermore, as D approaches its critical maximum value, the yield coefficient decreases. One possible reason for this discrepancy may be the relatively high Substrate Concentration characteristic of high dilution rates. Under such conditions, the substrate often does not limit cell growth, and the cells making up the population may alter their metabolic pathways, utilizing a different environmental limiting factor. Another reason could be insufficiently efficient mixing; we will examine this issue in Chapter 9.

FIG. 7.10. Experimental data on the growth of Aerobacter cloacae in a continuous reactor, demonstrating the deviation of cell mass concentration from zero at dilution rates exceeding the calculated critical value. [Reprinted from: Herbert D. et al., The Continuous Culture of Bacteria: A Theoretical and Experimental Study, J. Gen. Microbiol., 14, 601 (1956).]