systems, growth-related kinetic expressions are sometimes approximated by first-order equations of the form kS, where k is a constant for that system. However, at high substrate concentrations [equation (11.7)], Monod kinetics approach zero order (since S0 = 1, the rate is unaffected by substrate concentration). Table 11.5 provides some half-saturation and other coefficients. (Although the discussion so far has focused on the carbon and energy source as the limiting nutrient, the same approach can be used for other requirements, such as dissolved oxygen, as indicated in the table; see "Multiple Substrates" in Section 11.7.4.)
Note that the Monod equation has the same form as the Michaelis-Menten equation used to describe enzyme kinetics (Section 5.3.1). However, unlike Michaelis-Menten kinetics for enzymes, which can be derived from fundamental chemical kinetic principles, the Monod expression for growth is empirical—an approximate fit to observed results.
Example 11.7 Assuming that an organism grows according to Monod kinetics with a maximum growth rate of 10 per day and a half-saturation coefficient of 5 mg/L, how fast would it be growing if the substrate concentration were 100 mg/L? What if it dropped to 20 mg/L?
Organism |
Substrateb |
T (°C) |
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