where K, is the half-inhibitory coefficient (mg/L). Note that when S ^ K,, the added term becomes 1, leaving the Monod expression. Also, when S = K,, this term becomes 2 in
equation (11.34), and m thus becomes half of the Monod value. In the Andrews model, growth rate approaches zero asymptotically as substrate increases. Some other models incorporate an inhibitory level above which there is no growth; this has been found to provide a better fit for growth on toluene, for example, which compromises the cell membrane at higher concentrations.
Product Inhibition Products of cell metabolism can accumulate in the organism's environment and produce inhibitory effects. In some cases this may be a general effect, such as a decrease in pH. In other cases it may be a specific toxic product that is inhibitory, such as the release of ammonia and hydrogen sulfide from proteins, nitrite produced by ammonium oxidizers, or ethanol produced by fermentations. In the case of composting, accumulation of heat leading to excessively high temperatures is also, in a sense, an example of product inhibition.
Other Inhibitory Agents Other toxic chemicals present naturally or as contaminants in the organism's environment may exert inhibitory effects but not serve as substrates. These might include heavy metals, toxic organics, or chlorine (perhaps added for disinfection). Ultraviolet light or other radiation can also be inhibitory. Depending on its mode of action, one way to model the effect of the concentration (I) of an inhibitory substance is to use another modification of the Monod expression:
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