Effect of cooperativity on microbial growth

The classical Monod equation for the specific growth rate of a microbial population can be derived by assuming a single substrate enzyme-catalysed reaction (Michaelis-Menten kinetics) as the rate-limiting step in microbial growth. In some cases the enzyme which catalyses the rate-limiting step in microbial growth may have more than one substrate binding site and the binding of one substrate molecule to the enzyme facilitates the binding of the next substrate molecule (cooperativity). The presence of cooperativity changes the form of the Michaelis-Menten equation for enzyme-catalysed substrate reactions and also the Monod equation for microbial growth. The number of interacting active sites on an enzyme molecule is an additional parameter in this case. In this article, the cooperative growth model for n interacting sites on the enzyme is derived and compared with the classical Monod model.