S

where Vm is the maximum reaction rate (concentration time-1), and is proportional to the total mass of enzyme in the soil (and hence to the total active biomass), and Km is the Michaelis-Menton, or half-saturation, constant and is the substrate concentration at which the reaction occurs at half the maximum velocity, Vm/2. Km is inversely related to enzyme-substrate affinity, which tends to have higher values in soil than in aqueous solutions and to decrease when soil slurries are shaken; therefore Km is inversely proportional to diffusivity.

Figure 16.2 illustrates how Michaelis-Menton kinetics contain both first- and zero-order regions.

Substrate concentration, A

FIGURE 16.2 Graphical expression of the Michaelis-Menton kinetic parameters for an enzymatic reaction.

Substrate concentration, A

FIGURE 16.2 Graphical expression of the Michaelis-Menton kinetic parameters for an enzymatic reaction.

At high substrate concentrations (S >> Km), the equation simplifies to f = (9)

dt which describes a zero-order reaction, and under very low substrate concentrations (S << Km), the equation simplifies to dS Km S

dt K, m which describes a first-order reaction. Because of the combined linear and exponential forms of S in the equation, the Michaelis-Menton cannot be solved for St analytically; however, solutions are easily calculated iteratively using spreadsheet software.

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