thus,
½ES¼ESk 1 =ðk 2 þk 3 Þ: ð 13 : 11 Þ(k 2 +k 3 )/k 1 is defined as the Michaelis constant (Km).
Equation 13.11 becomes [ES]=ES/Km, and Equation 13.10 is converted
toV=(k 3 /Km)ES,orV=(kcat/Km)ES,aswellasV=(Vmax/Km)ES as an
alternative.
kcat, the maximal catalytic rate constant, is usually expressed as the number
of metabolite molecules formed by an enzyme molecule in 1 s (or simply in
units ofs^1 ) and is one of the intrinsic properties of a given enzymatic reaction.
However, it is not always readily determined in vitro, for example, in
microsomal assays, since the quantities of the individual enzymes involved
are usually unknown. In contrast, the protein concentrations are easily
determined. Thus,Vmax, an alternative tokcat, expressed in nmol/min/mg and,
is more readily determined. However, there is a subtle difference betweenkcat
and Vmax due to the differences between defined and undefined enzyme
quantities.Vmax,in contrast to the constantkcat, will likely vary for a given
enzymatic reaction, due to the potentially variable enzyme content in the
enzyme preparations.
13.3.2 Experimental Design
Prior to enzyme kinetic investigation, the linearity of the relationship between
the metabolite formation and the enzyme quantity and reaction time should be
determined. The time courses and enzyme concentration dependencies of CYP
activities are often linear when determined at concentration ranges for
microsomal proteins of 0.2–2 mg/mL, although this should be confirmed for
each metabolic pathway being studied.
As the rates for CYP-mediated reactions are usually either low or moderate
from a standard enzymology perspective, the reaction time for the linearity
assay could be extended to 60 min, or longer. Six time points for such assays
are common, for example, 0, 5, 15, 30, 45, and 60 min.
After the testing for linearity (at typically 0.2 or 1 mg/mL of microsomal
proteins and a 15- or 30-min period of incubation), experiments to determine
other parameters can be designed. The rationale for a suitable assay condition is
that such a condition will permit the formation of quantifiable amounts of the
metabolites without markedly depleting (i.e., by less than 20%) the substrate.
Estimates of Km and Vmax with reasonable accuracy probably require
detection of the rates of metabolite formation with substrate concentrations
spanning the range from 0.3 to 3 KmappKmappis the apparent value ofKm.
Unfortunately, theKmappmust be determined, since it is not readily predicted.
The alternative, therefore, is the use of a default set of substrate concentra-
tions, based largely on the general understanding of the kinetic characteristics
of metabolic enzymes, particularly CYP-mediated reactions (Guengerich,
426 DETERMINATION OF METABOLIC RATES AND ENZYME KINETICS