possibly CYP3A4, at very high theophylline concentrations. The observed
biphasic kinetics, as indicated, could be either due to the contribution of
multiple enzymes or to atypical kinetics. The key to differentiating between
these possibilities is to resolve whether single or multiple enzymes are involved.
Although biphasic in the HLM preparations (Campbell et al., 1987), the
kinetics of theophylline 8-hydroxylation mediated by each of the responsible
CYP enzymes including cDNA-expressed CYP1A2, CYP2D6, CYP2E1, and
CYP3A4, was indeed monophasic, suggestive of a multiple enzyme involve-
ment rather than atypical enzyme kinetics.
13.3.3.2 Computational Approach Computational nonlinear regression ana-
lysis, in which the data points in the Michaelis–Menten plots are directly fitted,
is the preferred approach for analysis of metabolic kinetic data. Such an
approach should be utilized as often as possible, given its unbiased nature.
Regression analyses for the determination ofKmandVmax,orCLint(orKm/
Vmax) are described below, for the SigmaPlot (Version 9.0, Syst Inc.) software.
The data, including substrate concentrations, metabolite concentrations,
and the calculated rates of metabolite formation, are entered, and Regression
Wizard is selected in the pop-up menu of Statistics. Hyperbola and single
rectangular with two parameters are chosen for Equation Category and
Equation Name, respectively, followed by Next.XYPair is selected and the
variables for the equation, y=ax/(b+x), are assigned. The independent
variable x is designated as the substrate concentrations (mM) and the
dependent variabley as the rates (or the means of rates) of metabolite
formation, respectively. The constants of the equation,aandb, thus represent
VmaxandKmin Eq. 13.7. Following the selection of Finish, the nonlinear
regression analysis is performed with a default option setting (automatic initial
parameter estimations with the constraints ofa>0 andb>0, no weight fit,
and iterations of 200 with the step size of 1 and the tolerance of 1e-10).
Representative results of such analysis, in which the data in Table 13.3 were
analyzed, are provided in Table 13.4.
TABLE 13.3 Data transformations for enzyme kinetic characterization.
Primary data Transformed dataS(mM) Va(nmol/min/mg) V/S(mL/min/mg) 1/S(L/mM) 1/V(L/nmol/min/mg)
10.0 2.0 0.202 0.10 0.50
20.0 3.9 0.196 0.05 0.26
50.0 8.9 0.178 0.020 0.11
100.0 15.8 0.158 0.010 0.063
200.0 22.2 0.111 0.005 0.045
500.0 31.2 0.0624 0.002 0.032
(1000.0) (30.0) (0.0300) (0.001) (0.033)
aMean (N= 3); the data in parentheses, due to potential substrate inhibition, were detected but not
used for parameter determination.
430 DETERMINATION OF METABOLIC RATES AND ENZYME KINETICS