Drug Metabolism in Drug Design and Development Basic Concepts and Practice

protein or enzyme should be largely based on the requirement to achieve a
measurable overall rate of the metabolism at low micromolar substrate
concentrations, that is, 1 or 10mM, together with the need to minimize
nonspecific protein binding (Li et al., 2003; Naritomi et al., 2001).
For a fixed-time study, samples are usually run in triplicate, to enable
standard deviations to be calculated. In studies with five or six time points, for
example, 0, 10, 30, 45, 60, (90) min, duplicate samples are adequate (Li et al.,
2003). The time-course studies are preferred for the determination ofin vitro
t1/2, although estimates are possible using two time points (Zhao et al., 2005).
The last time point, and preferably the last two time points selected ideally
should permit 50% or more of compound disappearance.
In a single exponential decay model,

Ct=C 0 ¼expðketÞð 13 : 1 Þ

whereCt, is the concentration of the parent compound at timet;C 0 , the initial
incubation concentration; andke, the elimination rate constant.
Ct/C 0 =R, the relative concentration at timet

lnR¼ket; thus ke¼lnR=t:

Therefore,keis the slope of a linear regression curve in a semilog plot
(Fig. 13.1a), while thet1/2is the time whenR= 0.5, or

t ¼lnR=ke

t 1 = 2 ¼ðln 0: 5 Þ=ke; or

t 1 = 2 ¼ 0 : 693 =ke:

ð 13 : 2 Þ

As shown in Table 13.1, the reaction periodtand the corresponding amount
(or concentration) of remaining compoundRare tabulated for the construction
of plots fort1/2determination (Fig. 13.1). Althoughkeis readily estimated in
the semilog plots, it is preferably calculated through a fitting of the data with
the model of a single exponential decay, using computer software. Many
application software packages are commercially available, including Scientist,
SigmaPlot, WinNonlin, ADAPT II, and KaleidaGraph (Holleran et al., 2003;
Slaughter et al., 2003). SigmaPlot (Version 9.0, Syst Inc.) is selected as the
demonstration software throughout this text due to its applicability, flexibility
and user-friendly operation.
After the raw data, that is, the time points and the corresponding
determined quantities, are entered into a SigmaPlot data sheet, Regression
Wizard under Statistics is selected. Exponential decay and single with two
parameters are chosen for Equation Category and Equation Name,
respectively, followed by Next.XYPair is selected following the assignments
of the independent variablexas timetand the dependent variableyasR(the
remaining amount relative to that at time 0), to the equation (y=aexp(bx)).

420 DETERMINATION OF METABOLIC RATES AND ENZYME KINETICS