maximal rate of metabolism) for each metabolic
reaction, using substrate saturation plots (using the
familiar algebra and, because of enzyme satura-
tion, finding that Cl^0 int¼Vmax=Km). However, for
compound X, the situation is more complicated
because we know that the Cl^0 int(drug disappear-
ance) actually is due to several combined biotra-
nsformation pathways (i.e. Cl^0 intðtotalÞ¼Cl^0 int1þ
Cl^0 int2þCl^0 int3þL), thus complicating any Km
andVmaxdeterminations from a simple substrate
saturation plot.
To determine the Cl^0 intof compound X, we are
able to use thein vitrohalf-life method, which is
simpler than finding all the component Cl^0 intvalues.
When the substrate concentration is much smaller
thanKm, the Michaelis–Menten equation simpli-
fies from velocity ðVÞ¼Vmaxð½SÞ=ðKmþ½SÞ,
because [S] (substrate concentration) becomes
negligible. Furthermore, under these conditions,
thein vitrohalf-life (T 1 = 2 ¼ 0 :693/Kel) can be mea-
sured, and this, in turn, is related to the Michaelis–
Menten equation through the relationship velocity
(V)¼volumeKel(wherevolume is standardized
for the volume containing 1 mg of microsomal
protein). When bothVandVmaxare known, then
Kmis also found. Although simpler than finding a
complicatedCint, one caveat of thein vitrohalf-life
method is that one assumes that the substrate
concentration is much smaller thanKm. It may be
necessary to repeat the half-life determinations at
several substrate concentrations, and even model
the asymptote of this relationship, because very
low substrate concentrations that are beneath bio-
chemical detection may be needed to fulfill the
assumptions needed to simplify the Michaelis–
Menten equation.
Note also that in thisin vitroapplication, intrin-
sic clearance, like all conventional mathematical
evaluation of clearances, has units of
volumetime^1. It is obtained fromVmaxand
Km measurements, where Vmax has units of
masstime^1. The definition of intrinsic clear-
ance asVmaxKm^1 should not be confused with
the historically prevalent calculation ofkel(the
first-order rate constant of decay of concentration
in plasma), calculated fromkel¼Vmax/Km, where
Vmaxis the zero-order rate of plasma concentration
decay observed at high concentrations andKmaxis
the concentration of plasma at half-maximal rate of
plasma level decay.
Once thein vitrointrinsic clearance has been
determined, the next step, scalingin vitrointrinsic
clearance to the whole liver, proceeds as follows:in vivoCl^0 int¼in vitroCl^0 intweight microsomal
protein=g liverweight liver=kg body weightThe amount of microsomal protein per gram
liver is constant across mammalian species
(45 mg g^1 liver). Thus, the only species-
dependent variable is the weight of liver tissue
per kilogram body weight.
In vivo, hepatic clearance is determined by fac-
toring in the hepatic blood flow (Q), the fraction of
drug unbound in the blood (fu) and the fraction of
drug unbound in the microsomal incubations
(fuðincÞ) against the intrinsic clearance of the drug
by the whole liver (thein vivoC^0 int). Thefuand
fuðincÞare included when the drug shows consider-
able plasma or microsomal protein binding
(Obach, 1996b). Several models are available for
scalingin vivointrinsic clearance to hepatic clear-
ance, including the parallel tube model or sinusoi-
dal perfusion model, the well-stirred model or
venous equilibration model and the distributed
sinusoidal perfusion model (Wilkinson, 1987).
Thus far, for compound X, we have obtained
good results in this context with the simplest of
these, the well-stirred model (see Table 8.1 for the
equations, with and without significant plasmaTable 8.1 Equations for predicting hepatic clearance using the well-stirred model
In the absence of serum or In the presence of significant In the presence of both serum and
microsomal protein binding serum protein binding microsomal protein binding
Clhepatic¼
QCl^0 int
QþCl^0 int
Clhepatic¼
QfuCl^0 int
QþfuCl^0 int
Clhepatic¼
QfuCl^0 intfuðincÞ
QþfuCl^0 intfuðincÞ82 CH8 PHASE I: THE FIRST OPPORTUNITY FOR EXTRAPOLATION FROM ANIMAL DATA