Drug Metabolism in Drug Design and Development Basic Concepts and Practice

binds to equivalent sites on each protein subunit. However, the advent of
more sensitive analytical techniques allowing both accurate and precise
metabolite quantification at very low amounts has resulted in the identification
and reporting of numerous examples of sigmoidicity in drug metabolizing
enzymes.
In this case, the homotropic cooperativity occurs with a monomeric enzyme
through substrate binding to both a catalytic and an effector site, and these
sites may not be equivalent (Shou et al., 1999). This results in two Km
parameter estimates and twoVmaxparameter estimates, as discussed below.
One of the most commonly used equations describing sigmoidal kinetic profiles
is the Hill equation (Eq. 4.5):

v¼

Vm½SŠn

K^0 þ½SŠn

ð 4 : 5 Þ

This equation allows a description of sigmoidal kinetics, while requiring the
estimation of only a few parameters. In this case,Vmhas the same meaning as
in the Michaelis–Menten equation and though K^0 is analogous, it is not
equivalent toKm(unlessn= 1) sinceK^0 is comprised of both Kmand the
interaction factors (Shou et al., 1999). The coefficient nis called the Hill
coefficient since it measures relative cooperativity and reflects the degree of
sigmoidicity observed (i.e., the greater thenvalue, the more cooperativity and
sigmoidicity are observed). It should be noted that the nvalue does not
necessarily equal the number of binding sites for substrate since it frequently is
not an integer. However, the Hill equation and its resulting parameters are
useful in comparing substrates that induce sigmoidal kinetics since the
efficiency of the reaction (Vmax/K^0 ) and cooperativity (n) can be compared
for different substrates of the same enzyme.
To gain additional insight into the substrate–enzyme interactions occurring
during sigmoidal kinetics, including the events occurring at each of the
substrate binding sites, other equations have been developed for describing
sigmoidal kinetics of drug metabolizing enzymes that also allow estimation of
twoKmvalues (Km1andKm2) and twoVmaxvalues (Vm1andVm2) (Korzekwa et
al., 1998). This equation (Eq. 4.6) allows estimation of the events occurring at
each of the distinct subsites within the active site binding pocket.

v¼

Vm1½SŠ

Km1 þ

Vm2½SŠ^2

Km1Km2

1 þK½Sm1Šþ ½SŠ

2

Km1Km2

ð 4 : 6 Þ

As implied above, this equation allows for estimation of theKmandVmax
parameters associated with each binding site, and as such, is more informative.
It should be realized, however, that in order to accurately estimate these four
parameters, substantially more data points may be needed than are needed to
estimate parameters using Equation 4.5.

96 ENZYME KINETICS