Drug Metabolism in Drug Design and Development Basic Concepts and Practice

researchers have incorrectly fit these types of data by either ignoring (and thus,
omitting) the data points after the apex in which the velocity is declining or
they have simply applied the Michaelis–Menten equation to the entire data set.
Lin et al. (2001) in some comprehensive work have demonstrated the necessity
to fit the entire data set to the proper equation and have also presented the
hazards of failing to fit the data properly. This equation is extremely useful and
can be used with datasets containing a limited (<15) number of data points. If
the researcher wishes to obtain additional information about the processes
occurring during substrate inhibition kinetics, Lin et al. (2001) have provided a
more complex equation (Eq. 4.9) that requires substantially more data points
but that provides much greater detailed kinetic parameter estimates regarding
this type of kinetics.

v¼

Vm K^1 SþabK½SiKŠS



1

Sþ

1

KSþ

1

Kiþ

½SŠ

aKSKi

ð 4 : 9 Þ

It should be noted that in this case,Ksis approximately equal toKmandKiis
the dissociation constant of the substrate binding to the ‘‘inhibitory’’ region
within the enzyme active site. Also,arepresents the factor by which the
dissociation (KsandKi) of substrate at both sites changes when a second
substrate molecule is bound, whereasbis the factor by whichVmaxchanges
upon binding of the second substrate molecule. Thus, one gains additional
information as to the degree to which the binding of the second substrate
molecule altersKmandVmax.
One must also realize that ternary complex situations exist, such as with the
glucuronosyl transferases that involve the enzyme–aglycone–glucuronic acid
complex and that substrate inhibition may also occur in these systems. In this
case, a different equation is required to adequately describe substrate inhibition
(Eq. 4.10).

Vm½AŠ½BŠ

KiAKmBþKmB½ŠþA KmA½ŠþB ½ŠA½ŠðB 1 þK½BsibŠÞ

ð 4 : 10 Þ

However, in this case,Ksibis a constant that defines the strength of inhibition
and is not a dissociation constant.

4.5.3 Heterotropic Cooperativity

4.5.3.1 Heterotropic Activation In the case of heterotropic activation, the
addition of another compound to the incubation mixture results in an
increased velocity for substrate turnover without increasing the amount of
enzyme present. This result is in contrast to the inhibition interaction that is
typically expected when two substrates are coincubated. Again, this

ATYPICAL KINETICSALLOSTERIC EFFECTS 99