Drug Metabolism in Drug Design and Development Basic Concepts and Practice

both substrate and inhibitor are competing for the enzyme active site and their
binding is mutually exclusive. When the inhibitor is bound to the enzyme, the
complex is incapable of reacting (turning over substrate).
In this case, formation of EI is a dead-end complex and the only way to
generate catalytically active enzyme is for the reformation of E+I. Because
competitive inhibition has no effect onVmax, a change (increase) inKmmust
occur and thus this type of inhibition is characterized as ‘‘an increase inKm.’’
However, to assist in characterization of inhibitors it may be more
straightforward and simpler to describe competitive inhibition as a decrease
inVmax/Kmwith no change in the apparentVmax. The equation for defining
competitive inhibition is listed below as Equation 4.12.

v¼

Vmax½SŠ

Kmð 1 þK½IŠiÞþ½ŠS

ð 4 : 12 Þ

In this equation,VmaxandKmhave their usual meanings and [I] is the free
inhibitor concentration.Kiis the inhibition constant and is equal toKi= [E][I]/
[EI]. Note that the equation is of the same form as the Michaelis–Menten
equation and can be rewritten as the following (Eq. 4.13):

v¼

Vappmax½SŠ

Kmappþ½SŠ

ð 4 : 13 Þ

whereVmaxappandKmappare the apparent values ofVmaxandKm, respectively, and
are the values as they appear in the presence of the inhibitor. Thus,Vmaxapp¼Vmax
andKmapp¼Kmð 1 þ½IŠ=KiÞ, then (Eq. 4.14) follows:

Vmax appapp

Kappm

¼

Vmax

Km

1 þ½KIŠi

ð 4 : 14 Þ

From Equation 4.14, it thus becomes apparent that in the case of
competitive inhibition, the apparent value ofVmax/Kmis decreased by the
factor (1+[I]/Ki) andVmaxremains unchanged. It should be noted, that this is
frequently also stated as ‘‘competitive inhibition results in an increase inKm
with no change inVmax.’’

4.7.3 Mixed Inhibition

In the case of mixed inhibition, both specific and catalytic effects are present
and thus, bothVmaxapp=Kappm andVmaxappare altered. Thus, both the maximal velocity
and the concentration at which half-maximal velocity is achieved are changed
as compared to the absence of inhibitor. As can be seen in Scheme 4.3, the
mechanism that produces mixed inhibition is much more complex than that of
competitive inhibition since the formation of an enzyme–inhibitor complex is
not necessarily a dead-end reaction. In this case, substrate can bind to the

ENZYME INHIBITION KINETICS 103