Drug Metabolism in Drug Design and Development Basic Concepts and Practice

enzyme–inhibitor complex that can subsequently dissociate to form an
enzyme–substrate complex that can undergo catalysis to produce product.
It is apparent from Scheme 4.3 that the inhibitor cannot only ‘‘compete’’
with substrate for binding to the enzyme but bind to an enzyme molecule that
subsequently binds a substrate molecule also or to an enzyme-substrate
complex to affect catalytic turnover. These multiple binding mechanisms help
explain the effects of mixed inhibition on bothVmaxandKm. The effects of
mixed inhibition on the velocity of the reaction can be described by the
following mixed inhibition equation (Eq. 4.15):

v¼

Vmax½SŠ

Kmð 1 þ½KIŠiÞþ½ŠðS 1 þ½KIŠiÞ

ð 4 : 15 Þ

whereVmax,KmandKihave their usual meanings. Following the format used
for competitive inhibition, one can also develop equations for describing the
apparentKmandVmaxresulting from mixed inhibition of the reaction. In this
case, theVmaxappresulting from mixed inhibition can be described with (Eq. 4.16):

Vmaxapp¼

Vmax

1 þ½KIŠi

ð 4 : 16 Þ

Likewise, the resultingKappm can be described with (Eq. 4.17):

Kappm ¼

Kmð 1 þK½IicŠÞ

1 þK½IiuŠ

ð 4 : 17 Þ

where Kic is the competitive portion of the inhibition and Kiu is the
uncompetitive portion of the inhibition.
And finally, the ratio ofVmaxapptoKmappcan be described with (Eq. 4.18):

Vmaxapp

Kappm

¼

Vmax

Km

1 þK½IicŠ

ð 4 : 18 Þ

4.7.4 Noncompetitive Inhibition

Pure noncompetitive inhibition (decrease inVmaxwith no change inKm)is
seldom observed in enzyme kinetics studies, except in the case of very small
inhibitors, such as protons, metal ions, and small anions. For noncompetitive

SCHEME 4.3 Mixed inhibition (Kic¼Kicompetitive andKiu¼Kiuncompetitive).

104 ENZYME KINETICS