Drug Metabolism in Drug Design and Development Basic Concepts and Practice

16.2.6 Data Analysis

Nonlinear curve fitting of enzyme kinetic data was accomplished with the
Enzyme Kinetics module of either Grafit version 5.0 (Erithacus Software Ltd,
Horley Surrey, UK) or Sigmaplot version 9.0 (SPSS, Inc., Chicago, IL).
When the behavior of inhibition is identified, appropriate equations
(velocity reduction or % inhibition) can be used for quantitative inhibition
of a metabolite formed in the presence of the inhibitor (Table 16.3). Figure 16.2
shows plots for each type of inhibition and graphic determinations for theirKi.
IC 50 is an estimate to evaluateKiwhen the substrate concentration approaches
Km.IC 50 equals to two units ofKifor both competitive and uncompetive
inhibitions, and to one unit ofKifor noncompetitive inhibition. However, the
IC 50 value cannot be used as an estimate ofKiin the mixed type inhibition, due
to the interference of factorsa(Scheme 16.1), which is a change in binding
affinity of inhibitor to enzyme (Segel, 1997; Shou et al., 2001).
For determination of enzyme kinetic parameters, replicates ofn=3were
run at eight substrate concentrations to obtainKmand replicates ofn=3were
run at eight inhibitor concentrations in the presence of substrate concentra-
tion approachingKmto generate IC 50 value. Known inhibitors were usually
run in parallel as positive controls. IC 50 parameters were obtained by curve
fitting of nonlinear regression to observed data using Equation 16.2, whereVo
is the uninhibited velocity,vis the observed velocity,sis the slope factor, and
[I] is the inhibitor concentration. Alternatively, the inhibition of enzyme
activity can be expressed as percentage of control activity. Figure 16.3 and
Table 16.4 show the curve fitting of inhibition of six individual CYP activities

TABLE 16.3 Enzyme inhibition kinetics from the kinetic model in Scheme 16.1:
types of enzyme inhibition, velocity and % of enzyme activity (% Control) for the
metabolism of substrate (S) in the presence of an inhibitor (I), and relationship
between [S] and [I] in different types of inhibition as [S] = Km.

Inhibition type y_(velocity) Percentage of Control

Relationship

(IC 50 andKi)

([S] =Km)

Competitive
([ESI] = 0)

Vmax½SŠ

Km 1 þ½KIŠi



þ½ŠS

Kmþ½SŠ

Km 1 þ½KIŠi



þ½ŠS

IC 50 =2Ki

Noncompetitive
(a=1)

Vmax½SŠ

Km 1 þK½IŠi



þ½ŠS 1 þK½IŠi

 Kmþ½SŠ

ðKmþ½ŠÞS 1 þ½KIŠi

 IC 50 =Ki

Uncompetitive
([EI] = 0,a=1)

Vmax½SŠ

Kmþ½ŠS 1 þ½KIŠi

 Kmþ½SŠ

Kmþ½ŠS 1 þK½IiŠ

 IC 50 =2Ki

Mixed type (a6¼1) Vmax½SŠ
Km 1 þ½KIŠi



þ½ŠS 1 þa½IKŠi

 Kmþ½SŠ

Km 1 þ½KIŠi



þ½ŠS 1 þa½KIŠi

 IC 50 ¼ð^2 aaþK 1 iÞ

REVERSIBLE INHIBITION 523