Enzymes - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 347

We can develop the following equation for the rate of enzymatic conversion:

r max ½ S

r P ¼ (8.54)

1þ ½I K I ðK m þ½ S Þ

or

r 0 max ½

K m þ½

S

r P ¼ (8.55)

S

where

r max
1þ ½

r 0 max ¼ (8.56)

K I I

The net effect of noncompetitive inhibition is a reduction in r max . High substrate concentra-
tions would not overcome noncompetitive inhibition. Figure 8.12 illustrates the noncompet-
itive rate as compared with the Michaelis e Menten kinetics. Other reagents need to be added
to block binding of the inhibitor to the enzyme. In some forms of noncompetitive inhibition
r max is reduced and K m is increased. This occurs if the complex ESI can form product.
Uncompetitive inhibitors bind to the ES complex only and have no affinity for the enzyme
itself. The scheme for uncompetitive inhibition is
K m

k 2

E + S ES E + P

+
I

(8.57)

K I

ESI

r P

r max

No inhibition

r max

r max = '

1 + [I]
K I

Noncompetitive inhibition

1
2 r max
r max

1
2 '

0

[S] = K m

0

[S]

FIGURE 8.12 Comparison of Michaelis e Menten and noncompetitive inhibition enzyme kinetics.