Enzymes - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 348

K m ¼ ½

E ½ S

(8.58)

½ ES

K I ¼ ½

ES ½ I

(8.59)

½ ESI

½ E 0 ¼½ E þ½ ES þ½ ESI (8.60)

and

r p ¼ k 2 ½ ES (8.61)

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

r max ½ S

r P ¼ (8.62)

1þ ½

K I I

K m þ ½

S

or

r 0 max ½

K 0 m þ½

S

r P ¼ (8.63)

S

where

r max
1þ ½

r 0 max ¼ (8.64)

K I I

K m
1þ ½

K 0 m ¼ (8.65)

K I I

The net effect of uncompetitive inhibition is a reduction in both r max and K m values. Reduc-
tion in r max has a more pronounced effect than the reduction in K m , and the net result is
a reduction in reaction rate. Uncompetitive inhibition is described in Fig. 8.13 .
High substrate concentrations may cause inhibition in some enzymatic reactions, known
as substrate inhibition. Substrate inhibition is graphically described in Fig. 8.14 .
The reaction scheme for uncompetitive substrate inhibition is

K m

k 2

E + S ES E + P

+
S

(8.66)

K S2

ES 2