Enzymes - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 350

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

r max ½ S

r P ¼ (8.71)

2
K S 2

þ ½

S

K m þ½ S

At lowsubstrate concentrations, [S] 2 << K S2 , and inhibition is dominant. The rate in this case is

K m þ½

r max ½ S

r P ¼ (8.72)

S

At high substrate concentrations, [S] >> K M , and inhibition is dominant. The rate in this case is

r max
1þ ½

r P ¼ (8.73)

K S 2

S

The substrate concentration resulting in the maximum reaction rate can be determined
by setting d r P
d

¼

0 . The [S] max is given by

½ S

p

K m K S 2

max ¼

(8.74)

S

8.2.5. Effects of pH and Temperature
8.2.5.1. pH Effects
Certain enzymes have ionic groups on their active sites, and these ionic groups must be in
a suitable form (acid or base) to function. Variations in the pH of the medium result in
changes in the ionic form of the active site and changes in the activity of the enzyme and
hence the reaction rate. Changes in pH may also alter the three-dimensional shape of the
enzyme. For these reasons, enzymes are only active over a certain pH range. The pH of
the medium may affect the maximum reaction rate, K m , and the stability of the enzyme. In
some cases, the substrate may contain ionic groups, and the pH of the medium affects the
affinity of the substrate to the enzyme.
The following scheme may be used to describe pH dependence of the enzymatic reaction
rate for ionizing enzymes.

-

E + H +

K a2

K m

k 2

EH + S EHS EH + P

(8.75)

H +

K a1

+

EH 2