Biomedical Engineering Reference
In-Depth Information
Figure 7.18
The three regimes of the enzymatic reaction.
Integrating this relation and substituting the result in (7.21) yields the parabolic
kinetics
2
t
(7.32)
[
P
]
=
k k E S
[
] [ ]
1 2
0
0
2
After this early stage, the reaction acquires a steady state rate, according to the
Michaelis-Menten approach
d ES
d t
[
]
=
0
We integrate (7.21) to obtain the linear form
[
P
]
=
at b
+
Using continuity considerations, the preceding equation can be rewritten as
t
æ
ö
0
[
P
]
=
k V
[ ]
S
t
t
-
(7.33)
ç
÷
1 max
0
0
è
ø
2
This linear form corresponds to the second regime in Figure 7.18. At the end
of the reaction, the substrate S becomes depleted, the concentration [
S
] may be ne-
glected in (7.20), and the equation collapses to
d ES
[
]
= -
(
k
+
k
) [
ES
]
2
-
1
d t
