Biomedical Engineering Reference
In-Depth Information
50
Positive
40
30
Negative
20
10
0
0 102030405060708090100
q
s
FIGURE 8.29
Velocity of product appearance for cooperative reactions using Eq. (8.138). Positive: The para-
meters used for the positive cooperativity are
K
1
¼
0
:
001,
K
1
¼
0
:
00001, K
2
¼
0
:
1,
K
3
¼
0
:
05,
K
3
¼
0
:
00002,
K
4
¼
0
:
3, and
E
¼
7
:
The parameters used for the negative cooperativity are
K
¼
1,
K
1
¼
0
:
2, K
2
¼
0
:
1,
K
¼
0
:
01,
0
1
3
K
3
¼
0
:
4,
K
¼
0
:
02, and
E
¼
7
:
4
0
The overall reaction can exhibit positive or negative cooperativity depending on the param-
eter values. For positive cooperativity, one case is the slow binding of
S
þ
E
to form
C
1
(
K
1
is
small), and the binding of
K
3
is large), which increases the overall
reaction. For negative cooperativity, one case is when the binding of
S
þ
C
1
to form
C
2
is fast (
S
þ
E
to form
C
1
(
K
1
is
large) slows the binding of
K
3
is small), which slows the overall reaction.
Figure 8.29 illustrates positive and negative cooperativity. Notice the sigmoidal shape for the
reaction rate for a positive cooperativity in Figure 8.29, where the negative cooperativity has
a hyperbolic shape like the other reaction rates illustrated before.
S
þ
C
1
to form
C
2
(
8.7 EXERCISES
1.
For the reaction given in Eq. (8.1) and with
q
A
ð
0
Þ¼
15,
q
B
ð
0
Þ¼
8,
q
P
ð
0
Þ¼
0, and
K
¼
3,
q
P
:
2.
For the reaction given in Eq. (8.1) and with
solve and simulate the solution for
q
A
ð
0
Þ¼
10,
q
B
ð
0
Þ¼
20,
q
P
ð
0
Þ¼
0, and
K
¼
5,
q
A
:
3.
For the reaction given in Eq. (8.13) and with
solve and simulate the solution for
q
A
ð
0
Þ¼
10,
q
B
ð
0
Þ¼
20,
q
P
ð
0
Þ¼
0,
K
1
¼
7, and
K
1
¼
5, solve and simulate the solution for
q
A
:
4.
For the reaction given in Eq. (8.13) and with
q
A
ð
0
Þ¼
18,
q
B
ð
0
Þ¼
5,
q
P
ð
0
Þ¼
0,
K
1
¼
10, and
K
1
¼
4, solve and simulate the solution for
q
P
:
5.
For the reaction given in Eq. (8.13) and with
q
A
ð
0
Þ¼
30,
q
B
ð
0
Þ¼
10,
q
P
ð
0
Þ¼
0,
K
1
¼
1, and
K
1
¼
0
:
1, solve and simulate the solution for
q
B
:
6.
Show that Eq. (8.24) follows from Eq. (8.23).
7.
For the reaction given in Eq. (8.25) and with
q
A
ð
0
Þ¼
10,
q
B
ð
0
Þ¼
20,
q
P
ð
0
Þ¼
0,
K
1
¼
4
K
1
¼
2, a ¼
2, and b ¼
1, simulate the solution for
q
A
:
8.
For the reaction given in Eq. (8.25) and with
q
A
ð
0
Þ¼
30,
q
B
ð
0
Þ¼
10,
q
P
ð
0
Þ¼
0,
K
1
¼
8
K
1
¼
3, a ¼
1, and b ¼
3, simulate the solution for
q
P
:
Continued
