Biomedical Engineering Reference
In-Depth Information
Consider an enzyme catalyzed reaction between a substrate,
S
, modifier,
M,
and enzyme,
, synthesizing product,
,as
E
P
ð
8
:
124
Þ
are the intermediate complexes.
6
Note that we
have eliminated the reverse reaction from the product to the intermediate complex. Another
variation of allosteric reaction eliminates the product from forming through
where
C
¼
SE
,
C
¼
ME
, and
C
¼
SME
1
2
3
C
:
3
The equations that describe the system in Eq. (8.124) are
q
S
¼
K
1
q
C
1
þ
K
4
q
C
3
K
q
S
q
E
K
q
S
q
C
2
1
4
q
M
¼
K
3
q
C
2
þ
K
6
q
C
3
K
q
M
q
E
K
q
M
q
C
1
3
6
q
C
1
¼
K
q
S
q
E
þ
K
6
q
C
3
K
1
ð
þ
K
Þ
q
C
1
K
q
M
q
C
1
1
2
6
ð
8
:
125
Þ
q
C
2
¼
K
3
q
M
q
E
þ
K
4
þ
K
5
ð
Þ
q
C
3
K
3
q
C
2
K
4
q
S
q
C
2
q
C
3
¼
K
q
S
q
C
2
þ
K
q
M
q
C
1
K
4
ð
þ
K
þ
K
6
Þ
q
C
3
4
6
5
q
P
¼
K
2
q
C
1
þ
K
5
q
C
3
We eliminate
q
E
from Eq. (8.125) by using
q
E
¼
E
0
q
C
1
q
C
2
q
C
3
, giving
q
S
¼
K
1
þ
K
1
q
S
ð
Þ
q
C
1
þ
K
4
þ
K
1
q
S
ð
Þ
q
C
3
K
1
q
S
E
0
K
4
K
1
ð
Þ
q
S
q
C
2
q
M
¼
K
3
þ
K
3
q
M
ð
Þ
q
C
2
þ
K
6
þ
K
3
q
M
ð
Þ
q
C
3
K
3
q
M
E
0
K
6
K
3
ð
Þ
q
M
q
C
1
q
C
1
¼
K
q
S
E
K
q
S
q
C
2
þ
K
6
ð
K
q
S
Þ
q
C
3
K
1
ð
þ
K
þ
K
q
M
þ
K
q
S
Þ
q
C
1
1
0
1
1
2
6
1
ð
8
:
126
Þ
q
C
2
¼
K
q
M
E
K
3
q
M
q
C
1
þ
K
4
ð
þ
K
K
3
q
M
Þ
q
C
3
K
ð
q
M
þ
K
3
þ
K
q
S
Þ
q
C
2
3
0
5
3
4
q
C
3
¼
K
4
q
S
q
C
2
þ
K
6
q
M
q
C
1
K
4
þ
K
5
þ
K
6
ð
Þ
q
C
3
q
P
¼
K
q
C
1
þ
K
q
C
3
2
5
with nonzero initial conditions of
q
S
ð
0
Þ¼
S
0
,
q
M
ð
0
Þ¼
M
0
, and
q
E
ð
0
Þ¼
E
:
0
6
This model is adapted from Rubinow, page 89.
