Biomedical Engineering Reference
In-Depth Information
by enhancing or reducing the overall reaction. Hemoglobin is a prime example of a cooper-
ative reaction involving the storing of oxygen in red blood cells.
A simple cooperative reaction is given by the following model:
ð
8
:
133
Þ
using the variables previously defined. The equations that describe this system are given by
q
S
¼
K
1
q
C
1
þ
K
3
q
C
2
K
q
S
q
E
K
q
S
q
C
1
1
3
q
C
1
¼
K
q
S
q
E
þ
K
3
q
C
2
þ
K
q
C
2
ð
K
1
þ
K
Þ
q
c
1
K
q
S
q
C
1
1
4
2
3
ð
8
:
134
Þ
q
C
2
¼
K
3
q
S
q
C
1
K
3
q
C
2
q
P
¼
K
q
C
1
þ
K
q
C
2
2
4
using the quantities previously defined. The quantity
q
E
is removed using
q
E
¼
E
q
C
1
q
C
2
,
0
giving
q
S
¼
K
1
ð
þ
K
q
S
Þ
q
C
1
þ
K
3
ð
þ
K
q
S
Þ
q
C
2
K
E
q
S
K
q
S
q
C
1
1
1
1
0
3
q
C
1
¼
K
E
q
S
þ
K
3
q
C
2
þ
K
ð
K
q
S
Þ
q
C
2
K
1
ð
þ
K
K
q
S
Þ
q
c
1
K
q
S
q
C
1
1
0
4
1
2
1
3
ð
8
:
135
Þ
q
C
2
¼
K
3
q
S
q
C
1
K
3
q
C
2
q
P
¼
K
q
C
1
þ
K
q
C
2
2
4
with nonzero initial conditions of
q
S
ð
0
Þ¼
S
0
, and
q
E
ð
0
Þ¼
E
:
The quasi-steady-state approx-
0
q
C
1
¼
q
C
2
¼
0, yielding
imation is found from Eq. (8.135) with
0
¼
K
1
E
q
S
þ
K
3
q
C
2
þ
K
ð
K
q
S
Þ
q
C
2
K
1
ð
þ
K
K
q
S
Þ
q
c
1
K
q
S
q
C
1
0
4
1
2
1
3
ð
8
:
136
Þ
0
¼
K
q
S
q
C
1
K
3
q
C
2
3
Equation (8.136) is solved for
q
C
1
and
q
C
2
, giving
K
i
M
E
0
q
S
K
i
M
K
s
M
þ
K
i
M
q
S
þ
q
q
C
1
¼
2
S
ð
8
:
137
Þ
2
S
K
i
M
K
s
M
þ
K
i
M
q
S
þ
q
E
q
0
¼
q
C
2
2
S
K
s
M
¼
K
1
þ
K
2
K
i
M
¼
K
3
þ
K
4
where
and
:
The velocity of the reaction is given by
K
1
K
3
K
2
K
i
M
E
0
q
S
K
i
M
K
s
M
þ
K
i
M
q
S
þ
q
2
S
K
i
M
K
s
M
þ
K
i
M
q
S
þ
q
K
4
E
0
q
V
¼
K
2
q
C
1
þ
K
4
q
C
2
¼
þ
2
S
2
S
ð
8
:
138
Þ
K
i
M
þ
K
¼
E
q
S
K
q
S
0
2
4
K
i
M
K
s
M
þ
K
i
M
q
S
þ
q
2
S
