Biomedical Engineering Reference
In-Depth Information
Quasi-Steady-State Approximation to the Reaction Rate
The quasi-steady-state approximation is found from Eq. (8.126) with
q
C
1
¼
q
C
2
¼
q
C
3
¼
0,
yielding
0
¼
K
1
q
S
E
K
q
S
q
C
2
þ
K
6
ð
K
1
q
S
Þ
q
C
3
K
1
ð
þ
K
þ
K
6
q
M
þ
K
q
S
Þ
q
C
1
0
1
2
1
0
¼
K
3
q
M
E
0
K
3
q
M
q
C
1
þ
K
4
þ
K
5
K
3
q
M
ð
Þ
q
C
3
K
3
q
M
þ
K
3
þ
K
4
q
S
ð
Þ
q
C
2
ð
8
:
127
Þ
0
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
Equation (8.127) can be solved for
q
C
1
and
q
C
3
using the D-Operator method or the graph
theory method from Rubinow, giving
8
<
:
0
1
9
=
;
q
S
E
0
K
1
K
3
K
i
6
q
S
þ
K
i
3
K
1
4
K
i
6
þ
K
1
@
A
þ
K
i
6
q
M
6
K
i
M
K
K
q
C
1
¼
D
ð
8
:
128
Þ
8
<
9
=
K
K
3
q
S
þ
K
K
4
K
i
3
þ
K
1
1
1
K
6
K
s
M
þ
q
M
E
q
M
q
S
0
:
;
q
C
3
¼
D
where
K
1
K
2
S
3
K
i
6
þ
q
M
D
¼
q
0
@
1
A
<
:
=
;
K
K
3
K
i
6
K
s
M
þ
K
i
3
K
K
4
K
i
6
þ
K
1
1
1
K
6
K
i
M
þ
q
S
0
1
þ
q
M
K
i
6
þ
K
1
K
3
K
i
M
þ
K
1
4
K
i
3
þ
K
1
@
A
þ
q
6
K
s
M
2
M
K
K
0
@
1
A
þ
K
s
M
K
i
3
K
4
K
i
6
þ
K
1
1
6
K
i
M
K
K
8
<
9
=
0
@
1
A
þ
K
i
3
K
i
M
K
K
4
K
i
6
þ
K
1
1
þ
q
M
K
s
M
K
6
K
i
3
:
;
þ
K
i
M
q
2
M
