Biomedical Engineering Reference
In-Depth Information
2.3. Forward Reaction, Conservation of Total Number of Molecules
Now consider the reaction
k
A
¶l
B
,
[12]
where
n
0
+
n
1
=
n
= const. Since the total number
n
is conserved, the system is
defined by only one variable. We will use
n
2
as the single variable to define this
system. For the reaction above:
p nt knnpnt knn pn t
.
(,) ( )(,) ( )( ,)
=
+
+
[13]
2
2
2
2
2
This leads
1
to:
¬
s
F
s
F
-
F zt knF kz
(,)
=
+
+
kn zF kzz F
( )
+
+
-
-
2
2
2
2
2
--
s
z
s
z
®
2
2
s
F
=
kn z
( )
s
F kz
( )
z
.
[14]
2
2
2
z
1
Based on these elementary reactions, larger chemical networks can be built up.
The results above are summarized in Table 1.
Table 1
Reaction type
F
=
s
s
F
I
A
¶l
k
A
+
B
kz
(
z
)
12
z
1
H
s
F
B
¶l
0
s
(
z
)
II
1
z
1
s
s
F
A
¶l
k
B
III
kn z
(
)
F
kz
(
z
)
2
2
2
z
2
(
n
1
+
n
2
=
n
= const., in terms of
n
2
)
¶¶l
k¶¶
k
1
s
F
s
F
A
B
kz
(
z
)
+
k z
(
z
)
IV
12
1
11
2
s
z
s
z
k
1
2
1
