Biomedical Engineering Reference
In-Depth Information
To remove
q
S
o
in Eq. (8.77), we assume a constant total substrate
q
ST
¼
q
S
i
þ
q
S
o
, and with
q
S
o
¼
q
ST
q
S
i
, we have
q
S
i
¼
K
q
S
i
q
E
þ
K
1
q
ES
i
þ
B
oi
q
ST
q
Si
ð
Þ
B
io
q
S
i
1
¼
K
1
q
S
i
q
E
þ
K
1
q
ES
i
B
oi
þ
B
io
ð
Þ
q
S
i
þ
B
oi
q
ST
ð
8
:
78
Þ
q
ES
i
¼
K
1
q
S
i
q
E
K
1
þ
K
2
ð
Þ
q
ES
i
q
P
i
¼
K
q
ES
i
þ
D
oi
q
P
o
D
io
q
P
i
2
K
1
q
S
i
q
E
þ
K
1
q
ES
i
¼
V
max
q
S
i
þ
K
M
We can substitute the quasi-steady-state approximation,
Þ
q
S
i
ð
(based on Eq. (8.47)), into Eq. (8.78) and get
V
max
q
S
i
þ
K
M
q
S
i
¼
Þ
q
S
i
B
oi
þ
B
io
ð
Þ
q
S
i
þ
B
oi
q
ST
ð
0
1
ð
8
:
79
Þ
V
max
q
S
i
þ
K
M
@
A
q
S
i
þ
B
oi
q
ST
¼
Þ
þ
B
oi
þ
B
io
ð
q
E
ð
0
Þ
and
where
q
ES
i
¼
q
P
i
¼
q
S
i
ð
0
Þ
q
S
i
q
ES
i
:
þ
K
M
q
S
i
1
8.4.3 Carrier-Mediated Transport
Now consider carrier-mediated transport, where an enzyme carrier in the cell membrane
has a selective binding site for a substrate, which, when bound, transports the substrate
through the membrane to be released inside the cell. Many also refer to this process as
facilitated diffusion. Carrier-mediated transport does not use energy to transport the sub-
strate but depends on the concentration gradient. Without carrier-mediated transport, the
substrate cannot pass through the membrane.
Carrier-mediated transport differs from diffusion, since it is capacity-limited and diffu-
sion is not. That is, as the quantity of the substrate increases, the carrier-mediated transport
reaction rate increases and then saturates, where regular diffusion increases linearly with-
out bound, as shown in Figure 8.20.
Figure 8.21 illustrates carrier-mediated transport, described by
ð
8
:
80
Þ
where
S
o
and
S
i
are the substrate outside and inside the cell,
C
o
is the carrier on the outside
of the membrane, C
is the carrier on the inside of the membrane,
P
o
is the bound substrate
i
and carrier complex on the outside of the membrane, and
P
i
is the bound substrate and
