Biomedical Engineering Reference
In-Depth Information
1
V(0)
q
I
(0)
=
b
50
q
I
= 0
q
I
= 10
40
q
I
(0)
=
a
q
I
= 30
30
q
I
(0)
=
0
20
10
0
0 102030405060708090100
1
q
S
(0)
0
q
s
FIGURE 8.27
(Left) Velocity of product appearance for a substrate, enzyme, and enzyme inhibitor using
K
s
M
¼
K
i
M
¼
Eq. (8.121).
V
max
¼
50,
3, and
3
:
(Right) Lineweaver-Burk plot, where b > a.
inhibitor enzyme. As shown, increasing the quantity of the enzyme inhibitor shows a
slower synthesis of the product,
P
1
:
Keep in mind that all of the substrate will eventually
be synthesized into the
P
1
but it does so more slowly.
To obtain the Lineweaver-Burk equation for this system, we take the reciprocal of
Eq. (8.121), giving
K
s
M
1
V
¼
1
1
q
S
þ
q
I
K
i
M
1
þ
1
ð
8
:
122
Þ
V
max
and at
t
¼
0, we have
K
s
M
1
V
ð
1
V
max
1
q
S
ð
þ
q
I
ð
0
Þ
Þ
¼
1
þ
1
ð
8
:
123
Þ
0
0
Þ
K
i
M
The plot of the Lineweaver-Burk equation is shown on the right side of Figure 8.27 for
three values of the quantity of the enzyme inhibitor. One again, the relationship between
1
V
ð
1
q
s
ð
1
V
ð
axis is a constant
as the quantity of the enzyme inhibitor is increased. Additionally, the slope of the line
increases as the quantity of the enzyme inhibitor is increased, which is indicative of a slow-
ing reaction rate.
vs
:
is a straight line. Further, we note that the intercept of the
0
Þ
0
Þ
0
Þ
8.6.2 Allosteric Activators and Inhibitors
Next, consider the noncompetitive allosteric modifier that binds with an enzyme on
a regulatory site and a substrate that binds with the enzyme on the active site. The
effect of a modifier on the reaction is to either increase or decrease the activity of
the enzyme.
