Biomedical Engineering Reference
In-Depth Information
8.2.2 Estimation of the Michaelis-Menten Parameters
The reaction rate given by Eq. (8.47) contains two parameters,
V
max
and
K
M
, and is
given by
V
max
q
S
q
S
þ
K
M
V
max
1
V
¼
Þ
¼
ð
8
:
48
Þ
ð
þ
K
M
q
S
One can estimate
V
max
and
K
M
by first taking the reciprocal of Eq. (8.48), giving
¼
K
M
V
þ
1
V
1
q
S
1
ð
8
:
49
Þ
V
max
max
which is called the Lineweaver-Burk equation. By plotting
1
V
1
q
S
against
, a straight line results
1
as shown in Figure 8.9, with the ordinate-intercept as
Since the
substrate changes as a function of time, the Lineweaver-Burk equation is usually carried
out with the initial value of substrate,
V
max
and the slope as
K
M
:
q
S
ð
0
Þ
—that is,
þ
1
V
ð
1
q
S
ð
1
V
max
Þ
¼
K
M
ð
8
:
50
Þ
0
V
max
0
Þ
The method to generate data for the Lineweaver-Burk equation is to perform a series of
experiments that increase the quantity of substrate, while keeping the amount of enzyme
constant. Recall at
V
¼
V
max
2
While estimation of the
parameters from the Lineweaver-Burk plot looks attractive, any measurement error is
amplified by the transformation, thus giving poor estimates of the parameters.
,
q
S
¼
K
M
:
If
q
S
K
M
, then
V
¼
V
max
:
1
V(0)
K
M
V
max
1
V
max
1
K
M
0
1
q
S
(0)
-
FIGURE 8.9
A Lineweaver-Burk plot.
