substrate, the lower the substrate concentration range in
which the enzyme is effective. As we will soon see, enzyme
activity in the cell can be modulated by regulatory molecules
that bind to the enzyme and alter the
K
m
for a particular sub
strate.
K
m
values for several enzymesubstrate combinations
are given in
Table 62
and, as you can see, can vary over
several orders of magnitude.
Enzyme Name
Substrate
K
m
(
M
)
k
cat
(sec
uni2212.bold
1
)
Acetylcholinesterase
Acetylcholine
9
uni00D7
10

5
1.4
uni00D7
10
4
Carbonic anhydrase
CO
2
1
uni00D7
10

2
1
uni00D7
10
6
Fumarase
Fumarate
5
uni00D7
10

6
8
uni00D7
10
2
Triose phosphate isomerase
Glyceraldehyde3phosphate
5
uni00D7
10

4
4.3
uni00D7
10
3
b
lactamase
Benzylpenicillin
2
uni00D7
10

5
2
uni00D7
10
3
K
m
and
k
cat
Values for Some Enzymes
Table 62
Figure 69
The Linear Relationship Between
V
max
and
Enzyme Concentration.
The linear increase in reaction veloc
ity with enzyme concentration provides the basis for determining
enzyme concentrations experimentally.
V
max
V
max
=
k
3
[E]
Enzyme concentration [E]
141
Chapter 6

Enzymes: The Catalysts of Life
Figure 610
The Lineweaver–Burk DoubleReciprocal Plot.
The reciprocal of the initial velocity, 1/
v
, is plotted as a function of
the reciprocal of the substrate concentration, 1/[S].
K
m
can be calcu
lated from the
x
intercept and
V
max
from the
y
intercept.
Slope
=
K
m
/
V
max
y
intercept
=
x
intercept
=
1/
v
1/[S]
1
K
m
V
max
V
max
v
1
K
m
1
V
max
1
1
[S]
=
+

Equation 612 on page 140 is known as the
Lineweaver–
Burk equation.
When it is plotted as 1/
v
versus 1/[S], as in
Figure 610
, the resulting
doublereciprocal plot
is linear
in the general algebraic form
y
uni003D
mx
uni002B
b
, where
m
is the
slope and
b
is the
y
intercept. Therefore, it has a slope (
m
)
of
K
m
/
V
max
, a
y
intercept (
b
) of 1/
V
max
, and an
x
intercept
(
y
uni003D
0) of

1/
K
m
. (You should be able to convince yourself
of these intercept values by setting first 1/[S] and then 1/
v
equal to zero in Equation 612 on page 140 and solving for the
other value.) Therefore, once the doublereciprocal plot has
been constructed,
V
max
can be determined directly from the
reciprocal of the
y
intercept and
K
m
from the negative recip
rocal of the
x
intercept. Furthermore, the slope can be used to
check both values.
Thus, the Lineweaver–Burk plot is useful experimentally
because it allows us to determine the parameters
V
max
and
K
m
without the complication of a hyperbolic shape. (
Key
Technique, page 142
, shows an experimental setup for
determining these kinetic parameters for hexokinase, the en
zyme catalyzing the phosphorylation of glucose on carbon
atom 6 to begin the degradation of glucose in the glycolytic
pathway.)
glucose
uni002B
ATP
++
¡
hexokinase
glucose
@
6
@
phosphate
uni002B
ADP
(613)
PROBLEM:
Hexokinase is an important enzyme in energy
metabolism because it catalyzes the first step in the exothermic
degradation of glucose. Understanding the kinetics of this reac
tion will help us to better understand its role in energy produc
tion in the cell. But how do scientists experimentally determine
the kinetic parameters of
K
m
and
V
max
for an enzyme such as
this?