enzyme reactions that proceed in two steps, the parameter K M is given
by the ratio of the rates (eqn 7.44).
(7.50)
When the enzyme operates under the condition that k f 2 << k 1b , then the
equation reduces to:
(7.51)
In this case, K M is a measure of the affinity of the enzyme for its substrate.
However, for many enzymes this limit of the rates does not hold and the
interpretation of K M is not straightforward, especially when the enzyme
undergoes a multistep process.
To describe the enzyme activity, a more general rate constant, k cat , is
used to describe the limiting rate under saturating conditions. When the
mechanism is complex, this parameter represents a function of several
rate constants. However, for a simple two-step reaction, the new parameter can be equated to the forward rate of the second step (k cat = k 2 ).
In this case the Michaelis–Menten equation (eqn 7.45) can be written in
terms of k cat :
(7.52)
The parameter k cat is a first-order rate constant and is called the turno9er
number as it is equivalent to the number of substrate molecules that are
converted to product within a certain time when the enzyme is saturated
with substrate. Together with the K M value, the k cat provides a measure
of the kinetic efficiency of the enzyme (Table 7.3). When the substrate
concentration is small compared to K M , this relationship can be simplified:
(7.53)
The initial velocity is now dependent upon the concentrations of the two
reactants: the total enzyme and substrate. This relationship is a secondorder rate equation with the ratio k cat /K M being a second-order rate
constant. One way to compare the efficiencies of different enzymes or
the turnover of different substrates by one enzyme is to make use of the
ratio k cat /K M , termed the specificity constant. The upper limit of this ratio
is the rate at which the enzyme and substrate can diffuse together in an
V
k
K
k
0
[ ]
=
+
≈
cat total
M
cat total
[E ][S]
S
[E ][ [S]
E ][S]
M
cat
M
total
K
k
K
[
=
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
V
k
K
S
k
f
0
2 [
]
[ ]
[
=
+
=
E ][S
E ][
total
M
cat
total S S
S
M
]
[ ]
K +
K
k
k
f
f
M =
2
1
K
k
k
k
f
b
f
M =
+
2
1
1
156
PART I
THERMODYNAMICS AND KINETICS
9781405124362_4_007.qxd 4/29/08 10:41 Page 156
by the ratio of the rates (eqn 7.44).
(7.50)
When the enzyme operates under the condition that k f 2 << k 1b , then the
equation reduces to:
(7.51)
In this case, K M is a measure of the affinity of the enzyme for its substrate.
However, for many enzymes this limit of the rates does not hold and the
interpretation of K M is not straightforward, especially when the enzyme
undergoes a multistep process.
To describe the enzyme activity, a more general rate constant, k cat , is
used to describe the limiting rate under saturating conditions. When the
mechanism is complex, this parameter represents a function of several
rate constants. However, for a simple two-step reaction, the new parameter can be equated to the forward rate of the second step (k cat = k 2 ).
In this case the Michaelis–Menten equation (eqn 7.45) can be written in
terms of k cat :
(7.52)
The parameter k cat is a first-order rate constant and is called the turno9er
number as it is equivalent to the number of substrate molecules that are
converted to product within a certain time when the enzyme is saturated
with substrate. Together with the K M value, the k cat provides a measure
of the kinetic efficiency of the enzyme (Table 7.3). When the substrate
concentration is small compared to K M , this relationship can be simplified:
(7.53)
The initial velocity is now dependent upon the concentrations of the two
reactants: the total enzyme and substrate. This relationship is a secondorder rate equation with the ratio k cat /K M being a second-order rate
constant. One way to compare the efficiencies of different enzymes or
the turnover of different substrates by one enzyme is to make use of the
ratio k cat /K M , termed the specificity constant. The upper limit of this ratio
is the rate at which the enzyme and substrate can diffuse together in an
V
k
K
k
0
[ ]
=
+
≈
cat total
M
cat total
[E ][S]
S
[E ][ [S]
E ][S]
M
cat
M
total
K
k
K
[
=
⎛
⎝
⎜ ⎜
⎞
⎠
⎟ ⎟
V
k
K
S
k
f
0
2 [
]
[ ]
[
=
+
=
E ][S
E ][
total
M
cat
total S S
S
M
]
[ ]
K +
K
k
k
f
f
M =
2
1
K
k
k
k
f
b
f
M =
+
2
1
1
156
PART I
THERMODYNAMICS AND KINETICS
9781405124362_4_007.qxd 4/29/08 10:41 Page 156