Chemistry Reference
In-Depth Information
in equation (2).
K
2
−→
ES
E
+
P
(2)
K
1
−
←−
K
−
1
K
2
−→
E
+
S
ES
E
+
P
(3)
When reactions (1) and (2) are combined into reaction (3), a model for enzyme catalysis is
obtained. First, the enzyme (
E
) and substrate (
S
) come together to form an ES complex; the
reaction occurs by which the substrate is converted into the product of the reaction and then
the ES complex is broken apart, yielding enzyme (
E
) plus product (
P
).
The Michaelis-Menten model assumes that only a negligible amount of ES complex
reverts to reactants (i.e.
k
1
k
−
1
in equation (1)). The rate of formation of product (shown
in equation (4)) can be determined from equation (2) in the mechanism written above:
Rate of formation of product is
K
2
[
S
]
(4)
and the rate of formation of the intermediate ES (equation (5)) can be determined from
equations (1) and (2) in the mechanism written above:
Rate of formation of
ES
=
K
1
[
E
][
S
]
−
(
K
2
+
K
1
)[
ES
]
(5)
Using the steady-state approximation, that is, the assumption that the concentration of
intermediates (ES) stays constant while the concentrations of reactants and products change,
the equation for the rate of formation of the product can be calculated as follows:
δ
[
P
]
δ
K
2
[
E
0
][
S
]
[
S
]
=
(6)
t
+
K
m
Here [
E
0
] is the initial concentration of free enzyme, [
S
] is the substrate concentration
and
K
m
is a constant specific to a given enzyme known as the Michaelis-Menten constant.
The value of
K
m
relates to the rate constants shown in equations (1) and (2), as given by the
following equation:
K
−
1
+
K
2
K
m
=
(7)
K
1
The Michaelis-Menten constant (
K
m
) is very important, because it can be determined
experimentally and describes the catalytic power of an enzyme.
K
m
can also be used to
predict the rate of an enzyme-catalyzed reaction when the starting conditions (enzyme and
substrate concentration) are known.
The major contribution of Henri
14
was to think of enzyme reactions in two stages. In the
first, the substrate binds reversibly to the enzyme, forming the ES complex. In the second
reaction, the enzyme catalyzes the chemical step and releases the product.
Enzymes can catalyze up to several million reactions per second. Enzyme rates depend
on solution conditions and substrate concentration. Conditions that denature the protein
reduce or eliminate enzyme activity. Such conditions are high temperature, extreme pH
or high salt concentrations. Raising substrate concentration tends to increase activity. To
