13.1 Catalysis
577
The Michaelis–Menten Mechanism
Michaelis and Menten proposed a mechanism for enzyme catalysis. 11 For the case of
a single reactant R and a single product P, 12 this mechanism is
(1) E + R ER
(13.1-40a)
(2) ER − → E + P
(13.1-40b)
where E stands for the enzyme and ER stands for the enzyme-reactant complex. Many
biochemistry textbooks refer to the reactant as the substrate, but we will continue to
call it the “reactant.” Since we have not included a reverse reaction for the second step,
this mechanism will give a rate law for the forward reaction.
The application of the steady-state approximation to obtain the rate law for the
Michaelis–Menten mechanism was first carried out by Briggs and Haldane. 13 The two
differential rate equations are
d[ER]
dt
k 1 [E][R] − k
1 [ER] − k 2 [ER]
(13.1-41a)
d[P]
dt
k 2 [ER]
(13.1-41b)
The steady-state approximation is invoked by setting the right-hand side of
Eq. (13.1-41a) equal to zero. An unknown but significant fraction of the enzyme is
in the combined form ER, so that [E] will differ significantly from the total concentration of the enzyme, given by
[E] total [E] + [ER]
(13.1-42)
The total concentration of reactant is generally much larger than the enzyme concentration and is thus much larger than [ER], so that to a good approximation we can write
[R] [R] total − [ER] ≈ [R] total
(13.1-43)
When we substitute [E] total − [ER] into the right-hand side of Eq. (13.1-41a) in place
of [E], set the result equal to zero, and solve for [ER], we obtain
[ER]
k 1 [E] total [R]
k
1 + k 2 + k 1 [R]
(13.1-44)
Exercise 13.9
Verify Eq. (13.1-44).
The rate law for the forward reaction is obtained by substituting Eq. (13.1-44) into
Eq. (13.1-41b). This rate law is called the Michaelis–Menten equation:
forward rate
d[P]
dt
k 2 [E] total [R]
K m + [R]
(Michaelis−Menten
equation)
(13.1-45)
11 L. Michaelis and M. L. Menten, Biochem. J., 49, 333 (1913).
12 Many biochemistry textbooks denote the reactant by S (for “substrate”) and its concentration by [S]
instead of [R]. No good reason is given for calling a reactant a “substrate.”
13 G. E. Briggs and J. B. S. Haldane, Biochem. J., 19, 338 (1925).
577
The Michaelis–Menten Mechanism
Michaelis and Menten proposed a mechanism for enzyme catalysis. 11 For the case of
a single reactant R and a single product P, 12 this mechanism is
(1) E + R ER
(13.1-40a)
(2) ER − → E + P
(13.1-40b)
where E stands for the enzyme and ER stands for the enzyme-reactant complex. Many
biochemistry textbooks refer to the reactant as the substrate, but we will continue to
call it the “reactant.” Since we have not included a reverse reaction for the second step,
this mechanism will give a rate law for the forward reaction.
The application of the steady-state approximation to obtain the rate law for the
Michaelis–Menten mechanism was first carried out by Briggs and Haldane. 13 The two
differential rate equations are
d[ER]
dt
k 1 [E][R] − k
1 [ER] − k 2 [ER]
(13.1-41a)
d[P]
dt
k 2 [ER]
(13.1-41b)
The steady-state approximation is invoked by setting the right-hand side of
Eq. (13.1-41a) equal to zero. An unknown but significant fraction of the enzyme is
in the combined form ER, so that [E] will differ significantly from the total concentration of the enzyme, given by
[E] total [E] + [ER]
(13.1-42)
The total concentration of reactant is generally much larger than the enzyme concentration and is thus much larger than [ER], so that to a good approximation we can write
[R] [R] total − [ER] ≈ [R] total
(13.1-43)
When we substitute [E] total − [ER] into the right-hand side of Eq. (13.1-41a) in place
of [E], set the result equal to zero, and solve for [ER], we obtain
[ER]
k 1 [E] total [R]
k
1 + k 2 + k 1 [R]
(13.1-44)
Exercise 13.9
Verify Eq. (13.1-44).
The rate law for the forward reaction is obtained by substituting Eq. (13.1-44) into
Eq. (13.1-41b). This rate law is called the Michaelis–Menten equation:
forward rate
d[P]
dt
k 2 [E] total [R]
K m + [R]
(Michaelis−Menten
equation)
(13.1-45)
11 L. Michaelis and M. L. Menten, Biochem. J., 49, 333 (1913).
12 Many biochemistry textbooks denote the reactant by S (for “substrate”) and its concentration by [S]
instead of [R]. No good reason is given for calling a reactant a “substrate.”
13 G. E. Briggs and J. B. S. Haldane, Biochem. J., 19, 338 (1925).