Physical Chemistry Third Edition

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 thesubstrate, 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 concentra-

tion of the enzyme, given by

[E]total[E]+[ER] (13.1-42)

The total concentration of reactant is generally much larger than the enzyme concen-

tration 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 theMichaelis–Menten equation:

forward rate

d[P]

dt



k 2 [E]total[R]

Km+[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).