Introduction to Enzyme and Coenzyme Chemistry - E-Library Home

Methods for Studying Enzymatic Reactions 55
The Michaelis–Menten model for enzyme kinetics assumes that the
following steps are involved in the enzymatic reaction: reversible formation of
the enzyme–substrate (ES) complex, followed by conversion to product:
Michaelis–Menten Model
k 1 k 2
E + S ES E + P
k −1
There are several assumptions implicit in this model: that the enzyme binds only
a single substrate; that there is only one kinetically signiWcant step between the
ES complex and product formation; and that product formation is irreversible.
Despite the fact that these assumptions are not strictly correct for most
enzymes, this proves to be a useful model for a very wide range of enzymes.
Derivation of a rate equation uses a kinetic criterion known as the steady state
approximation: that the enzymatic reaction will quickly adopt a situation of
steady state in which the concentration of the intermediate species, ES, remains
constant. Under these conditions the rate of formation of ES is equal to the rate
of consumption of ES. The other criterion that is used is that the total amount
of enzyme in the system E 0 , made up free enzyme, E, and enzyme–substrate
complex, ES, is constant. The derivation is as follows:
Derivation of Michaelis–Menten equation
Steady state approximation: Rate of formation of ES = Rate of breakdown of ES
k1 [E] [S] = k 2 [ES] + k −1 [ES]
Total amount of enzyme [E] 0 = [E] + [ES]
k 1 [E] 0 [S] − k 1 [ES] [S] = k 2 [ES] + k −1 [ES]
k 1 [E] 0 [S]
[ES] =
k 1 [S] + k 2 + k −1
k
= k cat [E] 0 [S]
2 [E] 0 [S]
Rate of production of P = k 2 [ES] =
k −1 + k 2
K M + [S]
+ [S]
k 1
v
v max
v max [S]
Observed rate v =
K M + [S]
v max /2
where v max = k cat [E 0 ]
K [S]
M