8 8
FIG U R E 6-3
pH dependence of the rates of enzyme-catalyzed reactions, (a) Optimal
activity at alkaline pH. (b) Optimal activity of acidic pH.
Effect o f Concentration o f Enzyme and Substrate
The reaction rate is directly proportional to the con-
centration of the enzyme if an excess of free substrate
molecules is present. Thus, enzyme-substrate interactions
obey the mass-action law. For a given enzyme concen-
tration, the reaction velocity increases initially with in-
creasing substrate concentration. Eventually, a maximum
is reached, and further addition of substrate has no effect
on reaction velocity (v) (Figure 6-4). The shape of a plot
of v versus [S] is a rectangular hyperbola and is character-
istic of all nonallosteric enzymes (Chapter 7). At low sub-
strate concentrations, the reaction rate is proportional to
substrate concentration, with the reaction following first-
order kinetics in terms of substrate concentration.
Michaelis-Menten Treatment o f the Kinetic
Properties o f an Enzyme
A model for enzyme kinetics that has found wide appli-
cability was proposed by Michaelis and Menten in 1913
and later modified by Briggs and Haldane. The Michaelis-
Menten equation relates the initial rate of an enzyme-
catalyzed reaction to the substrate concentration and to
a ratio of rate constants. This equation is a
rate equation,
chapter 6
Enzymes I: General Properties, Kinetics, and Inhibition
FIG U R E 6-4
Plot of substrate concentration versus initial velocity of an enzyme-
catalyzed reaction. Segment A: At low substrate concentration, the
reaction follows first-order kinetics with respect to substrate concentration;
v =
k[S], where
is a reaction rate constant. Segment B: At high
substrate concentration, maximum velocity (Vmax) is attained (saturation
kinetics), and any further increase in substrate concentration does not
affect the reaction rate; the reaction is then zero-order with respect to
substrate but first-order with respect to enzyme.
K m
is the value of [S]
corresponding to a velocity of ^
VmM .
derived for a single substrate-enzyme-catalyzed reaction.
In the reaction
E + S <=* E S ^ E + P
an enzyme E combines with substrate S to form an ES
complex with a rate constant
The ES complex formed
can dissociate back to E and S with a rate constant k_i,
or it can give rise to a product P and regenerated enzyme
with a rate constant
In the latter process, the formation
of product is essentially irreversible; the reverse reaction
(E + P
ES) does not occur to any appreciable extent.
- 2
is much less than
which corresponds to a
large, negative AG in going from ES to E + P.
In the Michaelis-Menten expression, [ET] represents
the total concentration (in moles per liter) of enzyme, equal
to [E] + [ES]. Therefore, the concentration of free enzyme
[E] is equal to [ET] —
[ES], The following assumptions
are made:
1. In the reaction mixture, [S] is greater than [E],
However, [S] is
so large that all enzyme
molecules are in the ES form, but [S] must
be sufficiently large that [S] does not rapidly become
so small that [S] < [E]. Excess concentration of
substrate is the most common condition in enzymatic
studies in which the catalyst is present at very low
concentration. Under these conditions, [ES] rapidly
becomes constant, so that the rate of formation of ES
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