6.3 Kinetics of Enzymes Catalyzing
Two-Substrate Reactions
Most enzymatic reactions involving two-substrate reac-
tions show more complex kinetics than do one-substrate
reactions. Examples are catalyzed by dehydrogenases and
aminotransferases. Hydrolytic reactions are bisubstrate re-
actions in which water is one of the substrates. The change
in water concentration is negligible and has no effect on the
rate of reaction. A two-substrate reaction can be written
as
Enzyme
Substrate A + Substrate B <
>
Product C + Product D
The enzyme-substrate interactions can proceed by either
single-displacement
or
double-displacement reactions
(commonly known as “ping-pong” reactions). A substrate
reaction proceeding by way of a single-displacement re-
action can be shown by
E + A ^ EA
or
E + B ^ EB
EA + B ^ EAB
or
EB + A ^ EAB
EAB ^ C + D
Note that the ternary complex EAB can be formed in two
different ways. If the formation of EAB can occur with
either substrate binding first, the reaction is known as
a
random
single-displacement reaction. Many reactions
catalyzed by phosphotransferases are of this type. If a par-
ticular substrate must bind first with the enzyme before
the second substrate can bind, the reaction is known as
an
ordered
single-displacement reaction. Many reactions
catalyzed by dehydrogenases are of this type. The values
for
Km
and Vmax for each substrate can be obtained from
experiments in which the concentration of one substance
is held constant at saturating levels while the concentra-
tion of the second substrate is varied. Kinetic analyses can
distinguish between these types of reactions.
In a double-displacement reaction, at first only one sub-
strate is bound; the release of one product and covalently
modified enzyme (E*) follows. E* then combines with the
second substrate to form a second product. Reactions cat-
alyzed by aminotransferases are of this type. In this mech-
anism, no ternary complex EAB is formed. The double
displacement reaction sequence is shown below:
(Substrate 1)
(Product 2)
92
6.4 Inhibition
Enzyme inhibition is one of the ways in which enzyme ac-
tivity is regulated experimentally or naturally. Most ther-
apeutic drugs function by inhibition of a specific enzyme.
Inhibitor studies have contributed much of the available
information about enzyme kinetics and mechanisms. In
the body, some of the processes controlled by enzyme
inhibition are blood coagulation (hemostasis), blood clot
dissolution (fibrinolysis), complement activation, connec-
tive tissue turnover, and inflammatory reactions.
Enzyme inhibitors are
reversible
or
irreversible.
Reversible Inhibition
In reversible inhibition, which is further subdivided into
competitive, noncompetitive, and uncompetitive types, the
activity of the enzyme is fully restored when the inhibitor
is removed from the system (by dialysis, gel filtration, or
other separation techniques) in which the enzyme func-
tions. In reversible inhibition, equilibrium exists between
the inhibitor, I, and the enzyme, E:
E + I ^ El.
The equilibrium constant for the
dissociation
of the
enzyme-inhibitor complex, known as the inhibitor con-
stant
K
\, is given by the Equation
ram
[EIJ
Thus,
K\
is a measure of the affinity of the inhibitor for
the enzyme, somewhat similar to the way in which
Km
reflects the affinity of the substrate for the enzyme.
In
competitive inhibition,
the inhibitor is a structural
analogue that competes with the substrate for binding at
the active site. Thus, two equilibria are possible:
E + S ^ E S ^ E + P
and
E + I ^ EL
A modified Michaelis-Menten equation that relates the
velocity of the reaction in the presence of inhibitor to the
concentrations of substrate and inhibitor can be derived:
Vmax [S]
V
= ------------------------
[S] +
Km
(l + g )
In this relationship,
Km
is modified by a term that includes
the inhibitor concentration, [I], and the inhibitor constant,
chapter 6
Enzymes I: General Properties, Kinetics, and Inhibition
