90
chapter 6
Enzymes I: General Properties, Kinetics, and Inhibition
so that
k
- 1
Km = - ± = Ks.
k\
8
. When
k
2
k—
i, the rate of dissociation of ES to E
and S is low, so that products are usually formed. For
practical purposes, the reaction sequence can be
thought of as consisting of two irreversible reactions:
E + S ^ E S ^ - E + P
The overall reaction rate is always determined by
[ES]. At low values of [S], ES is formed by a
second-order reaction whose rate is proportional to
[E][S]. At high values of [S], [ES] is constant and
the rate is determined by the first-order breakdown
of ES to product.
9. When [S]
Km,
the characteristic property of the
turnover number
for an enzyme can be invoked.
This number provides information on how many
times the enzyme performs its catalytic function per
unit time, or how many times it forms the ES
complex and is regenerated (turned over) by yielding
product. The turnover number can be determined
from ymax and [ET], We know that
d(P)
- j 1 = Vmm =
k
2
[ES] = k
2
[ET]
at
under saturation conditions. Therefore, if [ET] is
increased n-fold while [S] > [ET] is maintained,
then Vmax will also increase n-fold. The rate is
proportional to (or first order with respect to) [ET].
The kinetic constant k2, denoted as
kCM
under
saturation conditions, provides the value for the
turnover number. For example, if a reaction mixture
contains an enzyme at a concentration of x molar,
and the product is formed at a rate such that its
concentration increases by
y
molar per second when
the enzyme is saturated,
kCdi
= —
per second.
x
This means that
y /x
substrate molecules are
converted to product molecules every second.
Correspondingly, the time required for a single
conversion is x
/y
seconds. Turnover numbers for
most enzymes usually range from
1
to
1 0 4
per
second. A few enzymes have turnover numbers
above 10
5
(Table 6-1). The ability of a cell to
produce a given amount of product by an enzymatic
reaction during its life span is proportional to the
turnover number and the number of molecules of
that enzyme in the cell. Because turnover numbers
T A B L E 6-1
Turnover Numbers of Some Enzymes
Enzyme
Turnover Number
(per second)
Catalase
5xl0
6
Carbonic anhydrase
6
x l
0 5
Acetylcholinesterase
2.5 xlO
5
a-Amylase
1.9 xlO
4
Lactate dehydrogenase
lxlO
3
/3-Galactosidase
2 xlO
2
Chymotrypsin
1 0 2
Phosphoglucomutase
2 1
Tryptophan synthase
2
Lysozyme
0.5
can be measured only for pure enzymes, the activity
of an enzyme is expressed as specific activity,
defined as micromoles (/xmol) of substrate converted
to product per minute per milligram (mg) of enzyme
protein. The International Union of Biochemistry
recommends use of the unit known as
katal
(kat);
one katal is the amount of enzyme that converts one
mole of substrate to product per second. In clinical
disorders, the activity of a variety of enzymes is
measured in biological fluids. For this purpose, the
activity is usually defined as that quantity of enzyme
which catalyzes the conversion of
1
/./mol of
substrate to product per minute under a defined set
of optimal conditions. This unit, referred to as
the
International Unit
(U), is expressed in terms
of U/mL of biological specimen (e.g., serum),
orU/L.
10. When [S] <
3
C
Km,
the rate of product formation
increases linearly with increase of [S]. In other
words, the reaction is first order with respect to [S].
The rate is also proportional to [ET] (since doubling
[Ej] should double [ES]); thus, the reaction velocity
at low values of [S] becomes
v =
k \
E][S].
It can also be shown that
k' = ^ ,
Km
a fact that must be included in a description of any
model of enzyme activity.
In summary, the rate equation for an enzyme
reaction must satisfy a second-order dependence on
[S][Et] when [S] is small as well as a first-order
