section 7.2
Allosteric Enzyme Regulation
117
FIGURE 7-10
Hill plots for myoglobin and hemoglobin. A slope of 1.0 for myoglobin is
consistent with noncooperative oxygen binding, whereas a slope of
2.8
for
hemoglobin is indicative of cooperative oxygen binding.
of 1 for the Hill coefficient is indicative of noncooperativity;
as we will see with hemoglobin, values greater than
1
indi-
cate positive cooperativity, and values less than
1
indicate
negative cooperativity.
A molecule of hemoglobin (Hb) can bind four molecules
of oxygen, and therefore four equilibrium expressions can
be written to describe the dissociations of Hb02, Hb(02)2,
Hb(
0
2
)
3
, and Hb(02)4. For simplicity, we consider an equi-
librium in which № (
0 2 ) 4
dissociates into deoxyhemoglobin
and four molecules of oxygen:
Hb(0
2 ) 4
— Hb + 402
(7.9)
The equilibrium constant for Reaction (7.9) is:
K
_ [Hb] [0
2 ] 4
[H b(o2)4]
(7.10)
Based upon considerations similar to those for myoglobin
dissociation, the value for
Y
is
(■
Po
2 ) 4
(Po2f
+ (P
5 0 ) 4
(7.11)
A plot of
Y
versus
Pq2
yields a sigmoidal curve, indicat-
ing cooperative binding of oxygen to hemoglobin. A general
expression for the dissociation of oxyhemoglobin to deoxy-
hemoglobin and oxygen may be written as
Hb(02)„ ^ Hb + n 0
2
(7.12)
where
n
is the number of molecules of oxygen. The equilib-
rium constant for reaction (7.12) is
and
[Hb] [P2]
[Hb(02)„]
(PoJ1
(P02r +
(
P50)n
(7.14)
Rearrangement of Equation (7.14) yields
The Hill equation is obtained by taking the logarithm of both
sides:
=
n
log
Po2
- n
log
P5(j
A plot of log(T/l —
Y)
versus log
Pq2
yields a straight
line with a slope of
n,
the Hill coefficient. For hemoglobin,
n
= 2.8 (Figure 7-10), which signifies that the binding of
oxygen to hemoglobin exhibits positive cooperativity.
From a physiological point of view, the cooperative oxygen
binding characteristics of hemoglobin are eminently suited
for the transport of oxygen from the lungs to the tissues.
In the alveolar spaces of the lungs, the partial pressure of
oxygen is about 100 Torr, and about 97% of the hemoglobin is
combined with oxygen (i.e., 97% saturation with 0 2). As the
oxygenated blood passes through the tissue capillaries, where
the partial pressure of oxygen often falls below 40 Torr (in
actively exercising muscle, the
Po2
is about 20 Torr), about
30% of the oxygen is unloaded from oxyhemoglobin to tis-
sue cells. This process is cooperative, so that as 0
2
is re-
leased from oxygen-saturated hemoglobin because of a drop
in
Po2,
the loss of a single
0
2
molecule causes rapid release
of the remaining ones. Similarly in the lungs, the affinity of
hemoglobin for binding the first
0
2
molecule is low; how-
ever, once this molecule is bound, the affinity increases. Myo-
globin, in conformity with its storage function, has higher
affinity for oxygen than does hemoglobin at any partial pres-
sure of oxygen (Figure 7-9).
X-ray studies have shown that oxyhemoglobin (R form)
and
deoxyhemoglobin
(T
form)
have
different three-
dimensional conformations. However, no changes in the
tertiary structure of the individual subunits have been ob-
served. The molecular mechanisms of cooperative binding of
oxygen are known, and the details of this process along with
other ligand interactions with hemoglobin are discussed in
Chapter 28.
Theoretical Models for Allosteric Effect
Two theoretical models for allosteric effects have been
proposed to explain the mechanism for ligand-protein co-
operative interactions: the concerted (or symmetry) model of
Monod, Wyman, and Changeux and the sequentially induced-
fit model of Koshland. The nomenclature associated with
allosterism and cooperativity originated from the concerted
model. Both models assume that
1. Each subunit of an oligomeric protein exists in two
forms, T and R, which bind the ligand with low and high
affinity, respectively; and
2. The T ^ R transformations involve noncovalent bonds
and result in changes in the quaternary structure of the
enzyme.
