Biology Reference
In-Depth Information
Eq. (7-6). Curve T follows the classic sigmoid shape of a positive
cooperative system, as in human hemoglobin. In this context, the curve
labeled D corresponds to the noncooperative dimeric species of
hemoglobin, and curve T corresponds to the cooperative tetrameric
species. In Figure 7-4, the solid lines are calculated from a mathematical
model that Ackers and his collaborators developed based upon the
observed oxygenation linked dimer-tetramer association of hemoglobin
(next paragraph). The data points between the T and D curves are the
actual experimental observations of the fractional saturation with O
2
determined at different hemoglobin concentrations. The lower the
concentration, the closer the data points approach the dimer-binding
curve (D). The higher the concentration, the closer the data points
approach the tetramer-binding curve (T).
We shall now present a conceptual description of the Ackers model.
Hemoglobin tetramers are formed from two identical
α
2
β
2
2
αβ
ab
dimers. These
dimers undergo a reversible association equilibrium, 2
ab $ a
2
b
2
.
+O
2
The
association reaction has such a large association constant
that it is, in effect, complete and virtually irreversible. In addition, the
major structural transformation associated with O
2
binding occurs at the
interface between the two
a þ b $ ab
+2O
2
α
2
β
2
(O
2
)
+O
2
dimers. The linkage between the dimer to
tetramer subunit assembly and the O
2
binding properties of dimeric and
tetrameric hemoglobin are shown in Figure 7-5. Each vertical arrow
depicts an oxygenation step, and each horizontal arrow depicts a
hemoglobin dimer-tetramer association step. For example, the
horizontal arrow at the top represents the reaction that forms an
unoxygenated
ab
α
2
β
2
(O
2
)
2
2
αβ
O
2
+O
2
+2O
2
α
2
β
2
(O
2
)
3
+O
2
ab
dimers. The vertical arrow in the lower right depicts the reaction that
combines a triply-oxygenated hemoglobin tetramer (
a
2
b
2
hemoglobin tetramer from two unoxygenated
2
αβ
(O
2
)
2
α
2
β
2
(O
2
)
4
a
2
b
2
(O
2
)
3
) with O
2
FIGURE 7-5.
The oxygenation linked 2ab $ a
2
b
2
subunit
assembly scheme.
(Reprinted with permission from Mills, F.C.,
Johnson, M.L., and Ackers, G.K. [1976].
Oxygenation-linked subunit interactions in
human hemoglobin: Experimental studies on
the concentration dependence of oxygenation
curves. Biochemistry, 15, 5350-5362.
#
1976
The American Chemical Society.)
to form a quad-oxygenated hemoglobin tetramer (
a
2
b
2
(O
2
)
4
).
Ackers and coworkers derived a mathematical model, Eqs. (7-18) and
(7-19) below, for the fractional saturation of hemoglobin undergoing the
oxygenation linked 2
ab $ a
2
b
2
subunit assembly scheme shown in
Figure 7-5. These equations represent a weighted average of a four-
binding-site Adair equation [Eq. (7-16)], describing the oxygen-binding
properties of the tetrameric hemoglobin (
a
2
b
2
), and an analogous
two-binding-site Adair equation describing the oxygen-binding
properties of the dimeric hemoglobin (
). The relative weights for these
two Adair-binding equations are determined by the hemoglobin dimer
to tetramer association reactions and are themselves a function of
both the O
2
and hemoglobin concentrations (see Figure 7-6).
ab
The model yields the following result for the fractional saturation:
q
ðX
2
Þ
2
X
2
0
þ X
4
0
4
0
K
2
X
4
½
þ
Hg
X
2
=ð
4
X
4
Þ
Y
¼
q
ðX
2
Þ
;
(7-18)
2
4
0
K
2
X
4
½
X
2
þ
þ
Hg
