Biology Reference
In-Depth Information
E
XERCISE
7-4
Derive the limit in Eq. (7-10) from the Hill equation (7-9) by verifying the
following steps:
(a) Show that for n
>
1,
n
1
dY
nk
½
O
2
O
2
¼
2
:
d
½
n
ð
1
þ
k
½
O
2
Þ
(b) Use part (a) to show that for n
>
1
dY
n
1
O
2
¼
½
¼
:
lim
lim
0
nk
O
2
0
d
½
½
O
2
!
0
½
O
2
!
D. The Adair Equations
Shortly after World War I, osmotic pressure measurements by G. S.
Adair and sedimentation equilibrium measurements by T. Svedberg
demonstrated that human hemoglobin is a distinct molecule with a
molecular weight of approximately 67,000 daltons, and not simply a
mixture of aggregates. It was subsequently established that hemoglobin
contains four polypeptide chains and four oxygen-binding sites,
and that hemoglobin binds O
2
in a cooperative fashion, as
described above. Thus, it became evident that Hill's equation, with no
intermediates, does not explain the experimental data. Consequently,
Adair formulated an equation for the fractional saturation of O
2
assuming that hemoglobin contained four oxygen-binding sites while
allowing for all of the intermediate oxygenation stages. Adair's reaction
scheme with intermediates is as follows:
þ
$
Hb
4
O
2
Hb
4
O
2
Hb
4
þ
2O
2
$
Hb
4
ð
O
2
Þ
2
(7-11)
Hb
4
þ
3O
2
$
Hb
4
ð
O
2
Þ
3
Hb
4
þ
4O
2
$
Hb
4
ð
O
2
Þ
4
:
The fractional saturation equation has four equilibrium-binding
constants, one for each reaction defined in Eq. (7-11). Because of the
effect of cooperativity, the values of these binding constants are
different. According to the law of mass action, these equilibrium
constants are defined as:
K
4i
¼
½
Hb
4
ð
O
2
Þ
i
i
¼
1
;
2
;
3
;
4
;
(7-12)
i
½
Hb
4
½
O
2
and are commonly referred to as product Adair-binding constants.
The subscript 4 refers to tetrameric hemoglobin, discussed in the next
