Biology Reference
In-Depth Information
section. The Adair's four-site fractional saturation function in terms of
the product Adair-binding constants is:
2
3
4
1
4
K
41
½
O
2
þ
2K
42
½
O
2
þ
3K
43
½
O
2
þ
4K
44
½
O
2
4
:
¼
Y
4
(7-13)
2
3
1
þ
K
41
½
O
2
þ
K
42
½
O
2
þ
K
43
½
O
2
þ
K
44
½
O
2
Heuristical
ly
, this equation reflects the concept that the fractional
saturation Y of an entity with four binding sites must take into account
the occupation of each of the sites. We present the derivation of
Eq. (7-13) later in the chapter.
Eq. (7-11) is often written in the form:
Hb
4
þ
O
2
$
Hb
4
O
2
þ
$
ð
Þ
2
Hb
4
O
2
O
2
Hb
4
O
2
(7-14)
Hb
4
ð
O
2
Þ
2
þ
O
2
$
Hb
4
ð
O
2
Þ
3
Hb
4
ð
O
2
Þ
3
þ
O
2
$
Hb
4
ð
O
2
Þ
4
:
The equilibrium constants, called stepwise Adair-binding constants (lower-
case k's), are:
½
Hb
4
ð
O
2
Þ
i
k
4i
¼
i
¼
1
;
2
;
3
;
4
:
(7-15)
½
Hb
4
ð
O
2
Þ
i
1
½
O
2
The four-site fractional saturation function in terms of the stepwise
Adair-binding constants is:
2
3
4
½
þ
½
þ
½
þ
½
1
4
k
41
O
2
2k
41
k
42
O
2
3k
41
k
42
k
43
O
2
4k
41
k
42
k
43
k
44
O
2
4
:
Y
4
¼
2
3
1
þ
k
41
½
O
2
þ
k
41
k
42
½
O
2
þ
k
41
k
42
k
43
½
O
2
þ
k
41
k
42
k
43
k
44
½
O
2
(7-16)
The stepwise binding constants are thus related to the product
Adair-binding constants as:
K
4i
¼
k
41
k
42
...
k
4i
;
i
¼
1
;
2
;
3
;
4
:
(7-17)
For example, if i
¼
3, then K
43
¼
k
41
k
42
k
43
;ifi
¼
2, then K
42
¼
k
41
k
42
, and
so on.
Adair-binding equations continue in common use today. We emphasize
that the only assumption needed for their derivation is that tetrameric
human hemoglobin contains four oxygen-binding sites.
E. Coupling Between Subunit Assembly and Oxygen Binding
In the 1970s, Gary K. Ackers and coworkers first theoretically predicted
and then experimentally observed another interesting property of O
2
binding by hemoglobin: That it is dependent upon the concentration of
