Biology Reference
In-Depth Information
Adair's four-site fractional saturation model from Eq. (7-13).
The rationalization of Eq. (7-20) is presented in Section V.
Observe that the mean number of bound O
2
molecules N is the
fractional saturation, Y, times the number of binding sites (i.e., four for
hemoglobin tetramers and two for hemoglobin dimers). Combining this
observation with Eq. (7-20) and a mathematical statement of the total
concentrations of all the species present in solution (i.e., the binding
polynomial
), an equation for the fractional saturation of O
2
is easily
derived. In this example, the fractional saturation function for
X
a
2
b
2
tetramers [e.g., the T curve in Figure 7-5 and Eqs. (7-13) and (7-16)] is:
N
4
¼
1
4
½
O
2
@
ln
X
1
4
½
O
2
@ X
4
4
Y
4
¼
O
2
¼
O
2
:
(7-21)
@½
X
4
@½
2
3
4
Using the expression
X
4
¼
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
from Eq. (7-19)] and calculating the appropriate derivatives, Eq. (7-21)
now yields Adair's four-site fractional saturation function:
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
Y
4
¼
4
:
(7-22)
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
The analogous fractional saturation for
ab
dimers (e.g., the D curve in
Figure 7-4) is:
N
2
¼
1
2
½
O
2
@
ln
X
1
2
½
O
2
@X
2
2
Y
2
¼
O
2
¼
(7-23)
@½
X
2
@½
O
2
2
1
2
K
21
½
O
2
þ
2K
22
½
O
2
Y
2
¼
2
:
(7-24)
1
þ
K
21
½
O
2
þ
K
22
½
O
2
Equation (7-24) is analogous to the form of Eq. (7-22), except that it
applies to dimeric hemoglobin with two binding sites instead of
tetrameric hemoglobin with four binding sites.
E
XERCISE
7-5
Use the expressions for
X
4
and
X
2
given by Eq. (7-19):
2
3
4
X
4
¼
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
2
X
2
¼
1
þ
K
21
½
O
2
þ
K
22
½
O
2
to:
(a) Supply the calculations deriving Eq. (7-22) from Eq. (7-21); and
(b) Supply the calculations deriving Eq. (7-24) from Eq. (7-23).
