Biology Reference
In-Depth Information
In order to understand the mechanistic relationships involved in the
hemoglobin subunit coupling, it is essential to understand the exact
meaning of the average macroscopic Adair-binding constant for the first
O
2
being bound to either of the oxygen-binding sites. It is not the binding
constant to either the
a
b
subunit. To understand this last
statement, consider a dimeric hemoglobin that contains two nonidentical,
distinguishable oxygen-binding sites, such as the
subunit or the
a
subunit and the
b
subunit. In solution, four possible oxygenation states exist. The states
containing none and two O
2
molecules are the same as the previous
example. The other two states include the one where the O
2
is bound to the
a
subunit. If we assume
the intrinsic binding affinities of the individual subunits are K
subunit and the one where the O
2
is bound to the
b
and K
,we
a
b
can write the four-term binding polynomial as:
2
X
2
¼
1
þ
K
a
½
O
2
þ
K
b
½
O
2
þ
K
K
b
½
O
2
:
(7-28)
a
By applying Eq. (7-20) to Eq. (7-28) we obtain the fractional saturation
function for dimeric hemoglobin in terms of the Adair-binding constants
of the individual
a
and
b
subunit binding constants:
2
ð
K
a
þ
K
b
Þ½
þ
2K
a
K
b
½
1
2
N
1
2
O
2
O
2
Y
2
¼
¼
2
:
(7-29)
1
þð
K
a
þ
K
b
Þ½
O
2
þ
K
a
K
b
½
O
2
By comparing the forms of Eqs. (7-24) and (7-29), it is apparent that the
average macroscopic Adair-binding constant for the first O
2
being bound
to either of the oxygen-binding sites is equal to the sum of the intrinsic
binding affinities of the individual subunits
K
21
¼
K
a
þ
K
b
:
(7-30)
Before leaving the subject of utilizing binding polynomials to derive
fractional saturation functions, we need to consider one additional case:
When a protein has two identical binding sites and there is a cooperative
interaction between them. In this situation, the binding of the first ligand
(e.g., O
2
) will enhance or inhibit the binding of the second ligand, even
though the binding sites are identical in the unbound species. An example
of this might be where the two binding sites are physically close to each
other and the ligands are highly charged. The binding of the second ligand
would be somewhat inhibited by the charge of the first ligand (i.e., it
would be a negatively cooperative system). There would again be four
possible ways to put the two identical ligands onto the molecule:
Unbound, a ligand on the first site, a ligand on the second site, and a
ligand on both sites. The binding polynomial for this system is given by:
X ¼
2
1
þ
K
i
½
X
þ
K
i
½
X
þ
K
c
ð
K
i
½
X
Þ
;
(7-31)
where K
i
is the intrinsic affinity for either site and K
c
is the cooperativity
constant. The ligand concentration is expressed as [X] because the
