Biology Reference
In-Depth Information
is constant at constant temperature. The higher the drug concentration,
the higher the concentration of drug-bound receptors should be for the
quotient to remain unchanged. As the drug concentration increases,
a point will be reached where virtually all of the receptors will be
saturated with the drug. When this occurs, further increases in drug
concentration will produce no additional effect.
To understand the action of a drug, it is important to understand how
the fractional saturation of the receptor is related to the c
on
centration of
the unbound drug. The receptors' fractional saturation, Y, is the
concentration of the drug-receptor complex divided by the total receptor
concentration:
½
Drug
Receptor
K
a
½
Drug
½
Receptor
Y
¼
¼
½
Receptor
þ½
Drug
Receptor
½
Receptor
þ
K
a
½
Drug
½
Receptor
K
a
½
Drug
½
Drug
=
K
d
¼
¼
K
d
:
(7-5)
1
þ
K
a
½
Drug
1
þ½
Drug
=
In the special case of hemoglobin-oxygen binding, human hemoglobin
can at most bind four O
2
molecules, and the coordinative bond between
the O
2
molecule and the central ferrous ion in the heme is very weak.
The number of oxygenated sites depends strongly upon the level of O
2
present (i.e., upon the partial O
2
pressure). In the lungs, where the
partial pressure of the O
2
is relatively high, the prevailing form is the
oxygenated hemoglobin that causes arterial blood's pure
red color. Traveling through the capillaries of the tissues, where the O
2
partial pressure is low,
2
the oxygenated hemoglobin is subjected to
considerable deoxygenation. This is the basic mechanism of the
so-called hemoglobin shuttle: hemoglobin loads O
2
in the lungs,
transports it to the tissues, where it is released, and the cycle repeats. In
muscles, the O
2
is taken up by myoglobin, where it is then
available to rapidly provide the large amounts of O
2
required by active
muscles.
The molecular reaction mechanisms involved in O
2
binding to
hemoglobin and myoglobin are the most thoroughly studied in
biochemistry, and are the test cases for every mathematical model of
binding reactions and cooperativity. If we replace the drug with O
2
and
the receptor with myoglobin in Eq. (7-5), the mathematical model applies
to the binding of O
2
by myoglobin. The fractional saturation of
myoglobin is described by:
K
a
½
O
2
½
O
2
=
K
d
Y
¼
O
2
¼
K
d
:
(7-6)
1
þ
K
a
½
1
þ½
O
2
=
2. The O
2
in the tissues is used to oxidize glucose to carbon dioxide and water.
As a result, the partial pressure of the O
2
decreases, and the partial pressure of
the CO
2
increases.
