Biomedical Engineering Reference
In-Depth Information
many times data analysis by nonlinear regression could correlate well with experi-
mental results. Cooperative interaction between ligand and receptor can be written
in a series of interactions
k
k
1
k
non
,
on
2
on
R
+
L
RL
⋅
→⋅
RL
+
L
RL
⋅
→⋅
RL
+
L
RL
⋅
2
n
−
1
n
k
k
k
1
off
2
off
n off
,
Interaction of one ligand with
N
types of binding sites can be represented as
k
jon
RLRLj
+
⋅
; 1...
=
n
j
j
k
joff
or they can also be a combination of all three of these schemes and can be not well
explained by a simple bimolecular reaction such as (7.1). In addition, the concen-
tration of receptors on a cell and the dissociation constant could modify in many
physiological and pathophysiological situations; the receptor concentration can re-
flect functional receptor modifications, and the dissociation constant can reflect
genetic alterations of the receptor. Consider the transport of O
2
in the body, which
occurs through a binding to a transporter (nearly 97% of O
2
is carried by hemo-
globin inside red blood cells) along with the dissolution in plasma (1.5-3% of O
2
).
Each hemoglobin molecule has four heme groups, each of which binds a molecule
of O
2
in a reversible reaction to form oxyhemoglobin (HbO
2
).
Hb
+
4O
⇔
Hb(O )
2
2
4
This reaction assumes that the subunits of Hb are fully cooperative, that is, if
one subunit binds oxygen, they all must bind oxygen, or if one releases oxygen,
they must all release oxygen. However, this assumption of total cooperativity pro-
duces a very steep curve and does not agree with the experimental results. Consider
a general binding interaction of Hb with oxygen:
Hb
+
n
O
⇔
Hb(O ) or [ ]
P
+
n L
[
]
⇔
[
P
:
L
]
2
2
n
n
where [
P
] is the unliganded protein (hemoglobin), [
L
] is the ligand (oxygen), and
[
P
:
L
] is the concentration of the protein:ligand complex (hemoglobin with oxygen
bound). At any equilibrium condition, the rate constant is
[][]
[
n
PL
K
=
(7.9)
]
D
PL
:
n
Defining the fraction,
Y
, of protein that is in complex with a ligand (e.g., hemo-
globin molecules that are saturated) is:
