Biomedical Engineering Reference
In-Depth Information
0
(7.3)
Δ=
G
TK
ln
D
where
T
is the temperature and
R
is the gas constant. A small
K
D
value corresponds
to a large negative free energy (i.e., the reaction is thermodynamically favored). If
the receptors have a high affinity for the ligand, the
K
D
will be low, as it will take
a low concentration of ligand to bind half the receptors.
K
D
spans a wide range
from10
−6
(low affinity) to 10
−15
M (high affinity or tight binding). However, (7.1)
is not of practical significance as it requires the concentration of unoccupied recep-
tor, [
R
], at any given time. Alternatively, assuming that the receptors do not allow
for more than one affinity state or states of partial binding, the fractional receptor
occupancy (fraction of all receptors that are bound to ligand) at equilibrium as a
function of ligand concentration can be determined. The ligand bound receptor is
called,
Bound
(
B
) and the unbound ligand is called
Free
,
L
0
. Both of these are mea-
surable experimentally. Substituting these measurable terms into (7.2),
LR
0
[]
(7.4)
=
K
D
B
Each cell has a specific number of receptors, for a specific ligand, at a given
physiological state. Receptors are either free or bound to the ligand. In other words,
Total receptors
=
free receptors
+
receptors bound to the ligand
For any given cell, the total receptors present can be termed as the maximal
number of binding sites,
B
max
. Hence,
[]
max
BRB
=+
(7.5)
Hence (7.4) can be rewritten as
(
)
LB
−
B
(7.6)
o
max
=
K
D
B
This can be rearranged to obtain
LB
.
B
=
0m x
(7.7)
KL
+
D
0
It is possible to estimate the
B
max
and
K
D
from (7.7). Plotting (7.7) gives a
hyperbolic curve, which is a typical response of many biological reactions. This
type of equation is popularly referred to as the Michaelis-Menten equation and is
often valid for many reactions including transport of substrates, enzyme-catalyzed
