Biomedical Engineering Reference
In-Depth Information
IC
[L]
50
(1.4)
K
=
i
æ
ö
1
+
ç
÷
è
K
ø
D
where
[L] is the concentration of the radioligand used in the assay
K
D
is the afi nity of the radioligand for the receptor
It should be noted that IC
50
values are dependent on the concentration and the afi nity of the
radioligand. Care should be taken when comparing IC
50
values unless the same radioligand and
radioligand concentration have been used in all binding experiments. In contrast,
K
i
is a constant
for the ligand with respect to the receptor. It provides a useful measure of the total afi nity, but by
itself it tells little about the details of the molecular recognition.
1.3 PARTITIONING OF
D
G
The driving forces for ligand-protein recognition are electrostatic interactions (ion-ion, ion-dipole,
and dipole-dipole), lipophilicity/hydrophobicity, and shape complementarity. In order to understand
the nature and the relative contributions of the different forces it is an useful approximation to partition
Δ
G
into a sum of free energy contributions, as shown in Equation 1.5. Several different partitioning
schemes have been proposed in the literature. The partition used here is essentially that suggested by
Williams on the basis of studies by Page and Jencks (see Further Readings).
D=D
GG G G G G
+D
+D
+D
+D
(1.5)
transl+rot
conf
polar
hydrophob
vdW
•
Δ
G
transl+rot
accounts for the restrictions of translational movements (movements in
x
-,
y
-,
and
z
-directions) and restrictions of rotations (about the
x
-,
y
-, and
z
-axes) of the “whole”
molecule from the unbound to the bound state.
Δ
•
G
conf
is the difference in the conformational free energies between the unbound and
bound states due to conformational restrictions in the ligand-protein complex.
Δ
•
G
polar
is the free energy change due to interactions of polar functional groups in the bind-
ing cavity of the protein.
Δ
•
G
hydrophob
accounts for the binding free energy due to the hydrophobic effect.
Δ
•
G
vdW
gives the difference in free energy due to van der Waals (vdW) interactions in the
bound and unbound states.
In the following sections, the different terms in Equation 1.5 and their magnitudes will be discussed
in more detail and illustrated in terms of ligand-protein recognition.
1.3.1
D
G
transl+rot
—T
HE
F
REEZING
OF
THE
O
VERALL
M
OLECULAR
M
OTION
Outside the binding cavity in the protein, the ligand tumbles freely in the aqueous solution through
rotations and translations of the entire molecule. Since the freedom of translation and rotation in the
binding cavity becomes severely restricted through formation of the ligand-protein complex, these
motions to a large extent become frozen (i.e., three rotational and three translational degrees of
freedom are lost). In terms of thermodynamics this leads to a decrease in entropy resulting in a more
negative
Δ
S
and consequently a more negative
T
Δ
S
. According to Equation 1.3 this gives a more
G
transl+rot
is a
free energy cost, which must be overcome by the favorable binding forces to make the formation of
positive
Δ
G
. Thus, the loss of freedom of translation and rotation opposes binding and
Δ
