Molecular Recognition in Ligand–Protein Binding - Drug Design and Discovery - page 17

Global energy
minimum

Δ G =- RT In K

Δ G conf

Bioactive
conformation

FIGURE 1.2 The equilibrium determining the afi nity of a ligand.

The free energy difference is related to the equilibrium constant K by Equation 1.1.

D=- GTK ln

(1.1)

where
R is the gas constant (8.315 J/K/mol)
T is the temperature in kelvin

A higher afi nity implies a larger positive value of K , and, thus, a larger negative value of G .

In medicinal chemistry, the afi nity of a ligand is most often given as an inhibition constant K i
or by an IC 50 -value. Since K = 1/ K i the free energy difference in terms of K i can be written as in
Equation 1.2.

Δ

D= GRTK ln

(1.2)

i

Δ G has an enthalpic component ( Δ H ) as well as an entropic component ( Δ S ) according to Equation 1.3.

D=D-D GHTS (1.3)

A higher afi nity (a more negative Δ G ) corresponds to a smaller value of the inhibition constant K i

(most often given in nM or μ M). A K i of 1 nM corresponds to a Δ G of −53.4 kJ/mol at 310 K and

a K i of 1 μ M to −35.6 kJ/mol. Furthermore, using Equation 1.2 it can be calculated that a change

in G by 5.9 kJ/mol alters K i by a factor of 10. An example of the size of this energy in terms of

molecular structural change is shown in Figure 1.3. A conformational change of the ethyl group
in ethyl benzene from a perpendicular conformation with respect to the phenyl ring (the lowest
energy conformation) to a conformation with a coplanar
carbon skeleton increases the energy by 6.7 kJ/mol. Thus,
even modest changes in the conformation (the shape) of a
ligand can result in a signii cant decrease in the afi nity, a
fact that should carefully be taken into account in ligand
design (for further discussions on ligand conformations,
see Section 1.3.2).
IC 50 expresses the concentration of an inhibitor that dis-
places 50% of the specii c binding of a radioactively labeled
ligand in a radioligand experiment. The IC 50 value can be
converted to an inhibition constant K i by the Cheng-Prusoff
equation (Equation 1.4).

Δ

H H

H

CH 3

H

CH 3

0.0 + 6.7 kJ/mol

FIGURE 1.3 Conformational energies
of ethyl benzene.