It is of utmost importance to understand the affinity of a ligand for a protein and to keep in mind that the affinity is defined by the equilibrium between the unbound ligand and the unbound protein on one side and the ligand-protein complex on the other, as shown in Figure 1.2. Thus, thermodynamics governs the basic physicochemical principles of molecular recognition.
The affinity of the ligand for the protein is given by the free energy difference (AG) between the ligand-protein complex (the right-hand side in Figure 1.2) and the "free" (unbound) ligand and the "free" (unbound) protein (the left-hand side). Water plays an important role on both sides of the equilibrium as will be discussed below.
It should be noted that the ligand exists as a mixture of conformations with different shapes on the left-hand side but in a single well-defined conformation on the right-hand side. The protein conformation may also change between the left- and right-hand sides of the equilibrium and the water structure is different on the two sides of the equilibrium.
FIGURE 1.2 The equilibrium determining the affinity of a ligand.
The free energy difference is related to the equilibrium constant K by Equation 1.1.
R is the gas constant (8.315 J/K/mol) T is the temperature in kelvin
A higher affinity implies a larger positive value of K, and, thus, a larger negative value of AG. In medicinal chemistry, the affinity of a ligand is most often given as an inhibition constant Ki or by an IC50-value. Since K = 1/Ki the free energy difference in terms of Ki can be written as in Equation 1.2.
AG has an enthalpic component (AH) as well as an entropic component (AS) according to Equation 1.3.
A higher affinity (a more negative AG) corresponds to a smaller value of the inhibition constant Ki (most often given in nM or |M). A Ki of 1 nM corresponds to a AG of -53.4 kJ/mol at 310 K and a Ki of 1 ||M to -35.6 kJ/mol. Furthermore, using Equation 1.2 it can be calculated that a change in AG by 5.9 kJ/mol alters Ki 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 significant decrease in the affinity, a fact that should carefully be taken into account in ligand design (for further discussions on ligand conformations, see Section 1.3.2).
IC50 expresses the concentration of an inhibitor that displaces 50% of the specific binding of a radioactively labeled ligand in a radioligand experiment. The IC50 value can be converted to an inhibition constant Ki by the Cheng-Prusoff equation (Equation 1.4).
FIGURE 1.3 Conformational energies of ethyl benzene.
[L] is the concentration of the radioligand used in the assay KD is the affinity of the radioligand for the receptor
It should be noted that IC50 values are dependent on the concentration and the affinity of the radioligand. Care should be taken when comparing IC50 values unless the same radioligand and radioligand concentration have been used in all binding experiments. In contrast, Ki is a constant for the ligand with respect to the receptor. It provides a useful measure of the total affinity, but by itself it tells little about the details of the molecular recognition.
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