Measurements of affinity with binding studies

The interaction of ligands with receptors can be quantified as the strength of attraction between the ligand and the receptor (affinity) and also as the observation of the change in the receptor system as a result of the binding. Binding studies quantify the proportion of receptor occupied by ligand for any given concentration of ligand. This method requires a tracer molecule, the disposition of which, whether bound to the receptor or not, can be discerned. If the ligand is a tracer itself (i.e. radioligand), then the binding can be measured directly (saturation binding). However, since most ligands are not radioactive, an indirect method, namely the effect of a non-radioactive ligand on a bound tracer molecule, is used to determine the affinity of the non-radioactive ligand.

Binding experiments primarily yield information about affinity although there are techniques which also yield estimates of efficacy (vide infra). The first step is to characterize the saturation binding of a tracer radioligand. Once this is done, the effects of other ligands on the binding of the tracer ligand can furnish information regarding the molecular interaction of the ligand with the receptor and the concentrations at which these interactions occur. Detailed descriptions of methods to optimize and quantify binding are beyond the scope of this chapter (see Limbird 1996; Klotz 1997; Winzor and Sawyer 1995). Simultaneous comparison of total and non-specific (not receptor related) binding yields a sigmoid saturation curve (preferable to linear transformations—see Klotz 1982,1997; Klotz and Hunston 1984). In general, the effect of ligand-binding on a single bound concentation of radioligand yields a sigmoid displacement curve.

For competitive antagonism with the tracer ligand, whereby both the radioactive and non-radioactive ligand compete for the same site on the receptor, parallel displacement of the tracer curve is produced (see Fig. 8.2a). The displacement of different concentrations of radioligand is shown in Fig. 8.2b; a characteristic pattern is observed, whereby the ligand reduces the radioactive ligand binding completely to non-specific (nsb) levels and the IC5o (concentration producing 50% inhibition of the binding) is linearly related to the concentration of the radioligand (Cheng and Prusoff 1973).

Ki and Kd refer to the equilibrium dissociation constants of the receptor-antagonist and receptor-radiolabel complex, respectively and [A] the concentration of radiolabel. Under ideal conditions, a system independent measure of affinity (Ki) can be derived.

In the case where the antagonism precludes binding of the radioligand (either by noncompetitive or pseudo-irreversible interaction), a depression of the saturation binding curve is obtained with no dextral displacement (see Fig. 8.2c). The displacement curves are still depressed to non-specific levels but there is no increase in the IC50 with increasing radioligand concentration (see Fig. 8.2d).

Another type of ligand interaction, whereby the tracer and non-radioactive ligands bind to distinctly different sites on the receptor, is termed allosteric. The effects on saturation binding can be very similar to competitive ligands except that they are saturable, that is, when the 'allosteric' site for the ligand is saturated, the effect is maximal. The maximal effect on the affinity of the tracer ligand is given by a cooperativity factor (denoted a) which can be inhibitory (i.e. a ligand with a = 0.1 produces a maximal 10-fold decrease in the affinity of the tracer ligand) or potentiating (i.e. a = 10 leads to a 10-fold enhancement of tracer affinity). Figure 8.3a shows the effect of an allosteric modulator with a = 0.1 on saturation binding. Figure 8.3b shows the resulting displacement curve. A characteristic of allosteric inhibition is the potential to not decrease radioligand completely to non-specific levels. Also, the relationship between radioligand concentration and allosteric ligand IC50 is hyperbolic

Fig. 8.2 Effects of antagonists on tracer ligand binding. (a) Effect of a simple competitive antagonist on a saturation binding curve of a tracer ligand. Parallel shifts to the right with no diminution of maxima result. (b) Effects of a range of concentrations of a simple competitive antagonist on a various single concentrations of tracer ligand. Binding is diminished to nsb levels with shifts to the right of the IC50 for inhibition. (c) Effect of a non-competitive antagonist (binding of antagonist precludes binding of tracer ligand) on a saturation binding curve for a tracer ligand. (d) Effects of a range of concentrations of a non-competitive antagonist on various single concentrations of tracer ligand. Binding is diminished to nsb levels with no shift to the right of the IC50 for inhibition.

Fig. 8.2 Effects of antagonists on tracer ligand binding. (a) Effect of a simple competitive antagonist on a saturation binding curve of a tracer ligand. Parallel shifts to the right with no diminution of maxima result. (b) Effects of a range of concentrations of a simple competitive antagonist on a various single concentrations of tracer ligand. Binding is diminished to nsb levels with shifts to the right of the IC50 for inhibition. (c) Effect of a non-competitive antagonist (binding of antagonist precludes binding of tracer ligand) on a saturation binding curve for a tracer ligand. (d) Effects of a range of concentrations of a non-competitive antagonist on various single concentrations of tracer ligand. Binding is diminished to nsb levels with no shift to the right of the IC50 for inhibition.

and not linear:

An allosteric enhancer shifts the saturation binding curve to the left (Fig. 8.3c) with a corresponding increase in ordinate values for tracer binding in the displacement curve (Fig. 8.3d).

The most sensitive method of detecting allosteric effects through ligand binding is to examine the rate of tracer ligand association and dissociation in the presence of the suspected allosteric ligand. The rationale for this idea is that an allosteric ligand will affect a conform-ational change in the receptor which will, in turn, alter the orthosteric association and/or dissociation constant of the tracer ligand. In theory, allosteric ligands can either decrease both the association and dissociation constant of the tracer ligand. Therefore, kinetic experiments may detect allosteric effects that may not otherwise be detected in equilibrium binding experiments. For example, the allosteric modulator Tetra-W84 decreases both the association

Fig. 8.3 Effects of allosteric ligands on tracer ligand binding. (a) Effect of an allosteric modulator with a = 0.1 on a saturation binding curve of a tracer ligand. Parallel shifts to the right with diminution of maxima result until a 10-fold maximum shift is obtained. (b) Effects of a range of concentrations of the same allosteric modulator on a various single concentrations of tracer ligand. Binding may not be diminished to nsb levels with higher concentrations of tracer ligand and limited shifts to the right of the IC50 for inhibition are observed up to a maximum value. (c) Effect of an allosteric enhancer (increased affinity) on a saturation binding curve for a tracer ligand. (d) Effects of a range of concentrations of allosteric enhancer on various single concentrations of tracer ligand. Binding of tracer is increased by the allosteric enhancer up to the maximal asymptote for tracer binding.

and dissociation rate constants of [3H]-N-Methylscopolamine at muscarinic acetylcholine receptors (Chapter 18), an allosteric effect clearly detected in kinetic experiments (Kostenis and Mohr 1996). However, since both rate constants are affected, there is no obvious change in the equilibrium affinity of the tracer in the presence of Tet-W84, thus equilibrium binding does not detect the allosteric effect of this ligand.

Assuming the kinetics of the allosteric ligand are faster than the tracer ligand (as is almost always the case), the observed rate of dissociation of the tracer ligand ([A]), in the presence of the allosteric ligand ([C]) is given by (Christopoulos 2000):

where a is the allosteric constant (maximal change in affinity imparted by the allosteric ligand to the the tracer ligand) and Kc is the equilibrium dissociation constant of the allosteric ligand-receptor complex. The rate of dissociation of the tracer ligand from the receptor is given by koffA in the absence of C and fcoffAC in the presence of C. It can be seen that, with increasing concentrations of allosteric ligand, there will be a linear change in the observed dissociation rate constant.

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