Determining the position of each of the competition binding curves is crucial to the identification of the receptors present in the cell/tissue. This is because the position of the competition binding curve is (at least in part) dependent upon the affinity of the competing ligand for the receptor(s) present. As explained further below, by identifying the position of the competition binding curve and completing appropriate analyses, it is possible to calculate the affinity of the ligand for the receptor(s) present and ultimately determine which receptor subtypes are present.

The position of steep sigmoidal and shallow sigmoidal competition binding curves is typically expressed in terms of an IC₅₀ value – the concentration of competing ligand that reduces %Specific binding of the radioligand by 50% – and can be read directly from the competition binding curve or determined using computer-assisted analysis by fitting the data to a one-site binding model. Biphasic competition binding curves (the most common form of multiphasic binding, that contain two clear phases of binding separated by a clear point of inflection) will have two IC₅₀ values – IC₅₀(1) for the first phase of binding (at the lower concentrations of the competing ligand) and IC₅₀(2) for the second phase of binding (at the higher concentrations of the competing ligand). IC₅₀(1) and IC₅₀(2) can be read directly from the competition binding curve or determined using computer-assisted analysis by fitting the data to a two-site binding model.

IC₅₀ values are not a reliable measure of the affinity of the competing ligand for the receptor – this is because the IC₅₀ value depends upon not only on the affinity of the competing ligand but also on the concentration and affinity of the radioligand. The higher the concentration of radioligand used, the higher the concentrations of competing ligand required to outcompete the radioligand and the higher the IC₅₀ value. Nevertheless, IC₅₀ values can be used to calculate the absolute affinity of the competing ligand for the receptor (K_i) present by applying the Cheng-Prusoff (1973) equation:

where
K_i = the affinity of the competing ligand for the receptor(s) present(the ‘i’ indicates the affinity value was determined from a competition (inhibition) binding study)

IC₅₀ = the concentration of competing ligand that reduces radioligand binding by 50% (determined from the competition binding curve)

[radioligand] = the concentration of radioligand used in the competition binding study

K_d of radioligand = the affinity of the radioligand for the receptors – typically determined from a previously-completed saturation binding study

Application of the Cheng-Prusoff equation to generate K_i values (true measure of affinity) is appropriate for IC₅₀ values generated from steep sigmoidal and biphasic competition binding curves, but not shallow sigmoidal competition binding curves. That is, although a single IC₅₀ value can be readily derived from a shallow sigmoidal curve, it represents the binding of the competing ligand to at least two receptor subtypes with different affinities – so the single K_i value derived from the IC₅₀ value of a shallow sigmoidal curve is a ‘composite K_i value’ which does not faithfully represent the true affinity of the competing ligand for either receptor subtype (Note though that the ‘composite K_i value’ will lay between the two true K_i values). Calculating the two true K_i values for a shallow competition binding curve requires fitting the data to a two site binding model (to generate two IC₅₀ values) and using the Cheng-Prusoff equation (to convert each IC₅₀ value into a K_i value).

From the Cheng-Prusoff equation, notice that if the [radioligand] used is very low (compared to K_d of radioligand) then the quotient [radioligand]/K_d of radioligand approaches zero, the value of the denominator approaches 1, and the K_i value approximates the IC₅₀ value. That is, when the [radioligand] << K_d of radioligand then the visually-determined IC₅₀ value (read directly from the competition binding curve) can be used as a good approximation of the K_i value for the competing ligand.

In SPIKESmate, the [radioligand] << K_d of radioligand, and thus the logIC₅₀ values obtained directly from the competition binding curves can be used as a direct approximation of the affinity (logK_i value) of the ligand for the receptor(s) present (i.e. no need to apply the Cheng-Prusoff equation).

As mentioned above, the K_i value is a measure of the affinity of the competing ligand for the receptor – it is often expressed as a –logK_i value. The K_i value is determined by applying the Cheng-Prusoff equation to the IC₅₀ values read/determined from the competition binding curve, as indicated above. The units of the K_i value are molar concentration, consistent with the idea that the K_i value is the concentration of ligand that will occupy 50% of receptors in the absence of any competing ligand. Thus, the lower the K_i value, the higher the affinity of the ligand for the receptor.

Comparison of the –logK_i values obtained for a range of receptor-selective competing ligands in a competition binding study to their known –logK_i values (obtained from competition binding studies using pure populations of recombinant human M receptor subtypes), together with a process of elimination and summation can be used to determine which M receptor subtypes are present in a cell/tissue.

The comparison involves determining the absolute difference between the single –logK_i value obtained for a competing ligand in a cell/tissue to each of the known –logK_i values for that competing ligand at each of the receptor subtypes (e.g. M₁, M₂, M₃, M₄ and M₅). If for any of the comparisons, the absolute difference in –logK_i values is  1.0 unit then it is highly unlikely that any of those receptor subtypes are present in the cell/tissue.

For example, a competition binding study determined that the –logK_i value of MT-3 in a cell/tissue was 6.3. This value of 6.3 is then compared to the known –logK_i values of MT-3 at M₁, M₂, M₃, M₄ and M₅ receptors (6.7, 5.9, 6.0, 8.1 and 6.0, respectively) – providing absolute differences of 0.4, 0.4, 0.3, 1.8 and 0.3. Of these differences only the difference of 1.8 at the M₄ receptor subtype is ≥ 1.0 unit. The conclusion drawn from the MT-3 competition binding curve (and –logK_i value of 6.3) is that the cell/tissue does not contain a significant population of M₄ receptors – i.e. the use of MT-3 has enabled us to eliminate the possibility that the cell/tissue contains M₄ receptors. Although MT-3 has thus been useful in the example to eliminate the M₄ receptor subtype, it does not provide any definitive additional information regarding which receptor(s) are present – there could be any combination of M₁, M₂, M₃ and/or M₅ receptors present. Determination of which receptor subtypes are present requires applying this elimination process to the –logK_i values obtained visually to a range of other receptor-selective ligands (e.g. potentially to each of pirenzepine, methoctramine, darifenacin and S-secoverine) until all receptor subtypes have been eliminated except for the receptor subtypes present.

Only relatively rarely can the use of a –logK_i value obtained from a single competing ligand successfully identify which receptor is present in a cell/tissue – that is, only in the instance where the competing ligand is highly selective for the single receptor present (e.g. MT-3 binding to a cell/tissue containing a pure population of M₄ receptors, S-secoverine binding to a cell/tissue containing a pure population of M₅ receptors or DAU-5884 binding to a cell/tissue containing a pure population of M₂ receptors).