Insurmountable antagonists

Historically, Gaddum and colleagues [3] devised a method to measure the affinity of insurmountable antagonists based on a double reciprocal linear transformation. With this method, equiactive concentrations of agonist in the absence ([A]) and presence ([A ]) of a noncompetitive antagonist ([B]) are compared in a double reciprocal plot... 

FIGURE 6.19 Use of the clextral displacement produced by an insurmountable antagonist to estimate dose ratios and subsequent pA2 values. Response according to model for orthosteric noncompetitive blockade (Equation 6.31 with Emax = 1, t = 3, Ka = 0.3 pM, Kb = 1 pM) for 1 pM and 3 pM antagonist. Dose ratios measured at response = 0.24 for 1 pM antagonist and response = 0.15 for 3pM antagonist. Resulting pA2 values are close estimates of the true pKB (6.0) as modified by the [A]/Ka term (see Equation 6.37). 

A characteristic of hemi-equilibria is the observation of a depressed plateau of maximal responses. Thus, while a truly insurmountable antagonist will eventually depress the concentration-response curves to basal levels hemi-equilibrium conditions can produce partial but not complete inhibition of the agonist maximal response. This is shown in Figure 6.21. 

If there is no receptor reserve for the system, then an insurmountable antagonist, whether allosteric or orthosteric, will produce immediate depression of the agonist concentration-response curve with no concomitant shift to the right. Under these circumstances,... 

As with insurmountable orthosteric antagonists, the shift to the right of concentration-response curves produced by allosteric insurmountable antagonists can be used to calculate a pA2 value, and in turn this can be related to the pKB of the antagonist. A concentration of antagonist equal to the pA2 (i.e., concentration = 10-pA2) causes a dose ratio of 2, leading to the following equality ... 

Method for Estimating Affinity of Insurmountable Antagonist (Dextral Displacement Observed)... 

FIGURE 12.13 Calculation of a pA2 value for an insurmountable antagonist, (a) Conner ation-response curve for control (filled circles) and in the presence of 2 jiM antagonist (open circles), (b) Data points fit to logistic functions. Dose ratio measured at response value 0.3 (dotted line). In this case, the DR = (200nM/50nM = 4). 

Responses in the absence and presence of an insurmountable antagonist that causes dextral displacement of the concentration-response curve. 

It is worth examining the possible magnitudes of the error with various scenarios. The maximal value for [A]/Ka can be approximated, assuming a system where response is directly proportional to receptor occupancy. Under these circumstances, Response = 0.3 = [A]/Ka/([A]/Ka + 1), which in this case is [A]/Ka = 0.5. Therefore, the pA2 is pKB + Log (2) (i.e., the pA2 will overestimate the affinity of the antagonist by a maximal factor of 2). If the insurmountable antagonist is allosteric antagonist that reduces the affinity of the receptor for agonist (a < 1), then the error will be <2. However, if the modulator... 

As with insurmountable orthosteric antagonists (see Section 6.4), in systems with a receptor reserve for the agonists there will be a measurable dextral displacement of the concentration-response curves either with or without concomitant depression of the maximal response. Under these circumstances, a useful method for determining the affinity of allosteric insurmountable antagonists is to measure the pA2 (-log of the molar concentration that produces a twofold shift to the right of the agonist concentration-response curve). It can be shown that for allosteric noncompetitive antagonists, the pA2 is related to the pKB with the relation (see Section 7.8.4)... 

Kenakin, T.P., Jenkinson, S., and Watson, C. (2006). Determining the potency and molecular mechanism of action of insurmountable antagonists../. Pharmacol. Exp. Ther. 319 710-723. 

TABLE 13.9 Responses in the Absence and Presence of an Insurmountable Antagonist That Causes Dextral Displacement of the Concentration-Response Curve... 

General Procedure The response to the agonist is determined in the absence and presence of a range of concentrations of the insurmountable antagonist. The data points may be fit to logistic functions (for observation of trends this isn t necessary for calculation of IC50). 

A concentration of agonist is chosen and the response to that concentration (expressed as a fraction of control) is plotted as a function of the concentration of antagonist to form an inhibition curve. This curve is fit to a function and the midpoint (IC50) calculated this is an estimate of the affinity of the insurmountable antagonist. To detect a possible allosteric increase in affinity of the antagonist with agonist concentration, more than one concentration may be chosen for this procedure. 

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