If the insurmountable antagonist is allosteric antagonist that reduces the affinity of the receptor for agonist (a < 1), then the error will be <2. Therefore, the pA2 is pKB + Log (2) (i.e., the pA2 will overestimate the affinity of the antagonist by a maximal factor of 2). Under these circumstances, Response = 0.3 = /Ka/(/Ka + 1), which in this case is /Ka = 0.5. The maximal value for /Ka can be approximated, assuming a system where response is directly proportional to receptor occupancy.
It is worth examining the possible magnitudes of the error with various scenarios. Responses in the absence and presence of an insurmountable antagonist that causes dextral displacement of the concentration-response curve. Dose ratio measured at response value 0.3 (dotted line). įIGURE 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. Method for Estimating Affinity of Insurmountable Antagonist (Dextral Displacement Observed). A concentration of antagonist equal to the pA2 (i.e., concentration = 10-pA2) causes a dose ratio of 2, leading to the following equality. Īs 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. 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. 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. Ī characteristic of hemi-equilibria is the observation of a depressed plateau of maximal responses. Resulting pA2 values are close estimates of the true pKB (6.0) as modified by the /Ka term (see Equation 6.37). Dose ratios measured at response = 0.24 for 1 pM antagonist and response = 0.15 for 3pM antagonist. 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. įIGURE 6.19 Use of the clextral displacement produced by an insurmountable antagonist to estimate dose ratios and subsequent pA2 values. With this method, equiactive concentrations of agonist in the absence () and presence () of a noncompetitive antagonist () are compared in a double reciprocal plot. Historically, Gaddum and colleagues devised a method to measure the affinity of insurmountable antagonists based on a double reciprocal linear transformation.
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