Agonist concentration

Dose-response curves depict the response to an agonist in a cellular or subcellular system as a function of the agonist concentration. Specifically, they plot response as a function of the logarithm of the concentration. They can be defined completely by three parameters namely, location along the concentration axis, slope, and maximal asymptote... 

Black and Leff [11] presented a model, termed the operational model, that avoids the inclusion of ad hoc terms for efficacy. This model is based on the experimental observation that the relationship between agonist concentration and tissue response is most often hyperbolic. This allows for response to be expressed in terms of... 

FIGURE 3.7 Principal components of the operational model. The 3D array defines processes of receptor occupation (plane 1), the transduction of the agonist occupancy into response (plane 2) in defining the relationship between agonist concentration, and tissue response (plane 3). The term a refers to the intrinsic activity of the agonist. 

It can be seen that if KA< v then negative and/or infinite values for response are allowed. No physiological counterpart to such behavior exists. This leaves a linear relationship between agonist concentration and response (where Ka = v) or a hyperbolic one (KA>v). There are few if any cases of truly linear relationships between agonist concentration and tissue response. Therefore, the default for the relationship is a hyperbolic one. 

The antagonism is quantified by measuring the ratio of equiactive concentrations of agonist measured in the presence of and absence of the antagonist. These are referred to as dose ratios (DRs). Usually, ECS0 concentrations of agonist (concentration producing 50% maximal... 

A more rigorous version of this method has been presented by Kauman and Marano [8], In this method, the slopes from a range of equiactive agonist concentration plots are utilized in another regression (see Section 6.8.8) ... 

In cases where there is a substantial receptor reserve such that there is a measurable dextral displacement of the concentration response curves, then another reliable method for determining the affinity of the noncompetitive antagonist 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 purely noncompetitive antagonists the pA2 is related to the pKB with the relation (see Section 6.8.10)... 

Therefore, a double reciprocal plot of equiactive agonist concentrations in the presence (1/[A ] as abscissae) and absence (1 /[A] as ordinates) of antagonist should yield a straight line. The equilibrium dissociation constant of the antagonist is calculated by... 

The relationship between equiactive agonist concentrations in the absence and presence of antagonist to yield a dose ratio of 2 ([B] = 10-pAi) is then calculated by equating... 

Similarly, receptor occupancy equal to the occupancy above (agonist concentration [A ]) in the presence of the test antagonist and a reference antagonist [B ] is given as... 

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,... 

Van Der Graaf, P. H., and Schoemaker, R. C. (1999). Analysis of asymmetry of agonist concentration-response curves. J. Pharmacol. Toxicol. Methods 41 107-115. 

A target agonist concentration is chosen. For this example, a concentration of 0.3 mM agonist was used. This approximates the concentration that produces an 80% maximal response. The antagonist is tested against the response produced by 0.3 pM agonist. 

General Procedure Dose-response curves to a full agonist are obtained in the absence and presence of the antagonist. At a level of response approximately 30% of the maximal response of the depressed concentration response curve, an equiactive dose ratio for agonist concentrations is measured. This is used to calculate a pA2. 

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