Antagonists dose-response curves

Fig. 8. Agonist, dose—response curves, (a) For an agonist where a value of 10 M is indicated at the concentration giving 50% response, (b) For an agonist alone, Aq, and in the presence of increasing amounts of irreversible receptor antagonists, B—F. There is a progressive rightward shift of the dose—response curve prior to reduction of maximum response. This pattern is consistent with the presence of a receptor reserve.

FIGURE 6.1 Effects of antagonists on agonist dose-response curves, (a) Surmountable antagonism with no diminution of maxima and no limiting antagonism (competitive antagonists). 

One shortcoming of Schild analysis is an overemphasized use of the control dose-response curve (i.e., the accuracy of every DR value depends on the accuracy of the control EC o value). An alternative method utilizes nonlinear regression of the Gaddum equation (with visualization of the data with a Clark plot [10], named for A. J. Clark). This method, unlike Schild analysis, does not emphasize control pECS0, thereby giving a more balanced estimate of antagonist affinity. This method, first described by Lew and Angus [11], is robust and theoretically more sound than Schild analysis. On the other hand, it is not as visual. Schild analysis is rapid and intuitive, and can be used to detect nonequilibrium steady states in the system that can corrupt... 

To apply this method, the pECS0 values of the control and shifted dose-response curves and the corresponding concentrations of antagonist [B] values associated with those pECjgS are used to construct a Clark plot [10] according to the equation... 

When an antagonist produces parallel shifts to the right of the dose-response curve with no diminution of the maximal response, the first approach used to quantify potency is Schild analysis (see Section 6.3.1). In cases where the value of a is low (i.e., a = 0.01), a tenfold concentration range of the antagonist would cause shifts commensurate with those produced by a simple competitive antagonist. 

Antagonists can produce varying combinations of dextral displacement and depression of maxima of agonist dose-response curves. The concentration-related effect of an antagonist on the system response to a single concentration of agonist constitutes what will be referred to as an inhibition curve. One of the most straightforward examples... 

In the presence of a competitive antagonist, the EC50 of the agonist dose-response curve will be shifted to the right by a factor equal to the dose ratio. This is given by the Schild equation as [B]/Kb-I-1, where the concentration of the antagonist is [B] and KB is the equilibrium dissociation constant of the antagonist-receptor complex ... 

FIGURE 11.14 Data set consisting of a control dose-response curve and curves obtained in the presence of three concentrations of antagonist. Panel a curves fit to individual logistic functions (Equation 11.29) each to its own maximum, K value, and slope. Panel b curves fit to the average maximum of the individual curves (common maximum) and average slope of the curves (common n) with only K fit individually. The F value for the comparison of the two models is 2.4, df = 12,18. This value is not significant at the 95% level. Therefore, there is no statistical support for the hypothesis that the more complex model of individual maxima and slopes is required to fit the data. In this case, a set of curves with common maximum and slope can be used to fit these data. 

FIGURE 11.16 Control dose-response curve and curve obtained in the presence of a low concentration of antagonist. Panel a data points. Panel b data fit to a single dose-response curve. SSqs = 0.0377. Panel c data fit to two parallel dose-response curves of common maximum. SSqc = 0.0172. Calculation of F indicates that a statistically significant improvement in the fit was obtained by using the complex model (two curves F = 4.17, df=7, 9). Therefore, the data indicate that the antagonist had an effect at this concentration. 

Dose-response curves to the agonist carbachol are obtained in the presence and absence of the antagonist scopolamine. The data are given in Table 12.6a. Responses are contractions of rat trachea resulting from muscarinic receptor... 

General Procedure Dose-response curves to a full agonist are obtained in the absence and presence of the noncompetitive antagonist. From these curves, equiactive concentrations of full agonist are compared in a linear regression (see Section 12.2.1). The slope of this regression is used to estimate the KB for the noncompetitive antagonist. 

General Procedure Dose-response curves are obtained for an agonist in the absence and presence of a range of concentrations of the antagonist. The dextral displacement of these curves (ECSo values) are fit to a hyperbolic equation to yield the potency of the antagonist and the maximal value for the cooperativity constant (a) for the antagonist. 

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