Experimental and theoretical comparisons between the classical Schild analysis and a new alternative method to evaluate the pA2 of competitive antagonists.

The Schild analysis is undoubtedly the most frequently used powerful diagnostic tool to investigate the nature of an antagonist and, consequently, to evaluate its potency, often expressed as pA2. Nevertheless, different reasons often prevent the experimenter from applying this analysis, leading to use an inhibition curve for the antagonist and to evaluate its potency by means of several approaches, which are generally considered theoretically invalid. In a recent work, a new theoretical approach, mathematically analogous to the Schild one, has been shown. By means of a simplified experimental protocol based on an antagonist inhibition curve (following a control concentration-response curve for the agonist), this method allows a linear regression analysis, giving a slope value absolutely equivalent to the Schild slope and a reliable estimation of the pA2 of a competitive antagonist. In this paper, this new method has been compared with the Schild analysis, to determine the parameters of potency relative to well-known competitive antagonists, on different in vitro isolated preparations. In strips of guinea pig isolated gastric smooth muscle, pirenzepine antagonised the effects of bethanechol. In guinea pig isolated ileum, atropine blocked the contracturant effects of carbamylcholine, while in electrostimulated ileum segments, the inhibitory responses to alpha-methylnoradrenaline were reduced by idazoxan. Finally, in guinea pig isolated spontaneously beating atria, the negative inotropic effects of 5'-N-ethylcarboxamidoadenosine were antagonised by 8-cyclopentyl-1,3-dipropylxanthine. The parameters of potency, relative to all the above competitive antagonists and expressed as pA2, resulted almost equivalent, when calculated by the Schild analysis or by the alternative method. Furthermore, when tested also for the well-known irreversible alkylating agent dibenamine in rat aortic rings stimulated by noradrenaline, the alternative method furnished a profile of clear nonlinearity, unmasking the nature of the antagonism. Finally, the relationships between the results calculated by the alternative analysis or by the Schild analysis and different levels of computer-generated "random noise" (affecting the shape and the position of theoretical curves) were also evaluated, in order to know the robustness of the new method. The two methods proved reliable and almost equivalent in robustness, when applied with different levels of "random noise". These results confirm the Schild analysis as the most accurate tool to study antagonists, since this analysis can furnish the highest number of information and observations on the behaviour of an antagonist. Nevertheless, when limiting conditions prevent a classical Schild analysis and impose the use of an inhibition curve, the new method probably represents the most preferable experimental approach. Indeed, it allows to calculate the antagonist potency, after the evaluation of a slope parameter giving an important information about the possible nature of the antagonism.