A Test of the Null Equation for Functional Antagonism

Abstract

I The quantitative model for functional antagonism and synergism has been tested by studying its abilitv to fit data obtained from the functional antagonism of (-)-isoprenaline by muscarinic agonists on guinea-pig isolated atria.

Effects of Spasmogens on Relaxant Dose-Response Curves to Full or Partial Agonists at β-Adrenoceptors of Guinea Pig Isolated Trachea

“…The difference between histamine and spon taneously developed tone on the one hand and carbachol and methacholine on the other excludes the possibility that the effects of inducing tone is in reality due to the indomethacin used to abolish intrinsic tone, rather than to the spasmogen. In neither of the classic theoretical treatments of func tional antagonism, namely those by van den Brink [1973a, b] and MacKay [MacKay, 1981;Emmerson and MacKay, 1973], is al lowance made for the situation in which drugs that produce the same response or state cause different degrees of antagonism, although it is fair to state that neither model is explicitly claimed to accommodate 'antag onists' acting via different receptors (in this case histamine Hi and muscarinic cholinoceptors). In addition, no simple way of incor porating such a modification into the theo ries can be envisaged as yet.…”

A comparison of effects measured with isotonic and isometric recording: II. Concentration‐effect curves for physiological antagonists

“…Both types of drug are agonists but act at different receptors with different effector mechanisms, though these seem likely eventually to converge at the final step involving effects on the intracellular concentration of calcium ions. The situation has been variously described as ‘physiological’, ‘independent’ or ‘functional’ antagonism and although there has been much speculation about possible mechanisms these are not fully understood ( Ariens et al ., 1957 ; Van den Brink, 1973a , 1973b ; Mackay, 1981 ; Emmerson & Mackay, 1981 ; Hughes & Mackay, 1985 ; Goodall et al ., 1986 ; Lew, 1995 : Lew & Flanders, 1999 ).…”

Experimental testing of Mackay's model for functional antagonism in the isolated costo‐uterus of the rat

“…Several modifications to the approach used by Emmerson & Mackay (1981) to test the model experimentally would provide a better indication of the applicability of the model. The major modifications adopted in the present study were as follows.…”

“…Mackay's model for functional antagonism has been quantitatively tested (Emmerson & Mackay, 1981) by examining its ability to describe cholinoceptor agonist concentration-state data obtained in the presence and absence of (-)-isoprenaline in guineapig isolated atrial preparations. Concentration-state data from the pair ofcholinoceptor agonist curves was substituted into the general form of the null equation and multiple linear regression analysis used to estimate a, P and y.…”

“…Concentration-state data from the pair ofcholinoceptor agonist curves was substituted into the general form of the null equation and multiple linear regression analysis used to estimate a, P and y. On the basis that the general form of the null equation satisfactorily described the experimental curves and that the estimated values of (a -1), P and y were generally significant, Emmerson & Mackay (1981) suggested that the functional antagonism was Type I. However, they found that the estimated values of ax, P and y did not satisfy the requirement for Type I functional antagonism that (a-1)2 = 4*p1y.…”