Dennis Mackay

AN ANALYSIS OF FUNCTIONAL ANTAGONISM AND SYNERGISM

1 A method is described for deriving null equations for functional antagonism and synergism. These null equations relate together the concentrations of agonist required to produce equivalent states of a cell or tissue in the presence and in the absence of a functional interactant 2 In one particular case the null equation leads to conclusions which are very similar to those reached by an earlier author who did not use the null method. However, the null equations give a clearer insight into the quantitative aspects of functional interaction. 3 It is concluded that the use of functional antagonism to estimate affinity constants and relative intrinsic efficacies of agonists has serious limitations. On the other hand, it may be possible to use the null equations, or similar principles, to test the validity of postulated mechanisms and sites of action of functional interactants.

Agonist potency and apparent affinity: interpretation using classical and steady-state ternary-complex models

The relative potencies of agonists have been used in the past to classify receptors. This could be justified on the basis of ideas and equations developed using the occupancy model of drug action. Although attempts have been made recently to develop methods of analysis based on other models, these have not been entirely satisfactory. In this article Dennis Mackay explores possible interpretations of relative potency, apparent affinity and efficacy on the basis of a steady-state ternary-complex model. He concludes that use of these quantities to classify receptor-transducer systems may not be entirely dependable. However the steady-state model can explain why use of agonists to classify receptors has been successful in the past and why properties of agonists deduced from ligand binding studies may differ from their properties deduced from experiments on intact tissues.

Quantification of the characteristics of antagonists exhibiting both competitive antagonism and functional interaction.

1 Null equations have been derived which, when applied to log10 concentration‐tissue state curves for an agonist determined in the presence and absence of a competitive antagonist which also exhibits functional interaction, allow quantitation of the characteristics of the competitive and functional interactant effects. 2 Both the affinity constant of the antagonist for its receptors and numerical values characterizing the functional interaction can be obtained. 3 The null equations have been tested in a model system by using a mixture of papaverine hydrochloride (either 5 or 20 μM) and methyl atropine bromide (10 nM) to mimic a competitive antagonist which also shows functional interaction. 4 Agreement between values derived directly and indirectly from the model is good and validates the use of the null equations.

Diffusion of labelled substances through isolated rat diaphragm

1 The rate of diffusion of [14C] sucrose through rat diaphragm muscle is dependent on the period of preliminary soaking of the muscle in Krebs solution at 36° C. The ratio of the length of the diffusion path through the diaphragm to its geometrical thickness appears to fall from 4.39 ± 0.38 (S.E. of the mean) to 2.23 ± 0.18 after about 6 h of soaking. 2 The area of the diaphragms available for diffusion is apparently constant at 0.3–0.4 of their total area. 3 The measured thickness of the diaphragms increases by about 20% on soaking. 4 Entry of [131I] iodide into the muscle fibres is detected as a fall in both steady state and non‐steady state rates of diffusion through the diaphragm. 5 Entry of [14C‐methyl] decamethonium into the muscle cells is not evident from such diffusion studies in normal Krebs solution.

A TEST OF THE NULL EQUATION FOR FUNCTIONAL ANTAGONISM

1 The quantitative model for functional antagonism and synergism has been tested by studying its ability to fit data obtained from the functional antagonism of (−)‐isoprenaline by muscarinic agonists on guinea‐pig isolated atria. 2 The general form of the null equation has been shown to fit the experimental curves satisfactorily. 3 Functional interaction between (–)‐soprenaline and muscarinic agonists on atria has been shown to be type I although there does seem to be a discrepancy between values of the functional affinity constants. KA1F and KA2F estimated in two different ways. 4 The affinity constants, KA. of the muscarinic agonists for their receptors have been estimated by use of the selective irreversible antagonist propylbenzilylcholine mustard. The discrepancy between KAF (i.e. both KA1F and KA2F) and KA is small for pentyltrimethylammonium which is an agonist of low intrinsic efficacy. By contrast the discrepancy between KAF and KA is much greater for methyl‐furmethide and oxotremorine both of which have much higher intrinsic efficacies. These results are as predicted by the model. 5 It is suggested that the discrepancy between KA1F and KA2F may be due to the limited ability of the equation

A new method for estimating dissociation constants of competitive and non-competitive antagonists with no prior knowledge of agonist concentrations.

1 A method is presented which enables the dissociation constant (K1) of a competitive, pseudo‐irreversible or non‐competitive antagonist‐receptor complex to be estimated without knowledge of agonist concentrations. 2 The technique has been tested using sets of concentration‐response data which simulated these various types of antagonism. 3 The points for each set of simulated data could be plotted both as agonist concentration‐response curves at fixed antagonist concentrations and vice versa, producing paired data sets. 4 pK1‐values were estimated from such paired data sets using appropriate graphical and computer curve‐fitting methods. 5 For competitive antagonism, for each paired data set the computer curve‐fitting techniques gave the same value for pK1, assuming drug‐receptor interaction to be 1:1 and agonist concentrations to be known. 6 When agonist concentrations were assumed unknown, pK1s could not be estimated by the conventional method (using agonist dose‐ratios) but could still be obtained (for competitive, pseudo‐irreversible and non‐competitive antagonism) by the new method. 7 This new method should be especially useful for measuring dissociation constants of antagonists against neuronally‐ or ionophoretically‐released agonists. It may also be useful when agonist is applied exogenously, especially if suitable drugs are not available to block agonist uptake and/or metabolism.

Analysis of the binding of fluorescent ligands to soluble proteins: Use of simultaneous non-linear least squares regression to obtain estimates of binding parameters

The binding of three fluorescent ligands (warfarin, dansylsarcosine and 1-anilino-8-naphthalene sulphonate) to human albumin was analysed using simultaneous non-linear least squares regression analysis. Both mock and actual fluorescence data were examined and the results indicated that reliable estimates of the binding parameters as well as the molar fluorescence of bound ligand could be obtained. The advantage of this method of analysis is that it makes full use of all the experimental data and it eliminates the need for the graphical procedures usually employed to estimate the molar fluorescence of bound ligand and its binding constants. This type of analysis can be extended to other systems where some physical property of the bound ligand varies with increasing protein concentration.

Similarity between μ-opioid receptors in mouse vas deferens and guinea-pig ileum

1 The effects of the opioid receptor agonist RX783006 and of the opioid receptor partial agonist (+)‐meptazinol have been examined on electrically‐induced twitch responses of the guinea‐pig isolated ileum and of the mouse isolated vas deferens. 2 Log10 concentration‐tissue state curves were determined for (+)‐meptazinol and for RX783006, alone, in combination and, when appropriate, in the presence of naloxone (30 nM). 3 Analysis of these log10 concentration‐tissue state curves using the null equations derived and verified in the previous paper allows quantitation of the characteristics of the interaction of (+)‐meptazinol with the opioid receptors in these tissues. 4 The results indicate that the apparent differences in the actions of (+)‐meptazinol on isolated electrically‐stimulated guinea‐pig ileum and mouse vas deferens can be accounted for without the need to postulate differences between μ‐opioid receptors in these two tissues.

Quantification of the actions of agonists that simultaneously act on a particular type of receptor and have separate functional interactant properties

1 Null equations have been derived which allow quantification of the agonist properties of a compound that is able to modify the state of a tissue simultaneously by interacting with a particular type of receptor and by other means. 2 Parameters can be estimated which separately characterize the agonist properties of the compound and its functional interactant effect. 3 The null equations have been tested in a model system by using a mixture of papaverine (5 μM) and hexyltrimethylammonium bromide (30 μM) to mimic an agonist which also has functional antagonist properties. 4 The values obtained for the various parameters measured directly and indirectly are in good general agreement, confirming the validity of the model.

Rate of onset and offset of neuromuscular block in the isolated rat diaphragm.

Waud (1967) has suggested that the rate of action of tubocurarine applied directly to a motor endplate is limited by diffusion, although his conclusion is contrary to that reached earlier by del Castillo & Katz (1957). However, it is generally agreed that when tubocurarine is added to a solution bathing an isolated rat diaphragm the rate of onset and offset of neuromuscular blockade is likely to be limited by the rate of diffusion of the drug molecules to their site of action (Paton & Waud, 1964). Nevertheless, attempts to prove this have not been entirely successful (Holmes, Jenden & Taylor, 1951 ; Creese, Taylor & Tilton, 1959). It is also of interest that the rate of onset of blockade is commonly seen to increase with successive applications of the same concentration of tubocurarine (Chou, 1947; Godfrey, Mogey & Taylor, 1950; Holmes et al., 1951). The effect is obvious even when the tissue is washed for prolonged periods between applications of tubocurarine (Fig. 1). If the muscle is regarded as an infinite sheet of uniform thickness exposed on both sides to the drug solution at zero time then predicted curves can be constructed for the onset and offset of neuromuscular blockade by methods similar in principle to those used by Hill & Macpherson (1954). These curves (predicted on the basis of a diffusion model) can then be compared with those observed experimentally.