The relationships between chemical structure, biological activity, affinity, and efficacy in compounds related to acetylcholine

Abstract

The present work describes an attempt to study the effects of changes in chemical structure on the affinity and efficacy of compounds related to acetylcholine. Although the absolute measurement of either of these properties is extremely difficult in principle for agonists, Stephenson suggested that if two series of compounds were prepared, one purely antagonist and the other agonist, changes in affinity with structure could easily be measured in the series of antagonists, and might be applicable to corresponding agonists. From these, and from the experimentally determined changes of activity with structure it might be possible to deduce something about the changes of efficacy with structure.Compounds related to acetylcholine seemed to be the simplest to study, the series of agonists containing an intact acetyl or methyl group and the series of antagonists being the analogous diphenylacetyl, or diphenylmethyl derivatives. Some benzilyl derivatives were also prepared.From the theory of Arrhenius, the relationship between the association constant, K, for the drug and receptor, and the free energy change on adsorption (Δ F) isΔ F = -RTlogₑK (20)or log₁₀ K = (- ΔF)/2.3RT (20a)In the series R⁺NMe₃ R'⁺NMe₃R⁺NMe₂ Et R'⁺NMe₂ EtR⁺NMe Et₂ R'⁺NMe₂ EtR⁺NMeEt₂ R'⁺NMeEt₂R⁺NEt₃ R'⁺NEt₃let it be assumed that the change in the free energy of adsorption is only dependent on the substitution in the onium group, i.e. that the free energy of adsorption is made up of components which are additive, the contribution from the portion R (whatever it may be) being unaffected by changes in the onium group: this implies that there is no interaction between R and the individual substituents on the quaternary nitrogen atom. We can then write, if the free energy of adsorption for R⁺NMe₃ is ΔF, and for R'NMe₃ ΔF', the free energy of adsorption ofR⁺NMe₂ Et = ΔF + a R'⁺NMe₂ Et = ΔF' + aR⁺NMeEt₂ = ΔF + b R'⁺NMeEt₂ = ΔF' + bR⁺NEt₃ = ΔF + c R'⁺NEt₃ = ΔF' + cwhere "(a)" is the free energy change brought about by replacing ⁺NMe₃ by R⁺NMe₂ Et, "(b)" the change for replacing ⁺NMe₃ by NMeEt₂ and "(c)" the change for replacing ⁺NMe₃ by ⁺NEt₃.The value of K for the series of antagonists have been determined experimentally; in the series R⁺NMe₃, R⁺NMe₂ Et etc., let these be K, Kₐ, Kb and Kc. It should then follow thatlog K = (- ΔF)/2.3RT (20a)log Kₐ = (- ΔF + a)/2.3RT (20b)therefore,log Kₐ/K = (-a)/2.3RT (21Values can similarly be obtained for "b" and +c ". These values should be the same regardless of the nature of R, and this can be investigated by using more than one series of antagonists.In the series of agonists, R⁺NMe₃ etc., the absolute value of the affinity or the free energy of adsorption cannot be determined in these experiments but the change in the free energy of adsorption produced by altering the cationic head should be the same, a, b and c, as in the series of antagonists. Suppose that the two compounds K⁺NMe₃ and R⁺NMe₂ Et have affinity constants K and Kₐ and that the equipotent molar ratio for R⁺NMe₂ Et relative to R⁺NMe₃ is n, i.e. n molecules of the R⁺NMe₂ Et are needed in order to produce the same response as one molecule of R⁺NMe₃. Then the stimulus,S = (e K A)/(1 +KA) = (eₐ Kₐ Aₐ)/(1+KₐAₐ) (22)where e is the efficacy of R⁺NMe₃ and A the concentration producing the response, and eₐ the efficacy of R'⁺NMe₂ Et and Aₐ the concentration producing the same response: the value Aₐ/A will be n.If the proportion of receptors occupied by the drug is relatively small, the expression KA = y/l-y will approximate to y and hence the stimulusS = ey = e AK (23)The expression above then becomes e K A = eₐKₐAₐ and hence the ratio of the efficacies,e/eₐ = (KₐAₐ)/KA = Kₐ/K n. (24)But the ratioKₐ/K = 10⁻[ᵃ/².³ ᴿᵀ] (25)which has been determined in the experiments with the antagonists. The value of (n), the equipotent molar ratio, Has been determined experimentally and hence the ratio can be calculated.