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) is

Δ F = -RTlogₑK (20)

or log₁₀ K = (- ΔF)/2.3RT (20a)

In the series R⁺NMe₃ R'⁺NMe₃

R⁺NMe₂ Et R'⁺NMe₂ Et

R⁺NMe Et₂ R'⁺NMe₂ Et

R⁺NMeEt₂ R'⁺NMeEt₂

R⁺NEt₃ R'⁺NEt₃

let 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 of

R⁺NMe₂ Et = ΔF + a R'⁺NMe₂ Et = ΔF' + a

R⁺NMeEt₂ = ΔF + b R'⁺NMeEt₂ = ΔF' + b

R⁺NEt₃ = ΔF + c R'⁺NEt₃ = ΔF' + c

where "(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 that

log K = (- ΔF)/2.3RT (20a)

log Kₐ = (- ΔF + a)/2.3RT (20b)

therefore,

log Kₐ/K = (-a)/2.3RT (21

Values 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 stimulus

S = 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 ratio

Kₐ/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.