A theory of drug action is developed on the assumption that excitation by a stimulant drug is proportional to the rate of drug-receptor combination, rather than to the proportion of receptors occupied by the drug. The properties of a drug can then be specified by two rate constants:
k
1
, the association rate constant, and
k
2
, the dissociation rate constant; the ratio
k
2
/
k
1
═
k
e
corresponds to the reciprocal of the ‘affinity’. The value of
k
e
then determines potency, and
k
2
determines whether the drug is a powerful stimulant (
k
2
high), a partial agonist with ability both to excite and to antagonize (
k
2
moderate) or an antagonist with vestiges of stimulant action (
k
2
low). Qualitatively such a theory accounts for the persistence of effect of an antagonist on a tissue; for the characteristic sequence of excitation followed by block with drugs such as nicotine; for certain forms of tachyphylaxis; and for the vestiges of stimulant action possessed by classical antagonists. The theory has been tested on the guinea-pig ileum with acetylcholine and histamine as agonists, hyoscine, mepyramine and atropine as antagonists and alkyltrimethylammonium compounds as partial agonists, and it was corroborated in the following respects: 1. The dose-response curve of acetylcholine or histamine has the predicted form, if it is determined with an auxotonic rather than with an isotonic lever. 2. The rates of offset and of onset of antagonism, expressed in terms of change of receptor occupation by the antagonist, follow an exponential course from which
k
1
and
k
2
can be measured. Values of
k
2
/
k
1
so obtained agree with those obtained from the intensity of antagonism at equilibrium. The rate of onset of action increases in proportion to the antagonistic dose ratio finally achieved. The rate of offset of action is independent of the intensity of the antagonism or of the time taken to achieve it, up to dose ratios of 20 to 100. Diffusion barriers do not appear to contribute significantly to the time course of action of drugs such as hyoscine or mepyramine except at high dosage. 3. With the alkyltrimethylammonium compounds (hexyl to dodecyl): (
a
) the rate of onset and offset of antagonistic action fell with increasing potency. (
b
) The excitation produced always reached a peak response soon after injection which faded thereafter to a lower equilibrium value, with a time constant comparable with that predicted from the atropinic action. The rate and proportion of fade increased with dose. The dose-response curve for
peak
responses is bell-shaped, but not that for equilibrium responses. (
c
) The slope of the foot of the dose-response curves of the series and the magnitude of the maximum equilibrium responses correlated with the estimates of
k
1
and
k
2
, respectively, obtained from analysis of the atropinic action. The alkyltrimethylammonium compounds could be specified by a
k
1
which is constant and a
k
2
diminishing by a factor of about 2∙5 for each methylene group added. It is suggested that association is determined by the cationic head, and dissociation by shorter-range binding forces. 4. The responses to strong stimulants, such as histamine or acetylcholine, cannot be fully described in these terms. Following exposure to them the ileum is
non-specifically
desensitized. This desensitization is detectable with small doses, increases with dose and duration of exposure, and differs in its course to recovery from a specific antagonism. 5. A similar desensitization follows the removal of potassium from the fluid in which the ileum is immersed, and the two forms of desensitization summate. If potassium-free solution is applied rapidly, a contraction of the ileum occurs, indistinguishable from that due to acetylcholine. It is suggested as a working hypothesis of stimulant action that the drug ion exchanges with potassium at the receptor, and is then released from the receptor in exchange for potassium derived intracellularly, so that the chemoceptive action involves an extraction of potassium from the tissue. The implications of rate theory and of non-specific desensitization for theories of drug action are discussed.
Initial Inoculum and the Severity of COVID-19: A Mathematical Modeling Study of the Dose-Response of SARS-CoV-2 Infections
