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A System of Models for the Action of Drugs Applied Singly or Jointly to Biological Organisms

J. R. Ashford and J. M. Cobby
Biometrics
Vol. 30, No. 1 (Mar., 1974), pp. 11-31
DOI: 10.2307/2529614
Stable URL: http://www.jstor.org/stable/2529614
Page Count: 21
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A System of Models for the Action of Drugs Applied Singly or Jointly to Biological Organisms
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Abstract

This paper is concerned with a system of mathematical models for the action of drugs when applied singly or jointly. The models are based upon the concepts of "sites of dosage" and "sites of action" of drugs and of "physiological systems" which may be affected by drugs at sites of action. A drug may have one or more sites of action and at each such site may affect one or more physiological systems. Two or more drugs may have common sites of action. The action of a drug at any particular site is assumed to take place as a result of the "occupation of receptor", an occupied receptor behaving differently from an unoccupied receptor. The occupation of receptors is governed by the "law of mass action" and depends upon the concentration of the drugs at the site of action. If two or more drugs act the same site, they compete for receptors at that site. The effect of occupying receptors at a site is to change the "activity" of the corresponding physiological system. This change may not be capable of direct assessment, but may be revealed by a change in the state of the system, which is assumed to be a monotonic function of the change of activity. The action of a drug when applied alone is considered in the light of this conceptual framework. It is shown that if the state of a system is a monotonic function of the concentration of the drug, a model involving a single site of action of the drug is appropriate. If, as is sometimes observed, the relationship is nonmonotonic, with a single extremum, a two site representation is required. The extension of the basic models to the joint action of two drugs is then discussed, in terms of the number of sites of action of each drug separately and whether or not certain sites of action are common to each drug. A feature of this approach is that the joint action is completely determined by the action of the separate drugs and the existence or otherwise of common sites. The classification of models for the joint action of drugs is then considered. It is shown that if the transfer of the drugs from sites of dosage to sites of action is regarded as a separate phenomenon, a classification in terms of the concentrations of drugs at their sites of action can be formulated in very simple terms. This classification embraces all the major distinctions which are present in alternative systems and enables some further light to be thrown on concepts such as synergism and antagonism. The application of the models is illustrated by an analysis of data concerning the effect of alcohol and meprobamate on human subjects.

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