## The Operational Model Of Drug Action

While Stephenson's treatment of drug receptor-mediated response can be used to fit data to molecular models, it still utilized efficacy essentially as a fitting parameter tailored to make experimental data fit the model. This arbitrary nature of efficacy led Black and Leff to postulate a new model of drug action based on observed effects of drugs in tissues; they called this approach the operational model of drug action [12]. This model is based on the premise that the efficacy term emerges from an experimentally observed behavior of pharmacological systems, specifically the saturable relationship between receptor stimulation and observed response. An example of the shape of such a relationship is shown in Fig. 1.2b. The hyperbolic shape of this relationship forms the basic premise of this model; the ligand occupied receptor [AR] activates the cellular stimulus-response cascade with a general equilibrium dissociation constant denoted KE (this is the concentration of [AR] complex producing 50% maximal response):

The more efficient is the process from production of [AR] to response, the smaller is KE. Substituting mass action for the production of [AR] yields the equation for the operational model:

Response

'max

The constant used to characterize the propensity of a given system and a given agonist to yield response is the ratio [Rt]/Kg; this is denoted t. Substituting for t yields the working equation for the operational model:

Response

'max

It can be seen that tissue response is now a function of biologically related quantities, namely the receptor density [Rt ] and KE, concentration of occupied (activated) receptor available for interaction with the cellular machinery mediating tissue response.

At this point, it should be pointed out that the unknown nature of the biochemical reactions linking receptor occupancy and tissue response is not an impediment to the system-independent measure of drug activity. This is because of the null method. Thus, when comparisons of agonists are made in the same tissue at equal levels of response, then the impact of the biochemical cascade translating receptor occupancy and tissue response is removed since their effects are the same for both agonists. Under these circumstances, ratios of receptor affinities (i.e., KA) and/or ratios of efficacies (ratio of t values) become unique identifiers of the particular agonist-receptor pairs. Up to this point, only agonism has been discussed, but receptor theory also has provided a number of models to describe the antagonism of agonist response. It is worth considering these before discussion of 7TM receptor mechanisms.

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