The relationship between receptor-effector unit heterogeneity and the shape of the concentration-effect profile: pharmacodynamic implications.

The apparent concentration-effect relationship is the ensemble of many effector units (such as individual cells or channels) that do not always exhibit a uniform stimulus-effect relationship. This concept is substantiated by many observations of heterogeneity in receptor-effector populations including hormone secreting cells, response to hormonal stimuli, activity pattern of second messengers, stimulus-evoked synaptic currents, and single ion channels. The relationship between drug concentration and magnitude of pharmacologic response is commonly described by the sigmoidal Emax model which was derived from the Hill equation. The sigmoidicity factor (N) in this model is assumed to be a pure mathematical parameter without physiological connotations. This work demonstrates that the numerical value of N (measured empirically) is the product of two factors: (i) the degree of heterogeneity of the effector subunits, i.e., the elemental component that upon drug stimulus contributes its pharmacological effect independently and does not interact with other subunits (it could range from a single receptor up to a whole tissue), and (ii) value of N*--the shape factor of the subunits' concentration-effect relationship. A special case of this approach occurs when N* > 5, which is an on-off case. Here N is determined by the distribution (density equation) of the subunit values. In case of heterogeneity of the microparameters of the effector subunits the apparent N will always have a lower value than N*. According to this theory it can be concluded that without knowledge of the distribution of the microparameters no mechanistic interpretation can be deduced from the apparent N value. If in the future N* can be determined by theoretical or experimental methods, the distribution function relating N* to N can be calculated. The relevance of this theory is increased in view of the progress being made in advanced research techniques which may enable us to determine the concentration-effect relationship at the level of the individual effector unit.