Bidirectional collision coupling in the regulation of the adenylate cyclase. The allozyme hypothesis for receptor function

Donald E Macfarlane

doi:10.1016/S0026-895X(25)15184-5

A mathematical analysis is presented of an extension of the collision coupling model for the regulation of the adenylate cyclase. The analysis assumes that the adenylate cyclase is switched on by a brief interaction with an agonist-occupied activating receptor. It remains on until it is switched off either by a brief interaction with an agonist-occupied deactivating receptor or with a postulated basal deactivating system. Only one species of agonist-receptor complex accumulates, so that agonist binding conforms to the Langmuir isotherm. Both the activation step and the deactivation step are regarded as being irreversible, and the complete on/off cycle requires a source of driving energy from the cell. The analysis gives an economical account of the relationship between the intrinsic activity of an agonist (I) and its pharmacological shift ratio (P) (the ratio of concentrations of the agonist needed for half-maximal occupancy of the receptor and half-maximal effect on the adenylate cyclase). The dose-response relationships are 'normal', that is, have the shape of the Langmuir isotherm. Both I and P are shown to be simple functions of the coupling factor (Fc), which is defined in terms of the rate constant of the basal deactivating system (B) and the planar concentration of receptors (R). These relationships are: Fc = KcR/B; I = Fc/(Fc + 1); P = Fc + 1. Two or more agonists acting on different activating receptors interact to reduce their apparent coupling factors. The coupling factor for agonists which deactivate adenylate cyclase (F'c) includes a term dependent upon the activating agonist being used. The deactivating intrinsic activity (I') and pharmacological shift ratio (P') are related to F'c in the same way as those for activating agonist. Slowly and rapidly reversing antagonists are demonstrated to have an effect which is less than their occupancy of the receptor by a factor related to the pharmacological shift ratio of the agonist used. The trajectory with which the activity of the adenylate cyclase approaches its equilibrium value after the addition of an agonist is a complex function, but initially the rate constant of this trajectory exceeds that of the binding of the agonist to its receptor by a factor related to Fc and the final occupancy of the receptor. The model is compatible with many of the general features of the control by multiple receptors of the adenylate cyclase observed in the intact cell. It predicts that interventions that alter B will increase or decrease the sensitivity of the cell to all agonists operating on the adenylate cyclase system, and that activating and deactivating agonists will synergistically accelerate the consumption of driving energy. The model may be applicable to other pharmacological systems in which the receptors are allozymes, i.e., catalysts which are regulated by external stimuli.

Bidirectional collision coupling in the regulation of the adenylate cyclase. The allozyme hypothesis for receptor function

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