Mathematical analysis of the control of neurotransmitter release by presynaptic receptors as a supplement to experimental data.

The quantitative analysis of receptor-mediated effects is based on experimental concentration-response curves in which an independent variable, the concentration of a receptor ligand, is linked with a dependent variable, the biological response. The steps that intervene between the ligand-receptor interaction and the subsequent biologic effect, i.e. modulation of transmitter release in our examples, are largely unknown. Nevertheless, the shape of a concentration-response curve may give some insights into the nature of the relation between receptor occupancy and ensuing response. The shape of the concentration-response curve can be evaluated by nonlinear regression analysis of the data points of the independent and dependent variable. If possible, the model applied should be mechanistically derived from a physical or chemical law, underlying the biological condition. For instance, the inherence of the Law of Mass Action allows to call the model mechanistic. The presence of spare receptors for an agonist must induce an alteration of the shape of the concentration-response curve as compared to a symmetric bimolecular concentration-binding curve. Evaluation methods which neglect the alteration of the geometrical form of concentration-response curves due to non-proportionality between receptor occupation and relative response do not seem appropriate to quantify spare receptors. The "general response function" may allow a mechanistic interpretation of the occupancy-response relationship. This function estimates roughly the number of "non-spare" receptors and of spare receptors on a functional unit that contribute to the response.