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 experime ntal concentration-response curves in which an independent variable, the co ncentration of a receptor ligand, is linked with a dependent variable, the biological response. The steps that intervene between the ligand-receptor i nteraction and the subsequent biologic effect, i.e. modulation of transmitt er release in our examples, are largely unknown. Nevertheless, the shape of a concentration-response curve may give some insights into the nature of t he relation between receptor occupancy and ensuing response. The shape of t he concentration-response curve can be evaluated by nonlinear regression an alysis of the data paints of the independent and dependent variable. If pos sible, the model applied should be mechanistically derived from a physical or chemical law, underlying the biological condition. For instance, the inh erence 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 b imolecular concentration-binding curve. Evaluation methods which neglect th e alteration of the geometrical form of concentration-response curves due t o non-proportionality between receptor occupation and relative response do not seem appropriate to quantify spare receptors. The "general response fun ction" may allow a mechanistic interpretation of the occupancy-response rel ationship. This function estimates roughly the number of "non-spare" recept ors and of spare receptors on a functional unit that contribute to the resp onse.