Mathematical modelling and quantification of the autoinhibitory feedback control of noradrenaline release in brain slices.

Concentration-response curves, reflecting alpha 2-autoreceptor-mediated inhibition of [3H]-noradrenaline release by exogenous noradrenaline in rat cerebral cortex and rabbit hippocampus slices, were analysed in order to test the usefulness of a mathematical model describing the relation between the independent variable, exogenous noradrenaline, and the dependent variable, inhibition of release. This model was based on the assumption of direct proportionality between receptor occupation and response, implying that there is correspondence between the shape of a concentration-binding curve and a concentration-response curve. The experimental concentration-response curves were obtained by different approaches: noradrenaline release from brain slices prelabelled with [3H]-noradrenaline was elicited electrically either by pseudo-one-pulse (POP) stimulation or by stimulation with 36 pulses applied with a frequency of 3 Hz. POP stimulation avoids autoinhibition by released noradrenaline and, therefore, was a suitable touchstone for the applied mathematical model which evaluates by nonlinear regression analysis two primary parameters: the dissociation constant between noradrenaline and the alpha 2-adrenoceptor and the biophase concentration of noradrenaline which reflects the extent of autoinhibition and should be zero under POP conditions. In rat cerebral cortex tissue, the corresponding biophase concentration of endogenous noradrenaline was indeed estimated to be zero and the dissociation constant was Kd = 10(-7.62 +/- 0.14) mol/l. With 3 Hz stimulation, the biophase concentration was 10(-7.80 +/- 0.05) mol/l, which has to be interpreted with respect to a simultaneously estimated Kd of 10(-7.63 +/- 0.12) mol/l.(ABSTRACT TRUNCATED AT 250 WORDS)