Neurotransmitter release: development of a theory for total release based on kinetics

According to the calcium-voltage hypothesis for the control of neurotransmitter release, a molecule (or molecular complex) must be activated by membrane depolarization, after which the activated molecule can bind calcium and initiate release. In this study, we have examined properties of the kinetics of phasic release resulting from a set of differential equations that characterize the calcium-voltage hypothesis. It was found that, in accord with experiments, an important feature is the approximate constancy of the shape of the graph for the kinetics of phasic release at various depolarizations and extracellular calcium concentrations. The shape constancy allowed us to obtain an explicit and relatively simple analytical formula for the total transmitter release (quantal content) by approximating the differential equations of the model. This formula shows a saturating sigmoidal dependence on both intracellular and extracellular calcium concentrations. The formula thus agrees with various experiments. Moreover, it agrees with, and provides meaning to, earlier phenomenological expressions for the dependence of release on calcium concentration. In particular, the formula provides an expression for the maximal release in terms of kinetic parameters from the calcium-voltage model, and thereby allows one to supplement earlier kinetic tests of the calcium-voltage hypothesis with further tests focused upon the dependence of total release on depolarization.