A THEORETICAL-STUDY OF CALCIUM ENTRY IN NERVE-TERMINALS, WITH APPLICATION TO NEUROTRANSMITTER RELEASE

The dependence of miniature end-plate potential frequencies (mepp) and evoked neurotransmitter release (epp) on extracellular Ca concentration (Ce) and on depolarization was analyzed. The observed dependence of depolarization-induced mepp and epp on Ce results from a combination of 3 processes: Ce-dependent entry of Ca into the terminal, removal of intracellular Ca and the release of neurotransmitter as a function of intracellular Ca. Because the entry process is of central concern, the experimental findings of Cooke, Okamoto and Quastel were selected for intensive study. Previously suggested equations in which entry grows without bound as Ce increases are rejected-including the commonly used equation that follows from employment of the Nernst equilibrium potential. Qualitative features of the experiments are best fit by an entry equation that saturates as a function of Ce, with a saturation level that increases with depolarization. To apply the new theoretical results, a study was made of the slope of curves giving log neurotransmitter release as a function of log Ce. The observed maximum slope of these curves is generally less than the product of the release co-operativity exponent n and the entry co-operativity exponent r. Maximum facilitation is a suitable measurement for the ascertainment of n, while duration of facilitation plays the corresponding role for r. An explanation is given of the differing effects of reduction in Ca influx by presynaptic inhibition and by the extracellular addition of divalent ions. The differing dependences of the slope on Ce that are observed in epp and mepp do not preclude a common mechanism, with the same dependence on internal Ca.