A theoretical study of calcium entry in nerve terminals, with application to neurotransmitter release

This study is concerned with explaining the dependence of miniature end-plate potential frequencies (mepp) and evoked neurotransmitter release (epp) on extracellular calcium concentration (C_e) and on depolarization. The key feature of the analysis is the recognition that the observed dependence of depolarization-induced mepp and epp on C_e results from a combination of three processes: C_e-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 & Quastel (1973) have been selected for intensive study. Previously suggested equations in which entry grows without bound as C_e increases are rejected-including the commonly used equation that follows from employment of the Nernst equilibrium potential. It is shown that the qualitative features of the experiments are best fit by an entry equation that saturates as a function of C_e, with a saturation level that increases with depolarization. In order to apply the new theoretical results, a study is made of the slope of curves giving log neurotransmitter release as a function of log C_e. It is shown that 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 shown to be 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. In addition, it is shown that the differing dependences of the slope on C_e that are observed in epp and mepp do not preclude a common mechanism, with the same dependence on internal Ca.