The statistical parameters underlying acetylcholine (ACh) release were studied using Ca2+ and Sr2+ ions to promote ACh secretion. Experiments were performed at frog neuromuscular junctions using electrophysiological recording techniques. Increases in asynchronous ACh release, reflected as the frequency of occurrence of miniature end-plate potentials (MEPPf), were evoked by high potassium depolarization in either Ca2+ or Sr2+ solutions. Increases in MEPPf mediated by Ca2+ were of very low probability and well-described by a Poisson distribution whilst similar MEPPf increases mediated by Sr2+ were best described as a simple binomial distribution. From the binomial distribution in Sr2+ solutions, values for the average probability of release (p) and the number of releasable ACh quanta (n) may be determined (whereby mean MEPPf = np). In Sr2+ solutions, values of p were independent of both bin width and of the value of n, suggesting that both n and p were stationary. Calculations of p using the simple binomial distribution in Sr2+ solutions gave theoretical values for the third moment of the mean which were indistinguishable from the experimental distribution. These results, in conjunction with Monte Carlo simulations of the data, suggest that spatial and temporal variance do not measurably affect the analysis. Synchronous ACh release evoked by nerve impulses (end-plate potentials, EPPs) follow a simple binomial distribution in both Ca26+ and Sr2+ solutions. Similar mean levels of synchronous ACh release (m, where m = np) were produced by lower values of P and higher values of n in Ca2+ as compared to Sr2+ The statistical analyses suggest the presence of two different Ca2+-dependent steps in the final stages of neurotransmitter release. The results are discussed in accordance with (i) statistical models for quantal neurotransmitter release, (ii) the role of Sr2+ as a partial agonist for evoked ACh release, and (iii) the specific loci that may represent the sites of Ca2+ and Sr2+ sensitivity.
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