The stochastic properties of spontaneous quantal release of transmitter at the frog neuromuscular junction

1. Earlier results showed that it is unlikely that spontaneous quantal release of transmitter at the frog neuromuscular junction is produced by a Poisson process.2. Data sets were tested, by using the u statistic, to see whether if they are assumed to be generated by a Poisson process, the mean interval is changing monotonically with time. By this critieria, some of the data sets are stationary, others are not.3. A variety of mathematical transforms are employed on empirical data sets to characterize the properties of the spontaneous quantal release.(a) The intensity function, which calculates the frequency distribution of all possible combinations of intervals, shows an excess of short intervals, without any sign of periodicity.(b) The variance-time curve, which estimates the accumulated variance of the series as a function of time into the series, lies significantly above the Poisson prediction.(c) The power spectrum, whether calculated on the intervals or on the number of intervals in time bins, deviates significantly from the Poisson prediction at the low frequencies.(d) The ln-survivor curve has two phases: a concave section for the short intervals, and a roughly linear section for the intervals of greater length.These transforms indicate that the min.e.p.p.s are clustered.4. A series of models for spontaneous quantal release were considered.(a) A Poisson model. Rejected because of consistent failure to fit the data.(b) A periodic model. Rejected because the intervals should be ordered rather than clustered.(c) A time-dependent model, in which quantal release is governed by a Poisson process with a mean interval that is oscillating in time. This model will generate clustering; by the transforms the model can be shown to closely fit the data. However, an autocorrelation of min.e.p.p. amplitudes shows that there is a relationship between the amplitudes and their position in the series. This is not predicted by the time-dependent oscillating model.(d) A branching Poisson model, in which a primary release, generated by a Poisson process, is likely to be followed by one or more subsidiary releases from the same site. The parameters of the branching model can be determined from ln-survivor curves. Theoretical curves, created with these parameters, give power spectra, variance-time curves, and ln-survivor curves that strongly resemble those calculated from the data. The model also predicts a significant autocorrelation of amplitudes.5. Min.e.p.p.s recorded with an extracellular electrode also fit well to a branching Poisson model.6. The effects of raised [Ca(2+)](o) on the intervals between min.e.p.p.s were studied. In our experiments the change in extracellular solution did not produce any notable change in release statistics.7. The effects of elevated [K(+)](o) on the intervals between spontaneous releases were studied. Depolarization of the nerve terminal increases the frequency of primary releases and decreases the chance of having subsidiary releases.8. Possible physical mechanisms by which quantal release of transmitter from a nerve terminal would fit a branching Poisson model are described.