Quantal behaviour of synaptic transmission can be statistically examined using the Fourier line spectrum of the histogram of synaptic potentials

Combining principal component and spectral analyses with the method of moments in studies of quantal transmission

This chapter considers methods for measurements of postsynaptic responses and simple approaches to the estimation of parameters of quantal release in synapses of the central nervous system of vertebrates. The use of these methods is illustrated by the analysis of single-fibre and "minimal" monosynaptic postsynaptic potentials (PSPs) or currents (PSCs) recorded from neurons of the frog spinal cord and rat hippocampus. First, we briefly discuss traditional methods of the response measurements using peak amplitudes or areas, further focusing on a novel method based on multivariate statistical techniques of the principal component analysis (PCA). This approach provides typically better signal-to-noise ratios and is able to separate two or more response components, which can arise due to activation of more than one presynaptic fibre, axon collaterals, receptor subtypes or spatially separated transmission sites. Second, spectral analysis is introduced as the method of choice to verify whether the amplitude fluctuations of the postsynaptic responses have a quantal nature and to obtain estimations of the "basic" quantal parameters, i.e. the quantal size (Q) and mean quantal content (m), without introducing assumptions on release statistics. Third, we show how the method of moments could be applied in the framework of the Poisson and binomial models to estimate the basic quantal parameters and parameters p and n, which reflect the release probability and maximum number of quanta released (or the number of effective release sites), respectively. Fourth, we show that the analysis of the moments can also be instrumental to reveal non-uniformity of release probabilities and compare how several competing models of neurotransmitter release fit to multiple experimental data sets.

Calibration of an autocorrelation-based method for determining amplitude histogram reliability and quantal size

1. We describe a method, based on autocorrelation and Monte Carlo simulation, for determining the likelihood that peaks in synaptic amplitude frequency histograms could have been a result of finite sampling from parent distributions that were unimodal. 2. The first step was to calculate an 'autocorrelation score' for the histogram to be tested. A unimodal distribution was fitted to the test histogram and subtracted from it. The resulting difference function was smoothed and its autocorrelation function calculated. The amplitude of the first (non-zero lag) peak in this autocorrelation function was taken as the autocorrelation score for that histogram. The score depends on the sharpness of the histogram peaks, the equality of their spacing and the number of trials. 3. The second stage was to generate large numbers of random samples, each of the same number of trials as the histogram, from a unimodal generator distribution of similar shape. The autocorrelation score was calculated for each sample and the proportion of samples with scores greater than the histogram gave the likelihood that the histogram peaks could have arisen by sampling artifact. 4. The method was calibrated using simulated non-quantal and quantal histograms with different signal-to-noise ratios and numbers of trials. For a quantal distribution with four peaks and a signal-to-noise ratio of 3, a sample size of about 500 trials was needed for 95% of samples to be distinguished from a non-quantal distribution. 5. The ability of the autocorrelation method to distinguish quantal from non-quantal distributions was compared against two conventional statistical tests, the chi 2 and the Kolmogorov-Smirnov goodness of fit tests. The autocorrelation method was more specific in extracting quantized responses. The Kolmogorov-Smirnov test in particular could not distinguish quantal distributions with multiple peaks even if the peaks were very sharp. 6. The improved discrimination of the autocorrelation method proved important when applied to experimental data recorded from hippocampal synapses. Of thirty-three histograms that were significantly different from smooth distributions by the autocorrelation method (P < 0.05), only seventeen were significantly different using the chi 2 test and only two when using the Kolmogorov-Smirnov test. 7. The autocorrelation method also gave an estimate of histogram peak spacing or quantal size. Using simulated quantal distributions, we showed that this estimate was likely to be correct within a few per cent for distributions that gave P < 0.01 by autocorrelation scoring.

Noise deconvolution based on the L1-metric and decomposition of discrete distributions of postsynaptic responses

A statistical approach to analysis of amplitude fluctuations of postsynaptic responses is described. This includes (1) using a L1-metric in the space of distribution functions for minimisation with application of linear programming methods to decompose amplitude distributions into a convolution of Gaussian and discrete distributions; (2) deconvolution of the resulting discrete distribution with determination of the release probabilities and the quantal amplitude for cases with a small number (< 5) of discrete components. The methods were tested against simulated data over a range of sample sizes and signal-to-noise ratios which mimicked those observed in physiological experiments. In computer simulation experiments, comparisons were made with other methods of 'unconstrained' (generalized) and constrained reconstruction of discrete components from convolutions. The simulation results provided additional criteria for improving the solutions to overcome 'over-fitting phenomena' and to constrain the number of components with small probabilities. Application of the programme to recordings from hippocampal neurones demonstrated its usefulness for the analysis of amplitude distributions of postsynaptic responses.

Quantal analysis of synaptic transmission in the central nervous system

In the past year, important advances have been made in the understanding of quantal neurotransmission at central synapses. These include new statistical tests for the significance of quantal peaks in synaptic amplitude histograms, greater understanding of possible sources of quantal variance, and new attempts to undertake a rigorous quantal analysis of neurotransmission.