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

Abstract

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.