Estimation of the variance of the variance: implications for multiple-probability fluctuation analysis at central synapses

Abstract

Synapses play a crucial role in information processing in the brain. Amplitude fluctuations of synaptic responses can be used to extract information about the mechanisms underlying synaptic transmission and its modulation. In particular, multiple-probability fluctuation analysis uses the variance and mean amplitude of postsynaptic responses, recorded at different probabilities, to estimate the number of functional releasing sites, the mean probability of release and the amplitude of single quantal responses. We investigated the best estimators of the variance of the variance in order to improve the estimates of quantal parameters. We used simulations of synaptic transmission to test the accuracy and reliability of estimators under different experimental conditions. For central synapses, which generally have a low number of releasing sites, the amplitude distribution of synaptic responses is not normal, thus the use of a theoretical variance of the variance based on the normal assumption is not a good approximation. However, appropriate estimators can be derived for the population and for limited sample sizes using a more general expression that involves higher moments and introducing unbiased estimators based on the h-statistics. Our results are likely to be relevant for various applications of fluctuation analysis when few channels or releasing sites are present.