Limits of quantal analysis reliability: quantal and unimodal constraints and setting of confidence intervals for quantal size

Abstract

An accurate objective method for determining the reliability of estimates of quantal size (Q) at central synapses was developed. To do this, distributions of amplitudes of postsynaptic responses were simulated by convolving a number of discrete amplitudes separated by equal increments Q with gaussian noise, after which the value of Q was estimated by the maximum likelihood method under different constraints on the discrete distribution. It was shown that the likelihood function (LF) had several local maxima under the quantal constraint, and, if the value of the ratio between Q and the standard deviation of the noise (sigma) was less than 3, the global maximum of the LF corresponded to a biased estimate of Q lying in a range of values less than 1.5 sigma. The best estimates of Q were obtained when unimodal discrete distributions of amplitudes resulting from the maximum likelihood method were selected. However, this method also gave biased estimates when Q/sigma was less than 1.5-2.3. The limit of reliability depended on the number of discrete components and the sample size. To calculate confidence intervals for the quantal size, different numbers and weights of components were used to simulate amplitude histograms with different values of Q/sigma. Three data sets were used to illustrate the procedure.