Doubts about quantal analysis.

TO THE EDITOR: In an impressive series of articles, Korn and co-workers (e.g., Faber and Korn 1988; Faber et al. 1992, 1995; Korn et al. 1981, 1982, 1987; reviews in Korn and Faber 1991, 2005) described electrophysiological recordings performed on goldfish Mauthner cells and adjacent inhibitory interneurons. In their founding article, published in the Journal of Neurophysiology, Korn and colleagues (1982) developed a formal analysis of the amplitude fluctuations of inhibitory postsynaptic potentials (IPSPs) produced by directly evoked presynaptic impulses. According to these analyses, the IPSPs follow a binomial distribution whose parameters can be determined unambiguously. In particular, Korn and co-workers claimed that the value of n obtained by selecting the binomial distribution that best fit the data was equal to the number of stained presynaptic boutons that had been counted anatomically (see Fig. 1, redrawn from Korn et al. 1982). They suggested that a single bouton can release only one quantum of transmitter per impulse; this idea has been influential but has remained controversial. The aim of this letter is to raise doubts about the validity of aspects of this seminal paper, rather than to review the subsequent literature on “one bouton one quantum,” which has accreted around it. The very close agreement that Korn and co-workers obtained between the anatomically counted number of synapses and the n deduced from indirect analyses of electrophysiological recordings (see Fig. 1) is almost miraculous considering: 1) the difficulty of manually extracting precise slopes from zigzagging electrophysiological recordings that display fluctuations at two or three different scales (see Fig. 5 in Korn et al. 1982). Indeed, Korn and colleagues were ultimately led to develop automated procedures (Ankri et al. 1994; Korn et al. 1993) and 2) the lack of precision in the histograms that describe the slopes’ distributions. On average, one histogram represented data pooled from 160 events and such data were used to discriminate between, say, binomial parameters n 17 and n 18. My main objection to the work of Korn et al. is derived from a close examination of their published theoretical curves. As I will show, several theoretical curves were simply not what Korn and co-workers claimed them to be. Other curves, given as unique solutions to an optimization algorithm on n and p were not unique because curves for other n and p values would have fit the data just as well. The inadequacy of the theoretical curves provided by the authors could not be perceived by the average reader because readers were not given the precise numerical values of the parameters needed to generate the curves. In the present work, an extensive exploration of the parameter space was performed, allowing me to evaluate the hidden parameters, and cast doubt on some of the authors’ claims. M E T H O D S