Statistical methods for assessing the dimensions of synaptic vesicles in nerve terminals

Chemical transmission between neurons occurs by the release of neurotransmitter packaged within vesicles of the presynaptic neuron onto a postsynaptic target. The amount of transmitter contained within a vesicle is in part regulated by the size of the vesicle. Thus, it is of general interest to quantify the dimension of vesicles in understanding the basic principles of chemical synaptic transmission. These vesicles can only be measured by electron microscopic techniques. Obtaining the true dimensions of synaptic structures is therefore complicated by stereological considerations. In this study, we suggest improved methods for determining the distributions (and mean sizes) for populations of vesicle diameters by mathematical processes involving (1) an implicit inversion of the empirical data distribution, (2) an explicit inversion approach, and (3) an approach based on substituting the empirical distribution into the inversion formula and then isotonizing using an iterated convex minorant algorithm. These procedures provide distributions that better represent the true population distributions (and means) for comparisons with other data sets of vesicle diameter measures.