Analysis and implications of equivalent uniform approximations of nonuniform unitary synaptic systems

Real synaptic systems consist of a nonuniform population of synapses with a broad spectrum of probability and response distributions varying between synapses, and broad amplitude distributions of postsynaptic unitary responses within a given synapse. A common approach to such systems has been to assume identical synapses and recover apparent quantal parameters by deconvolution procedures from measured evoked (ePSC) and unitary evoked postsynaptic current (uePSC) distributions. Here we explicitly consider nonuniform synaptic systems with both intra (type I) and intersynaptic (type II) response variability and formally define an equivalent system of uniform synapses in which both uePSC and ePSC amplitude distributions best approximate those of the actual nonuniform synaptic system. This equivalent system has the advantage of being fully defined by just four quantal parameters: n, the number of equivalent synapses; p, the mean probability of quantal release; μ, mean; and σ², variance of the uePSC distribution. We show that these equivalent parameters are weighted averages of intrinsic parameters and can be approximated by apparent quantal parameters, therefore establishing a useful analytical link between the apparent and intrinsic parameters. The present study extends previous work on compound binomial analysis of synaptic transmission by highlighting the importance of the product of p and μ, and the variance of that product. Conditions for a unique deconvolution of apparent uniform synaptic parameters have been derived and justified. Our approach does not require independence of synaptic parameters, such as p and μ from each other, therefore the approach will hold even if feedback (i.e., via retrograde transmission) exists between pre and postsynaptic signals. Using numerical simulations we demonstrate how equivalent parameters are meaningful even when there is considerable variation in intrinsic parameters, including systems where subpopulations of high- and low-release probability synapses are present, therefore even under such conditions the apparent parameters estimated from experiments would be informative.