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 s ynapses, and broad amplitude distributions of postsynaptic unitary response s within a given synapse. A common approach to such systems has been to ass ume identical synapses and recover apparent quantal parameters by deconvolu tion procedures from measured evoked (ePSC) and unitary evoked postsynaptic current (uePSC) distributions. Here we explicitly consider nonuniform syna ptic 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 o f the actual nonuniform synaptic system. This equivalent system has the adv antage of being fully defined by just four quantal parameters: (n) over til de, the number of equivalent synapses; (p) over tilde, the mean probability of quantal release; <(<mu>)over tilde>, mean; and <(<sigma>)over tilde>(2) , variance of the uePSC distribution. We show that these equivalent paramet ers are weighted averages of intrinsic parameters and can be approximated b y apparent quantal parameters, therefore establishing a useful analytical l ink between the apparent and intrinsic parameters. The present study extend s previous work on compound binomial analysis of synaptic transmission by h ighlighting the importance of the product of p and mu, and the variance of that product. Conditions for a unique deconvolution of apparent uniform syn aptic parameters have been derived and justified. Our approach does not req uire independence of synaptic parameters, such as p and mu from each other, therefore the approach will hold even if feedback (i.e., via retrograde tr ansmission) exists between pre and postsynaptic signals. Using numerical si mulations 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 pre sent, therefore even under such conditions the apparent parameters estimate d from experiments would be informative.