Probability of quantal transmitter release from nerve terminals: theoretical considerations in the determination of spatial variation

The release of transmitter occurs in discrete quantal units, such that the number released (m) is equal to the number available (n) times the average probability of release (p). Although a common method of estimating these parameters is to use simple binomial statistics, results may be biased if there is spatial or temporal variation in n and p (vars p, vart n, vart p). The problem arises in the simultaneous analysis of five variables, which is impractical due to the complexity and margin of error involved. The proposed solution is to eliminate two variables (vart n, vart p) by assuming stationarity and to obtain the required information from the first three moments of m. The resulting quadratic equation gives two solutions, p1 and p2. Computer simulation of quantal output as a function of vars p indicates that p1 is the better estimator of p when vars p is small, but that p2 is better when vars p is large. This changeover or "inflection" occurs at points which correspond to the maximum vars p obtainable by unimodal distributions of p (larger vars p being obtained by bimodal distributions). Comparison of the simulated histogram of m with those predicted by p1 and p2 shows that p1 provides the better fit, whether vars p is large or small. This discrepancy indicates that histogram analysis is unable to distinguish the appropriate estimate. The major limitations in the procedure can be met by assuming (1) stationarity (which can be attained and tested experimentally), and (2) normal distribution of p (since vars p is then less than "inflection" point, p1 will always be the correct estimate). The overall findings demonstrate that vars p and unbiased estimates of n and p may be calculated, provided reasonable assumptions are made. This in turn should allow the continued use of quantal parameters for describing transmitter release.