The probability of quantal secretion within an array of calcium channels of an active zone

A Monte Carlo analysis has been made of calcium dynamics in submembranous domains of active zones in which the calcium contributed by the opening of many channels is pooled. The kinetics of calcium ions in these domains has been determined using simulations for channels arranged in different geometries, according to the active zone under consideration: rectangular grids for varicosities and boutons and lines for motor-nerve terminals. The effects of endogenous fixed and mobile buffers on the two-dimensional distribution of free calcium ions at these active zones are then given, together with the extent to which these are perturbed and can be detected with different affinity calcium indicators when the calcium channels open stochastically under an action potential. A Monte Carlo analysis of how the dynamics of calcium ions in the submembranous domains determines the probability of exocytosis from docked vesicles is also presented. The spatial distribution of exocytosis from rectangular arrays of secretory units is such that exocytosis is largely excluded from the edges of the array, due to the effects of endogenous buffers. There is a steeper than linear increase in quantal release with an increase in the number of secretory units in the array, indicating that there is not just a local interaction between secretory units. Conditioning action potentials promote an increase in quantal release by a subsequent action potential primarily by depleting the fixed and mobile buffers in the center of the array. In the case of two parallel lines of secretory units exocytosis is random, and diffusion, together with the endogenous calcium buffers, ensures that the secretory units only interact over relatively short distances. As a consequence of this and in contrast to the case of the rectangular array, there is a linear relationship between the extent of quantal secretion from these zones and their length, for lengths greater than a critical value. This Monte Carlo analysis successfully predicts the relationship between the size and geometry of active zones and the probability of quantal secretion at these, the existence of quantal versus multiquantal release at different active zones, and the origins of the F1 phase of facilitation in synapses possessing different active zone geometries.