Calcium triggered neurotransmitter release is distinguished from other types of cellular exocytosis by its fast on and off kinetics and its precise spatial localization. To address the importance of the precise geometrical relationship among the vesicles, the Ca channels, and the proteins of the release machinery on neurotransmitter release, I developed a Monte Carlo simulation of Ca diffusion and reaction with nanometer spatial and nanosecond temporal resolution. I first examined the simple case of a single vesicle and its associated Ca channel. I found that the vesicle acts as a diffusion barrier, altering the shape of the Ca microdomain around the vesicle. Therefore, Ca-sensor(s) for release would be exposed to markedly different [Ca], varying by up to 13-fold, depending on their position around the vesicle. Using simple models of Ca triggered release, I showed that, due to the brevity of the Ca influx, the binding kinetics of the Ca-sensor rather than its equilibrium affinity determines receptor occupancy. Also, redundant copies of the binding sites could account for apparent differences in Ca-sensor affinities between synapses. I further showed that the random positioning of the Ca-sensor molecules around the vesicle can result in the emergence of two distinct populations of vesicles with low and high release probability. To study the case of multiple channels and vesicles, I constructed a geometrically realistic model of the active zone in frog neuromuscular junction. By tracking all Ca ions as they enter though particular channels and diffuse in the terminal, I showed that on average only 2-6 open Ca channels are required to produce experimentally observed channel cooperativity in this preparation. I then systematically compared the functional consequences of low and high number of open channels per action potential in this active zone. Modeling suggested that, while a low number of open channels reduced the energy needed to restore [Ca] after influx and decreased the delay of release, it resulted in high trial-to-trial variability of the number of vesicles released, which was not consistent with the experimental observation. I proposed a short-term lateral inhibition of fusion by each vesicle released to resolve this paradox
