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Synaptic transmission between neurons is governed by a cascade of stochasticreaction-diffusion events that lead to calcium-induced vesicle release ofneurotransmitter. Since experimental measurements of such systems arechallenging due their nanometer and sub-millisecond scale, numericalsimulations remain the principal tool for studying calcium dependent synapticvesicle fusion, despite limitations of time-consuming calculations. In thispaper we develop an analytical solution to rapidly explore dynamical stochasticreaction-diffusion problems, based on first-passage times. This is the firstanalytical model that accounts simultaneously for relevant statistical featuresof calcium ion diffusion, buffering, and its binding/unbinding reaction with avesicular sensor. In particular, unbinding kinetics are shown to have a majorimpact on the calcium sensor's occupancy probability on a millisecond scale andtherefore cannot be neglected. Using Monte Carlo simulations we validated ouranalytical solution for instantaneous calcium influx and that throughvoltage-gated calcium channels. Overall we present a fast and rigorousanalytical tool to study simplified reaction-diffusion systems that allow asystematic exploration of the biophysical parameters at a molecular scale,while correctly accounting for the statistical nature of molecular interactionswithin cells, that can also serve as a building block for more general cellsignaling simulators.

A first-passage approach to diffusion-influenced reversible binding: insights into nanoscale signaling at the presynapse