Close agreement between deterministic versus stochastic modeling of first-passage time to vesicle fusion.

Ca-dependent cell processes, such as neurotransmitter or endocrine vesicle fusion, are inherently stochastic due to large fluctuations in Ca channel gating, Ca diffusion, and Ca binding to buffers and target sensors. However, previous studies revealed closer-than-expected agreement between deterministic and stochastic simulations of Ca diffusion, buffering, and sensing if Ca channel gating is not Ca dependent. To understand this result more fully, we present a comparative study complementing previous work, focusing on Ca dynamics downstream of Ca channel gating. Specifically, we compare deterministic (mean-field/mass-action) and stochastic simulations of vesicle exocytosis latency, quantified by the probability density of the first-passage time (FPT) to the Ca-bound state of a vesicle fusion sensor, following a brief Ca current pulse. We show that under physiological constraints, the discrepancy between FPT densities obtained using the two approaches remains small even if as few as ∼50 Ca ions enter per single channel-vesicle release unit. Using a reduced two-compartment model for ease of analysis, we illustrate how this close agreement arises from the smallness of correlations between fluctuations of the reactant molecule numbers, despite the large magnitude of fluctuation amplitudes. This holds if all relevant reactions are heteroreaction between molecules of different species, as is the case for bimolecular Ca binding to buffers and downstream sensor targets. In this case, diffusion and buffering effectively decorrelate the state of the Ca sensor from local Ca fluctuations. Thus, fluctuations in the Ca sensor's state underlying the FPT distribution are only weakly affected by the fluctuations in the local Ca concentration around its average, deterministically computable value.