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

Ca²⁺-dependent cell processes, such as neurotransmitter or endocrine vesicle fusion, are inherently stochastic due to large fluctuations in Ca²⁺ channel gating, Ca²⁺ diffusion, and Ca²⁺ binding to buffers and target sensors. However, previous studies revealed closer-than-expected agreement between deterministic and stochastic simulations of Ca²⁺ diffusion, buffering, and sensing if Ca²⁺ channel gating is not Ca²⁺ dependent. To understand this result more fully, we present a comparative study complementing previous work, focusing on Ca²⁺ dynamics downstream of Ca²⁺ 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 Ca²⁺-bound state of a vesicle fusion sensor, following a brief Ca²⁺ 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 Ca²⁺ 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 Ca²⁺ binding to buffers and downstream sensor targets. In this case, diffusion and buffering effectively decorrelate the state of the Ca²⁺ sensor from local Ca²⁺ fluctuations. Thus, fluctuations in the Ca²⁺ sensor's state underlying the FPT distribution are only weakly affected by the fluctuations in the local Ca²⁺ concentration around its average, deterministically computable value.