Close agreement between deterministic vs. 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, prior studies revealed closer-than-expected agreement between deterministic and stochastic simulations of Ca2+ diffusion, buffering and sensing, as long as Ca2+ channel gating is not Ca2+-dependent. To understand this result more fully, we present a comparative study complementing prior 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 the fluctuation amplitudes. This holds if all relevant reactions are heteroreaction between molecules of different species, as is the case for the 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+ sensors state underlying the FPT distribution are only weakly affected by the fluctuations in the local Ca2+ concentration around its average, deterministically computable value. Statement of SignificanceMany fundamental Ca2+-dependent cell processes are triggered by local Ca2+ elevations involving only a few hundred Ca2+ ions. Therefore, one expects large Ca2+ concentration fluctuations, which are ignored by deterministic reaction-diffusion modeling approaches. However, more accurate stochastic approaches require tracking trajectories of individual Ca2+ ions and its binding targets, which is very computationally expensive. This study reveals conditions under which Ca2+-dependent processes like secretory vesicle fusion can be modeled using efficient deterministic approaches, without sacrificing significant accuracy. We find that deterministic methods can accurately predict the delay to the fusion of a neurotransmitter-containing vesicle, as long as the number of Ca2+ ions is above about 50. We reveal factors that explain the limited impact of stochastic fluctuations in this case.