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

Synaptic transmission between neurons is governed by a cascade of stochastic calcium ion reaction-diffusion events within nerve terminals leading to vesicular release of neurotransmitter. Since experimental measurements of such systems are challenging due to their nanometer and sub-millisecond scale, numerical simulations remain the principal tool for studying calcium-dependent neurotransmitter release driven by electrical impulses, despite the limitations of time-consuming calculations. In this paper, we develop an analytical solution to rapidly explore dynamical stochastic reaction-diffusion problems based on first-passage times. This is the first analytical model that accounts simultaneously for relevant statistical features of calcium ion diffusion, buffering, and its binding/unbinding reaction with a calcium sensor for synaptic vesicle fusion. In particular, unbinding kinetics are shown to have a major impact on submillisecond sensor occupancy probability and therefore cannot be neglected. Using Monte Carlo simulations we validated our analytical solution for instantaneous calcium influx and that through voltage-gated calcium channels. We present a fast and rigorous analytical tool that permits a systematic exploration of the influence of various biophysical parameters on molecular interactions within cells, and which can serve as a building block for more general cell signaling simulators.

Automated summary

The paper introduces an analytical solution for exploring dynamic stochastic reaction-diffusion problems, considering important statistical features of calcium ion diffusion, buffering, and binding/unbinding reactions with a calcium sensor for synaptic vesicle fusion simultaneously. The kinetics of unbinding are shown to significantly impact submillisecond sensor occupancy probability. This analytical tool allows systematic exploration of the influence of various biophysical parameters on molecular interactions within cells, serving as a building block for more generalized cell signaling simulators.