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

Maria Reva,Denis S Grebenkov,David A Digregorio

doi:10.1038/s41598-021-84340-4

Abstract

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.

Highlights

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
We demonstrate the validity of the analytical solution by Monte Carlo simulations and study the effects of the sensor’s kinetics and geometrical properties of the synapse on the probability of the single site occupancy
We tested the importance of Ca2+ sensor koff for action potentials (APs)-evoked synaptic vesicles (SVs) fusion by solving reaction–diffusion equations by a finite-element method

Summary

Introduction

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. An analytical solution to this problem was found and coupled with a Markovian jump process to model buffering and calcium influx[18] Despite its advantages, this hybrid method does not account for the Ca2+sensor’s binding and unbinding kinetics, which is of crucial importance for the vesicle release dynamics, as shown below (Fig. 1). An extension to multiple calcium ions and its limitations are discussed To our knowledge, this is the first analytical solution for a stochastic reaction–diffusion problem that accounts simultaneously for binding/unbinding kinetics of a single binding site sensor in the presence of competing buffer species, and accurately predicts target occupancies following stochastic influx from ion channels, as compared to particle-based Monte Carlo simulations. This approach is applicable to a wide range of biochemical processes within cells that operate via diffusion-influenced reactions

Methods

Results

Conclusion