Partial mean-field model for neurotransmission dynamics

TL;DR

This paper develops a hybrid modeling approach combining particle-based and continuum models to efficiently simulate neurotransmission dynamics, accurately capturing both stochastic low-copy-number effects and large-scale concentration changes.

Contribution

It introduces a new hybrid model that seamlessly integrates microscopic particle simulations with macroscopic PDEs for neurotransmission systems.

Findings

Hybrid model accurately approximates particle-based simulations

Efficiently captures stochastic effects in low-copy-number species

Demonstrates effectiveness in realistic neurotransmission scenarios

Abstract

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the stochastic-spatial particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.