Partial mean-field model for neurotransmission dynamics.

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 spatial–stochastic 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. • We study a system with two components that appear in strongly different abundance. • The starting model is a particle-based model for the two-component system. • We derive a mean-field model that couples a field model with a particle-based model. • The hybrid model is applied to the binding of calcium ions to presynaptic vesicles. • The hybrid model offers an accurate approximation of the full model in most cases. [ABSTRACT FROM AUTHOR]