  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.
