We study the effects of fast spatial movement of molecules on the dynamics of chemical species in a spatially heterogeneous chemical reaction network using a compartment model. The reaction networks we consider are either single- or multi-scale. When reaction dynamics is on a single-scale, fast spatial movement has a simple effect of averaging reactions over the distribution of all the species. When reaction dynamics is on multiple scales, we show that spatial movement of molecules has different effects depending on whether the movement of each type of species is faster or slower than the effective reaction dynamics on this molecular type. We obtain results for both when the system is without and with conserved quantities, which are linear combinations of species evolving only on the slower time scale.
"Scaling limits of spatial compartment models for chemical reaction networks." Ann. Appl. Probab. 25 (6) 3162 - 3208, December 2015. https://doi.org/10.1214/14-AAP1070