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.Comment: Published at http://dx.doi.org/10.1214/14-AAP1070 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
