  We propose a novel measure valued process which models the behaviour of
chemical reaction networks in spatially heterogeneous systems. It models
reaction dynamics between different molecular species and continuous movement
of molecules in space. Reactions rates at a spatial location are proportional
to the mass of different species present locally and to a location specific
chemical rate, which may be a function of the local or global species mass as
well. We obtain asymptotic limits for the process, with appropriate rescaling
depending on the abundance of different molecular types. In particular, when
the mass of some species in the scaling limit is discrete while the mass of the
others is continuous, we obtain a new type of spatial random evolution process.
This process can be shown, in some situations, to correspond to a
measure-valued piecewise deterministic Markov process in which the discrete
mass of the process evolves stochastically, and the continuous mass evolves in
a deterministic way between consecutive jump times of the discrete part.
