In this talk I will consider computational modeling of
diffusion-controlled reactions with applications mainly in molecular
cell biology. I will give a brief overview of the modeling involved,
in the non-spatial as well as in the fully spatial setting, and I
shall also mention some different means by which such models can be
simulated.

In the main part of the talk I will discuss convergence. Conditions
for the validity of spatial mesocopic modeling in general and of the
diffusion operator in particular will be emphasized. Defining the
mesoscopic Laplacian from a discrete Finite Element Method has its
definite advantages, but there are also some limitations. It has been
suggested that these are partially solved when switching to the Finite
Volume Method and a critical discussion of this idea will be offered.

I will finish by briefly discussing some problems were spatial
modeling truly changes the dynamics when compared to the well-stirred
case. Here we can expect an accurate description of the molecular
transport mechanism to be important.