  This chapter provides a brief introduction to the theory and practice of
spatial stochastic simulations. It begins with an overview of different methods
available for biochemical simulations highlighting their strengths and
limitations. Spatial stochastic modeling approaches are indicated when
diffusion is relatively slow and spatial inhomogeneities involve relatively
small numbers of particles. The popular software package MCell allows
particle-based stochastic simulations of biochemical systems in complex three
dimensional (3D) geometries, which are important for many cell biology
applications. Here, we provide an overview of the simulation algorithms used by
MCell and the underlying theory. We then give a tutorial on building and
simulating MCell models using the CellBlender graphical user interface, that is
built as a plug-in to Blender, a widely-used and freely available software
platform for 3D modeling. The tutorial starts with simple models that
demonstrate basic MCell functionality and then advances to a number of more
complex examples that demonstrate a range of features and provide examples of
important biophysical effects that require spatially-resolved stochastic
dynamics to capture.
