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
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