  Mathematical models are important tools to study the excluded volume effects
on reaction-diffusion systems, which are known to play an important role inside
living cells. Detailed microscopic simulations with off-lattice Brownian
dynamics become computationally expensive in crowded environments. In this
paper we therefore investigate to which extent on-lattice approximations, so
called Cellular Automata models, can be used to simulate reactions and
diffusion in the presence of crowding molecules. We show that the diffusion is
most severely slowed down in the off-lattice model, since randomly distributed
obstacles effectively exclude more volume than those ordered on an artificial
grid. Crowded reaction rates can be both increased and decreased by the grid
structure and it proves important to model the molecules with realistic sizes
when excluded volume is taken into account. The grid artifacts increase with
increasing crowder density and we conclude that the computationally more
efficient on-lattice simulations are accurate approximations only for low
crowder densities.
