In biological cells, molecules are transported actively or by diffusion and react with each other when they are close.
The reactions occur with certain probability and there are few molecules of some chemical species. Therefore, a stochastic model is more accurate compared to a deterministic, macroscopic model for the concentrations based on partial differential equations.
At the mesoscopic level, the domain is partitioned into voxels or compartments. The molecules may react with other molecules in the same voxel and move between voxels by diffusion or active transport. At a finer, microscopic level, each individual molecule is tracked, it moves by Brownian motion and reacts with other molecules according to the Smoluchowski equation. The accuracy and efficiency of the simulations are improved by coupling the two levels and only using the micro model when it is necessary for the accuracy or when a meso description is unknown.
Algorithms for simulations with the mesoscopic, microscopic and meso-micro models will be described and applied to systems in molecular biology in three space dimensions.