Figure 1.

Classes of mathematical models for biochemical processes in cells and their applicability and assumptions. Well-mixed systems: The underlying biochemical processes with cells are stochastic transformations. However, a deterministic mathematical description may be applicable depending on the number of molecules N of each molecular species in the volume (or area) of interest. This number must be large (N≫1) for a deterministic approach to provide an accurate representation. Basically, the expected stochastic fluctuations of the molecule number (ΔN, the magnitude of intrinsic fluctuations is on the order of N^1/2) must be small relative to the absolute number for a deterministic description to be an acceptable assumption. Spatially heterogeneous systems: The well-mixed assumption implies that there is no significant spatial heterogeneity in the system. If this is not true but there are well-defined spatial regions that are homogeneous, then a compartment-based model may be used instead of a fully spatial model.