FIGURE 9:

Summary of the impact of spatial modeling and simulation approaches on quantitative (small, medium, large) and qualitative (major/minor) biochemical behavior. For quantitative behavior, our tree structure separates parameter and geometry regimes to specifically identify the scale of change observed and expected. For qualitative behavior, we note that, especially for reaction-network elements and stochastic effects, observing major changes also depends on additional parameter specifications, but in a less predictable way than the spatial effects (e.g., relative sizes of distinct rates or copy numbers). Minor changes are the default, as we observe for models with purely reversible reactions (rxns). The test cases range from very simple problems (U1: bimolecular association in 3D, 2D, and from 3D to 2D, U2 crowding) via intermediate tests (I1: exploiting membrane localization to stabilize protein–protein interactions; I2: increasing stochastic fluctuations in a system with multiple steady states) to applications that combine different spatial features (A1: stochastic effects in gene expression; A2: spatial and temporal oscillations in MinCDE). Various tools have been applied in the test cases: U1: ODE, PDE, SSA/Gillespie, particle-based (NERDSS, Smoldyn); U2: particle-based (NERDSS, eGFRD); I1: ODE, PDE, SSA/Gillespie, particle-based (NERDSS, Smoldyn); I2: ODE, SSA/Gillespie, particle-based (NERDSS); A1: ODE, PDE, SSA/Gillespie, particle-based (NERDSS, MCell, Smoldyn); A2: PDE, particle-based (Smoldyn). A detailed description of the theoretical basis and the features offered by these tools/methods can be found in Supplemental Table S2.