FIGURE 2:

Demands on spatial approaches and their extensibility. (a) For all spatial models, in addition to treating fundamental reaction types in all dimensions (3D, 2D,1D) and between all dimensions (for instance molecular exchange between bulk [3D] and surfaces [2D]), they must specify an equation of motion, typically diffusion, and boundary conditions on the system geometry. (b) More advanced treatments of curved and complex boundaries require additional care for treating reactions and diffusion. (c) Single-particle spatial methods can be classified based on the model they use and further whether they support large time steps. In both models, the ability to take large time steps generally requires reaction probabilities (p_react) that are determined by finding analytical solutions for the fraction of diffusive trajectories that are reactive (not all collisions lead to reactions when the microscopic rate k_a<∞). In the volume-reactive methods here, short-time step approximations are used, except MCell, which is described in the text. (d) Single-particle methods have the capacity to build in higher-resolution features, although these will alter their equation of motion, requiring new definitions of p_react. We note that PDE-based models can also expand beyond purely diffusive dynamics. In Supplemental Table S2, we summarize features available in commonly used software tools.