The use of a structured population - a spatial distribution of individuals in the form of either a set of islands or a diffusion grid - determines the dynamical processes that can take place in complex systems.
From this relation, we chose diffusion grid size nc = 50 μm, and consequently, each diffusion grid contains 10 × 10 × 10 cells.
For instance, at each time-step within a diffusion grid, the total amount of nutrients consumed should be considerably smaller than available nutrients.
Spatially, cell actions took place on a cell grid with single-cell resolution (5 μm), while nutrient distributions were followed on a diffusion grid at lower spatial resolution (∼15 to 60 μm).
After each cell state update, the diffusion coefficient is updated: the diffusion coefficient in each community diffusion grid (15 μm × 15 μm × 15 μm, maximally containing 3 × 3 × 3 = 27 cells of size 5 μm × 5 μm × 5 μm) is assumed to be proportional to the occupancy of that grid, changing from 0 to 20 μm/s.
To ensure stability of the finite-difference equations for diffusion, the diffusion grid-size (nc) and the time-step (dt u ) for the diffusion equation have to satisfy (Iserles, 2009) (9) d t u < 1 2 (n c ) 2 D, where D is the diffusion constant in the region of interest.
Equation (3) states that S, the amount of limiting nutrient in a diffusion grid, depends on three processes: i) diffusion of nutrient with diffusion constant D, ii) uptake of nutrients (Walther et al., 2005) by cells (U), and iii) in cooperative communities, release of nutrients by the partner population (Q).
In equations (4) and (5), n u and n q are the number of consuming and releasing cells within the diffusion grid, respectively, K MM is the Michaelis-Menten constant for uptake, v m is the maximum uptake rate per cell, and ρ is the release rate per cell.
This inconvenience can be solved using anti-diffusion grids which are installed in the X-ray apparatus eliminating about 90% of this radiation.
Decoupling the transport problem from the underlying 3D geological model results in a significant computational efficiency while minimizing numerical diffusion and grid orientation effects (Thiele et al. 1997; Samier et al. 2001).
