Fig 1.
The 2D or 3D system is divided in well-mixed boxes. At every time step Δt, (i) the metabolic activity of the organisms is calculated using either thermodynamic flux analysis (TFA) or neural networks (NNs), then (ii) the diffusion of metabolites is approximated by the Crank-Nicolson method (CN) or crowding-lattice Boltzmann method (cLBM), and finally (iii) the behavior and spatial distribution of the microbial cells are computed using an individual-based modeling (IbM) approach. In step (iii), solid arrows indicate the cell motion, while dashed arrow indicates that cell division will take place. Since the uptake and diffusion of the metabolites are faster processes than the cell division and shoving (S1 Text IbM rules), steps (i) and (ii) can be simulated during a time tl using a smaller time step ΔtCN (ΔtCN ≤ Δt). Step (iii) is computed when tl = Δt. The simulation ends when the final simulation time tsim is reached.
Fig 2.
Dynamics of the mutualistic community E. coli ΔmetB: methionine-secreting mutant of S. enterica (meth+) with an initial composition of 99:1.
(A) Total biomass. (B) The average volume fraction occupied by the cells (i.e. crowding conditions) in their corresponding box. (C) The species ratio convergence of meth+. Three initial crowding conditions were tested: 2% (using a box height Δz = 0.18 mm), 20% (Δz = 0.018 mm), and 40% (Δz = 0.009 mm). Closed symbols represent simulations where the crowding effect was taken into account (), while open symbols represent simulations where the crowding was neglected (
). Error bars show the standard deviation in five independent simulations.
Fig 3.
Availability of methionine and fitness as a function of the distance from the production point in crowded environments.
The microbial community was composed by E. coli ΔmetB and methionine-secreting mutant of S. enterica. (A) Schematic representation of the spatial distribution of the species. (B) Average amount of methionine available per box (inset) enlarged graph assuming that E. coli cells are inactive, and (C) fitness of active E. coli cells (inset) enlarged graph at different crowding conditions. Error bars show the standard deviation in the system (one independent simulations).
Fig 4.
Dynamics of the community E. coli—S. enterica with metabolic variability.
(A) Fitness and (B) relative abundance of meth+ computed after 26 h. Three different initial crowding conditions were tested: 2% (Δz = 0.18 mm), 20% (Δz = 0.018 mm), and 40% (Δz = 0.009 mm), with initial frequencies of 70, 60, and 50 meth+ cells. Closed symbols represent simulations where the crowding effect was taken into account, while open symbols represent simulations where the crowding was neglected. (C) Snapshot of the spatial distribution of cells in one simulation repetition at t = 0h and t = 26 h. Only 1 out of 20 bacterial spots, colony A, where inoculated with 70 meth+ cells, the initial crowding conditions were set as 40%. (D) Dynamics of the relative abundance of the species predicted in 20 different regions of the system (the time is represented on the x axis of each quadrant, while the relative abundance is on the y axis). Error bars show the standard deviation in five independent simulations.
Fig 5.
Dynamics of the biofilm growth of two E. coli species with different EPS production level.
(A) Spatial distribution at t = 0 h of E. coli cells WT and eps mutant (eps+ or eps++). (B) Snapshots of the space occupied only by the cells and the metabolic regions in the vertical layer (0.06 mm, y, z) of biofilms Beps+ and Beps++ at 25 h. (C) Fitness of the eps mutant relative to WT. (D) Total biomass and (E) the acetate produced by the microbial community at 25 h. Closed symbols represent simulations where the crowding effect was taken into account (), while open symbols indicate simulations where the crowding was neglected (
). Error bars show the standard deviation in five independent simulations.
Table 1.
Parameters used for the simulation of community models 1 and 2.