Fig 1.
The basic structure of an iDynoMiCS 2.0 model.
Interaction with the program takes place through the GUI or command line terminal. A protocol file specifying a model can be loaded to initialize the simulator. If parameters are missing from the protocol file, a default is loaded or the user is queried if no default exists. Scheduling ensures predictable handling of the compartments and the order of processes occurring within them. A species library is kept such that properties and/or behavior that are identical for agents of the same species can be looked up from the library. The simulator further ensures that the model state is saved at the end of each global time step. Spatially explicit and well-mixed compartments can be connected. Solute concentration fields are stored as matrices, which include local solute concentrations, local diffusivity and reaction rates. The collective of agents represents the biofilm, agents may have many properties depending on user specifications, basic properties are species, mass and position of the agent. Processes act upon the information in the model system and describe the processes occurring in the model such as mechanical interactions or diffusion, or generate output from the active model state. For this figure, colors are used to distinguish between the different elements of iDynoMiCS 2.0. The core elements are orange, input elements are blue, output elements are green and helper algorithms and data structures are yellow.
Fig 2.
Different agent shapes in iDynoMiCS 2.0.
Dashed lines indicate sphere-swept volumes of ‘dots’ or line-segments. Dots are mass-points indicating position and orientation of agents. Solid lines indicate mechanical interactions between points (forces between points modeled as springs): Collision interaction (b-c), spine interaction responsible for the rigidity of rod-shaped agents (d1-2 and e1-2), connecting interactions (d2-e1, e2-f, f-g). α is the angle between two elements of a filament. This angle can be counteracted by a torsion spring applying forces on d1, d2 and e1. L1 and L2 are the moment arms. The torsion spring applies force until the angle α reaches 180°, aligning the three points.
Fig 3.
iDynoMiCS 2.0 was capable of simulating large 3D biofilms.
A nitrifying biofilm was initiated with 1,000 Ammonium Oxidizing Organisms (red) and 1,000 Nitrite Oxidizing Organisms (blue) in a 500x500x500 μm domain. Growth kinetics were adopted from Hubaux et al. [49]. Both species produced EPS particles (gray semi-transparent). Agents that dropped below 20% of their division mass as a result of endogenous respiration (maintenance metabolism) became inactive (black). The 175-day biofilm contained 1.02×107 agents (bacteria and EPS particles).
Fig 4.
Comparing steady states in BM3.
Steady state organic carbon (Chemical Oxygen Demand, COD) and ammonium concentrations in the bulk liquid for the three different BM3 cases (HA: High ammonium, SC: Standard case, LA: Low ammonium) across 7 model implementations (W: a one-dimensional continuum biomass model run on the AQUASIM software [53] and developed by Peter Reichert and Oskar Wanner [54,55], M1: a variant of the W model with a fixed boundary-layer thickness by Eberhard Morgenroth et al. [56], DN: a two-dimensional cellular automaton model developed by Daniel Noguera and colleagues [57], CP: a two-dimensional individual-based model, with biomass spreading via shoving, developed by Cristian Picioreanu and colleagues [58], NUFEB: a three-dimensional individual-based model by Li et al. [21], iD: an individual-based model by Lardon et al. [17] (iDynoMiCS 1), iD2: iDynoMiCS 2.0, either with shoving algorithm similar to iD or the new Force-based Mechanics). Data and analysis are included in Table I in S1 Text.
Fig 5.
Biofilms promote altruism case study.
Rate Strategist (RS, blue) and Yield Strategist (YS, red) competitions using the shoving algorithm in BacSim [59] (reproduced from “Kreft J-U (2004). Biofilms promote altruism. Microbiology 150: 2751–2760” with permission) were replicated in iDynoMiCS 2.0 with its force-based mechanics. Cells were initially placed in alternating, equidistant positions with increasing density from 5 cells per strategy (Scenario 1: a-b), 10 cells each (Scenario 2: e-h) to 50 cells each (Scenario 3: i-l and c-d). iDynoMiCS 2.0 panels show local oxygen concentration as a linear gray-level gradient from zero oxygen (0 mg L-1, white) to a maximum concentration (Sox_bulk = 1 mg L-1, black). Block 1 shows 3-week-old biofilms. Block 2 zooms into panels i and j. Block 3 shows 10-week-old biofilms developed from the 3-week-old biofilms shown in the same position on the left.
Fig 6.
Filaments rule and gave Rate Strategists an advantage.
Rate Strategists (RS, blue) and Yield Strategists (YS, red) competed in a 3D biofilm domain (200x200x12.5 μm) for 3 weeks. In the first 4 rows, different strategies competed. Column 1 corresponds to spherical cell scenarios in Fig 2 of Ref [59] but were now simulated in 3D. In column 2, RS formed filaments and in column 3, YS formed filaments. Filaments won regardless of strategy. In column 4, both formed filaments and RS won or likely won. The last 3 rows show single species ‘controls’ with 10, 20 or 100 initial agents. The first two columns show simulations with spherical YS or RS agents while the last two columns show filament forming YS or RS agents. See Fig 7 for corresponding time courses. Duplicate simulations are shown in Fig G in S1 Text. The filamentous microbes incorporate a basic life cycle in which initially spherical agents extend into rod shaped agents to further extend into multi-segmented filaments as described in S1.14.
Fig 7.
Growth curves corresponding to competitions of Rate Strategists (RS, blue) and Yield Strategists (YS, red) in Fig 6.
Duplicates are plotted with dashed lines. Divergence between replicates is most visible in panels g and p. In panel p, it is too early to definitely call the outcome of competition, but it is likely that RS would win given the biofilm structure after 3 weeks (Fig 6P).