Qualitative model.

<p>Factions (a) decide whether to cooperate or defect. Then (b) raw resource is collected, which (c) is either reduced (for defectors) or redistributed according to power (for cooperators). Power grows (d) proportional to resource, with a defection bonus, and (e) is normalised so that the total power remains constant. This effectively reduces power for some and increases it for others, potentially changing their behaviour next round.</p

Characteristic behaviour of our model.

<p>a) Defection behaviour with state formation and collapse. Defection is shown in grey, cooperation in white, and the leading faction in black (which always cooperates). b) The power of factions over time. c) The resource of factions over time. The power and resource of the non-leader factions converge, with the result that periodic coordination and defection periods occur. (Parameters: , , and .)</p

Conversion between quantitative scores and qualitative indicators of model fit.

<p>Scores are ‘State formation’ (), ‘Periodicity’ (), ‘State size’ (), and ‘Capital stability’ () defined precisely in Methods. “Match” and “Deviate” are both acceptable fits to the historic data.</p

Long term payoff for strategies taking into account future payoff in the two player version of the game, averaged over many iterations.

<p>“aggressive” and “passive” are defined in the main text, as are the payoffs .</p

Payoff structure for the two player version of the game, when <i>p_ij</i>.

<p>In this case <i>j</i> should always cooperate.</p

Effect of parameters/model extensions on the qualitative dynamics.

<p>The plots are shaded to show whether model qualitatively behaves as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0096523#pone-0096523-g002" target="_blank">Figure 2</a>. The model either matches (solid), deviates (dense hatching) or fails (thin shading). The qualitative fit is based on quantitative scores (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0096523#s4" target="_blank">Methods</a>). Firstly, ‘State formation’ () is high when states are large and collapse rapidly to few factions. Secondly, ‘Periodicity’ () is high if there is periodic predictability to decisions. Thirdly, ‘State size’ () is high if state formation and collapse affect all factions. Finally, ‘Capital stability’ () is high if the leading faction does not change from the initial leader (relevant only for plots e–h). The qualitative model is matched if , , and . It deviates if , or . Otherwise the qualitative model fails. Also shown (where possible) is the parameter value from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0096523#pone-0096523-g002" target="_blank">Figure 2</a> (vertical line).</p

Schematic of a BSim model.

<p>BSim models consist of two main levels: 1. the individual agent (top) and 2. the shared environment (bottom). Individual agents are used to model any autonomous entity, such as a bacterium, outer membrane vesicle, etc, and contain an internal state vector which can change over time. BSim provides support for ordinary differential equations or user defined rules when specifying agent dynamics. Agents can sense various environmental factors as inputs and generate outputs within the local environment. The environment provides a shared medium in which agents can move, communicate (using chemical signaling), interact (through physical contact) with other agents or objects, and can be detailed and heterogeneous.</p

Multi-level effects of the <i>lac</i> operon.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042790#s3" target="_blank">Results</a> from a model of the <i>lac</i> operon that considers the states of individual cells as well as the population as a whole. A) Bimodal state distributions including the external inducer concentration and level of <i>lac</i> permease, . Since the model does not explicitly include an indicator, was used as a proxy measure. Low and high external inducer concentrations bias the population toward an uninduced or induced state respectively, and all concentrations see coexistence of states in the form of a bimodal distribution of . Dashed line indicates the overall population induction (average) that would be measured by purely observing at the population level, i.e., not taking into account the bimodal distribution of individual states. B) Effect of growth rate on coexistence of induced and uninduced states within the population. Line color indicates external inducer concentration, , (yellow = 30 M, green = 80 M, blue = 110 M,), solid and dashed lines indicate simulations where induction did and did not inhibit growth respectively. C) Bifurcation diagram showing bistability in the intracellular inducer concentration, . Red line illustrates the equilibrium state of in the deterministic GRN equations for a single cell as a function of external inducer, , computed via numerical continuation (solid and dashed lines indicate stable and unstable equilibrium respectively); blue line illustrates ensemble average concentration in a BSim simulation which incorporates this deterministic GRN and stochastic agent creation and removal in which was slowly varied (dashed lines indicate population minimum and maximum).</p

Synchronized genetic oscillators.

<p><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042790#s3" target="_blank">Results</a> from studying the synchronization of a population of 200 bacteria, each containing a repressilator GRN model <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0042790#pone.0042790-GarciaOjalvo1" target="_blank">[28]</a>. A) Repressilator GRN with external coupling. B–D) Simulations performed with a chemical field diffusivity of 100 and a cell wall diffusion constant of 1 . B) Left to right, simulation output for times 0, 5.5 and 40, where mins is the GRN period of oscillation. The color of the bacteria corresponds to their internal level of <i>lacI</i> mRNA, yellow for low and red for high. External autoinducer level is represented by the intensity of the blue field surrounding the bacteria. Initial mRNA and protein levels for each bacterium were chosen at random. However, synchronization quickly increases over time. Also see Video S2. C) Phase portraits for 3 pairs of bacteria. For clarity the first 2.5 hours of data, where the bacteria were extremely asynchronous, are omitted. Over time, each pair becomes more synchronized. D) Amplitude spectra for all bacteria with colors representing (amplitude) in arbitrary units (a.u.). The clear peaks correspond to the fundamental frequencies of the GRN where phase locked synchronization has occurred. E) Phase transition to synchronization as the cell wall diffusion constant is increased.</p

Describing complex spatial environments with meshes.

<p>A) User generated mesh that could be used to approximate a fibrous matrix, similar to that found in cotton wool. B) The same mesh loaded into a BSim environment. C) Torus shaped mesh used to influence behavioral characteristics of the bacteria. In this case, altering the output color they emit (blue outside and green inside the mesh). Also see Video S3.</p