Microbiota resident time in antibiotic-tolerant domination as a function of the: A–B) antibiotic action () and C–D) social interaction () parameters.

<p>Blue circles show the theoretical predictions obtained by determining the probability of the most probable path. Red circles are obtained by simulating the Langevin dynamics over iterations and averaged for noise realizations. Higher order-corrections can be included to increase the theoretical estimation accuracy.</p

Multistability and hysteresis in a simple model of the intestinal microbiota. A: phase diagram showing the three possible stability regions.

<p>Antibiotic-sensitive bacteria dominate when and antibiotic-tolerant bacteria dominate when and therefore these are regions of monostability. There is a region of bistability between the two regions where domination by either sensitives or tolerants is possible. B: schematic display of the hysteresis phenomenon explaining cases where antibiotic treatment produces altered microbiota (i.e. tolerants domination) that persists long after antibiotic cessation. C–F: mean density values obtained simulating the Langevin dynamics for a maximum time after an instantaneous change of the parameter (C and D) and (E and F). These averages are obtained over noise realizations. C, D and E, F show the antibiotic-tolerants or antibiotic-sensitives densities, respectively, as a function of the social interaction parameter () with or the antibiotic killing () with .</p

Most probable microbiota states change from bistable scenario to mono-stable coexistence with increasing noise.

<p>A: the bacterial density joint probability distribution determined by solving the Fokker-Planck equation (3) for four different values of the environmental noise. B: the bacterial densities at the peaks of as a function of the noise parameter . Red symbols are data from the numeric solution of the Fokker-Planck equation and the black solid lines are the exponential fit. Parameters used: and . The insets detail the linear regime.</p

The two-group model of the intestinal microbiota with antibiotic-sensitive and antibiotic-tolerant bacteria.

<p>Antibiotic sensitives can inhibit the growth of tolerants and both groups compete for the same growth substrate. Model parameters and represent the antibiotic sensitivity of sensitive and tolerant bacteria (where ), and represent their affinities to substrate and represents the inhibition of tolerants by sensitives.</p

Analysis of microbiota response to the antibiotic ciprofloxacin from three subjects [24] using singular value decomposition identifies antibiotic-sensitive and antibiotic-tolerant bacteria.

<p>A–C: fraction of variance explained by the five most dominant components. D–F: plot of each sample component 1 (green) and 2 (red) coordinates versus sample time. G–I: sorting of the phylotypes log2-transformed abundance matrix based on the correlation within the two principal component. Above (below) the green dashed lines, we display the time series of the top 20 phylotypes strongly correlated (anti-correlated) with component 1 and anti-correlated (correlated) with 2 and dropping (increasing) during treatment, which we identify as sensitves (tolerants). Subject 3 (C,F,I) displays absence of sensitive bacteria for a prolonged period of about 50 days after the first antibiotic treatment. This confirms the fact that microbiota response to antibiotic can differ from subject to subject. Additionally, it also supports our model prediction of remaining locked in a tolerant-dominated state after antibiotic treatment cessation.</p

Integration of Metabolic and Quorum Sensing Signals Governing the Decision to Cooperate in a Bacterial Social Trait

<div><p>Many unicellular organisms live in multicellular communities that rely on cooperation between cells. However, cooperative traits are vulnerable to exploitation by non-cooperators (cheaters). We expand our understanding of the molecular mechanisms that allow multicellular systems to remain robust in the face of cheating by dissecting the dynamic regulation of cooperative rhamnolipids required for swarming in <i>Pseudomonas aeruginosa</i>. We combine mathematical modeling and experiments to quantitatively characterize the integration of metabolic and population density signals (quorum sensing) governing expression of the rhamnolipid synthesis operon <i>rhlAB</i>. The combined computational/experimental analysis reveals that when nutrients are abundant, <i>rhlAB</i> promoter activity increases gradually in a density dependent way. When growth slows down due to nutrient limitation, <i>rhlAB</i> promoter activity can stop abruptly, decrease gradually or even increase depending on whether the growth-limiting nutrient is the carbon source, nitrogen source or iron. Starvation by specific nutrients drives growth on intracellular nutrient pools as well as the qualitative <i>rhlAB</i> promoter response, which itself is modulated by quorum sensing. Our quantitative analysis suggests a supply-driven activation that integrates metabolic prudence with quorum sensing in a non-digital manner and allows <i>P</i>. <i>aeruginosa</i> cells to invest in cooperation only when the population size is large enough (quorum sensing) and individual cells have enough metabolic resources to do so (metabolic prudence). Thus, the quantitative description of <i>rhlAB</i> regulatory dynamics brings a greater understating to the regulation required to make swarming cooperation stable.</p></div

Density-dependent scaling of <i>rhlAB</i> expression is controlled by quorum sensing autoinducers.

<p>A. Quorum sensing regulatory cascade in <i>P</i>. <i>aeruginosa</i> WT and in the quorum-sensing mutant, which lacks the genes encoding LasI and RhlI. Median is shown in thick lines with full range indicated by shaded area. All growth curves are aligned to OD = 0.01 at 10 hours. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004279#pcbi.1004279.s002" target="_blank">S2 Table</a> for lag times. B. Growth of the ∆<i>lasI</i>∆<i>rhlI</i> bacterial populations in carbon limitation media with 0.5 gC/L and different concentrations of auto inducer 1 X = 1 μM C12HSL and 5 μM C4HSL. 1X is estimated to be physiological and has recovered the WT level of rhamnolipid production in previous work [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004279#pcbi.1004279.ref019" target="_blank">19</a>]. C. GFP expression for each population. Populations that received higher levels of autoinducer express higher levels of GFP. D. P_<i>rhlAB</i> activity in different concentrations of autoinducer plotted against population density. Activity holds constant during phase I and rapidly shuts off at the onset of phase III. Phase I is shown in solid lines and phase III in dashed lines.</p

Quantitative analysis of <i>rhlAB</i> promoter dynamics and mathematical model of cooperation.

<p>A. Median of experimental data <i>rhlAB</i> promoter activity from phase I growth in different limitation media plotted against population density (OD). A similar slope is observed for all limitation media suggesting a consistent relationship between population density and <i>rhlAB</i> promoter activity. B. Median <i>rhlAB</i> promoter activity during growth under nutrient starvation over time. <i>rhlAB</i> promoter activity increases in iron starvation, is sustained in nitrogen starvation and is shutdown in carbon starvation. The mathematical model of growth systematically determined the start of starvation. Iron starvation initial condition 8.7 x 10^–6 gFe/L, nitrogen starvation initial condition 0.6 gN/L, carbon starvation initial condition 0.5 gC/L, all shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004279#pcbi.1004279.g003" target="_blank">Fig 3D</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004279#pcbi.1004279.g003" target="_blank">3F</a>. C. Median <i>rhlAB</i> promoter activity from phase II of nitrogen limited populations (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004279#pcbi.1004279.g003" target="_blank">Fig 3E</a>). Populations with higher density at the onset of starvation have higher <i>rhlAB</i> promoter activity during nitrogen starvation. D-F Mathematical model of <i>rhlAB</i> promoter activity compared to experimental data. The model is shown in thick lines and median experimental data is shown in thin lines. A model integrating nutrient starvation and population density is able to capture the many aspects of <i>rhlAB</i> promoter activity during periods of balanced and limited growth. D. Carbon limitation media. E. Nitrogen limitation media. F. Iron limitation media.</p

Conceptual model of cooperation by rhamnolipid secretion.

<p>Conceptual feed-forward supply-driven model of growth and <i>rhlAB</i> expression in <i>P</i>. <i>aeruginosa</i>. A slowdown in growth would lead to buildup of intracellular carbon metabolites. This buildup would trigger the expression of genes, in this case <i>rhlAB</i>, which would convert carbon metabolites into secreted rhamnolipids that can benefit the cell and the population. By only expressing <i>rhlAB</i> when there is a buildup of metabolites the cell never decreases the rate of biomass production, V_<i>x</i>.</p

Expression of <i>rhlAB</i> coincides with a slowdown in growth.

<p>A. Time-lapse imaging of swarming and GFP fluorescence driven by the P_<i>rhlAB</i> promoter. The colony grows until it reaches a critical size at ~5h and subsequently begins tendril formation. Before tendril formation, <i>rhlAB</i> expression is observed. B-D The time points where <i>rhlAB</i> expression starts and swarming motility starts are indicated by dashed vertical lines. B. The increase in total area of the swarming colony shows that swarming starts at ~5h. C. Cell density at the center of the colony increases exponentially until t = ~2h then growth rate slows down D. The <i>rhlAB</i> expression (GFP signal) at the center of the colony was normalized by cell density. <i>rhlAB</i> expression revealed that expression of biosurfactant synthesis genes starts ~3h before the onset of swarming. E. Growth curve of a <i>P</i>. <i>aeruginosa</i> population in synthetic liquid media (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004279#sec015" target="_blank">Synthetic Growth Media</a>) where all three growth phases occur. Phases I, II, and III are indicated with dashed lines. F. P_<i>rhlAB</i>–<i>gfp</i> expression of the population shown in E. over time. The majority of GFP production occurs during phase II, when the population growth rate has slowed. GFP measurements shown are corrected for autofluorescence (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004279#sec014" target="_blank">Correction of Autofluoresence in the <i>gfp</i> Signal</a>).</p