Expression of rhlAB Depends on Growth Phase

We analyzed the timing of rhlAB promoter activity directly in swarming colonies using fluorescent imaging and time-lapse video using a P_rhlAB-gfp reporter strain (Fig 1A) [39]. A colony of P. aeruginosa inoculated on a swarming plate first grows without moving until it reaches a certain critical size at ~5 h (Fig 1B). During the 2–5 h period expression at the colony center coincides with a decrease in growth rate that could be due to local nutrient depletion (Fig 1C and 1D). GFP levels continue to increase until ~5 h when we can observe a translucent ring of secreted rhamnolipids around the colony by eye. This is followed by the appearance of motile swarming tendrils shooting out from the colony. The secreted rhamnolipids lubricate the agar surface and allow the colony to slide over it.

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Fig 1. Expression of rhlAB coincides with a slowdown in growth.

A. Time-lapse imaging of swarming and GFP fluorescence driven by the P_rhlAB promoter. The colony grows until it reaches a critical size at ~5h and subsequently begins tendril formation. Before tendril formation, rhlAB expression is observed. B-D The time points where rhlAB 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 rhlAB expression (GFP signal) at the center of the colony was normalized by cell density. rhlAB expression revealed that expression of biosurfactant synthesis genes starts ~3h before the onset of swarming. E. Growth curve of a P. aeruginosa population in synthetic liquid media (see Synthetic Growth Media) where all three growth phases occur. Phases I, II, and III are indicated with dashed lines. F. P_rhlAB–gfp 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 Correction of Autofluoresence in the gfp Signal).

https://doi.org/10.1371/journal.pcbi.1004279.g001

In order to probe rhlAB expression more systematically, we turned to a batch culture system using shaken liquid media in a microtiter-based assay. This way we can simultaneously assess population density and gene expression using OD (optical density) and the P_rhlAB-gfp reporter respectively. Bacterial growth curves are typically described by four phases: lag phase, exponential phase (sometimes called “log” phase), stationary phase, and death phase. The definition of stationary phase often includes qualitatively distinct sub-phases of slowed growth and no growth, which can make analyzing responses to nutrient starvation difficult. To facilitate our analysis, we separate time series into three phases after lag phase. Phase I begins when the population becomes detectable by absorbance at 600 nm (OD, for optical density; detectable at 0.01 OD in this study) and grows exponentially at its maximum rate, μ_max. During this initial period, the cells have all nutrients required for biomass synthesis and thus achieve balanced growth. The start of phase II is defined by growth limitation, where an essential nutrient runs out and the population growth rate has slowed below μ_max. Phase III is when population density stops increasing and may actually decay. Fig 1E shows a representative growth curve with all three growth phases. The P_rhlAB-gfp construct enables tracking of rhlAB expression throughout the different phases of growth with high time resolution (Fig 1F). We corrected for P. aeruginosa secreted products that fluoresce in the GFP detection wavelengths, thus generating a compensated GFP signal from the P_rhlAB promoter over time (S1 Fig and Correction of Autofluoresence in the gfp Signal). Using population density and population level measurements of GFP assumes that rhlAB expression is homogenous across the population. To test if this assumption is valid, we used microscopy to measure single-cell expression levels at different stages of growth (S2 Fig). The up-regulation of rhlAB was simultaneous across the population rather than bimodal. Therefore, we concluded that the population-level measurements could be used to probe expression dynamics.

Growth Response to Nutrient Limitation

To better understand how a population responds to the entry into starvation we first analyze growth behavior in different limiting conditions. Our first growth limitation experiments set carbon as the growth-limiting nutrient in the media. We used varying concentrations of the carbon source (glycerol) and added a nitrogen source (ammonium sulfate) and iron (iron(II) sulfate) in excess. In these conditions, the population density and the length of phase I have a dose dependency with the initial amount of carbon, confirming that carbon is indeed the limiting nutrient (Fig 2A). Each growth curve follows the same phase I (exponential growth) with identical μ_max values (0.33 h^-1). We observed that once the carbon in the media is fully consumed, cell growth stops abruptly and the population shifts sharply from phase I to phase III (decay) without going through a period of slowed growth (phase II). We carried out additional growth experiments, now in limiting concentrations of nitrogen. As before, population density and phase I time scale with initial nitrogen concentration, confirming that nitrogen is the limiting nutrient (Fig 2B). In nitrogen starvation the growth rate drops at the end of phase I but, unlike carbon starvation, population density continues to increase until the end of our observation period (approximately 45 hours). Throughout this period of slowed growth (phase II), the growth rate is continually decreasing.

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Fig 2. Bacterial growth behavior under different limiting conditions in batch culture.

All growth curves are aligned to OD = 0.01 at 10 hours. See S2 Table for lag phase times. Shaded area represents full range; data lines represent the median. A. Growth of P. aeruginosa populations limited by carbon. The population transitions from phase I immediately to phase III when carbon is depleted with no observed period of slow growth. B. Growth behavior of populations limited by nitrogen. The populations abruptly transition from phase I to phase II when nitrogen is depleted. C. Growth behavior of populations grown in limiting concentrations of iron. The populations gradually transitions from phase I to phase II when iron is depleted from the media. For D-F the model is in thick lines and the data in thin lines. D. Mathematical model of growth in carbon-limited media. Growth halts when carbon is depleted from the media. E. Mathematical model of growth in nitrogen-limited media. Phase II growth is driven by an intracellular pool of nitrogen. F. Mathematical model of growth in iron-limited media. Phase II growth is driven by an intracellular pool of iron. G. Experimental scheme for testing growth behavior in the absence of extracellular carbon or nitrogen. H. Growth of the population that will be used in the depletion experiment. The population was grown to exponential phase in synthetic media rich in carbon, nitrogen and iron. I. Cells harvested from the population in H were washed and placed in one of the limiting media. The population without extracellular nitrogen is able to grow and increase in OD, while the population without extracellular carbon decays in OD. The data displayed is from a representative experiment from the biological replicates listed in S1 Table. The number of technical replicates is listed in S1 Table.

https://doi.org/10.1371/journal.pcbi.1004279.g002

Finally, we conducted experiments with iron as the growth-limiting nutrient. Increasing the amount of supplemented iron in the media increases both the population density and phase I, confirming that iron is the limiting nutrient (Fig 2C). Interestingly, the behavior under iron-limiting conditions was qualitatively distinct from both carbon and nitrogen limitation. In iron-limited growth there is still a transition from phase I to phase II, however this transition is gradual. The growth rate continually slows from μ_max, unlike the abrupt transition to phase II seen in nitrogen limitation. In the iron limitation titration, there is an uneven spacing between the curves; doubling the supplemented iron did not result in a doubling of total population density. This can be explained by a constant yield for iron (Y_Fe) and the presence of trace iron in the growth media. If trace iron is present then doubling the amount of supplemented iron will not double the total amount of iron in the system, but rather add to the trace amount already present. To test this explanation, we used the population density data from the iron titrations (Fig 2C), which fell on a line with slope Y_Fe (S3C Fig), to calculate the level of trace iron present in our non-iron supplemented media, Fe₀ = 1.4 x 10^–5 gFe/L. To additionally confirm the presence of trace iron in the media, we grew bacteria in media with no iron supplemented. As expected, the population was able to sustain a phase I (S4 Fig) in this medium and grew to the population density predicted by our trace iron calculation (S3C Fig). See S1 Table for information regarding biological and technical replicates.

Mathematical Model Suggests Growth with Internal Nutrient Pools

In order to investigate how the nutrient levels experienced by cells influence their growth, we created a mathematical model of P. aeruginosa growth kinetics. Using the data from the experiments described above where we manipulated the media composition such that carbon, nitrogen, or iron become limiting, we were able to construct a kinetic model based on mass conservation, where biomass production is a function of these three nutrients. Central to this model was the calculation of the yields of biomass produced (in units of OD) per amount of carbon (Y_C), nitrogen (Y_N) and iron (Y_Fe) consumed (S3 Fig). One benefit of this properly calibrated model is the calculation nutrient levels at any given time in the growth curve, which could not be directly measured with our assay.

Bacterial growth limitation due to depletion of an essential nutrient is commonly modeled using Monod kinetics, which requires two parameters: μ_max, the maximum specific growth rate, and K_s, the half-saturation constant [40,41]. In all of our nutrient limitations and titrations we observe the same μ_max in phase I independently of the initial nutrient concentrations. In order to satisfy this constraint, a Monod model would need to have a K_s value for each nutrient that is significantly below our lowest titration value (K_s<<0.063 gC/L, K_s<<0.0078 gN/L and K_S<<1.4 x 10^–5 gFe/L for carbon, nitrogen and iron respectively). In a Monod model, such a low K_s will give a very sharp transition from maximal growth to practically no growth. For carbon limitation we do observe this sharp transition behavior. This behavior is somewhat unexpected as the population might be predicted to slow in growth rate as carbon becomes increasingly scarce. This suggests that the half saturation constant value for carbon is indeed K_s<<0.063 gC/L and in order to measure its actual value we would need to monitor population density at OD values below the detection limit of our growth curve assay (OD = 0.01). Therefore, we instead model carbon (C) consumption as a step function with a constant yield Y_C (S3A Fig and Eq (2)). This model recapitulates the growth behavior observed in carbon limitation media (Fig 2D).

Nitrogen and iron limitation growth curves, on the other hand, are inconsistent with a Monod model even with a K_s value below the lowest titration concentration. Although there is a sharp transition in nitrogen limitation from phase I to phase II, the sustained growth in phase II is incompatible with a Monod model. A Monod model with a low K_s also cannot explain the gradual slowdown in growth rate observed in iron limitation. There are a few possible explanations for the observed curvature in the nitrogen and iron limitations that we can exclude based on the data. Firstly, consistent phase II behavior across titrations excludes the possibility of a toxic product accumulating, as the populations with higher cell densities are not more severely affected. For nitrogen, the yield calculations predict no contaminating trace nitrogen amounts (S3B Fig). The possibility of a contaminating trace nitrogen that is used only in phase II is also eliminated as this would result in the populations with lower cell densities growing much more than the populations with higher cell densities for a given amount of trace nitrogen, and instead phase II behavior is consistent across the titrations.

The nutrient source for phase II growth in nitrogen and iron limitation must scale with population density and is independent of the starting nutrient concentration. A model that fits these criteria is one where the transition from phases I to II represents a switch in cellular metabolism from growth on extracellular nitrogen or iron (upon complete depletion of the limiting nutrient from the media) to intracellular nitrogen or iron [42]. Such growth behavior has been observed before in the yeast Saccharomyces cerevisiae. S. cerevisiae could grow in the absence of extracellular nitrogen by using nitrogen-rich intracellular biopolymers, presumably protein, and decreasing the nitrogen-to-carbon ratio of its biomass composition [43].

To determine if a model of P. aeruginosa utilizing internal nutrient pools for growth, like S. cerevisiae, could explain the observed behavior, we created a mathematical model to account for an internal nitrogen pool, internal iron pool, and trace iron. In this model, the cells consume extracellular nutrients to produce biomass and maintain homeostatic levels of intracellular nutrient pools while growing exponentially (N_i, Fe_i) (Eq (3) and (5)). When the nitrogen or iron in the media is fully depleted, the cells switch to growth on the intracellular pool of the depleted nutrient, which then gradually decreases over time as the cells grow (Eq (4) and (6)). Because we cannot directly measure the size of the internal pool of nitrogen or iron, we normalize it by the size of the pool during balanced growth; both N_i, and Fe_i are dimensionless. Each cell enters phase II with N_i or Fe_i = 1 and this internal pool is then depleted for cell growth and diluted through cell division. The current growth rate of the population, μ(t), is dependent on the fraction of the internal pool in each cell. As the internal pool is depleted, growth slows from μ_max (Eq (7)).

The kinetics of biomass (X) (Eq (1)), growth and nutrient consumption of our different limiting nutrients are therefore given by: (1) (2) (3) (4) (5) (6) where μ(t) is the current specific growth rate. Nitrogen and iron use the same internal nutrient pool model.

We find that in addition to accounting for trace iron in the media and internal nutrient pools of nitrogen and iron, we also must postulate that the maximum growth rate while using internal nitrogen is lower than μ_max, here termed μ_max´. This postulation is required to explain the sharp transition from phase I to phase II observed in nitrogen limitation (Fig 2B). As the transition in iron limitation is more gradual, this postulation is not required for growth on internal iron and thus we do not assume a switch from μ_max to an alternative value (μ_max´) in iron limitation. Using this model, we are able to capture the dynamics observed in the experimental data (Fig 2D–2F). The equation set that determines μ(t) for the different nutrient conditions is given below

(7)

Nutrient Depletion Experiment Supports Model with Internal Nutrient Pools

To test our internal nutrient model experimentally, we designed a nutrient depletion experiment (Fig 2G). The experiment was only performed for carbon and nitrogen as trace iron prevents the depletion experiment for iron. Cells were grown to exponential phase in rich synthetic media (Fig 2H) and then harvested while still in balanced growth, washed, and separately inoculated in media lacking either carbon or nitrogen. As predicted by our model, the cells in media lacking nitrogen were able to grow and increase in population density (Fig 2I) whereas in the absence of carbon, the population transitioned immediately to phase III and population density started to decrease (Fig 2I), supporting our model that total carbon depletion causes transition to phase III. These results are consistent with the model for phase II of nitrogen limitation and phase III of carbon limitation. We were unable to perform this experiment for iron limitation in the same manner due to the fact that medium without supplemented iron contains trace amounts of this nutrient (S3C Fig). Nonetheless, the model with an internal iron pool is still able to describe the observed growth behavior in iron limitation (Fig 2F).

In summary, we developed a model of P. aeruginosa kinetics that successfully captures the observed growth dynamics. In total, the model has eight free parameters, which we were able to parameterize using growth curve experiments to derive the nutrient yields, Y_C, Y_N, and Y_Fe, as well as kinetic parameters (S5 Fig and S3 Table). We find that for carbon limitation, a Monod model (where growth slows with decreasing concentration of the limiting nutrient) with a very low K_s can explain the data, leading to a very sharp transition from exponential growth to no growth with virtually no slow down due to decreasing availability of carbon in the media (Fig 2D). The growth model also reveals that growth behavior in both nitrogen and iron limitation, under these conditions, is incompatible with an explanation using a Monod model. However, the behavior observed in these limiting conditions can be explained using a model of intracellular nutrient pools (Fig 2E and 2F), which is experimentally supported for nitrogen limitation (Fig 2I). A model using these intracellular nutrient pools is required to accurately capture bacterial growth dynamics and recapitulate the observed growth rate. This phenomenological model can be used to constrain the mechanisms of rhlAB expression responses we observe in nutrient limitations.

rhlAB Promoter Response to Nutrient Limitation and Population Density

Rhamnolipid production is a dynamic process and changes in rhlAB expression coincide with transitions between growth phases, which are difficult to capture experimentally. Our growth model provides us with an understanding of the conditions cells experience throughout growth and the growth rate response to changes in the nutrient environment. We can use this understanding to interpret the expression response of rhlAB under these conditions. Our measurements of GFP driven by the rhlAB promoter (Fig 3A–3C) were taken simultaneously with the population density measurements (Fig 2A–2C) in the different limiting nutrient conditions. Using GFP (Fig 3A–3C) and OD measurements (Fig 2A–2C), we calculated the promoter activity for rhlAB throughout the time series (Fig 3D–3F), with compensation for GFP dilution by cell division (see Promoter Activity Calculation). Note that promoter activity fluctuates more at the early time points because there is more noise at low OD measurements due to technical limitations of the equipment. We use our mathematical model of growth to systematically identify when the population exits phase I (exponential phase). In Fig 3, expression during phase I is shown in solid lines while expression that occurs after phase I (phase II or III) is shown in dashed lines. Our study and model of growth behavior in this media revealed that entry into phase II or III indicates starvation by the limiting nutrient, therefore promoter activity that occurs after phase I occurs during nutrient starvation.

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Fig 3. rhlAB promoter activity during different phases of growth in nutrient limitation batch culture.

GFP and promoter activity data are from the same growth curves shown in Fig 2. Phase I GFP data and promoter activity are shown in solid lines while data corresponding to phase II or III are shown in dashed lines. Phases were determined by the mathematical model for bacterial growth discussed in the text. A. Population rhlAB (GFP) expression in carbon limitation media. Expression only occurs during phase I. B. Population rhlAB (GFP) expression in nitrogen limitation media. Expression occurs during both phase I and phase II. C. Population rhlAB (GFP) expression in iron limitation media. Expression occurs during phase I, but the majority of GFP production occurs during phase II. Iron limitation hits the saturation for GFP in our conditions ~ 6.0923 x 10⁴ Arbitrary fluorescence units. D-F P_rhlAB activity (see Promoter Activity Calculation) from growth curves in different limitation media D. In carbon limitation growth curves rhlAB promoter activity occurs during phase I and drops to zero during phase III for all titrations. E. In nitrogen limitation growth curves promoter activity occurs during phase I and is sustained during phase II for all titrations after an initial decrease at the end of phase I. F. In iron limitation growth curves promoter activity occurs during phase I and increases at the onset of phase II for all titrations. G-I rhlAB promoter activity from limitation growth curves plotted against population density (OD). G. Promoter activity from carbon limitation growth curves increases with density during phase I. H. Promoter activity from nitrogen limitation increases with population density during phase I and shows consistent qualitative behavior in phase II at different population densities. I. Promoter activity in iron limitation growth curves also increases with population density during phase I and shows consistent qualitative behavior in phase II at different population densities. Median data is shown in lines with the full range of technical replicates indicated by shaded area.

https://doi.org/10.1371/journal.pcbi.1004279.g003

Previous work suggests that rhlAB expression occurs exclusively when carbon is in excess [23,36,44]. However, we unexpectedly observe appreciable rhlAB expression and promoter activity in carbon-limited media (Fig 3A and 3D and 3G). Expression in carbon-limited media occurs during phase I and promoter activity drops to zero when the population enters phase III. (The negative promoter activity values computed in carbon limitation media experiments (Fig 3D) are artifacts caused by a rapid increase in OD consistently occurring immediately before carbon starvation, coinciding with a shut off of rhlAB expression and beginning decay in the GFP signal.)

It is interesting that promoter activity increases throughout phase I, as it could be expected that there would be a constant level of expression during balanced growth and promoter activity would equilibrate quickly. However, increasing promoter activity during phase I is observed in all three limitation conditions (Fig 3D–3F, solid lines). This phase I promoter activity could be due to the fact that even during exponential growth there is carbon available in excess of what is needed for biomass production, and this carbon can be dedicated to rhamnolipid synthesis. The promoter activity in phase I increases with population density in all conditions suggesting that this expression is density dependent (Fig 3G–3I). By overlaying phase I of all conditions and plotting against population density we confirm a consistent slope across all conditions, suggesting that the mechanism driving the density dependent expression is the same in all three limitation conditions (Fig 4A).

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Fig 4. Quantitative analysis of rhlAB promoter dynamics and mathematical model of cooperation.

A. Median of experimental data rhlAB 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 rhlAB promoter activity. B. Median rhlAB promoter activity during growth under nutrient starvation over time. rhlAB 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 Fig 3D–3F. C. Median rhlAB promoter activity from phase II of nitrogen limited populations (Fig 3E). Populations with higher density at the onset of starvation have higher rhlAB promoter activity during nitrogen starvation. D-F Mathematical model of rhlAB 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 rhlAB promoter activity during periods of balanced and limited growth. D. Carbon limitation media. E. Nitrogen limitation media. F. Iron limitation media.

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In nitrogen limited media there is not a complete shutdown of expression after phase I. Instead, population level GFP continues to increase in phase II (Fig 3B). The promoter activity drops, but is sustained, with a second peak of activity occurring before tapering off to near zero (Fig 3E). In contrast, rhlAB promoter activity during phase II of iron limitation rapidly increases without an initial drop when the population enters phase II. Promoter activity of rhlAB decreases over time, but never reaches zero in our iron limitation condition (Fig 3F). The level of promoter activity reached in iron limitation is much higher than that in nitrogen limitation when the highest titrations are compared directly (Fig 4B). We also observe that even in nitrogen and iron starvation when promoter activity is sustained or induced, activity eventually shuts down, most likely due to the prolonged starvation experienced by the cell.

Similar behavior is observed for all titrations within each limiting media across a wide range of population densities (Fig 3G–3I). Therefore the limiting nutrient and the duration of starvation appear to be the main drivers of qualitative promoter behavior: shut down of activity in carbon starvation, sustained activity in nitrogen starvation, and induction of activity in iron limitation (Fig 4B). Although the qualitative behavior is determined by the limiting nutrient, a closer examination of promoter activity during nitrogen starvation reveals that populations with a higher density have higher rhlAB promoter activity even during starvation (Fig 4C). This suggests that the cells continue to use density-dependent information to modulate the dynamics of rhlAB promoter activity in nitrogen limitation.

Phenomenological Model of the Cellular Decision to Cooperate

To determine if our current understanding of the rhlAB promoter response was sufficient to explain the observed dynamics, we derived a mathematical expression of P_rhlAB-gfp promoter activity. The model contains three components. The first component implements the density-dependent up-regulation observed during balanced growth (Fig 4A). The second component implements the observation from here, and in previous work, that rhlAB is expressed under nutrient starvation when growth is limited, but not halted (Fig 4B, nitrogen and iron starvation) [23,36]. Since promoter activity under starvation is also a function of population density (Fig 4C), we use an additive model to describe the integration of population density and nutrient starvation induction. The third component implements a decrease in promoter activity that is observed under prolonged starvation by either nitrogen or iron (Fig 4B). Prolonged starvation shutdown is implemented using Hill kinetics.

Our mathematical model of bacterial growth predicts not only nutrient levels over time, but also the effect of these nutrient levels on growth rate. With an accurate prediction of μ(t), from the growth model, and an understanding of the nutrient environment the cells experience in phases II and III, we are able to use growth rate as an indicator of cell starvation. Therefore, expression under starvation is implemented by induction when μ(t) falls below μ_max (μ_max’ for nitrogen starvation)_. Promoter activity only occurs when carbon has not been depleted in the media. By using μ(t) as an indicator of starvation, rather than absolute nutrient values, our model remains flexible and can be adapted to multiple limitations of these nutrients or additional limiting nutrients. Two variables are required for converting the expression to GFP units and scaling the different components. The variable q_D is used to scale the density dependent activity component and is the same value for all nutrient conditions. The variable q_R is used to scale the starvation induced promoter activity. Consistent with our observations that expression under nutrient starvation depends on the limiting nutrient (Fig 4B), different values of q_R are required to achieve the observed levels of activity in nitrogen or iron limitation (q_RN and q_RFe respectively)

Activity during prolonged starvation shuts down progressively when μ(t) has decreased further and falls below a threshold fraction of μ_max, define here as k_g. We find again that the limiting nutrient has a great effect on promoter activity and to implement the appropriate shutdown in both nitrogen and iron limitation the values for k_g and h must be adjusted for each limitation (k_gN, h_N and k_gFe, h_Fe respectively). Although we must adjust for the different starvation conditions of nitrogen and iron, a parameterized three-component model of rhlAB expression (Eq (8)) is able to recapitulate the observed expression dynamics under our different nutrient limitations (Fig 4D–4F).

(8)

Although it is perhaps at first unsatisfying that the fitted parameters must be changed to account for behavior in both nitrogen and iron starvation, this ultimately supports that the internal state of the cell, which drives rhlAB promoter activity, is significantly different in these two conditions. By eye it is not clear if the growth rate and population size differences could be sufficient to explain the different behavior in the two starvation conditions. However, even by taking the observable differences into account we found no model or single parameter set that could sufficiently explain promoter activity in both starvation conditions simultaneously.

We find that this model is capable of capturing the observed dynamics and indicates that the metabolic signal for expression is potentially at different levels during nitrogen and iron starvation or that downstream regulation is different in these two limitations. The use of μ(t) from our growth model functions as an indicator of starvation and accurately predicts the response of the rhlAB promoter to nutrient starvation. Importantly, both density-dependent regulation and metabolic regulation are required in the model as non-digital regulatory components to recapitulate the observed expression dynamics in all nutrient conditions.

Experimental Test of the Role of Quorum Sensing

Previous work has shown that quorum sensing is required for rhlAB expression, however our observation of a gradual increase in rhlAB promoter activity as population density increases (Fig 4A) suggests a more nuanced role for quorum sensing in rhlAB expression. To confirm that quorum sensing does mediate the density-dependent component of rhlAB expression and to explore the effect of perceived density on rhlAB promoter activity, we utilized a quorum sensing mutant that does not produce the lasI/lasR nor rhlI/rhlR system autoinducers C₁₂HSL (N-(3-oxododecanoyl)-L-homoserine lactone) and C₄HSL (N-butyryl-L-homoserine lactone), respectively and we manipulated the levels of autoinducers in the medium. This strain (PA14 ∆lasI ∆rhlI attB::P_rhlAB-gfp) has the same P_rhlAB-gfp reporter as our wild-type strain (Fig 5A).

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Fig 5. Density-dependent scaling of rhlAB expression is controlled by quorum sensing autoinducers.

A. Quorum sensing regulatory cascade in P. aeruginosa 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 S2 Table for lag times. B. Growth of the ∆lasI∆rhlI 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 [19]. C. GFP expression for each population. Populations that received higher levels of autoinducer express higher levels of GFP. D. P_rhlAB 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.

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We first performed an extensive test of rhlAB induction across a wide range of autoinducer concentrations by varying the concentrations of each autoinducer independently (S6 Fig). The data revealed that although one autoinducer can compensate for a lack of the other, this requires very high levels of that single autoinducer, which are likely not biologically relevant. We also observed that when both autoinducers are increased in concentration, but kept in the same proportion, there is a consistent increase in rhlAB expression. We proceeded with a fixed 1:5 ratio of C₁₂HSL to C₄HSL used previously [36]. To isolate the density-dependent component of expression, the ∆lasI∆rhlI strain was grown in carbon-limited media complemented with different concentrations of C12HSL and C4HSL kept at a 1:5 ratio (Fig 5B).

Higher total levels of rhlAB expression were observed with higher concentrations of quorum sensing signal (Fig 5C). Importantly, promoter activity of rhlAB became constitutive during phase I (exponential growth) confirming that quorum sensing modulates expression during that phase (Fig 5D). In contrast to promoter activity of the wild-type PA14 strain (WT) during exponential growth, phase I promoter activity in the mutant is decoupled from population density (Fig 5D, compared with Fig 4A). The constitutive level of promoter activity in the mutant scales with the concentration of the autoinducers in the medium, as predicted from the relationship between population density and rhlAB promoter activity we observed and modeled in the WT.

We hypothesize that this phase I promoter activity behavior is the result of quorum sensing signals inducing promoter activity when there is a constant level of carbon-rich metabolites present inside the cell during balanced growth in this medium. Because the level of carbon-rich metabolites is constant, promoter activity is modulated only by changes in population density, sensed by quorum sensing signals. Quorum sensing regulation of rhlAB is confirmed here to not be a digital switch, but instead produces a graded rhlAB expression response. Also, the shutdown of rhlAB promoter activity due to carbon depletion occurs even in the presence of high levels of quorum sensing autoinducers (Fig 5D) demonstrating that carbon starvation is capable of overriding the quorum-sensing regulated induction. Using this mutant strain we were also able to confirm that quorum sensing signals scale rhlAB promoter activity during starvation by nitrogen or iron (S7 Fig).

Swarming Cooperation in Nutrient Limitation

We were able to identify the differential responses of the rhlAB promoter to different nutrient limitations and population densities in our liquid culture system. To test the effects of the identified rhlAB promoter responses on swarming cooperation, we grew swarming colonies of the ∆lasI∆rhlI quorum sensing null strain in different media conditions. Unlike in liquid culture experiments, the media used in swarming assays has to be a complex media where casamino acids serve as the carbon and nitrogen source. In our liquid culture system, we found iron limitation to be a potent inducer of rhlAB activity. To test if the integration of quorum sensing signals and iron limitation is required for swarming colony formation we tested several conditions with and without iron limitation and with and without quorum sensing signals. Without quorum sensing signals, the colony is unable to swarm regardless of whether iron is limiting (Fig 6A and 6B). As predicted from our liquid culture experiments and mathematical models, if a population has quorum sensing signals but lacks iron limitation, the colony does not have normally branching and does not travel far from the inoculation site (Fig 6C). This confirms that the significant induction of rhlAB promoter activity we observe under iron limitation in our liquid culture system is also key for rhamnolipid production in swarming colonies. Only when a population is provided with both quorum-sensing signals and iron limitation does successful swarming occur (Fig 6D). Swarming behavior in these four conditions supports our liquid culture data; significant production of rhamnolipids requires both quorum sensing signals and iron limitation. The observation that iron starvation facilitates swarming cooperation is consistent with our experiments showing that iron starvation induces higher rhlAB promoter activity than nitrogen starvation or quorum sensing signals alone (Fig 3F) and with previous reports [45,46]. Given these data the induction of rhlAB expression in swarming colonies (Fig 1D) is likely induced by iron limitation. We also tested the effect of nitrogen limitation, iron limitation, and additional quorum sensing signals on the WT. We found again that iron limitation is necessary for successful swarming while nitrogen limitation and additional quorum sensing signals only moderately affect swarming colony morphology (S8 Fig).

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Fig 6. Quorum sensing signals and iron limitation are required for swarming colony formation.

Quorum sensing signals and iron were supplemented in the agar swarming plates. Quorum sensing signals were supplemented at 1 μM C12HSL and 5 μM C4HSL. Iron was supplemented at 2.79*10^–4 gFe/L by addition of iron(II) sulfate. All swarms were done using the ∆lasI∆rhlI strain A. Populations that do not receive quorum sensing signals and are not in iron limiting conditions fail to swarm. B. Populations that do not receive quorum sensing signals and have iron limiting conditions fail to swarm. C. Populations that receive quorum sensing signals, but are not in iron limiting conditions do not swarm far from the inoculation site and do not form branching tendrils. This demonstrates the key role of iron limitation in rhamnolipid production and swarming colony formation D. Populations that receive quorum sensing signals and have iron limiting conditions exhibit WT swarming colony morphology with branched tendrils that extend to the edges of the plate.

https://doi.org/10.1371/journal.pcbi.1004279.g006

Single Cell Gene Expression

Cells of the P_rhlAB-gfp reporter were taken from a growth curve in a 96 well plate using the growth curve synchronization method described previously [59]. Cells were taken from the 96 well plate wells and mounted on agar pads of low melt agar (approximately 1.75% agar) with no nutrients. Cells were imaged for bright-field, GFP, and DsRed. A ratio of GFP to DsRed was used to determine expression level of rhlAB by GFP.

Correction of Autofluoresence in the gfp Signal

To correct for autofluorescence in the GFP signal, we measured the fluorescence of the unlabeled PA14 strain, which lacks the P_rhlAB-gfp reporter, in numerous experiments across multiple days and a range of conditions, and performed a linear regression on the logarithm of these data (S1A Fig). We found the OD data (OD₆₀₀) to be a good predictor of the autofluorescence. The fit of the autofluorescence (AF) is then a function of the OD₆₀₀ of the form:

We found a correlation coefficient r² = 0.97 using all data points that were OD₆₀₀>0.01. Using this function, we estimated the amount of autofluorescence in our reporter strains by using the OD₆₀₀. We then subtracted the calculated autofluorescence value from the total GFP signal to obtain a corrected GFP (S1B Fig).

Synthetic Growth Media

All synthetic media utilized glycerol as the sole carbon source, ammonium sulfate as the sole nitrogen source and Fe(II) sulfate (Acros Organics, Geel, Belgium) for iron supplementation. Base media contains 64 g/L of Na₂HPO₄.7H₂O, 15 g/L of KH₂PO₄, 2.5 g/L of NaCl, 1 mM of MgCl₂, 0.1 mM of CaCl₂ and carbon, nitrogen and iron concentrations depending on the limiting nutrient. Carbon limitation media: 0.5 gN/L, 2.79 *10^–4 gFe/L, carbon at listed concentration. Nitrogen limitation media: 3.0 gC/L, 2.79 *10^–4 gFe/L, nitrogen at concentration listed. Iron limitation media: 3.0 gC/L, 0.5 gN/L, iron at concentration listed.

Promoter Activity Calculation

Promoter activity was calculated as the change in population GFP per unit time divided by OD leading to the following expression [40,60]:

OD and GFP data are smoothed before calculating promoter activity using the 1-D digital filter using the function filter in Matlab with a window size of 5 timepoints. This calculation accounts for GFP dilution by cell division.

Time Lapse of Gene Expression in Swarming Colonies

Swarming motility and GFP expression were monitored at 37°C at 10 min intervals using a custom-made colony visualizer. The images acquired were processed using Matlab to quantify GFP signal and colony density.

Batch Culture Growth Curves

Starter cultures are inoculated into 3 mL of LB Miller from glycerol stock and incubated overnight at 37°C with shaking. 1 mL of this LB culture is taken, pelleted at 6000 rpm and re-suspended with 1x PBS. Pelleting and re-suspension in PBS is repeated twice before inoculation into the growth media at an OD600 of 0.0025. All growth curves are performed at 37°C in clear flat-bottom BD Falcon 96 well microtiter plates with 150 μL of media per well. Measurements were taken using a Tecan M1000 plate reader (Mannedor, Switzerland) every 10 minutes for the duration of the experiment. Quorum sensing autoinducers HSL and C4HSL used to induce rhlAB expression were obtained from Sigma-Aldrich, St. Louis, MO. Unless otherwise indicated, all growth curves are aligned to have OD 0.01 occur at 10 hours. The lag time for each growth curves is determined during this analysis and reported in S2 Table.

Mathematical Modeling and Parameter Fitting

The mathematical model was implemented as a system of ordinary differential equations in Matlab (the Mathworks, Natick, MA) and solved numerically using the ode45 function. Parameter fitting was carried out using the fminbnd function in a step-wise manner. The OD time series were fitted initially, since these data are independent of the GFP time series data. The goal function to be minimized was defined as: where i ∈ {1, N} represents all the data points used for the fit. The GFP data was fitted by first calculating the promoter activity from the data as explained in the main text followed by fitting with fminbnd to minimize the following function where P_i is the promoter activity calculated from the data and p_i is the promoter activity predicted by the model. Parameter sensitivity was performed for both the bacterial growth and rhlAB expression models and results are reported in S4 and S5 Tables.

Nutrient Depletion Experiment

Starter cultures and inoculation were performed as in Batch Culture Growth curves. Cells were grown to exponential phase in media with 3.0 gC/L, 0.5 gN/L and 2.79 *10^–4 gFe/L in 88 wells of a 96 well plate. All wells were harvested and the cells were pelleted and washed with PBS as in Batch culture growth curves. The harvested cells were then split and re-suspended either 1.2 mL of media without nitrogen (3.0 gC/L, 2.79 *10^–4 gFe/L) or 1.2 mL media without carbon (0.5 gN/L, 2.79 *10^–4 gFe/L) and grown in a 96 well plate in a Tecan M1000 plate reader as described in Batch Culture Growth curves.

P. aeruginosa Swarming Colonies

Swarming assays were performed as previously described [36]. Nitrogen was supplemented with ammonium sulfate at 0.5gN/L. Iron was supplemented using iron(II) sulfate at 2.79*10^–4 gFe/L. Quorums sensing autoinducers were added at the listed concentrations from liquid stock solutions.