Introduction

Interactions like cooperation and competition between different organisms govern ecosystem dynamics, influencing ecosystem composition [1], maintenance of biodiversity [1–4], and the microbiota–host relationship [5–9]. Despite the detailed knowledge of individual interaction mechanisms on the one hand [10,11] and large-scale sequencing based microbiome studies on the other hand [7–9,12,13], the fundamental problem in microbial ecology is the need for predictive model systems that combine experiments with theoretical modelling to explain how ecosystem dynamics emerge from interactions between single cells [14,15]. Simple bacterial model systems allow the elimination of distorting factors and enable the investigation of fundamental processes governing these dynamics, such as stochasticity, under well-defined experimental conditions [2–4,16,17].

In principle, cooperative [18,19] and competitive [10,20] interactions can occur between members of the same or of different species [21] and are mediated by various mechanisms [11,14,21–24]. Cooperative interactions are often realized by phenotypic heterogeneity, which is a division of labor within isogenic populations [24], in which only a subpopulation produces a public good. Competitive interactions are achieved indirectly by competition for resources such as nutrients and space [22] but can also act directly by production of bacteriocins [7]—protein-based toxins produced by many microbes [10].

One class of bacteriocins, the colicins, are synthesized only by a subpopulation of the producer strain [25–27]. The ColicinE2 is one of these heterogeneously produced colicins by E. coli. Here, similar to many other colicins [25], phenotypic heterogeneity is a consequence of the regulation via the noisy SOS response [26,28,29], which can be triggered by the inducing agent mitomycin C (MitC) [25], with higher MitC levels increasing the fraction of toxin producers [30]. The dynamics of ColicinE2 production have been investigated in detail [30]. Individual bacteria switch into the toxin-producing state stochastically [31]. Once a cell has switched into the producing state, it produces the toxin for approximately 60 min and subsequently releases the produced toxin into the environment upon cell lysis [30,32]. Cells that do not produce the toxin continue to reproduce. Hence, two different types of cells (toxin-producing and reproducing cells) are present, and a division of labor is established. Especially at small cell numbers, the stochastic switching dynamics can have important consequences. However, for large cell numbers, the stochastic nature of toxin production is less important, and the system approaches a steady state with constant producer fraction.

The combined action of the two cell types (toxin-producing and reproducing cells) can be seen as a specific type of indirect cooperation that does not rely on communication but in which the tuning of producer fractions is determined by the architecture of the gene regulatory network and its response to an external signal (MitC concentration) [30]. Hence, the production of ColicinE2 by E. coli incorporates both direct competition (by production of toxins) and cooperation (by means of division of labor/phenotypic heterogeneity).

The competition between colicinogenic and susceptible strains of bacteria has been studied as a model system for allelopathy [33–35]. Theoretical studies highlighted the importance of colicin production cost, toxin effectiveness, and initial strain ratios as determinants of the outcome of competition [33]. Furthermore, long-term coexistence of both strains was found to emerge only in structured habitats [33]. More recent studies included experiments and focused on coexistence and biodiversity of toxin producer, toxin-sensitive, and/or resistant strains [1,3–5, 36]. However, these studies mainly neglected the cooperative aspect of toxin production by the ColicinE2 producer strain (C strain). In particular, to our knowledge, the influence of heterogeneity and stochasticity in toxin production on competition outcome and C strain success is largely unexplored, and quantitative experimental validation of theoretical predictions remains lacking.

To address this problem, we employed an experimental approach using a stereoscopic microscope with zoom functionality, which enables investigations over multiple length-scales. In particular, this setup allowed us to correlate well-defined initial conditions with the macroscopic competition outcome of bacterial range expansions, hence, studying the impact of stochastic effects during initial colony formation on competition outcome. Computational modelling of the interaction by means of stochastic, spatially extended, lattice-based simulations supplemented the experiments. Using these two tools, we investigated the interaction of a C strain with a strain sensitive to the toxin (S strain) (Fig 1A). This system exhibits both indirect intra-strain cooperation between reproducers and toxin producers within the C strain population and inter-strain competition between the C and S strain, mediated via toxin action and denial of access to resources by spatial exclusion.

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Fig 1. Two-strain competition, strategies, and outcome.

C–S competition results in four competition outcomes. The competition outcome distribution changes with increasing inducer concentration. (A) Interaction between a toxin-producing strain (C strain) and a sensitive strain (S strain) is characterized by inter-strain competition (spatial exclusion and toxin action) and intra-strain cooperation within the C strain (division of labor between reproducers and toxin producers). (B) Possible outcomes of competition experiments between sensitive (magenta) and producer (green) cells after 48 h (scale bar = 1 mm). Mitomycin C (MitC) concentrations from left to right: 0.01/0.0/0.01/0.01 μg/ml). (C) Final fraction of C after competition (dot plot) and classified outcomes (pie plots) demonstrate a transition from coexistence and dominance of S (0.0 μg/ml MitC) to dominance of the producer strain (intermediate inducer concentrations, 0.005 and 0.01 μg/ml MitC) and failure of the toxin production strategy (high inducer concentration, 0.1 μg/ml MitC).

https://doi.org/10.1371/journal.pbio.2001457.g001

Our data revealed that the competition dynamics can be divided into two phases. In the initial phase of competition, at small cell numbers, stochastic effects originating from the stochastic toxin production dynamics and random initial positioning influenced the number of viable C clusters at the colony edge. In the second, deterministic phase, the degree of division of labor and the number of viable C clusters at the colony edge determined the final outcome of competitions.

Results

Mixed bacterial communities of fluorescently labelled C and S strains were prepared on solid growth media with an initial C:S ratio of 1:100. This ratio boosted the competitiveness of the S strain by facilitating spatial exclusion. At the same time, this ratio allowed us to investigate if and how the C strain is able to outcompete the S strain, in case the S strain is initially dominant in cell number. We imaged the communities using a stereoscopic microscope with a zoom function, which enabled us to acquire time-lapse recordings of the competition from the near single-cell level up to mature, macroscopic colonies. We then extracted colony area and colony composition using customized image and data analysis software (S1 Fig, Methods).

To assess the influence of cooperation within the C strain described above, as well as stochasticity in toxin production on competition outcome and C strain success, we performed range expansion experiments at four concentrations of the inducing agent MitC (0.0, 0.005, 0.01, 0.1 μg/ml). After 48 h of competition, we observed four qualitatively distinct outcomes based on the relative area occupied by the particular strain: domination by C or S, coexistence, and extinction of both strains (Fig 1B, S2 Fig and S1–S4 Videos). Domination signifies that one strain occupies over 90% of the colony area, coexistence denotes occupancies of between 10% and 90%, and occupation of a total area of less than 10⁶ μm² constitutes extinction. This was in contrast to competitions performed under well-mixed conditions (S3 Fig), in which toxin release by the C strain lead to a growth arrest of the S strain in all cases.

In our experiments, we observed a strong dependence of competition outcome distribution on the inducer concentration (Fig 1C). Without MitC, either S won, or the competition resulted in coexistence. At low inducer concentrations, C won in the majority of cases, while at high inducer concentrations C succumbed, and one observed either domination by S or extinction of both strains (Fig 1C). Hence, domination by C was only observed at intermediate inducer concentrations. Although we could identify clear differences between the outcome distributions, we unexpectedly observed multistability—the presence of multiple competition outcomes under similar initial conditions (the same inducer concentration).

To gain a mechanistic understanding of the interaction, we characterized the dynamics of the competition quantitatively. First, we analyzed the impact of stochastic effects in both toxin production and initial positioning on competition outcome (Fig 2). In a second step, we used experimental time-lapse data (Fig 3) as well as computational modelling (Fig 4) to investigate competition parameters that dictate the deterministic competition dynamics, such as growth rate, division of labor (toxin producer fraction) within the C strain, and toxin sensitivity. This enabled us to disentangle the influence of deterministic and stochastic effects and to identify the origin of multistability.

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Fig 2. Two-phase analysis of competition outcome determinants in experiments.

(A) The interaction dynamics are divided into two phases. In phase one, the stochastic switching from replication to toxin production of the ColicinE2 producer strain (C strain) determines the number of viable C clusters at the edge of the colony after 12 h, N_C,Edge. In phase two, the interaction follows deterministic dynamics in which N_C,Edge and MitC are suitable predictors for F_C, the fraction of the C strain after 48 h, whereas the spatial initial conditions only weakly influence F_C. (B) For intermediate mitomycin C (MitC) concentrations (as a proxy for toxin producer fraction), the average F_C is significantly increased. (C) The N_C,Edge—F_C diagram grouped and colored according to MitC concentrations. (D) Dependence of N_C,Edge on the average distance of C cells from the colony center R_C,0 (black squares) and the average distance of C cells from the C cell center D_C,0 (green circles) as proxys for initial spatial conditions. Data was binned into five equal-sized bins. (E) The relation between initial C cell number N_C,0 and N_C,Edge. (F) The effect of MitC concentration on average N_C,Edge. (Data points show the average value, error bars denote standard error). E/F data represent the average over all four MitC concentrations.

https://doi.org/10.1371/journal.pbio.2001457.g002

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Fig 3. Characterization of interaction dynamics.

The increase of the toxin producer fraction and not the ColicinE2 producer strain (C strain) growth rate determines the change in outcome distributions. Unless otherwise stated, colors indicate competition outcome (magenta: sensitive strain, green: producer strain, grey/black: coexistence), error bars represent mean ± standard deviation. (A) Sample image time series and corresponding area and relative fraction curves show C domination outcome (0.01 μg/ml MitC). Scale bar represents 400 μm. (B) Average expansion rates of single-strain colonies obtained in control experiments (no interaction). (C) Effective expansion rates of the entire S–C colony during competition (interaction present). Colors indicate the outcome of the competition: e.g., magenta indicates that >90% of S are present and responsible for colony expansion. (D) Temporal evolution of the producer fraction in the C population in high-resolution control experiments (Methods). (E), The dependence of transition time (time taken for C to capture more than 50% on the colonized area) on inducer concentration. (B, C, E: asterisks indicate significant differences as obtained by pairwise t-tests; not significant (ns): p > 0.05, ***: p < 0.001, for details see S1 Data).

https://doi.org/10.1371/journal.pbio.2001457.g003

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Fig 4. Theoretical analysis emphasizes the importance of intermediate toxin producer fractions for ColicinE2 producer strain (C strain) success.

(A) The four different competition outcomes in simulations (bright magenta: living S cells, dark magenta: growth-inhibited S cells, green: reproducing C cells, white: toxin-producing C cells). Scale bar = 1 mm. Values of the switching rate s_C from left to right: 0.001/0.02/0.001622/synchronicity scenario I. (B) The interaction scheme underlying the theoretical model (Methods). (C) C dominance phase diagrams for toxin effectivity s_S and toxin producer fraction. (D) The final fraction of the C strain (dot plot) and classified outcomes (pie and bar plots) after simulated competition at fixed s_S = 1,500 and in dependence on toxin producer fractions are in accordance with experimental results (Fig 1C). The color code represents competition outcome and is identical to that in Fig 1C.

https://doi.org/10.1371/journal.pbio.2001457.g004

Stochastic effects that are mainly important in this C–S competition are the random initial spatial positioning of the C strain within the C–S colony and the stochastic switching from the replicating to toxin-producing phenotype of C cells at low cell numbers (Fig 2A). Our method enabled us to precisely determine the position and number of C cells in initial colonies and subsequently analyze their influence on competition outcome. Surprisingly, we found that the fraction of C cells in the colony after 48 h F_C is only weakly correlated to various initial spatial measures, such as initial C cell number N_C,0, individual C cell distance to the colony center , average distance of C cells from the center R_C,0, and the average distance of C cells from the center of all C cells D_C,0 (Fig 2A dotted arrow, S4 Fig, Methods, and see S1 Data for correlation table).

In contrast, the second source of stochasticity, the stochastic toxin dynamics, was observed to strongly influence the final C fraction F_C (Fig 2B). For small cell numbers, stochastic switching has a big influence on the toxin production dynamics of individual C cells and can decide the fate of the single S–C communities. Qualitatively, this can be understood when considering different scenarios (S2 Fig): Early toxin production prevented C’s success in case there were too few C cells left to proliferate. Consequently, the S strain dominated or the whole S–C colony went extinct. In case of delayed toxin production, a considerable C strain population had formed, and enough reproducing C cells remained after toxin release to maintain the C strain population. This resulted in C domination or coexistence outcomes.

These observations inspired us to take a closer look at the initial phase of colony formation (phase one: t < = 12 h) where stochastic effects play an important role due to small cell numbers. We found that we could quantify our qualitative observations by N_C,Edge, the number of viable C cell clusters at the colony edge after 12 h. Linear regression showed that the buildup of viable C clusters at the colony edge was significantly influenced by each of the spatial variables N_C,0, R_C,0, D_C,0, and MitC as a proxy for the switching rate into the toxin-producing state (Fig 2D–2F, Methods, and S1 Data).

We found that variations in N_C,Edge together with the influence of the inducer concentration MitC, could explain the observed multistability (Fig 2C). As we will describe in the subsequent paragraphs, the deterministic dynamics were strongly influenced by the inducer concentration that determined the interaction regime. However, due to the stochastic nature of single-cell dynamics and initial spatial positioning, the formation of viable C cell clusters was subject to noise. Given a favorable deterministic regime (0.005, 0.01 μg/ml MitC), we can distinguish three cases: (1) N_C,Edge ≥ 1 lead to success of the C strain or transient coexistence, (2) N_C,Edge = 0 and there was no viable C cluster remaining lead to domination of the S strain, (3) N_C,Edge = 0 and there was no C cell cluster remaining and the random spatial distribution lead to unlikely but possible complete extinction. In cases of transient coexistence, growing C clusters were not large enough to cover over 90% of the area within the time-frame of our experiments but will take over in the long run. In the uninduced deterministic regime (0.0 μg/ml MitC), C success was prevented due to limited toxin action, and we only observed S success and coexistence with a linear dependence of F_C on N_C,Edge (Fig 2C). In the highly induced case (0.1 μg/ml MitC), buildup of viable C cell clusters was suppressed (Fig 2F), and depending on the spatial initial position of the S strain, S could survive, or we observed extinction.

To formally analyze the effects of the different variables, we employed a linear statistical model incorporating the variables MitC, N_C,Edge, N_C,0, R_C,0 and D_C,0 and their interactions to explain F_C (Methods, S1 Table). We found that significant effects stem from MitC, N_C,Edge, their interaction, and the interaction term of N_C,Edge and N_C,0. As expected from the previous results, large and medium effect sizes (based on η² statistic) were only attributable to MitC and N_C,Edge, respectively. In order to verify our findings with higher significance, we performed simulations (see below for details) with 16 random initial conditions IC, repeated 30 times each, over a range of 17 different switching rates s_C. Intriguingly, we could observe different outcomes of the competitions under the very same initial conditions (s_C = 0.02, example in S4C Fig), underlining the result that the spatial initial conditions do not fully determine the competition outcome. Analogously to our experimental analysis, N_C,Edge was determined, and the response variable F_C was modelled in a linear statistical model (Methods, S1 Table). Here, all variables and their interaction terms are statistically significant, but only s_C and N_C,Edge have large η² effect sizes (see S1 Table). This supports the experimental result that spatial initial conditions act only indirectly via N_C,Edge on the final C fraction F_C.

In order to probe the relation between stochastic and deterministic phases, we performed experiments (at 0.005 μg/ml MitC) and simulations with increased initial density, as inoculation density is known to influence colony pattern formation [37]. Intuitively, one expects a decrease in multistability, with competition outcome distributions becoming increasingly deterministic. However, our observations indicate a counteracting mechanism for intermediate densities (S5 Fig). For 2- and 4-fold initial density, S success was decreased, but we also observed an increased fraction of coexistence outcome in experiments. These cases of coexistence were believed to be transient, and are most likely explained by an increased S area that established before the toxin stops S’s growth. We speculate that during the 48 h of competition, the C strain did not have enough time to catch up, and the final fraction was below 90%. If we increased the density further, S’s head start might not have been enough to act against the increased probability to have high N_C,Edge values, and we observed mostly C success with few coexistence events. In contrast to these ambiguous results for the outcome distributions, we found a decrease in variance of the C fraction dynamics averaged over the time-course of the experiment, with increasing density (OD 0.1: 0.2146, OD 0.2: 0.1630, OD 0.4: 0.1231, OD 0.8: 0.1013) indicating more reproducible dynamics with increasing initial cell density. Note that the simulation results differed slightly from the experimental observations. First, with increasing initial cell density, spotting of the C-S mixture resulted in an increased coffee stain effect in experiments. Hence, the density is not homogeneously increased as is the case in the simulations. Secondly, in simulations in which viable C clusters were surrounded by dead S cells, preventing spatial expansion and dominance of the C strain, the total colony size remained very small, and the outcome was therefore classified as extinct.

Up to now, we have learned that stochastic effects in initial positioning and toxin production dynamics influence the number of viable C cell clusters at the colony edge after 12 h (N_C,Edge). Furthermore, we found that N_C,Edge together with the inducer concentration MitC determining the interaction dynamics of the second phase strongly predicts the outcome of competitions. However, an exact analysis of the influence of MitC on the deterministic dynamics in the second phase was missing. Therefore, we investigated competition parameters that dictate the deterministic competition using experimental time-lapse data and computational modelling.

In the first step, we evaluated the growth rates (area expansion rates) for both strains in the absence of the competing strain (Fig 3B, Methods). We found that the growth rates for S and the uninduced C strain were similar to those seen in previous studies [3], with C growing slightly faster on average. At high inducer levels, C’s growth rate falls considerably, owing to increased toxin release with concomitant lysis [30]. We speculate that the observed increased growth rate of the S strain can be attributed to selection for fast growing S cells at high MitC concentrations. We furthermore determined the growth rates of the entire colonies in competition experiments (Fig 3C). We found that in cases of final S strain dominance growth of the entire mixed colony is enhanced compared to the single S colony growth upon induction with MitC. Hence, competition may promote growth of S due to the selective effect of sublethal colicin concentrations (S3D Fig). In competition experiments that lead to final C strain dominance, the growth rate of the entire mixed colony is reduced compared to the single C strain colony growth rate. Here, although the C strain is dominating in the end, its growth is reduced by initial spatial exclusion by S, which restricts the territory available to the former.

The reduced effective growth of C in competition experiments emphasized that growth rate alone cannot explain its dominance at low inducer concentrations. Hence, we assessed the dependence of the second parameter, producer fraction within the C strain population, on MitC concentration using high-resolution microscopy (Fig 3D, Methods and S6 Fig). The dynamics of toxin production have been studied in detail for liquid environments using single-cell fluorescence time-lapse microscopy [30]. Here, the strongest population response is observed 75 min after induction, and it was found that the fraction of cells producing the toxin increases with the external stress level (MitC). While in the absence of external stress, only a basal producer fraction was found with few cells producing the toxin; low external stress resulted in a significant fraction of cells producing and releasing the toxin. In contrast, high MitC concentrations lead to a synchronized response of all cells [30]. We verified, that this correlation between the external stress level and the fraction of toxin-producing cells within the C strain population was also present for the experimental conditions used in this study (Fig 3D). In the absence of MitC, an intrinsically low producer fraction (7.0 ± 1.5%) was detected. At low MitC concentrations, the mean producer fraction increased to 14.5 ± 1.9% (0.005 and 0.01 μg/ml MitC combined), while the highest inducer concentration leads to a synchronized response (57.8 ± 3.2%) with a subsequent collective decrease in producer fraction due to cell lysis, in accordance with previous studies [30]. This suggested that the observed shift in competition outcome distribution with varying inducer concentration can be attributed to the change in toxin-producer fraction.

To verify that, indeed, increased toxin production was determining the interaction dynamics of the second phase, we repeated our competition experiments with a strain S_YFP that is genetically identical to the C strain but lacks the original colicin-producing pColE2-P9 plasmid and hence is not able to produce the toxin (Methods). Lysis in this strain is achieved through the additional lysis gene expression from a reporter plasmid encoding a yellow fluorescent protein (YFP) [30]. For this S_YFP–S competition, we found mostly dominance of the S strain and coexistence of both strains at all inducer concentrations (S7A Fig). Similar to this all-OFF scenario (no cell able to produce the toxin), also a scenario with all C cells producing the toxin (all-ON) reduced C strain success (S7B Fig). At a very high MitC concentration of 0.4 μg/ml, all cells produced the toxin simultaneously [30] which lead to the total extinction of both the C and S strain in nearly all competition experiments. This showed that, indeed, the change in producer fraction, and consequently the toxin amount released, was causing the shift in competition outcome distributions, and demonstrated the importance of division of labor for C strain success. To characterize individual interaction dynamics, we extracted the transition time from the relative occupied area curves (Fig 3E). The transition time was defined as the time it takes for C to capture more than half of the colonized area. We observed that average transition times were shorter for the higher inducer concentration and that long-term C dominance was possible only if the transition occurred early. This again emphasized that population fate was mostly determined in the initial phases of colony formation.

To corroborate our experimental finding of toxin-producer fraction as the key parameter of the second phase’s interaction dynamics determining C strain success, we developed a theoretical model of the competition and simulated the system with parameters we obtained in our experiments. We used a stochastic lattice-based model that enabled us to explicitly incorporate the stochastic positioning and phenotypic heterogeneity of the C strain (Methods and Fig 4). Phenotypic heterogeneity in the model is a result of stochastic switching [31] from the reproducing (normal) state C to the toxin-producing state C_on. Because of cell lysis accompanying toxin release, producing cells can only decay and cannot switch back in the model. Our numerical simulations reproduced the four different outcomes observed in competition experiments (Fig 4A, S5–S8 Videos) and demonstrated that dominance of the C strain could be achieved by only varying the switching rate s_C, i.e., the propensity of a reproducer cell to switch to the producing state (Fig 4C). In particular, upon altering s_C, which corresponds to varying the inducer concentration, we observed the same qualitative changes in the final C strain fraction and competition outcome as were seen in experiments (Fig 4D) for a constant toxin effectivity s_S. With low and high producer fractions, we observed no domination of the C strain, whereas the C strain took over for intermediate inducer concentrations. More explicitly, at ~50% toxin-producing C cells, we found mostly dominance of the C strain (Fig 4C) but also dominance of the S strain and coexistence of both strains. The question arose if one observed the same competition outcome if the C strain was able to release the toxin while growing, which is the case for other toxin-producing species [25]. In such a scenario, we found that the C strain dominates in nearly all cases (S7C Fig). Hence, the C strain is similarly successful if the toxin can be released without cell lysis by all toxin producers, even if the growth rate and the toxin sensitivity is reduced. This indicates that cell lysis bears a high cost for the toxin producer.

The third important interaction parameter, the toxin effectivity s_S, represents the total toxin impact and incorporates toxin amount released by the C strain and toxin sensitivity of the susceptible strain S. Because of its complexity, it is hard to exactly determine this parameter experimentally. However, its effect on the dynamics can be explored in the model. We simulated the system for a range of s_S and s_C values, yielding phase diagrams for each of the four competition outcomes (Fig 4C, S8A Fig). In agreement with our experimental findings, dominance of C was indeed prominent in regions of intermediate producer fractions. Furthermore, this held for a broad range of toxin effectivities s_S. Conversely, S dominance was most likely where C’s toxin production strategy failed. Coexistence was mostly found at low toxin producer fractions or low toxin effectivity. Extinction events occurred all over regions of the phase diagram where C prevailed and became more prominent for higher s_C values. However, the simple computational model could not reproduce the high incidence of extinction events seen in experiments at high inducer levels. A more detailed model incorporating the synchronicity of the toxin-production response to external stress yielded higher numbers of extinction events (S8B Fig and S9 and S10 Videos), highlighting the fact that population extinction at high producer fractions requires a synchronous response.

Taken together, the theoretical model clearly showed that only varying the switching rate and thereby the toxin producer fraction within the C strain population is sufficient to explain why the C strain can be dominant at intermediate inducer concentrations (= intermediate toxin producer fractions).

To explicitly test the influence of relative strain growth rate and toxin sensitivity, we repeated the competition of C with three other strains experimentally (at 0.005 μg/ml MitC) and varied the growth rate and toxin sensitivity parameters in simulations (Fig 5 and S9C Fig). Experimentally, this included altering the growth rate of the competitor and its sensitivity to the toxin (Methods). Boosting the growth rate of S (S_NFP) increased the effect of its competition strategy, spatial exclusion, and improved the S strain’s competitiveness considerably. Resistance to the toxin (R_RFP) neutralized the deleterious effect of C on its competitor and prevented dominance of C. Furthermore, increasing the resistant strain’s growth rate (R_NFP) enabled it to consistently prevail over C. These results (Fig 5B) were confirmed by our theoretical simulations, using the appropriate growth rates and toxin sensitivities for the competitor mutants obtained in experiments (S9A Fig and S2 Table). This underlined the ability of our model to accurately predict competition outcome distributions.

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Fig 5. ColicinE2 producer strain (C strain) dominance depends on the competitor’s strategy.

Experiments were performed at 0.005 μg/ml mitomycin C (MitC). Toxin resistance or induced growth enables the competitor to outcompete the C strain. Altering the background fluorescent marker expressed from fluorescent reporter plasmids in the respective strain, allows one to vary the growth rate of this strain. The expression of the red fluorescent protein (RFP) mCherry results in a significant growth rate reduction [3]. Strains indicated by no fluorescing protein (NFP) do not express a fluorescent protein. (A) Alternative competition strategies involving disablement of toxin action (R_RFP, R_NFP) and/or increased spatial exclusion (S_NFP, R_NFP) compared to the original toxin-sensitive strain (S strain) (S_RFP). (B) Experimental (top) and simulated competitions (bottom) yield similar outcome distributions.

https://doi.org/10.1371/journal.pbio.2001457.g005

Exploring the dependence of outcome probability on relative growth rate and toxin sensitivity further (S9C Fig), we found a trade-off between both parameters. The phase diagrams show a dividing line of coexistence along a diagonal axis that represents the growth rate and sensitivity trade-off. For instance, if a strain was sensitive and slow, it succumbed to the toxin producer. Conversely, a strain that was less sensitive did not need a high relative growth rate to thrive in competition. These insights can be used to predict the influence of growth rate changing fluorophore expression (S9A Fig) on the deterministic competition dynamics. The costly expression of red fluorescent protein (RFP) compared to no fluorescing protein (NFP) (S_RFP compared to S_NFP) [38] influenced competition outcome considerably (Fig 5, S9A Fig and S2 Table) in accordance to our theoretical results. Likewise, we expect the relatively small decrease in growth rate of the C strain compared to the corresponding wild-type strain due to fluorophore expression (Methods) to only weakly influence the interaction.

Taken together, the results show that stochastic and deterministic effects can be disentangled. In the first phase (t < 12 h), at low densities, stochastic effects of toxin production and spatial distribution influence the number of viable C cell clusters at the colony edge after 12 h (N_C,Edge). Together with a measure for the division of labor (MitC in experiments, s_C in simulations) the deterministic dynamics of the second phase can be well predicted. In this second competition phase, the strains simply expand in range afterwards, following deterministic dynamics governed by the effective fitness differences between the two strains [17].

Discussion

Our results clearly showed, how stochastic processes influenced the initial phase of colony formation and how effective fitness differences stemming from division of labor within the toxin-producing population dictated the deterministic interaction dynamics of the second phase.

We demonstrated that the outcome of competitions fought under the same condition is not fixed [33–35]. Instead, we could observe four different competition outcomes in our experiments. This multistability was a result of the stochastic toxin-production dynamics. This can be understood if we disentangle the dynamics into two distinct phases. In phase one, the stochastic toxin-production dynamics of individual cells at early time points determine the fate of a given S–C colony by affecting the number of viable C cell clusters at the colony edge N_C,Edge (phase one, Fig 2). In the second phase, the stochastic toxin production manifests itself in a constant toxin-producer fraction constituting the division of labor/phenotypic heterogeneity. The exact degree of heterogeneity sets effective fitness differences between both strains and, together with the number of C clusters at the colony edge, it dictates the deterministic macro dynamics and thereby competition outcome distributions (phase two, Fig 2).

As a result, in case of sufficient toxin action (0.005 and 0.01 μg/ml MitC), the effective fitness differences were so large that once a viable toxin-producer cluster had formed at the colony edge (N_C,Edge > 0), it took over the colony in the long run. Hence, the coexistence observed at 48 h was only transient, S never won as we observed N_C,Edge > 0, and the dynamics were fully determined by the initial phase.

However, in the case of limited toxin action (0.0 μg/ml MitC), the effective fitness difference was not as clear. The observed coexistence was persistent as the effective fitness differences were not large enough to let the C strain take over during the time-course of our experiments (S2 Video) and after prolonged competition (>48 h). Furthermore, in the absence of MitC, we observed few cases in which the S strain won, although we had observed N_C,Edge > 0. These cases were in accordance to previous studies that showed how inevitable random fluctuations due to genetic drift can cut off access to the exterior for similarly expanding colony domains [39]. Therefore, we conclude that for the uninduced case, the initial phase does not fully determine the outcome but predicts the final fraction of the C strain well (see also Fig 2C).

By taking advantage of the multiscale functionality of the presented experimental method, we could investigate both the parameters for the deterministic dynamics as well as the influence of stochasticity in toxin production and initial conditions. In addition, we are confident that this method can be used to investigate a variety of interaction types in detail, thereby advancing our fundamental understanding of bacterial interactions.

The computational model used in this study nicely complemented our experiments. When used with experimentally observed parameters, it was able to predict competition outcome distributions in good accordance with the experimental observations. Variations of toxin-producer fraction, growth rate, and the switch from sensitive to resistant strains showed outcome distributions similar to experiments. Furthermore, the model could be exploited to investigate conditions that we could not create experimentally, such as varying toxin effectivity s_S, replication of simulations with the very same initial conditions, and simulations of competitions with a non-lysing C strain.

Our conclusions about stochasticity as the origin of multistability are robust with respect to a wide range of different parameters influencing the deterministic interaction dynamics, such as toxin effectivity, growth rate, or exact switching rate. Obviously, the initial influence of stochasticity decreases with increasing density.

The observed trade-off between the beneficial effect of antibiotic production and the effective fitness disadvantage the producer strain exerts on itself is in accordance with Geradin et al. [36]. In this study, the fitness disadvantage was further increased by the presence of resistant bacteria.

In summary, our results show that stochasticity in the initial phase of colony formation can be the crucial factor that determines the ensuing population dynamics and consequently controls the final composition of the community. This is in accordance with a recent study of the effects of stochastic assembly on host-associated microbial communities [40] and underlines how random events at the single-cell level can influence the fate of microbial communities in the long run. Besides toxin production, there are many phenotypically heterogeneous traits in which decisions between one or another phenotype happen stochastically. Therefore, our findings are relevant for a broad range of microbial communities, in which the random choice between phenotypes during the initial phases of colony formation effectively fixes the community's composition and ultimate fate.

Methods

Statistical analysis

For the experimental data, the influence of N_C,0, R_C,0, D_C,0, and MitC on N_C,Edge was modelled after standardization using the following linear model.

For both experiment and simulation, the influence of the different factors MitC, N_C,Edge, N_C,0, D_C,0, and R_C,0 on final C fraction F_C was analyzed using a linear model that also incorporated interactions between these factors. For the experimental analysis, MitC was treated as a categorical variable to account for the qualitative difference between different induction regimes. The other variables were treated as continuous variables. The model had the explicit form:

Analysis of the simulation was performed analogously using the three variables s_C, N_C,Edge, and IC. Here all three variables were treated as categorical variables. The linear model had the explicit form:

Significance and effect sizes of the factors were analyzed using the Anova and EtaSq functions of the statistical programming language R (Version 3.2.3) that rely on the type I (sequential) sum of squares, where the order of terms in the model matters. Terms in the model are ordered according to the experimental design: MitC/s_C is externally tuned, N_C,Edge is found to be very important, exact spatial details/IC are of minor importance.

Supporting information

Acknowledgments

We thank M. Riley for the kind gift of the original S, R, and C strains and K. Jung for the kind gift of plasmid pBAD24-GFP and pmCherry. We also thank J.O. Rädler, E. Frey, D. Braun, A. Stöcker, D. Volbers. and A. Mader for their support and for fruitful discussions.