Low-Dose Ciprofloxacin Increases Bacterial Aggregation and Intestinal Expulsion.

For both Vibrio and Enterobacter, we empirically determined a ciprofloxacin dosage that induced clear changes in bacterial physiology and behavior in vitro, but that was below the apparent minimum inhibitory concentration. We first describe results of antibiotic exposure, in vitro and in vivo, for the Vibrio species.

From an initial survey of dose–response in rich media, we identified 10 ng/mL ciprofloxacin as an appropriate exposure for Vibrio populations. Growth of Vibrio in lysogeny broth in the presence of 1 ng/mL ciprofloxacin closely resembles that of the untreated control, while a concentration of 100 ng/mL is largely inhibitory (SI Appendix, Fig. S2A). An intermediate concentration of 10 ng/mL leads to a stable, intermediate optical density. Viability staining (Materials and Methods) after 6 h of incubation with 10 ng/mL ciprofloxacin identifies 30% to 80% of cells as alive (SI Appendix, Fig. S3 A and B), again consistent with this antibiotic concentration being sufficient to perturb the bacterial population without overwhelming lethality. Growth in the presence of 10 ng/mL ciprofloxacin induces marked changes in cell morphology and motility: Treated cells exhibit filamentation, making them considerably longer (mean ± SD 5.3 ± 3.1 μm) than untreated Vibrio (2.9 ± 0.9 μm) (SI Appendix, Fig. S2B). Swimming speed was also reduced compared to that of untreated cells (mean ± SD 11.4 ± 7.2 μm/s, untreated 16.9 ± 11.1 μm/s) (SI Appendix, Fig. S2C and Movies S3 and S4). We note also that 10 ng/mL ciprofloxacin is comparable to levels commonly measured in environmental samples (18).

While useful for illuminating the appropriate sublethal concentration to further examine, experiments in rich media conditions are not an optimal assay for comparison of in vitro and in vivo antibiotic treatments, as the chemical environments are likely very dissimilar. We therefore assessed effects of ciprofloxacin on bacterial populations in the aqueous environments of the flasks housing the larval zebrafish in comparison to populations in the intestines. In the flask water, as in the intestine, the only nutrients are fish derived. Oxygen levels are comparable to those in the larval gut, due to fast diffusion and the animals’ small size. Bacteria in flask water therefore constitute a useful baseline against which to compare antibiotic impacts on intestinal populations.

Vibrio was associated with germ-free zebrafish at 4 d postfertilization (dpf) by inoculation of the aqueous environment at a density of 106 cells/mL (Materials and Methods) and allowed to colonize for 24 h, which based on previous studies provides ample time for the bacterial population to reach its carrying capacity of ∼105 cells per gut (15). Animals and their resident Vibrio populations were then immersed in 10 ng/mL ciprofloxacin for 24 or 48 h or left untreated (Fig. 2 A and B). Vibrio abundances in the gut were assayed by gut dissection and plating to measure colony-forming units (CFUs) (Materials and Methods). Abundances in the flask water were similarly assayed by plating. We quantified the effect of the antibiotic treatment by computing the ratio of bacterial abundances in the treated and untreated cases, resulting in a normalized abundance (Fig. 2C). After a 24-h treatment, log10-transformed abundances in the flask water dropped by 0.98±0.4 (mean ± SD) compared to untreated controls, or 1 order of magnitude on average. In contrast, log10-transformed intestinal abundances showed a more severe reduction of 1.75±0.88 (Fig. 2C), or a factor of ∼60 on average, suggesting that the intestinal environment amplifies the severity of ciprofloxacin treatment. For the 48-h treatment, the declines in flask water and intestinal abundances were similarly severe (Fig. 2C). In terms of absolute abundances, pooled data from 24- to 48-h treatments give a mean ± SD of the log10-transformed Vibrio population of 3.1 ± 0.9 (n=40), compared to 4.9 ± 0.5 (n=42) for untreated specimens (Fig. 2D). Unpooled data are similar (SI Appendix, Fig. S3 E and F).

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Fig. 2.

Low-dose ciprofloxacin induces Vibrio aggregation and expulsion in vivo. (A) Schematic of the experimental timeline. (B) Schematic of the sampling scheme for plating measurements. (C) Normalized abundances (number of CFUs scaled by untreated medians) of water and gut populations. N values left to right: 8, 24, 7, 20, 6, 18, 5, 20. Water N values denote number of flasks; gut N values denote number of fish. (D) Histograms of gut CFUs with pooled data from 24- to 48-h treatments. Counts indicate the number of individual fish with a given log10 Vibrio CFUs. Dashed lines indicate the mean of each set, showing an ∼100-fold reduction in intestinal Vibrio abundance in antibiotic-treated fish. (E) Ensemble-averaged spatial distributions of log-transformed cell density as a function of distance along the gut axis, integrated over the perpendicular dimensions. (F) Maximum-intensity projections of 3D images of untreated (Top) and ciprofloxacin-treated (Bottom) Vibrio populations. Insets show viability staining of bacteria expelled from the gut, with green and magenta indicating living and dead cells, respectively. (G and H) Dynamics of in vivo Vibrio populations untreated (gray lines) and treated with 10 ng/mL ciprofloxacin (blue lines). (G) The 1D center of mass, normalized to intestine length. (H) Total image-derived Vibrio abundance. In both G and H, each curve represents a different zebrafish. Vertical dotted lines indicate the time of drug administration to the treatment cohort, t=0.67 h.

To assess the possibility that the intestine makes Vibrio more susceptible to ciprofloxacin-induced cell death, we embedded larval zebrafish in a 0.5% agarose gel, which allowed collection of expelled bacteria. After staining expelled bacterial cells with the viability dyes SYTO9 and propidium iodide, we imaged ejected material. We found no detectable difference between ciprofloxacin-treated and untreated populations (Fig. 2F, Insets). Similarly sizeable fractions of viable and nonviable cells are evident in both ciprofloxacin-treated and untreated populations; however, costaining of zebrafish host cells hindered exact quantification (SI Appendix, Fig. S4). This result suggests that the ciprofloxacin-induced population decline observed in vivo occurs independent of overt cell death and is a consequence of the response of living bacteria to the intestinal environment. We further note that the dose–response of the intestinal Vibrio abundance (SI Appendix, Fig. S5) mirrors the dose–response of the in vitro growth rate, implying that the larval gut does not significantly alter or concentrate ciprofloxacin. This is also consistent with the widespread use of zebrafish larvae as a pharmacological screening platform, as water-soluble chemicals readily enter and leave the animal (20, 21).

To investigate the causes of ciprofloxacin’s disproportionately large impact on in vivo bacterial abundance, we used light sheet fluorescence microscopy to directly monitor Vibrio populations within the intestine over several hours as they responded to antibiotic exposure. The 3D time-lapse imaging revealed that within hours of ciprofloxacin treatment, large numbers of bacteria became depleted from the anterior-localized planktonic and motile population (Movies S5 and S10). Cells were instead found in the midregion and distal region of the gut, where they appeared to be condensed into large multicellular aggregates prior to being expelled from the gut altogether (Movies S5 and S11). After 10 h of exposure, Vibrio populations in ciprofloxacin-treated hosts contained large, 3D aggregates localized to the posterior of the intestine, a feature not observed in untreated controls (Fig. 2 E and F) or in all previous characterizations of this strain (10, 15). We note also that in vitro, antibiotic-treated Vibrio does not form large aggregates (SI Appendix, Figs. S3 and S6 and Movie S4).

To determine whether the bacterial aggregation observed in vivo stems from a fundamentally different response to antibiotics at the single-cell level or different large-scale consequences of similar cell-level response, we generated in Vibrio a genetically encoded fluorescent reporter of the SOS pathway (SI Appendix, Fig. S7 and Materials and Methods), a DNA damage repair pathway induced by genotoxic agents such as ciprofloxacin (22, 23). Genes in the SOS regulon halt replication and enable DNA repair and also affect motility and biofilm formation (19, 24). In vitro, we found that treatment with 10 ng/mL ciprofloxacin strongly induced recN-based SOS reporter activity, with a heterogeneous response across individual cells (SI Appendix, Fig. S3 C and D). Within the intestine, SOS reporter activity was also heterogeneous, appearing in both planktonic and aggregated cells. Planktonic cells that were SOS positive appeared more filamented and less motile compared to SOS-negative cells within the same host (Movie S6). The activation of the SOS reporter in vitro and in vivo by ciprofloxacin (Movie S6 and SI Appendix, Fig. S3 C and D) suggests that in both cases a canonical SOS response is involved in the perturbation of Vibrio physiology.

Together, these data begin to reveal a mechanism by which the intestine amplifies the effect of low-dose ciprofloxacin. Individual Vibrio cells first undergo an SOS response that is associated with changes in cellular morphology and behavior. In the context of the mechanical activity of the intestine, these molecular and cellular-level changes then give rise to population-level aggregation and spatial reorganization throughout the entire length of the intestine, with the population shifting its center of mass posteriorly (Fig. 2G, n=4 per case). This process culminates in the expulsion of large bacterial aggregates from the host, causing a precipitous decline in total bacterial abundance (Fig. 2H).

Low-Dose Ciprofloxacin Suppresses Small Cluster Reservoirs Associated with Intestinal Persistence.

In contrast to Vibrio, Enterobacter is slower growing and nonmotile and naturally forms dense aggregates within the zebrafish intestine. Enterobacter populations have an in vivo growth rate of 0.27 ± 0.05 h⁻¹ (mean ± SD; SI Appendix, Fig. S1), compared to 0.8 ± 0.3 h⁻¹ for Vibrio (15). Based on conventional notions of antibiotic tolerance, we hypothesized that Enterobacter would be less affected by ciprofloxacin treatment than the fast-growing, planktonic Vibrio. However, as detailed below, we found this prediction to be incorrect; Enterobacter exhibits an even greater response to low-dose ciprofloxacin.

We first established in vitro that 25 ng/mL ciprofloxacin produces similar effects on Enterobacter growth to 10 ng/mL exposure on Vibrio. With the identical inoculation procedure used for Vibrio, log10-transformed Enterobacter abundance in the flask water dropped by 1.2 ± 0.4 (mean ± SD) compared to untreated controls after 24 h and dropped by 1.8±0.2 after 48 h (Fig. 3A). These values match well the values for Vibrio: 0.98 ± 0.37 for 24 h, 1.81 ± 0.5 for 48 h. Assays in rich media show a similarly reduced density between the 2 species (SI Appendix, Fig. S8) and an even lesser degree of cell death and damage in vitro for Enterobacter compared to Vibrio, with a viable fraction of ∼95% (SI Appendix, Fig. S9 A and B). As with Vibrio, in vitro growth measurements and viability staining both imply that low-dose ciprofloxacin treatment of Enterobacter induces growth arrest rather than widespread lethality.

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Fig. 3.

Low-dose ciprofloxacin collapses Enterobacter populations and suppresses small clusters in vivo. (A) Normalized abundances (number of CFUs scaled by untreated medians) of water and gut populations. N values left to right: 4, 20, 4, 20, 4, 19, 4, 20. Water N values denote number of flasks; gut N values denote number of fish. (B) Histograms of gut CFUs with pooled data from 24- to 48-h treatments. Counts indicate the number of individual fish with a given log10 Enterobacter CFUs. Dashed lines indicate the mean of each set, showing an ∼1,000-fold reduction in intestinal Enterobacter abundance in antibiotic-treated fish. (C) Total number of bacterial clusters in the intestine, quantified from 3D images (Materials and Methods). (D) Maximum-intensity projections of 3D images of untreated (Top) and ciprofloxacin-treated (Bottom) Enterobacter populations. Insets show viability staining of bacteria expelled from the gut, with green and magenta indicating living and dead cells, respectively.

Strikingly, low-dose ciprofloxacin treatment of fish colonized with Enterobacter (Materials and Methods) resulted in even greater reductions in abundance than in the case of Vibrio, with the majority of populations becoming nearly or completely extinct during the assay period (Fig. 3 A and B). Inoculation, treatment, dissection, and plating were performed as for Vibrio (Materials and Methods). Compared to untreated controls, log10-transformed intestinal abundances were reduced by 2.3 ± 1.1 after 24 h and by 3.2 ± 1.0 after 48 h (Fig. 3A). These reductions in intestinal abundances greatly exceeded the reductions of bacterial abundances in the flask water (Fig 3A). In terms of absolute abundances, pooled data from 24- to 48-h treatments give a mean ± SD of the log10-transformed Enterobacter population of 1.5 ± 1.0 (n=40), compared to 4.0 ± 1.0 (n=39) for untreated specimens (Fig. 3B); unpooled data are similar (SI Appendix, Fig. S9 C and D).

Live imaging of intestinal populations at single time points revealed ∼40% of treated hosts to be devoid or nearly devoid of Enterobacter, consistent with the plating-based measurements. In hosts that contained appreciable bacterial populations we observed a clear difference between treated and untreated specimens: Enterobacter populations in ciprofloxacin-treated hosts contained fewer small bacterial clusters and fewer individual planktonic cells than untreated controls (Fig. 3 C and D). We quantified this distinction using computational image analysis to identify each cluster (Materials and Methods), defining a single cell as a cluster of size 1. Bacterial populations in ciprofloxacin-treated animals contained ∼80× fewer clusters than untreated animals (Fig. 3C). Viability staining showed that there were no obvious differences in the viable fractions of bacteria expelled from the intestines of untreated and treated hosts (Fig. 3D, Insets and SI Appendix, Fig. S10). As with Vibrio, these observations suggested that the reduction in Enterobacter’s intestinal abundance was independent of cell death.

Previous studies of other naturally aggregated bacterial species have revealed that large bacterial aggregates are highly susceptible to expulsion from the gut (15, 25). To establish whether this is also the case for Enterobacter in the absence of low-dose ciprofloxacin treatment, we performed time-lapse 3D imaging (Materials and Methods). Indeed, in 2 of 5 hosts imaged for 3.5 h each, we observed events in which the largest bacterial aggregate was abruptly expelled from the intestine (Fig. 4A and Movie S7). These time-lapse movies also showed clear examples of cluster aggregation (Movie S8), in which single cells and small aggregates appear to come together and fuse, a process that is likely due to the rhythmic intestinal contractions that occur between frames. Importantly, smaller aggregates and planktonic cells that preferentially localize to the intestinal bulb are relatively undisturbed during these expulsion events, save for a few clusters that become incorporated into the large mass during its transit (Movie S7).

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Fig. 4.

Small bacterial clusters are required for recovery after large expulsion events. (A) Maximum-intensity projections of untreated Enterobacter populations before (Top, t=2 h from the start of imaging) and after (Bottom, t=3 h) an expulsion event (Movie S5). (Scale bar, 200 μm.) (B) Schematic of a kinetic model of bacterial cluster dynamics, illustrating its 4 constituent processes. (C) Image-derived time series of Enterobacter abundance in 5 untreated hosts showing sporadic large expulsion events.

Our observations suggest an explanation of how low-dose ciprofloxacin can lead to dramatic drops in Enterobacter abundance that moreover illuminates the more general question of how naturally aggregating bacterial species can persist in the vertebrate gut despite transport-driven expulsion. We provide both a qualitative and a quantitative description of the relevant dynamics, beginning with the following conceptual model: Single cells of Enterobacter replicate to form small clusters, which then aggregate to form larger clusters under the influence of intestinal flow. Large clusters are transported by the rhythmic contractions of the gut (15, 25, 26) and are stochastically expelled from the host (15, 25). The individual bacteria and small clusters that remain within the intestine serve as a reservoir that reseeds the next population, and the process of replication, aggregation, and expulsion repeats. Therefore, persistence within the intestine requires processes that generate single cells or small clusters; otherwise transport will eventually lead to extinction. This reseeding could take the form of 1) immigration of new cells from the environment, 2) passive fragmentation of clusters, or 3) active fragmentation in which single cells break away from a cluster surface during cell division. Immigration from the environment likely occurs even in established populations, but measurements in larval zebrafish suggest very low rates of immigration (27). We therefore suspected that more robust mechanisms must promote persistence. Supporting the active fragmentation mechanism, we found in untreated hosts examples of Enterobacter populations that contain an abundance of single cells, a single large aggregate, and a lack of midsized aggregates (SI Appendix, Fig. S9E). Following low-dose ciprofloxacin treatment, the planktonic cell reservoir associated with resilience to intestinal transport is depleted (Fig. 3C), most likely due to stalled Enterobacter division (SI Appendix, Fig. S8), leading to collapse of the resident bacterial population (Fig. 3 A and B).

A Quantitative Model of Bacterial Cluster Dynamics.

To solidify and test our conceptual picture, we developed a predictive mathematical model of bacterial cluster dynamics. We describe the framework of the model, its validation, and general insights it provides into perturbations and population stability. Drawing on ideas from nonequilibrium statistical mechanics and soft matter physics, we constructed a general kinetic model that describes the time evolution of a collection of bacterial clusters with varying sizes, illustrated schematically in Fig. 4B. We posit that 4 processes govern cluster dynamics: aggregation, fragmentation, growth, and expulsion. Each is described by a kernel that specifies its rate and size dependence: 1) Aggregation of a cluster of size n and a cluster of size m occurs with rate Anm, 2) fragmentation of a cluster of size n+m into clusters of size n and m occurs with rate Fnm, 3) growth (due to cell division) of a cluster of size n occurs with rate Gn, and 4) expulsion (removal by intestinal transport) of a cluster of size n occurs with rate En. Note that condensation of the population into a single massive cluster poises the system for extinction, for any nonzero En. The model is nonspatial and is inspired by well-established frameworks for nucleation and growth phenomena such as polymer gelation and colloidal aggregation (28). For example, sol-gel models describe a transition between dispersed individual units (“sol”) and a system-spanning connected network (“gel”) in materials capable of polymerization. In the thermodynamic limit of infinite system size, the model can be studied using standard analytic techniques (28). However, unlike polymer solutions and other bulk systems for which the possible number of clusters is effectively unbounded, our intestinal populations are constrained to have at most a few hundred clusters (Fig. 3C), necessitating the use of stochastic simulations (Materials and Methods).

In its general form, the model encompasses a wide range of behaviors that can be encoded in the various functional forms possible for the rate kernels Anm, Fnm, Gn, and En. Based on our observations and theoretical considerations elaborated in Materials and Methods, we made the following assumptions: 1) The rate of aggregation between 2 clusters is independent of their size, Anm = α; 2) fragmentation occurs only by separation of single cells and with a rate that is independent of cluster size, Fnm = β for m=1 and Fnm = 0 otherwise; 3) growth is logistic with a global carrying capacity, Gn=rn(1−N/K) with N the total number of cells, r the per capita growth rate, and K the carrying capacity; and 4) expulsion is independent of cluster size, En=λ. This model contains as special cases various simple models of linear polymers (29) and also resembles recent work modeling chains of Salmonella typhimurium cells in the mouse gut (30). As discussed in SI Appendix, these choices constitute the minimal model consistent with theoretical constraints and experimental phenomenology. More complex models are of course possible, but the requisite increase in the number of adjustable parameters would result in a trivial but meaningless ability to fit the observed data.

Even with the assumptions described above, the model needs 5 parameters: rates of aggregation, fragmentation, growth, and dispersal and a global carrying capacity. However, all of these parameters can be set by experimentally derived values unrelated to cluster size distributions. We measured Enterobacter’s per capita growth rate by performing time-lapse imaging of initially germ-free hosts that had been exposed to Enterobacter for only 8 h, capturing the exponential increase of a small founding population (SI Appendix, Fig. S1 and Movie S9), yielding r =0.27±0.05 h⁻¹ (mean ± SD across n=3 hosts). We identified expulsion events as abrupt collapses in Enterobacter abundance from time-lapse images (Fig. 3C and Movie S7) and set the expulsion rate equal to the measured collapse rate, λ=0.11±0.08 h⁻¹ (mean ± SE assuming an underlying Poisson process [Materials and Methods]). The model can be simulated to provide the mean and variance of the log10-transformed abundance distribution at a given time for a given set of parameters. Using this approach, we fitted static bacterial abundance measurements from dissection and plating at 72 h postinoculation (Materials and Methods) to determine the carrying capacity, K, and the ratio of fragmentation and aggregation rates, β/α. As discussed in Materials and Methods, the cluster dynamics should depend primarily on the ratio of β/α rather than either rate separately. This yielded log10K=5.0±0.5 and log10β/α=2.5±0.4.

The model therefore allows a parameter-free prediction of the size distribution of Enterobacter aggregates, plotted in Fig. 5A together with the measured distribution derived from 3D images, averaged across 12 untreated hosts. The 2 are in remarkable agreement. We also plot, equivalently, the cumulative distribution function P(size>n), the probability that a cluster will contain greater than n cells, again illustrating the close correspondence between the data and the prediction and validating the model. We emphasize that no information about the cluster size distribution was used to estimate any of the model parameters. We further note that the cluster size distribution is a stringent test of the model’s validity. Other cluster models predict different forms, typically with steep tails (29, 30). The linear chain model of ref. 30, for example, leads to an exponential distribution of cluster sizes that does not match the shallower, roughly power-law form of our data.

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Fig. 5.

A stochastic kinetic model predicts bacterial cluster sizes and generates a phase diagram for in vivo abundance. (A) The distribution of image-derived Enterobacter cluster sizes (gray circles) along with the prediction of our stochastic model (purple line). There are no free parameters in the fit; values were fixed by abundance, growth, and expulsion rate measurements independent of cluster size. Parameters: r =0.27 h⁻¹, λ=0.11 h⁻¹, α=0.1 h⁻¹, β=10^1.5 h⁻¹, K=10⁵. Error bars on experimental data are SDs across hosts. Shaded confidence intervals for the model prediction are bounds from parameter uncertainties. Inset shows the same experimental data and model plotted without binning as a reverse cumulative distribution. (B) Phase diagram of the log-transformed abundance, ⟨log10(N+1)⟩, showing the extinction transition (white dashed line). From best-fit parameter estimates, the in vivo state of untreated Enterobacter is overlaid as a gray circle and 25 ng/mL ciprofloxacin-treated Enterobacter as an orange circle; both circles are marked with “e.” Untreated Vibrio is located off the scale, indicated by the arrow, and 10 ng/mL ciprofloxacin-treated Vibrio is overlaid as a cyan circle marked with “v.” The doses for Enterobacter and Vibrio were established to be approximately equivalent in vitro. Parameters: λ=0.11 h⁻¹, α=0.1 h⁻¹, K=105 were fixed; r and β were varied on logarithmic grids.

The Abundance Phase Diagram and Extinction Transition.

Our kinetic model provides insights into the consequences of low-dose antibiotic perturbations on gut bacterial populations. We consider a general phase diagram of possible growth, fragmentation, aggregation, and expulsion rates and then situate Enterobacter in this space. For simplicity of illustration, we consider a 2D representation with one axis being the ratio of the fragmentation and aggregation rates, β/α, and the other being the ratio of the growth and expulsion rates, r/λ (Fig. 5B). As noted above and in Materials and Methods, the model in the regime studied should depend on the ratio β/α rather than on β or α independently. However, the roles of r and λ are not simply captured by their ratio. The expulsion rate nonetheless provides a scale to which to compare the growth rate, r, and we plot Fig. 5B using r/λ calculated for fixed λ=0.11 h⁻¹, the measured value. For completeness, we show a 3D r,λ,β/α phase diagram as in SI Appendix, Fig. S11 E and F. We numerically calculated the steady-state phase diagram of the model (Materials and Methods) and show in Fig. 5B the mean log-transformed abundance, ⟨log10(N+1)⟩. The regime of extinction (N=0) is evident (dark purple, with dashed white boundary).

The data-derived parameter values place untreated intestinal Enterobacter fairly close to the extinction transition (Fig. 5B). An antibiotic-induced growth rate reduction of ∼5× is sufficient to cross the boundary to the N=0 regime (i.e., to extinction), moving downward in Fig. 5B. This growth rate reduction, or an equivalent increase in death rate, reflects the conventional view of antibiotic effects. An ∼300× reduction in the balance between fragmentation and aggregation spurs an alternative path to extinction, moving leftward in Fig. 5B, reflecting a distinct mechanism resulting solely from changes in physical structure. The extinction transition in this direction corresponds to the condensation of the population into a single cluster, reminiscent of gelation phase transitions in polymer systems. As described above, low-dose ciprofloxacin causes a strong reduction in the number of small bacterial clusters, lowering β and possibly also r if fragmentation and individual cell division are linked. Conservatively assuming an equal effect along both axes, and fitting simulations to the 24-h treatment abundances (Materials and Methods), we find that the antibiotic reduces r and β/α by ∼10×. This drives the bacterial system through the phase boundary and well into the extinction regime (Fig. 5B, orange circle), consistent with our observations.

In contrast to Enterobacter, treatment of Vibrio with ciprofloxacin does not lead to widespread extinction after 48 h, suggesting that treated populations either lie safely at a new steady state away from the extinction boundary or are close enough to the transition so that dynamics are slow. To estimate model parameters for ciprofloxacin-treated Vibrio, we performed a 2-parameter fit of (β/α,r) to the 24-h treatment abundances. Because of Vibrio’s large population size (∼105 clusters), we modified the stochastic simulation procedure using a tau-leaping algorithm (Materials and Methods and SI Appendix, Fig. S12). We indeed find ciprofloxacin-treated Vibrio is located close to but safely inside the extinction boundary (Fig. 5B). Untreated Vibrio populations show no appreciable multicellular aggregation and are located off scale far to the upper-right side of the phase diagram (Fig. 5B, arrow).