A ‘rich-get-richer’ mechanism drives patchy dynamics and resistance evolution in antibiotic-treated bacteria

Abstract

Bacteria in nature often form surface-attached communities that initially comprise distinct subpopulations, or patches. For pathogens, these patches can form at infection sites, persist during antibiotic treatment, and develop into mature biofilms. Evidence suggests that patches can emerge due to heterogeneity in the growth environment and bacterial seeding, as well as cell-cell signaling. However, it is unclear how these factors contribute to patch formation and how patch formation might affect bacterial survival and evolution. Here, we demonstrate that a ‘rich-get-richer’ mechanism drives patch formation in bacteria exhibiting collective survival (CS) during antibiotic treatment. Modeling predicts that the seeding heterogeneity of these bacteria is amplified by local CS and global resource competition, leading to patch formation. Increasing the dose of a non-eradicating antibiotic treatment increases the degree of patchiness. Experimentally, we first demonstrated the mechanism using engineered Escherichia coli and then demonstrated its applicability to a pathogen, Pseudomonas aeruginosa. We further showed that the formation of P. aeruginosa patches promoted the evolution of antibiotic resistance. Our work provides new insights into population dynamics and resistance evolution during surface-attached bacterial growth.

Synopsis

Global resource competition and local collective survival lead to heterogeneous growth and development of bacterial colonies (or patchiness).

• Under intermediate antibiotic treatment, only a subset of colonies (the “rich”) with a sufficiently large initial seeding density survives.

• Surviving colonies benefit from the global pool of resource and grow larger (or get “richer”) than when all colonies survive (in the absence of an antibiotic).

• Local collective survival promotes the development of de novo mutants with enhanced antibiotic resistance.

Global resource competition and local collective survival lead to heterogeneous growth and development of bacterial colonies (or patchiness).

Introduction

Many bacteria form surface-attached communities (Costerton et al, 1995). During early development, these communities often consist of distinct microscopic subpopulations, or patches (Bjarnsholt et al, 2013; Kirketerp-Møller et al, 2008). For certain pathogens, these patches can emerge at infection sites, persist during antibiotic treatment, and develop into mature biofilms of patches up to ~mm in diameter (Costerton et al, 1999; O’Toole et al, 2000). Some well-documented examples are E. coli patches in urinary tract infections (Anderson et al, 2003; Justice et al, 2004; Mysorekar and Hultgren, 2006) and P. aeruginosa aggregates in chronic wound beds (Kirketerp-Møller et al, 2008), lung infections (Kolpen et al, 2022), and infections in the airways of cystic fibrosis patients (Lam et al, 1980; Rudkjøbing et al, 2012; Singh et al, 2000).

Patch formation has been shown to enable several bacterial pathogens, including Streptococcus, E. coli, Staphylococcus aureus, and P. aeruginosa, to evade phagocytic attack by host immune cells (Alhede et al, 2011; Alhede et al, 2020; Galdiero et al, 1988; Pettygrove et al, 2021). It can also modulate the activation and range of quorum-sensing signaling (Armbruster et al, 2017; Connell et al, 2014; Darch et al, 2018; Gao et al, 2016), which regulates the expression of virulence factors (O’Loughlin et al, 2013). Large patch size triggers Xylella fastidiosa cell differentiation, which is required for mergers with neighboring patches in biofilm development (Anbumani et al, 2021). Large patches can have a competitive advantage in vertical access to growth-limiting nutrients (Kragh et al, 2016). Last, patch formation can lead to an anaerobic interior environment (Wessel et al, 2014), which could modulate antibiotic tolerance (Lichtenberg et al, 2022).

Patch formation can arise from heterogeneity in the growth environment, such as the distribution of nutrients (Lichtenberg et al, 2022) or randomness in initial bacterial seeding. In addition, it can be facilitated by density-dependent bacterial interactions or bacteria-environment interactions. For example, Secor et al, found that polymers commonly found at infection sites can drive aggregation of P. aeruginosa at high densities in planktonic cultures (Secor et al, 2018). Zhao et al, showed that positive feedback between cell density and the deposition of surface attachment molecules secreted by cells can drive patchy growth of P. aeruginosa (Zhao et al, 2013). Rossy et al, showed that pili-mediated interactions of P. aeruginosa with mucus facilitate patch formation and subsequent biofilm development in a tissue-engineered lung infection model (Rossy et al, 2023).

These studies exemplify microscopic patch (group) formation with typical sizes of <100 μm. Though they have not considered the community context and heterogeneity between patches, they all involve or imply a role of cell density-dependent interactions. In the context of bacterial infections, cell density-dependent interactions are particularly relevant because pathogens frequently experience environmental stress such as host immune response and antimicrobial treatment (Lichtenberg et al, 2022). Under such conditions, bacteria often exhibit density-dependent survival (Udekwu et al, 2009): only populations at a sufficiently high density can survive. Density-dependent survival provides a bacterial population with collective survival (CS) to environmental stress lethal to individual cells. Myriad mechanisms could lead to the CS of a population, ultimately lowering the stressor dose per cell below lethal levels. Prominent examples include the distribution of the total stressor load among cells (Tan et al, 2012), the sharing of enzymes that inactivate the stressor (Meredith et al, 2015; Vega and Gore, 2014), or density-dependent regulation of these enzymes or phenotypes that are resilient to the stressor (Meredith et al, 2015).

If there are multiple groups (i.e., colonies) sharing the same resources, local CS would provide higher-density colonies with a growth advantage and further enhance their CS, constituting a ʻrich-get-richerʼ mechanism. Here, we demonstrate that under antibiotic treatment, such a ʻrich-get-richerʼ mechanism leads to heterogeneous growth and development of bacterial colonies (or patchiness) by amplifying an initial seeding heterogeneity in bacterial density: Only a subset of colonies (the “rich”) with a sufficiently large seeding density survives. Surviving colonies benefit from the global pool of resources and grow larger (or get “richer”) than when all colonies survive (in the absence of the antibiotic). Furthermore, local CS enables patch growth at seeding cell numbers insufficient for growth as well-mixed liquid cultures and, thus, promotes the development of de novo mutants with enhanced antibiotic resistance.

Results

Model formulation

To gain insight into the role of CS in patchy dynamics, we formulated models to account for two critical constraints (Fig. 1A): local, collective inactivation of the environmental stress (an antibiotic) and long-range resource competition. These two constraints are motivated by the widespread collective inactivation of environmental stress (e.g., antibiotics) (Cruz et al, 2007; Laman Trip and Youk, 2020; Lee et al, 2010; Meredith et al, 2018; Meredith et al, 2015; Ratzke and Gore, 2016; Sorg et al, 2016; Vega and Gore, 2014) and resource scarcity (Hood and Skaar, 2012; Morita, 1997) in microbial systems, with the assumption that collective inactivation of stress acts over shorter spatial scales compared to the diffusion length of growth-limiting nutrients. Individual bacteria are killed by the antibiotic at a sufficiently high concentration. Upon death, however, they release an enzyme that degrades the antibiotic. At a high local cell density, the released enzyme can remove the antibiotic fast enough to allow surviving cells to grow. This logic is motivated by the ubiquity of enzyme-mediated antibiotic inactivation, such as hydrolysis of $\beta$-lactams via $\beta$-lactamase (Bla) enzymes (Bush and Bradford, 2016), which was shown to lead to CS (Huang et al, 2016; Meredith et al, 2018; Tan et al, 2012). We consider that the cells are localized (i.e., non-motile). Nutrients are consumed by growing bacteria and partially recycled after antibiotic-induced cell death (Meredith et al, 2018). We assume the nutrients diffuse fast such that bacteria from different seeding locations experience long-range nutrient competition (Chacón et al, 2018) (see Appendix Table S1).

Figure 1. Model predicts the emergence of patchy growth from a ʻrich-get-richerʼ mechanism.

(A) Model formulation: We consider genetically identical bacteria with local, collective survival (CS). The bacteria engage in global (long-range) competition if resources are limited. A 6-by-6 grid community is defined with spatial heterogeneity in cell density per grid site (Appendix Fig. S1). We assume that CS acts over a shorter spatial scale (indicated with the dashed green double-headed arrow between two populations) compared to the diffusion length scale of growth-limiting nutrients. We implemented the model above in partial and ordinary differential equations to describe spatial and well-mixed, respectively, communities (see “Methods” and Appendix Notes for detail). (B) Collective survival (CS): CS is demonstrated by numerical simulations of well-mixed cultures with varied initial cell densities for different values of the initial antibiotic concentration ($a_0$). The cultures grew only when initialized with cell densities above a threshold, depending on $a_0$ (see Appendix Table S1 for the model parameters). The solid lines interpolating the data points were drawn to guide the eyes. (C) Patchy growth: Spatial simulations with CS (left, CS+), or without CS (right, CS−). The CS− case was implemented by setting the collective antibiotic inactivation rate constant (${\kappa }_b$) to zero (see “Methods”). $A_{th}$= 5 was applied as the minimum killing antibiotic concentration. Nutrients and antibiotics were added uniformly at t = 0. The simulated local population sizes (i.e., patch cell densities) with different $a_0$ (shown by orange numbers) but otherwise the same initial conditions and parameters were illustrated for t = 84, where a greater bubble radius represents a larger patch cell density. See Fig. EV1 for expanded results and Fig. EV3 for correlation graphs between initial and final patch cell densities, supporting the ʻrich-get-richerʼ notion. (D) Increased maximum patch cell density due to antibiotic treatment: The data from (C) was analyzed to reveal an increasing maximum final patch cell density with increasing $a_0$ values until a complete clearance is observed (green, CS+). Without CS, maximum final patch cell density is constant for $a_0\le A_{th}$ (gray dashed line) and zero for $a_0>A_{th}$ due to a complete clearance (purple, CS−). The solid lines interpolating the data points were drawn to guide the eyes.

We implemented the logic above using partial and ordinary differential equations to describe spatial and well-mixed communities, respectively (see “Methods” and Appendix Notes for details). We chose the model parameters such that the population will exhibit CS under intermediate antibiotic concentrations. Nutrients and antibiotics were added at t = 0. Simulated well-mixed populations grew only when starting with cell densities greater than a certain threshold, which increases with the initial antibiotic concentration ($a_0$) (Fig. 1B). All model parameters and variables were non-dimensionalized to simplify analysis. All the dimensionless variables and parameters can be mapped back to the original variables and parameters (see Appendix Notes; Table S1).

Model prediction: patchy growth emerges from a ʻrich-get-richerʼ mechanism

To simulate spatial growth, we initiated a square grid (6 × 6) of positions (Appendix Fig. S1A; “Methods”) with the heterogeneous number of seeding cells, where the cell density in each position was drawn from a truncated normal distribution (with a mean of 30 and standard deviation of 12, and replacing negative values with 0, also see Appendix Fig. S1B). The diffusivities of nutrients and the antibiotic-inactivating enzyme were chosen such that collective survival would be confined within single patches, while resource competition would be global across the community (Appendix Notes). This choice was due to the greater size of the inactivating enzyme compared to the nutrients as well as an anticipated hindrance of the enzyme dispersal due to the structure of the patches that produce them (“Methods”; Appendix Table S1). We have filled outside the grid uniformly with all model variables but cells for nearly one nearest neighbor distance. No-flux boundary condition was used, hence the outermost seeding sites had fewer interacting neighbors than the others. Nutrients and the antibiotic were added uniformly over space at t = 0, where $a_0$ was varied for different simulations. We then examined the resulting spatial dynamics at t = 84 (by which the growing patches were all determined, and their average growth rates were all reduced below 0.2-fold per unit time).

At $a_0\le$5, which was too low to kill individual cells, cells at all grid points survived, which led to unimodal growth (Fig. 1C, CS+, $a_0$= 0). At a high $a_0$(= 70), no cells survived (Figs. 1C and EV1, CS+). Intermediate $a_0$ values (20, 40, 50, 60) led to patchy growth, where cells at a fraction of the positions survived to form patches. The emerging patchy dynamics exhibit three features: the fraction of grid points leading to patch growth decreased with increasing $a_0$ (Fig. EV2A); the intermediate $a_0$ values led to the greatest variation of the final patch cell density (we used Gini inequality coefficient (Dorfman, 1979) to quantify patch cell density variation; see Fig. EV2B); the maximum final patch cell density increased with increasing $a_0$, due to weakened resource competition, until the latter was too high eliminating all cells (Fig. 1D, green for CS+; Fig. EV2C). The maximum final patch size could increase with increasing $a_0$ even when the total biomass produced by the community remained approximately constant (Fig. 1C, CS+ and Appendix Fig. S2, $a_0$ = 40). In summary, patchiness (measured by the Gini coefficient) is a function of $a_0$ (Fig. EV2B). The degree of patchiness is correlated with the fraction of the grid sites with no surviving bacteria (compare Fig. EV2A and  EV2B) and with the maximum final patch cell density (compare Fig. EV2A and  EV2C; see Appendix Notes). Consistent with the “rich-get-richer” mechanism, for intermediate $a_0$, only the patches with seeding densities higher than a threshold survived. Among surviving patches, a greater seeding cell density generally yielded a higher final cell density (Fig. EV3).

Figure EV1. Expanded results from the simulated grid communities in Fig. 1C.

Expanded results from the simulated grid community in Fig. 1C are presented. Local cell densities at different initial antibiotic concentrations ($a_0$; orange) are shown in both bubble graphs and histograms for t = 84. A larger bubble represents a larger local cell density.

Figure EV2. Three key features of patchy dynamics in simulated data.

We illustrate the three key features of patchy dynamics highlighted in this paper: (A) The fraction of grid positions leading to patch growth decreased with increasing initial antibiotic concentration ($a_0$), (B) the intermediate $a_0$ values led to the greatest final patch cell density variation, quantified using Gini inequality coefficient (Dorfman, 1979), (C) the maximum final patch cell density increased with increasing $a_0$, due to weakened resource competition, until the latter was too high eliminating all cells. As a measure of resource competition, for each value of $a_0$, we calculated an ‘average nutrient share’ by dividing the total initial nutrient concentration by the number of grid positions associated with a positive net growth at the final time point, t = 84 (A). The “$a_0$ versus max patch cell density” plot in (C) was reused from Fig. 1D. The gray dashed lines represent the killing threshold of the antibiotic concentration ($A_{th}=5$). The solid lines interpolating the data points were drawn to guide the eyes.

Figure EV3. Dependence of final patch cell density on the initial patch cell density or the total κ_bb.

The simulation data that yielded Fig. 1C was analyzed to map the initial (i.e., seeding) cell density to the final cell density for each grid site. Consistent with the “rich-get-richer” mechanism, (A) under killing initial antibiotic concentrations, $a_{0,}\left(\ge 20\mathrm{a}bove\right)$ patch survival was observed only at the sites with a seeding density above a threshold (~30). Above this threshold, a greater seeding cell density positively correlated with a higher final cell density. (B) Most data points that substantially deviate from the positive correlation belonged to edge sites of the grid, whose removal made the positive correlation stronger. (C) Total antibiotic removal rate at the grid sites was calculated by summing up ${\kappa }_{b}b$ over the course of the total simulation time (t = 0 - 84). The “total ${\kappa }_{b}b$” of patches had a linear positive correlation with their seeding cell densities (R² = 1). (D) The dependence of the final patch cell density on “total ${\kappa }_{b}b$” is similar to that on the initial patch cell density (B).

CS was critical for the patchy growth. When it was removed from the model, by removing the term for enzyme-mediated antibiotic inactivation, cells from all grid positions exhibited uniform growth or uniform death, depending on whether the initial antibiotic concentration, $a_0$, was above or below the killing threshold, $A_{th}$= 5 (Figs. 1C and EV1, CS−; Appendix Fig. S3A, CS−). Without CS, the maximum final patch cell density remained constant for $a_0$ values up to the threshold ($A_{th}$) and rapidly vanished for ${a_0>A}_{th}$ (Fig. 1D, purple for CS−).

When seeding heterogeneity was increased by leaving a fraction of the grid positions empty, in the absence of antibiotic the final cell densities of local populations emerging from inoculated grid positions were larger on average, due to reduced resource competition. However, these final cell densities have a narrow distribution, indicating the lack of substantial patchiness (Appendix Fig. S4A,B). This is because the growth of local subpopulations is capped by nutrient limitation (“Methods”) so that those with a relatively higher seeding cell density would not have a prolonged net growth advantage. In the presence of antibiotic, which triggers CS, the scope of patchy growth (defined as the range in which increasing $a_0$ monotonically increases the Gini inequality coefficient) shrunk as the fraction of empty positions increased (Appendix Fig. S4C–H). This is consistent with a reduced CS due to the lowered total seeding cell density. Yet, patchiness was stronger for $a_0$ values that allowed survival of bacteria only at some grid positions (compare Appendix Fig. S4 with Figs. 1C and EV1). These results further support the importance of CS for the generation of patchy dynamics.

Next, we analyzed the sensitivity to model parameters of the three features of patchy dynamics defined above. Briefly, we kept the default seeding density heterogeneity (Appendix Fig. S1) and varied the model parameters, one at a time, in a certain range and calculated the three features for each case for a certain range of $a_0$ (Fig. EV4A). We found that these three features were most sensitive to the antibiotic concentration killing threshold ($A_{th}$), the rate constant of antibiotic inactivation by the extracellular enzyme (${\kappa }_b$), and the maximum lysis rate ($\gamma$) (Fig. EV4B). The high sensitivity to these parameters underscores the importance of CS to the patchy dynamics, as these parameters are key to how a local population collectively responds to antibiotics.

Figure EV4. An analysis of the sensitivity of patchy dynamics to the model parameters.

(A) We varied the model parameters, one at a time, between the 0.25× and 4× their default values and repeated the spatial growth simulations. The coefficient of nutrient recycling from lysed cells, $\xi$, was an exception whose maximum value was 1. As key features of patchy growth, for each parameter varied and for a certain range of initial antibiotic concentration, $a_0$, (0 to 100 with increments of 2), we plotted the fraction of grid points leading to patch survival, maximum patch size, and the Gini inequality coefficient (Dorfman, 1979) to quantify final patch size variation (t = 84). The solid lines interpolate the data points and were drawn to guide the eyes. (B) For each tested value of a given parameter and each spatial dynamics feature examined in (A), the area under the curve (AUC) of the feature as a function of $a_0$ was calculated. The resultant AUCs were plotted against the fold-changes of the parameter value with respect to its default value ($p_0$). A lower and an upper threshold as the 0.5$\times$ and 1.5$\times$, respectively, of the AUC for $p_0$ were defined and illustrated by the dashed gray lines. $\gamma$, ${\kappa }_b$, and $A_{th}$, respectively, had the greatest three total number of AUC data points outside the threshold zone. This suggests that patchy growth dynamics was robust to changing the parameters except for the antibiotic concentration killing threshold $\left(A_{th}\right)$, the rate constant of antibiotic inactivation by the extracellular enzyme (${\kappa }_b$), and the maximum lysis rate ($\gamma$). Patchy dynamics depends on local CS and, hence, it is intuitive that $A_{th}$, ${\kappa }_b$, and $\gamma$ have the greatest influence on the patchy dynamics as they determine the collective response of a local population to antibiotics. Note that CS remains local as the diffusion coefficients of antibiotics ($D_a$), and the antibiotic-inactivating enzyme ($D_b$) always remained substantially smaller than that of nutrients $\left(D_n=1\right)$, despite their varied values.

Our findings were robust to different seedings sampled from the same cell density distribution (Appendix Fig. S5). The grid size (6 × 6 = 36 spots) chosen above was an example to study the general principles of the system. A larger community (14 × 14 = 196 spots) yielded qualitatively similar results (Appendix Fig. S6). We anticipate that our conclusions would apply unless the community size is too large compared to the length scale of resource competition (see Appendix Notes).

In our model, the population dispersal rate ($D_c$) accounts for the net outcome of cell motility and potential physical interactions between neighboring cells, including adhesion. Increasing $D_c$ reduced the patchy dynamics, leading to homogeneous growth across space for sufficiently large $D_c$ (Appendix Fig. S7A). At $a_0\le$40, the community’s total biomass yield was maximum (Appendix Fig. S7B). For $a_0\ge$70, again, no cells survived (Appendix Fig. S7B). For the intermediate $a_0$ values, spatial variation in cell density increased with increasing $a_0$, as long as $D_c$ allowed patch formation and maintenance (Appendix Fig. S7B).

Patchy growth emerged from the ʻrich-get-richerʼ mechanism in engineered E. coli

Next, we tested the model predictions using engineered E. coli (MC4100Z1) expressing BlaM, a variant of TEM-1 $\beta$-lactamase, from an inducible promoter on a plasmid (Tanouchi et al, 2012). BlaM lacks a periplasm-localization sequence; as such, it is entrapped in the cytoplasm. During a $\beta$-lactam antibiotic treatment, BlaM does not protect the producing cells. However, if enough bacteria lyse and the released BlaM degrade the $\beta$-lactam to below a lethal concentration before the entire population is cleared, the population can recover from the growth of survivors (Fig. 2A; Appendix Fig. S8). Thus, the death of a BlaM-expressing bacterium is “altruistic” (Tanouchi et al, 2012), and this single-cell trait is a critical component for the CS of the population.

Figure 2. Patchy growth emerged from the ‘rich-get-richer’ mechanism in engineered E. coli with synthetic CS.

(A) Experimental system: We used a $\beta$-lactam antibiotic (Carbenicillin, Carb) and an immotile E. coli strain (MC4100Z1) that expresses from an IPTG-inducible promoter a variant of TEM-1 $\beta$-lactamase gene (Tn3.2), named BlaM (Tanouchi et al, 2012) (Appendix Fig. S8). BlaM is localized in cytoplasm and does not confer resistance on the producing cell against a lethal treatment of $\beta$-lactams. A population of cells can exhibit CS, if sufficient BlaM is released by lysing cells and inactivates the $\beta$-lactam before a complete clearance of the population. (B) Verification of CS: Biomass (OD₆₀₀) was measured after 24 h incubation at 37 °C of well-mixed liquid cultures with different initial cell densities and for [Carb] (0, 3, 7.5, or 25 μg/ml). The cultures grew only with initial cell densities above a certain threshold, which was higher for greater [Carb]. Different symbols represent biological replicates, for which solid and open symbols show two technical replicates. The cross symbols illustrate the average of biological replicates after taking the mean value of their corresponding technical replicates, and the interpolating solid lines were drawn to guide the eyes. (C) Patchy growth: A grid of ~200 positions of cells was seeded on ~15 ml of agar containing different [Carb], using a robotic liquid handler (“Methods”). The initial number of cells in each position was drawn at random from one of three different cell density groups corresponding to 4 (low), 16 (medium), or 128 (high) cells, on average. Images were taken after ~72 h at 30 °C, and patch sizes (i.e., areas) were measured using a custom MATLAB routine (see “Methods”). Top and bottom panels are for the CS+ and CS− cases, respectively. The image data are representative of five technical replicates from three biological replicates (top) or two biological replicates with two technical replicates each (bottom). The histograms were plotted after pooling all the replicate data together. The representative images shown were equally processed for presentation purposes (see Appendix Notes), and Appendix Figs. S10 and S11 show the complete raw datasets. Scale bars: 5 mm. (D) Increased maximum patch size due to antibiotic treatment: Maximum final patch sizes were extracted from the data presented in (C). In agreement with the model predictions above (Fig. 1D), the maximum final patch size was, on average, up to more than two-fold greater with vs. without Carb treatment (green, CS+). Without CS, the maximum final patch size was virtually constant before rapidly vanishing for [Carb] >2.5 μg/ml (purple, CS−). Different symbols represent biological replicates, for which solid and open symbols and are technical replicates, except that square and diamond are for the same biological replicate (Appendix Figs. S10 and S11). The cross symbols illustrate the average of biological replicates after taking the mean value of their corresponding technical replicates, and the interpolating solid lines were drawn to guide the eyes.

To test CS, we inoculated well-mixed liquid cultures with varied initial cell densities and initial concentrations of carbenicillin (Carb, a $\beta$-lactam; concentration will be denoted using square brackets). The cultures grew only when inoculated at densities above a threshold, which increased with the initial [Carb] (Fig. 2B; Appendix Table S2). Bacteria without the BlaM-encoding plasmid exhibited a drastically reduced range of density-dependent survival (compare Appendix Fig. S9A,S9C). Bacteria carrying the plasmid but without induction also displayed a narrow CS range, but the reduction was less severe (Appendix Fig. S9B), presumably due to the leaky expression of BlaM from its lac/ara-1 promoter (Lutz and Bujard, 1997). In the following analysis, we used the bacteria without the BlaM-encoding plasmid as the control case and denoted as “CS−”, in alignment with our mathematical model analysis above.

To test the predicted spatial dynamics, we inoculated cells to a grid consisting of ~200 positions on the surface of LB agar containing different [Carb] (“Methods”). To enhance nutrient competition, we used 1/5 of the standard LB when preparing the agar plates. The initial number of cells in each position was sampled at random from one of three different cell density groups: low, medium, and high with an average of 4, 16, and 128 cells, respectively. The cell numbers were estimated from cell density measurements: $1.6\times {10}^9$ cells/ml per OD₆₀₀; the combination of the three numbers was chosen to ensure sufficient seeding heterogeneity. The resulting bacterial growth patterns after ~3 days were consistent with the model predictions. When the initial [Carb] was low ($\le$2 μg/ml), we observed nearly uniform growth from all grid positions; a sufficiently high [Carb] led to complete clearance; intermediate [Carb] led to patchy growth, where cells survived to form patches at a fraction of the grid points (Fig. 2C; CS+). For intermediate [Carb], locations seeded with higher cell densities were more likely to survive and form larger patches (Fig. 2C; CS+ histograms). Assuming that patch cell density and patch size are correlated, these results are in accordance with the ʻrich-get-richerʼ notion. As predicted (Fig. 1D), the maximum final patch size had a biphasic dependence on the initial [Carb], peaking for those that led to the widest variations in final patch sizes (Fig. 2D, CS+; see Appendix Fig. S10 for all the data). The CS− cells, exhibiting a much narrower scope of density-dependent survival (compare Appendix Fig. S9A and S9C), displayed patchy dynamics also over a much narrower range of [Carb] (Fig. 2C, CS−; Appendix Fig. S3B, CS−). Furthermore, the CS− cells exhibited no substantial increase in the maximum patch size for any [Carb] tested (Fig. 2D, CS−; see Appendix Fig. S11 for the complete set of data). These results suggest that BlaM-mediated CS promotes patchy dynamics by increasing the degree of patchiness and expanding the antibiotic concentration range over which patchy dynamics occurs. The time course of the data suggests that CS-driven antibiotic survival preceded the determination of the final patch sizes by the remaining nutrients (Appendix Fig. S12A).

Inoculating cells at well-defined grid points simplifies visualization and confers experimental controllability, but it is not a requirement for the resulting patchy dynamics. As an illustration, we conducted experiments by rigorously mixing the cells with the agar media prior to its solidification. The resource competition length scale is not anticipated to differ from that of the well-defined grid case (Appendix Notes). These experiments yielded a spontaneous emergence of patchy growth with qualitatively similar trends of patch areas as a function of the initial [Carb] (Fig. EV5). In contrast, the same experiment without the induction of BlaM expression narrowed the scope of patchy growth (Appendix Fig. S13), consistent with its narrower range of density-dependent survival (compare Appendix Fig. S9B and S9C). When a commercial blend of Bla was added in excess (at 10 μg/ml) to block Carb activity independently of CS, a uniform growth was observed instead of patchiness, further demonstrating the role of CS in the emergence of patchiness (Appendix Fig. S14). For intermediate [Carb] for which patchiness was high, using a ~2.3-fold higher agar concentration yielded similar results (Appendix Fig. S15, top panel). A motile strain expressing the same BlaM formed a thin lawn, instead of patches (Appendix Fig. S15, bottom panel), consistent with the model prediction (Appendix Fig. S7).

Figure EV5. Patchy dynamics emerged in response to Carb from a uniform seeding of CS+ E. coli.

16 ml of LB + agar (0.3%) was rigorously mixed with cells (MC4100Z1 with the BlaM-encoding plasmid) at ~39 °C and then solidified in 10 cm standard dishes. The aimed cell density after mixing was 3 × 10⁶ cells/ml (or OD₆₀₀ = ~ 1.88 × 10⁻³). BlaM expression was induced by adding IPTG (1 mM). Phase contrast microscopy (Keyence BZ-X710) images were taken after 48 h of growth at 30 °C. Darker color represents higher local cell density. Images of multiple fields of view were stitched using a built-in feature of the Keyence microscope software. The final images were shown after being downsized 100-times and consistently adjusted for their brightness and contrast for clarity in illustration (see Appendix Notes). Patch areas were quantified using a custom MATLAB code for object segmentation. The cross symbols illustrate the average from two biological replicates, which are shown by solid or open symbols, and the interpolating solid lines were drawn to guide the eyes. Kanamycin (50 μg/ml) was added for plasmid maintenance. “[Carb]” denotes the initial carbenicillin concentration. Scale bar: 2 mm.

Patchy growth emerged from the ʻrich-get-richerʼ mechanism in P. aeruginosa

The fundamental requirement for the ʻrich-get-richerʼ mechanism to drive patch formation is local CS coupled with global resource competition. To test the general applicability of the mechanism, we used a motility-deficient mutant (pilU^-) of the P. aeruginosa PA14 strain, which we found to exhibit CS in response to $\beta$-lactams ticarcillin (Tic) or piperacillin (Pip). Briefly, we inoculated well-mixed liquid cultures of varied initial cell densities and for different [Tic] or [Pip]. For both antibiotics, the cultures grew only when inoculated at cell densities above a certain threshold, which was higher for greater [Tic] and [Pip] (Fig. 3A,B; Appendix Tables S3 and S4). While its underlying molecular mechanisms are unclear, the observed CS can allow us to test the general applicability of the ʻrich-get-richerʼ mechanism in driving patchy dynamics.

Figure 3. Patchy growth emerged from the ʻrich-get-richerʼ mechanism in P. aeruginosa.

The experiments were performed as described for Fig. 2B, C. Here, instead of E. coli, we used a motility-deficient variant (pilU^-) of the P. aeruginosa PA14 strain. Instead of carbenicillin, ticarcillin (Tic) or piperacillin (Pip) (both $\beta$-lactams) were used as antibiotics. Other modifications were detailed below. (A, B, D) The cross symbols illustrate the average of biological replicates after taking the mean value of their corresponding technical replicates, and the interpolating solid lines were drawn to guide the eyes. (A) CS in response to Tic: As in Fig. 2B, biomasses (OD₆₀₀) of well-mixed liquid cultures with varied starting cell densities and [Tic] were measured after ~24 h at 37 °C. The cultures grew only with starting cell densities above a certain threshold, which was higher for greater [Tic]. Different symbols represent biological replicates, for which solid and open symbols show two technical replicates. (B) CS in response to Pip: As in (A), well-mixed cultures with different initial cell densities for various [Pip] were incubated at 37 °C for ~24 h, and then their biomass (OD₆₀₀) was measured. The cultures grew only when initialized with cell densities greater than a certain threshold, which depended on [Pip]. Different symbols represent biological replicates, for which solid and open symbols show two technical replicates. (C) Patchy growth: Spatial growth (Fig. 2C; “Methods”) experiments for Tic (top) or Pip (bottom) were set up with the following modifications. The three cell density groups were on average 400 (low), 800 (medium), or 4000 (high) cells per position. The incubation temperature was 37 °C. Patch areas were manually measured using ImageJ. For Tic (top), the image data are representative of three technical replicates from two biological replicates. For Pip (bottom), the image data are representative of four technical replicates from two biological replicates. All the replicates were pooled together to create the histograms. The representative photographs underwent processing for clarity in presentation (see Appendix Notes), and Appendix Figs. S16 and S17 have complete raw datasets. Scale bars: 5 mm. (D) Increased maximum patch size due to antibiotic treatment: The maximum final patch sizes for a given initial [Tic] (blue) or [Pip] (salmon) were determined from the data in (C). In accordance with the model predictions and the experimental results above (Figs. 1D and 2D), the maximum final patch size was up to ~two-fold larger with vs. without antibiotic treatment. Different symbols represent different biological replicates, for which solid and open symbols show technical replicates, when applicable (Appendix Figs. S16 and S17).

Next, we studied surface-attached communities of P. aeruginosa. Of note, P. aeruginosa was reported to land on surfaces from a planktonic phase in aggregates of various sizes, making this bacterium a natural fit to the spatial seeding heterogeneity implemented in our model and the experimental designs above (Kragh et al, 2016). We set up the experiments as described in the preceding section, except that the three cell density groups corresponded to an average of 400 (low), 800 (medium), or 4000 (high) cells in this case. The resulting bacterial growth patterns after ~3 days were again consistent with model predictions. In the absence of antibiotic treatment, we observed a uniform growth from all grid positions. A sufficiently high initial antibiotic concentration (30 μg/ml for Tic; 5 μg/ml for Pip) led to complete clearance. Intermediate antibiotic concentrations induced patchy growth, where cells grew to patches at a fraction of the grid points (Fig. 3C; Appendix Fig. S3B). Again, supporting the ʻrich-get-richerʼ notion, under intermediate antibiotic concentrations surviving patches mostly originated from higher seeding cell densities and larger patches were generally seeded with greater cell densities (Fig. 3C, histograms). As predicted (Fig. 1D), the maximum final patch size depended on the initial antibiotic concentration in a biphasic manner, peaking at those that yielded the largest variations in final patch sizes (Fig. 3D; see Appendix Figs. S16 and S17 for all the data). Again, CS likely dictated the survival in the presence of the antibiotic before the nutrient levels determined final patch sizes (Appendix Fig. S12B,C).

Patch growth promoted the emergence of elevated individual-level resistance in P. aeruginosa

Unlike our engineered E. coli BlaM system above, we did not a priori know a mechanism that confers on P. aeruginosa the observed CS in response to Tic and Pip (Fig. 3A,B). Hence, we did not have a well-controlled manner to eliminate the CS. Because a greater cell density means a larger population size, it could also mean a higher chance of having pre-existing, individually resistant mutants. If so, patches could result from the mutants that were individually resistant to the antibiotic treatment. However, our data suggest otherwise. Considering the Tic (10 μg/ml) treatment, the threshold cell density for well-mixed liquid cultures corresponds to ~ 30,000 cells (Fig. 3A; Appendix Tables S3 and S4). The maximum number of cells seeded per position on agar was 7.5-fold smaller, 4000 cells, and we observed multiple patches growing. If the growth of those patches was due to the selection of pre-existing mutants with individual-level resistance amongst their $\le$4000 founder cells, we would expect such mutants to be selected also in well-mixed liquid cultures with as low as 4000 cells initially.

Moreover, most patches originated from the positions seeded with 4000 cells (high-density group), and we typically had ~20 growing patches out of the ~70 positions inoculated with the high-density group (i.e., ~7%) (Fig. 3C, top panel). Given the measured frequency (<10⁻⁵) of spontaneous antibiotic-resistant mutants in P. aeruginosa (including PA14) (Oliver et al, 2000; Rodríguez-Rojas et al, 2010), the expected number of pre-existing mutants in a high-density group position is <4000 × 10⁻⁵ = 0.04. If we assume that the distribution of mutants (if any) in different patches follows the Poisson distribution, the frequency of patches containing at least 1 mutant is ~0.04 or less, which is much less than our observed frequency (20/70 = ~0.3). Hence, pre-existing resistant mutants alone cannot explain the initial growth of all patches. CS is likely the underlying reason for the initial growth of patches, in agreement with our modeling predictions and the experimental demonstrations with the engineered E. coli.

While the formation of patches did not require pre-existing resistant mutants, the growth of patches in the presence of antibiotic treatment creates an environment that can drive the emergence of resistant mutants. Indeed, studies have shown that P. aeruginosa infections frequently evolve antibiotic resistance during antibiotic treatment (Rossi et al, 2021; Trampari et al, 2021; Usui et al, 2022). To examine if new mutants have emerged in our experiments, we conducted a phenotypic analysis of the patches emerging in the presence of Tic (10 μg/ml). For each patch, we sampled and suspended cells in fresh liquid media with Tic (10 μg/ml) at an initial cell density substantially less than the threshold required for CS by ancestor PA14, 1.5 × 10⁴ cells/ml (or OD₆₀₀ = ~ 7 × 10⁻⁶) (Fig. 3A). Growth in this culture would indicate elevated individual-level resistance compared to the ancestor population.

Using this assay, we found that, among patches sampled after ~23 h (Sampling day 1), the fraction with elevated individual-level resistance, abbreviated as ʻresistant patchesʼ, was ~50% (Fig. 4). This result shows that the CS-driven patch formation promoted elevated individual-level resistance. The fraction of resistant patches remained at ~50% at ~72 h (Sampling day 3), the time at which we measured patch sizes (Fig. 3C,D). This finding suggests that the promotion of elevated individual-level resistance occurred within the first ~23 h.

Figure 4. Patch growth promoted the emergence of elevated individual-level resistance in P. aeruginosa.

The same experimental design as in Fig. 3 was used. For [Tic] = 10 μg/ml, we collected samples from individual patches after ~23 h (Sampling day 1) or ~72 h (Sampling day 3) incubation. The collected samples were separately diluted below the corresponding threshold for initial cell density for CS (1.5 × 10⁴ cells/ml; Fig. 3A) in fresh liquid media with or without Tic (10 μg/ml) and incubated as well-mixed cultures for ~16 h at 37 °C. Then, we determined the fraction of resistant patches, whose cultures grew with Tic (10 μg/ml). Circles and triangles denote data from two independent replicates. For each independent replicate, the error bars are centered at the fraction of resistant patches found for each sampling day and represent the 95% confidence intervals based on the formula $1.96\sqrt{p\left(1-p\right)/n}$, where $n$ is the number of samples and $p$ is the fraction of samples tested resistant. For 97% (92 of 95) of the resistant patches identified, their resistance was heritable for at least 17 generations in antibiotic-free media, suggesting a genetic change.

The elevated resistance we observed could be due to a non-genetic response to the antibiotic exposure in the experiment (a.k.a. phenotypic tolerance (Wiuff et al, 2005)) or a genetic change (i.e., evolution). The former is anticipated to be non-inheritable over many generations after the removal of antibiotics (Wiuff et al, 2005). Hence, to rule out phenotypic tolerance, for each sample that exhibited elevated individual-level resistance, we repeated our phenotypic analysis by first passaging the samples through a Tic-free culture for at least 17 generations. The results held for 97% (92 out of 95) of the resistant patches identified above, demonstrating a lasting heritability of their elevated resistance. This suggests that the elevated individual-level resistance was likely due to genetic mutations. We also tested patches that grew in the absence of Tic and did not detect any with such a lasting elevated resistance (Appendix Fig. S18). This result suggests that antibiotic treatment was required for the emergence of the lasting elevated individual-level resistance.

Last, we observed a large overlap between the size distributions of resistant versus sensitive patches while the largest patches were more likely resistant (Appendix Fig. S19). This finding suggests that elevated individual-level resistance does not heavily determine the patch size distributions, i.e., patchy growth.

In the phenotypic analysis above, we necessarily applied a population bottlenecking while suspending the samples at cell densities lower than the CS threshold. We estimate that 10⁻⁴–10⁻² and 10⁻⁷–10⁻⁵ of the patch populations were tested for Sampling day 1 and Sampling day 3, respectively. If the growth of a patch was solely due to the selection of pre-existing individually resistant mutants, the offspring of such mutants would dominate their patch population at the time of sampling. Thus, our reasoning that pre-existing individually resistant mutants alone cannot explain the initial growth of patches remains valid. This bottlenecking may have led to an underestimation of the true abundance of emerging mutants with elevated individual-level resistance if the patches consisted of their mixtures with ʻauthenticʼ-sensitive cells.

In theory, a pre-existing highly resistant mutant could generate a larger colony, which could serve as an antibiotic sink and lead to the generation of “satellite colonies” (Medaney et al, 2016). Given the mechanism, satellite colonies would center around the resistant colony. Nevertheless, our experimental images did not exhibit such a distinct pattern of colonies (Figs. 2 and 3; Appendix Figs. S10, S11, S16, and S17). Consistently, in our simulations a pre-existing highly resistant patch did not promote the survival of any other patch for CS− (Appendix Fig. S20, CS−). For CS+, a pre-existing highly resistant patch typically produced the maximum final cell density in its community by also rescuing a few other patches to much smaller final cell densities. The latter was more likely in the vicinity of, than farther away from, the highly resistant patch, consistent with the “satellite colonies” notion (Appendix Fig. S20, CS+). Furthermore, de novo emergence of highly resistant patches, as our experimental results suggest above (Fig. 4), did not have any noticeable effect on the simulated spatial dynamics (Appendix Fig. S21).

Discussion

Antibiotic responses of surface-attached bacteria with CS have implications for host invasion and colonization by pathogens. Pathogens often encounter sublethal doses of antibiotic factors (Algburi et al, 2017; Andersson and Hughes, 2014; Chaplin, 2010; Medzhitov, 2007) and resource limitation (Hood and Skaar, 2012; Morita, 1997). Such conditions can in turn drive patch formation to enhance the survival of P. aeruginosa against host immune system attacks, consistent with previous findings that larger aggregates are more likely to evade phagocytosis (Alhede et al, 2020).

Patches may facilitate the formation of antibiotic gradients by serving as a diffusion barrier, by enhancing antibiotic degradation, or both, and thus promote the evolution of elevated antibiotic resistance, based on previous reports that antibiotic gradients can facilitate resistance evolution (Baym et al, 2016; Hermsen et al, 2012). Consistent with this notion, we found that patch growth promotes the emergence of elevated individual-level resistance in ≤23 h of treatment (Fig. 4), which agrees with predominant observations that P. aeruginosa infections rapidly develop resistance to antibiotic treatment (Olivares et al, 2020; Rossi et al, 2021). This is a novel example of dissecting and bridging ecology (CS) and evolution (inheritable elevated individual-level resistance) in antibiotic responses of surface-attached P. aeruginosa communities. Our results suggest that CS in patches could allow the cells the time (or number of generations) needed for the mutants with elevated individual-level resistance to emerge. This occurred at initial cell numbers that would not support growth in well-mixed liquid cultures. We speculate that this could be due to the locality of CS on agar: Any molecules the cells secreted would have been confined to their diffusion length scales on agar, whereas they would have been rapidly homogenized to a low level in well-mixed liquid cultures.

$\beta$-lactam antibiotics, such as Tic and Pip, are often prescribed to treat P. aeruginosa infections (Glen and Lamont, 2021). Bla molecules were detected in clinical isolates of P. aeruginosa (Ciofu et al, 2000) and human lung infection samples (Giwercman et al, 1992). Patchy growth is promoted by CS. CS could be mediated by Bla under $\beta$-lactam treatment, but also occurs for P. aeruginosa against other classes of antibiotics (Mizunaga et al, 2005; Nicas and Bryan, 1978). Therefore, patchy growth of P. aeruginosa may emerge in response to a broad range of antibiotics, and our model could help explain the widespread patchiness of P. aeruginosa communities observed in patient specimens (Kirketerp-Møller et al, 2008; Kolpen et al, 2022; Lam et al, 1980; Rudkjøbing et al, 2012; Singh et al, 2000).

Physicians often prescribe $\beta$-lactams as first-line antibiotics to treat not only P. aeruginosa but also a broad spectrum of infections (Bush and Bradford, 2016; Fernandes et al, 2013). CS occurs for many bacterial species and against various antibiotics (Lee et al, 2010; Sharma and Wood, 2021; Sorg et al, 2016; Tan et al, 2012; Udekwu et al, 2009; Vega and Gore, 2014; Yurtsev et al, 2013; Yurtsev et al, 2016). CS is also implied by the observations of lower eradication rates of Helicobacter pylori when duodenal ulcer and gastritis patients were treated with antibiotics (Lai et al, 2003; Moshkowitz et al, 1995). Accordingly, patchy growth could occur generally in antibiotic responses of bacteria when CS acts over short spatial scales.

In a broader context, our study gives an example of how two competing interactions with different length scales shape ecological (i.e., population-level) dynamics and spatial patterns. Patchy growth emerges under resource limitation when CS acts in spatial scales shorter than the diffusion length scale of resources. Growth of bacteria in a patch locally enhances CS while globally inhibiting the further growth of its own type, creating short-range positive and long-range negative, i.e., scale-dependent, feedback. Scale-dependent feedback has been used to explain patchy growth of various bacteria by different means of local CS. One example is obligate collective substrate utilization, independently shown for Bacillus subtilis and Psychromonas (Ebrahimi et al, 2019; Ratzke and Gore, 2016). Another example is CS of Pantoea agglomerans, a human and plant pathogen (Cruz et al, 2007), desiccation stress to its host plant (Monier and Lindow, 2005). More generally, scale-dependent feedback was also proposed as a unifying mechanism for spontaneous patterning in morphogenesis (Murray, 2002), patchy growth in natural ecosystems such as arid land vegetation, ribbon forests, coral reefs, and mussel beds (Klausmeier, 1999; Rietkerk and van de Koppel, 2008). Thus, in other examples in nature, including non-microbial systems, if patchiness occurs in the presence of factors operating at differing spatial scales, the mechanisms delineated here could play an unrecognized role in patchiness and in its wide-ranging ecological and evolutionary consequences (Hansson et al, 1995; Johan van de Koppel et al, 2002; Wright, 1948).

Methods

Bacterial strains and growth media

E. coli MC4100Z1 with or without a plasmid that encodes an engineered cytoplasmic beta-lactamase (BlaM) (Tanouchi et al, 2012) or P. aeruginosa PA14 pilU^- (transposon insertion) was used. E. coli MG1655 with the same BlaM plasmid was used only for the experiment presented in Appendix Fig. S15.

In every experiment, bacteria were first streaked on an LB agar plate from their frozen glycerol stock, and a single colony was incubated overnight in liquid LB media. Liquid culture experiments were then inoculated through serial dilutions of an overnight culture. For the experiments with spatially extended communities, the overnight cultures were diluted in fresh liquid growth media and grown for 3–4 h at 37 °C and 225 r.p.m. Then, their appropriate dilutions were made in 11.6 g/l sodium chloride to prepare the cell suspensions loaded to the robotic liquid handler (Mantis by Formulatrix).

Unless otherwise noted, a low nutrient content LB (0.2 × LB: 2 g/l tryptone, 1 g/l yeast extract, and 11.28 g/l sodium chloride) was used. In the engineered E. coli experiments, kanamycin (50 μg/ml) and IPTG (1 mM) were added for the maintenance of the BlaM plasmid and for the induction of BlaM expression, respectively. In the P. aeruginosa experiments, gentamycin (15 μg/ml) was added for the maintenance of the transposon insert that disrupts the pilU gene. For the exogenous Bla experiment (Appendix Fig. S14), a commercially available blend (MilliporeSigma L7920-1VL) was dissolved in deionized water, filter sterilized (0.22 μm), and used in the same day.

Well-mixed liquid cultures

We grew 2–3 ml cells in 16 ml culture tubes at 37 °C and 225 r.p.m. The cultures used for Tic experiments were protected from light.

Spatially extended communities

In all, 15 ml growth media was solidified in each 35 mm well of a six-well dish. Agar densities were 0.5% and 1.5% for E. coli and P. aeruginosa experiments, respectively. LB with a reduced nutrient content (0.2 × LB) was used for enhanced resource competition and preventing patches to grow onto each other. Seeding droplet volume and initial nearest neighbor center-center separation for the grid positions were fixed at 0.1 μl and 2.25 mm, respectively.

The average number of cells ($n_c$) for different seeding cell density groups was estimated from the corresponding suspensions’ cell densities (OD₆₀₀). These values were converted to cell numbers based on our calibration ($1.6\times {10}^9$ cells/ml per OD₆₀₀ for E. coli, and 2.$1\times {10}^9$ cells/ml per OD₆₀₀ for P. aeruginosa).

The counting error for each cell density group, assuming that the number of cells per site is Poisson-distributed, would be the standard deviation ($\sigma$) of Poisson distribution, which is $\sigma =\sqrt{n_c}$. This would yield a trio of (4 $\pm$ 2), (16 $\pm$ 4), and (128 $\pm$ 11) cells for the E. coli experiments (Fig. 2; Appendix Figs. S10 and S11), and a trio of (400 $\pm$ 20), (800 $\pm$ 28), and (4000 $\pm$ 63) cells for the P. aeruginosa experiments (Figs. 3 and 4; Appendix Figs. S16–S19).

From the Poisson distribution, the greatest chance of leaving a grid site empty was $e^{-4}=0.018$, or 1.8%. Given that we seeded ~70 sites using each density group for each community, we did not anticipate leaving empty sites too often and this was supported by the images of the untreated communities in the end (Figs. 2 and 3; Appendix Figs. S10, S11, S16, and S17).

Tic resistance screening assays

Patch samples were collected and stored as frozen glycerol stocks. Later, the samples were inoculated at 30–10,000 cells/ml from their frozen stocks in 1–1.2 ml media (0.2 × LB). This suspension was split into two 500–600 μl aliquots. Tic was added to a 10 μg/ml final concentration into one of the aliquots (Fig. 4). Then, 200 μl from each group was transferred to a well of a 96-well plate in two replicates. The 96-well plate was then incubated in a plate reader at 37 °C (by shaking every 10 min). Each growth well was sealed with adding 50 μl mineral oil to minimize the evaporation of culture media. At the end of each assay, the samples that tested resistant and their antibiotic-free counterpart cultures were stored as frozen glycerol stocks. Later, to test the heritability of resistance, for 38% of the samples identified as resistant, their screening was repeated starting from those antibiotic-free frozen glycerol stocks. The remaining 62% was exposed to the inheritability test by growing in culture tubes in 2 ml liquid media prior to being frozen.

The control samples collected from no ticarcillin treatment case (Appendix Fig. S18) were screened as 2 ml (0.2 × LB) cultures in 16-ml culture tubes at 37 °C with shaking at 225 r.p.m. for 22.5–24.5 h.

Image analyses

For the E. coli communities (Figs. 2C,D and EV5; Appendix Figs. S10, S11, and S13), a custom MATLAB script was used for automated segmentation and area measurements of individual patches. The script first finds and subtracts the most common pixel intensity for all pixels, second uses “regionprops” for finding circular objects, touches up the objects via built-in functions of MATLAB for image analyses, and then eliminates the objects larger or smaller than user-defined bounds. For each case, the segmentation results were manually validated and corrected using ImageJ manual tools, as necessary.

For the P. aeruginosa communities (Fig. 3C,D; Appendix Figs. S16, S17, and S19), the sizes (i.e., areas) of the individual patches were manually measured using ImageJ.

A (28.3 mm × 28.3 mm) zone approximately in the center of each growth well was analyzed. This was to avoid our conclusions being affected by any boundary artefacts.

Mathematical model

Cell density (c):

$$\frac{\partial c}{\partial t}=\left(g-l\right)c+D_c{\nabla }^{2}c$$

Nutrient concentration (n):

$$\frac{\partial n}{\partial t}=\left(\xi l-g\right)c+{\nabla }^{2}n$$

Antibiotic concentration ($a$):

$$\frac{\partial a}{\partial t}=-{\kappa }_{B}ba{+D}_a{\nabla }^{2}a$$

Antibiotic-inactivating enzyme concentration (b):

$$\frac{\partial b}{\partial t}=lc-d_{b}b+D_b{\nabla }^{2}b$$

We implemented our model in a set of coupled partial differential equations (PDEs). These PDEs were written to describe the spatial and temporal evolution of cell density, nutrient concentration, antibiotic concentration, and antibiotic-inactivating enzyme concentration (We considered the antibiotic as a $\beta$-lactam, and its corresponding inactivating factor as a Bla enzyme). Here, $g$ and $l$ represent the growth and lysis functions, respectively, defined as $g=\frac{n}{1+n}\left(1-\frac{c}{c_m}\right)$ and $l=\left\{\begin{array}{cc}\hfill \gamma g,\hfill & \hfill ifa\ge A_{th}\hfill \\ \hfill 0,\hfill & \hfill else\hfill \end{array}\right)$. $c_m$ is the local population carrying capacity, $\gamma$ is the maximum lysis rate, and $A_{th}$ is the antibiotic concentration killing threshold (i.e., to cause lysis). All model variables were non-dimensionalized (see Appendix Notes). We implemented a local CS by setting the diffusion coefficient of the antibiotic-inactivating factor $\left(D_b\right)$ as 800-fold and 10,000-fold smaller than that of antibiotics $\left(D_a\right)$ and nutrients (which is $1$, because all the diffusion coefficients were normalized by the diffusion coefficient for nutrients during the nondimensionalization of the model), respectively. In other words, we assumed that the antibiotic-inactivating enzyme acts over a much shorter-range relative to the diffusion length scale of nutrients and antibiotics.

Simulations of the model were performed using MATLAB 2020a. Two-dimensional simulations were run for the spatial growth (Figs. 1C,D and EV1–EV4; Appendix Figs. S4–S7, S20, and S21). The numerical simulations were run in a 73-by-73-pixel spatial domain, where each pixel dimension was equivalent to a dimensionless spatial length of 0.1. Each local population was confined to a single pixel. The nearest neighbor distance was 0.9. The temporal scale used was a $2.5\times {10}^{-5}$ dimensionless timestep. For the well-mixed case (Fig. 1B), the same set of equations were used without the diffusion terms.

Author contributions

Emrah Şimşek: Conceptualization; Data curation; Software; Formal analysis; Validation; Investigation; Visualization; Methodology; Writing—original draft; Project administration; Writing—review and editing. Kyeri Kim: Formal analysis; Investigation; Writing—review and editing; Assisted in demonstrating collective survival and phenotypic screening of antibiotic resistance in the Pseudomonas aeruginosa experiments. Jia Lu: Formal analysis; Writing—review and editing; Performed Pseudomonas aeruginosa image analyses for patch size measurements. Anita Silver: Formal analysis; Investigation; Writing—review and editing; Assisted with parameter sensitivity analysis. Nan Luo: Software; Writing—review and editing; Produced the MATLAB implementation for the partial differential equation solver used. Charlotte T Lee: Formal analysis; Funding acquisition; Writing—review and editing; Commented on general ecology implications and assisted with manuscript revisions and results interpretation. Lingchong You: Conceptualization; Resources; Supervision; Funding acquisition; Writing—original draft; Writing—review and editing.

Source data underlying figure panels in this paper may have individual authorship assigned. Where available, figure panel/source data authorship is listed in the following database record: biostudies:S-SCDT-10_1038-S44320-024-00046-5.

Data availability

Source datasets and computer programming codes are available at https://github.com/youlab/Patchy_Dynamics.git.

The source data of this paper are collected in the following database record: biostudies:S-SCDT-10_1038-S44320-024-00046-5.

Disclosure and competing interests statement

The authors declare no competing interests. LY is an editorial advisory board member. This has no bearing on the editorial consideration of this article for publication.

Supplementary information

Expanded view data, supplementary information, appendices are available for this paper at 10.1038/s44320-024-00046-5.