## Introduction

Despite intensive study, antibiotic resistance remains an essential problem, in part due to the myriad of mechanisms by which cells can evade drug treatment. Classical tests, such as measurements of the minimum inhibitory concentration (MIC), are important for quantifying drug resistance, but can obscure single-cell level differences in resistance1. This is a significant problem because cell-to-cell differences in antibiotic resistance can establish concentration gradients, which can accelerate the resistance acquisition process2,3. In addition, subpopulations of antibiotic resistant or tolerant cells can decrease treatment efficacy4,5.

Individual cells can exhibit phenotypic differences in drug resistance even in the absence of community-level effects. For example, persister cells use dormancy or slow growth to evade antibiotic treatment1. Single-cell level resistance can also affect group growth. For instance, Streptococcus pneumoniae cells with chloramphenicol acetyltransferase can deactivate chloramphenicol, resulting in a decrease in both the intracellular and environmental chloramphenicol concentrations6. Bacteria also transiently express resistance-conferring genes such as drug export pumps or those that modify membrane permeability, resulting in cell-to-cell difference in susceptibility4,7.

Antibiotic efficacy can also be dependent on community-level phenomena. For example, the inoculum effect describes the cell density dependence of the MIC, where more dense cultures are less susceptible to antibiotics resulting in increases in the MIC8,9. Cell density plays an essential role in influencing group behaviors, such as quorum sensing and biofilm formation, which in turn can dramatically increase the antibiotic resistance of the population10,11. Furthermore, certain cells within a community may exhibit altruistic behavior, such as those that release resistance proteins upon death to enable other cells to survive10,12. These examples highlight the importance of cellular interactions and collective behavior in antibiotic resistance.

Bacterial efflux pumps are an important source of multidrug resistance13,14. These pumps export antibiotics from the cell, increasing their antibiotic resistance. Their expression can be taxing, reducing growth and imposing a fitness cost15,16; therefore, their expression is often regulated to limit the burden. The primary multidrug resistance efflux pump in E. coli is AcrAB-TolC. This pump is composed of three proteins that span the inner and outer cell membrane: a periplasmic linker protein AcrA, the inner membrane efflux transporter AcrB, and the outer membrane channel TolC17. Knocking out acrB, the pump protein responsible for substrate recognition and export via the proton motive force, leads to a significant increase in antibiotic susceptibility14,18. For instance, the MIC of E. coli ΔacrB to chloramphenicol is an eighth of that of wild type cells19. Complementing ΔacrB with the acrAB operon is sufficient to restore drug resistance15. Efflux pumps have been recognized to play a major role in clinical isolates in the emergence of resistant strains of E. coli, Salmonella enterica, and other pathogens, and thus have been identified as clinical targets20,21.

Recent studies have shown that AcrAB-TolC expression is heterogeneous across populations22,23, suggesting that differential pump expression exists even within isogeneic populations. Since the cost and benefit of expressing pumps can both be significant, these cell-to-cell differences may have important implications for bacterial populations. Here, we asked how efflux pump export of antibiotics affects the growth of neighboring cells and, ultimately, the composition of the population.

To accomplish this, we focused on differential expression of acrAB. We monitored single-cell growth rates using time-lapse microscopy, and analyzed growth of cells as a function of whether their neighbors have AcrAB-TolC efflux pumps. We found that individual bacteria that are surrounded by AcrAB-expressing neighbor cells will tend to grow more slowly than when the same cells are surrounded by ΔacrB neighbors under antibiotic exposure. By developing a mathematical model, we were able to characterize this effect and predict the cell growth in the presence of a different antibiotic. Furthermore, we tested co-cultures of E. coli and S. enterica serovar Typhimurium (hereafter referred to as S. typhimurium) and observed the same neighbor dependence, which has implications for the broader relevance of our findings since these results likely extend to mixed-species communities. This work contributes additional evidence for the critical role of single-cell level effects in antibiotic resistance.

## Results

To examine the effect of drug efflux on neighboring cells, we designed an experiment where ΔacrB cells were surrounded either wild type cells containing functional AcrAB-TolC pumps or by identical ΔacrB cells (Fig. 1A). We hypothesized that ΔacrB cells which had wild type neighbors would experience a higher local concentration of antibiotics due to drug efflux in their immediate vicinity, leading to a reduced growth rate relative to cells with neighbors lacking pumps. To test this, we conducted experiments with E. coli growing on agarose pads and measured single cell growth rates under different levels of antibiotic exposure.

To visualize the two cell types, we labeled the ΔacrB cells with red fluorescent protein (denoted ΔacrB-RFP) and wild type cells with green fluorescent protein (WT-GFP). Chloramphenicol is a broad-spectrum antibiotic which diffuses through the bacterial cell membrane and reversibly binds to the ribosome to inhibit protein synthesis. We quantified the growth rates of ΔacrB-RFP cells surrounded by either WT-GFP or ΔacrB-RFP neighbors. To do this, we mixed ΔacrB-RFP with WT-GFP cells in ratios of 1:5 and 5:1 to bias the community structure. Growth rates for cells were similar for both ratios for conditions with no chloramphenicol. However, under chloramphenicol treatment just below the MIC (1 μg/ml, Fig. S1), we found that the growth rate of ΔacrB cells with WT-GFP neighbors was lower than those with ΔacrB-RFP neighbors (Fig. 1B), indicating that the influence of drug efflux by neighboring cells is important in local growth inhibition. When we compared the growth of WT-GFP cells with WT-GFP or ΔacrB-RFP neighbors, we observed more modest differences in growth rates under chloramphenicol treatment. This is likely because cells with pumps are able to maintain low intracellular antibiotic concentrations regardless of their neighbors (Fig. 1C).

Building upon these results, we next conducted a series of experiments where we used ΔacrB as the strain background for both types of cells in the co-culture, allowing us to isolate the effect of efflux pumps independent of endogenous regulation. We tested microbial communities with ΔacrB-RFP cells and a ΔacrB strain overexpressing acrAB, which we labeled with green fluorescent protein (denoted AcrAB-GFP). We then monitored the growth of the ΔacrB-RFP cells surrounded by either AcrAB-GFP or ΔacrB-RFP neighbors. As before, we found that ΔacrB-RFP cells grow more slowly when they are in the vicinity of AcrAB-GFP neighbors than when they are surrounded by ΔacrB-RFP neighbors (Fig. 2A). Differences in the growth rate are apparent in measurements of cell length over time. As a negative control, we also measured ΔacrB-RFP cells mixed with ΔacrB-GFP cells and found no differences in growth rate (Fig. 2B).

To confirm our findings across measurements of hundreds of individual cells, we quantified the growth rates of single cells with ΔacrB-RFP or AcrAB-GFP neighbors. We found statistically significant differences in the growth rates in conditions where antibiotics were applied (Fig. 2C). In addition, we observed a shift in the mean growth rate in the opposite direction without antibiotic treatment, indicative of the cost of efflux pump expression. Under sub-MIC levels of chloramphenicol (0.2 μg/ml), the neighbor effect was more apparent than chloramphenicol concentrations near the MIC (1 μg/ml). This is likely because at the higher antibiotic concentration growth of both ΔacrB-RFP and AcrAB-GFP cells is impacted by chloramphenicol treatment. As expected, control experiments with ΔacrB-RFP and ΔacrB-GFP cells showed no statistical difference in growth rates, regardless of the antibiotic concentration (Fig. 2D). These results indicate that the AcrAB-TolC efflux pump plays a role in attenuating growth of neighboring cells in conditions where antibiotics are present.

Since competition will change the composition of cells in mixed species communities, we next extended our analysis to ask what the implications were for co-cultures. To do this, we compared the biomass of the ΔacrB-RFP cells at the start of the co-culture experiment to the end. More specifically, we quantified the relative abundance of the ΔacrB-RFP cells by comparing what fraction of the biomass they made up at the end divided by the fraction at the start. Thus, if there is no change in the composition of the co-culture then the relative abundance will be one; values below one correspond to AcrAB-GFP cells outcompeting the ΔacrB-RFP cells. When no antibiotic was applied we found that ΔacrB-RFP and AcrAB-GFP cells grew similarly and the relative abundances of the two strains were maintained near one (Fig. 3A). However, under chloramphenicol treatment the relative abundance of the ΔacrB-RFP cells decreased when they were surrounded by AcrAB-GFP cells, but not when they were in close proximity with other ΔacrB-RFP cells. We note that under these conditions there are still AcrAB-GFP cells, but since they are mixed in a ratio of 5:1, the AcrAB-GFP cells are comparatively rare. Control experiments with ΔacrB-RFP and ΔacrB-GFP co-cultures had relative abundance values near one regardless of the chloramphenicol concentration (Fig. 3B). Overall, these results indicate that proximity related inhibition from drug efflux can lead to rapid changes in the community composition.

To understand the impact of antibiotic export on neighboring cells, we developed a mathematical model to describe cell growth. The agent-based model applies a fixed spatial architecture to describe cell proximity. Within each cell, we used a system of ordinary differential equations to model changes in the intracellular antibiotic concentration due to drug efflux (Fig. 4A). Model parameters were estimated from measurements of cell density in the presence of antibiotics (Fig. S1). We found that cell growth and the intracellular antibiotic concentration are strongly influenced by the type of neighbors in the simulation (Fig. 4B). We next simulated a range of chloramphenicol concentrations and found that the growth rate decreased significantly for cells with higher efflux compared to cells with ΔacrB neighbors (Fig. 4C), in good agreement with the experimental results (Fig. 1B).

A key finding of the model is that the efflux rate is proportional to the neighbor effect. In other words, if the AcrAB-TolC pump exports a specific antibiotic well, then the neighbor effect will be more apparent than if the pump does not export it well. To test this, we conducted additional modeling and experiments with ciprofloxacin, which is a substrate of the AcrAB-TolC pump, but has a smaller fold reduction of the MIC than chloramphenicol for ΔacrB cells (Fig. S1B). Using parameter fits from experimental data, we lowered the efflux rate of wild type cells to model the lower efflux efficiency for ciprofloxacin. The simulated results show a decrease in the impact of neighbors on the focal cell’s growth rate (Fig. 4D). We confirmed this experimentally with ciprofloxacin, observing modest, but not statistically significant differences between the different neighboring cells (Fig. 4E). In an extension to the model, we explored how the neighborhood affected the focal cell’s growth rate. We observed that the overall number of neighbors was an important determining factor of the focal cell’s growth rate and the exact spatial arrangement of the neighbors played only a minor role (Fig. S4).

In microbial communities bacterial cross-species interactions are common. Therefore, we tested whether the neighbor effect was limited to our single-species co-cultures with E. coli or if it extended to cross-species interactions. E. coli (e.g. ETEC or STEC) and S. typhimurium are both foodborne pathogens and their co-existence can lead to mixed biofilm formation and a higher resistance against sanitization24. We investigated the growth of S. typhimurium co-cultured with E. coli WT-GFP or ΔacrB-RFP under conditions with and without chloramphenicol. Consistent with our results from the single-species co-cultures, we observed that S. typhimurium grows more slowly with E. coli WT-GFP neighbors than E. coli ΔacrB-RFP neighbors (Fig. 5). These results indicate that the neighbor effect generalizes to cross-species interactions.

## Discussion

Single cell level effects are important for bacterial growth and survival under antibiotic treatment. Here we focused on differences in antibiotic efflux as a mechanism for generating cell-to-cell differences in antibiotic survival. This work is motivated by recent studies showing that efflux pump expression is variable across cells within a bacterial population22,23. Using detailed quantitative measurements of single cell growth rates, we asked how differences in drug efflux affect the growth of neighboring cells. We found that ΔacrB cells have a lower growth rate when surrounded by cells with the AcrAB-TolC pump than when surrounded by like ΔacrB cells. This effect leads to a rapid shift in the community composition towards more resistant cells that occurs within a small number of generations. Further, the effect extends to E. coli and S. typhumirium co-cultures, suggesting that these findings are likely to be broadly relevant for mixed-species communities and stress tolerance mechanisms that work by exporting antibiotics or other compounds into the immediate vicinity.

Efflux pump expression can be burdensome to cells and there is a tradeoff between the benefit of pumps and their cost15. Under the conditions we tested here, the cost of pumps was modest and conditions with no antibiotics produced only minor differences in growth rates between ΔacrB-RFP and AcrAB-GFP cells; however, we note that as experiment durations are extended this burden will become more apparent. These cost and benefit tradeoffs will likely depend on the environment, as cells balance the burden of pump expression, the impact of their neighbors, and the local antibiotic concentration to maximize growth.

In the future, it will be interesting to study the interaction between drug efflux and other antibiotic resistance mechanisms that function at the single-cell level. Also, efflux pump expression is stochastic and can change over time in individual cells22,23, suggesting the potential for experiments that quantify how these dynamics affects growth of neighboring bacteria. The implications for the eventual evolution of permanent genetic changes that lead to antibiotic resistance are also an interesting area for future research. Single cell level effects and how bacteria interact, including their proximity, can have a profound impact on whether antibiotics are effective.

## Methods

### Strains and plasmids

We used BW25113 as the wild type strain of E. coli. BW25113 ΔacrB was derived from the Keio collection strain JW0451 (BW25113 ΔacrB::kanR)25, and we removed the kanamycin resistance marker using the pCP20 plasmid26. For Salmonella co-culture experiments we used the model strain S. typhimurium LT227.

Plasmids were constructed using the Gibson assembly method28. To distinguish the strains, we used fluorescent reporters encoded on plasmids. For RFP, we used the plasmid pBbA5k-rfp29, for GFP we used pBbA5k-sfgfp15, and for AcrAB-GFP we used pBbA5k-acrAB-sfgfp15, where acrAB and sfgfp are transcriptionally fused. All plasmids described above have an IPTG-inducible PlacUV5 promoter controlling gene expression, a medium copy p15A origin of replication, and kanamycin resistance marker. The plasmids were transformed into either the E. coli wild type strain (pBbA5k-sfgfp to make WT-GFP), E. coli ΔacrB strain (pBbA5k-rfp for ΔacrB-RFP; pBbA5k-acrAB-sfgfp for AcrAB-GFP; pBbA5k-sfgfp for ΔacrB-GFP), or S. typhimurium strain (pBbA5k-rfp).

### Growth conditions

E. coli and S. typhimurium were cultured in Luria Broth (LB) medium. For all experiments, overnight cultures were inoculated from a single colony in LB with 30 μg/ml kanamycin for plasmid maintenance. Overnight cultures were then grown at 37 °C with orbital shaking at 200 rpm. Before experiments, cultures were refreshed 1:50 in LB with kanamycin and grown at 37 °C with orbital shaking. After 5 h, we added 100 μM IPTG and then incubated an additional 2 h to induce fluorescent protein or AcrAB expression. For S. typhimurium, 100 μM IPTG was added after cultures were refreshed for 0.5 h and cells were grown for an additional 2 h induction. Co-cultures were mixed in ratios of 1:5 and 5:1 each for ΔacrB-RFP and WT-GFP or ΔacrB-RFP and AcrAB-GFP experiments (and control with ΔacrB-RFP and ΔacrB-GFP).

### Time-lapse microscopy

For imaging experiments, the co-cultures were placed on an agarose pad with 100 μM IPTG and with either 0, 0.2, 1 μg/ml chloramphenicol or 0.02, 0.1, 0.3 μg/ml ciprofloxacin for E. coli co-cultures, or 0, 1, 3 μg/ml chloramphenicol for the E. coli and S. typhimurium co-culture. We imaged at least three positions per pad, resulting in measurements of hundreds of single cells for each position (for n values for each case see Fig. S2). 1.5% low melting agarose pads were made using M9 minimal medium containing 0.2% glycerol, 0.01% casamino acids, 0.15 μg/ml biotin, and 1.5 μM thiamine. Cells were diluted and mixed at ratios as indicated above and placed on pads containing 100 μM IPTG and chloramphenicol or ciprofloxacin. Images were taken using a Nikon Ti-E microscope with 100x objective lens for 130 mins at 5 min intervals. The temperature of the microscope chamber was held at 32 °C for the duration of the experiment.

### Data analysis

Images were analyzed in Matlab. We used the automated image processing package SuperSegger30 to measure cell growth rates and identify neighboring cells. An individual cell’s lineage starts just after its mother has divided, forming it and a sister cell, and it ends when the cell divides into two daughter cells. Growth rate is defined as the natural log of the ratio of the length of the cell at the end of the lineage to its length at the start of the lineage, divided by the length of the lineage in minutes. Thus, the growth rate is the exponential rate constant31. Custom Matlab scripts were used to analyze growth data and neighbor effects. Statistical analysis of growth rates was performed in Matlab.

### Toxicity experiments

To determine the antibiotic toxicity of the strains, we added a final concentration of 0, 0.1, 0.2, 0.5, 1, 2, 5, or 10 µg/ml of chloramphenicol or 0, 0.05, 0.1, 0.2, 0.5, 1, 2, or 5 µg/ml of ciprofloxacin to each culture. The samples were sealed with evaporation-limiting membranes (Thermo Scientific AB-0580) and grown in 96-well plates at 37 °C with orbital shaking at 200 rpm. OD600 readings were taken with a BioTek Synergy H1m plate reader every 10 m for 18 h. The toxicity curves represent change in growth for the first 2 h for consistency with the length of the microscopy experiments. All experiments were performed in triplicates with biological replicates.

### Mathematical model

To simulate cell growth with different neighbors in the presence of antibiotics, we used an agent-based model with Moore neighborhood architecture to describe the spatial interactions between cells and the environment (Fig. 4A)32,33,34. We represent each cell with two ordinary differential equations describing intracellular antibiotic concentration (Eq. 1) and cell biomass (Eq. 2). The model assumes exponential growth, which is valid for the short durations (~2 h) over which modeling and experiments are conducted. The biomass equation has a term for the toxicity of the environment, which is derived from Van Impe et al.15,35,36.

$$\begin{array}{ccc}\frac{d{C}_{in}}{dt} & = & \frac{1}{6}(\,{\sum }_{j=1}^{all\,adjacent\,Neighbors}(\frac{1}{2}{K}_{out,j}+\frac{1}{2}{K}_{in}){C}_{in,j}+{\sum }_{k=all\,adjacent\,Neighbors+1}^{4}{K}_{in}{C}_{out})\\ & & +\,\frac{1}{12}(\,{\sum }_{j=1}^{all\,diagonal\,Neighbors}(\frac{1}{2}{K}_{out,j}+\frac{1}{2}{K}_{in})\times {C}_{in,j}+{\sum }_{k=all\,diagonal\,Neighbors+1}^{4}{K}_{in}{C}_{out})-{K}_{out}{C}_{in}\end{array}$$
(1)
$$\frac{dN}{dt}=\mu \cdot N\cdot (\frac{1}{1+{(\frac{{C}_{in}}{{K}_{c}})}^{{h}_{c}}})$$
(2)

The total antibiotic concentration at each time point is assumed to be equal to the antibiotic concentration in the environment and inside cells. We assume instantaneous diffusion within environments separated by a membrane.

$${C}_{total}={C}_{out}+\sum _{i=1}^{all\,cells}\,{C}_{in,i}$$
(3)

Our model focuses on the focal cell and its neighbors. Cin is the intracellular antibiotic concentration, and Cout is the extracellular concentration. N is biomass of the cell, and μ is the maximum growth rate. Kin and Kout are antibiotic entry and exit based on the presence of efflux pumps. We assume that if two cells are close together, the efflux from the neighbor will create a small area with a higher relative antibiotic concentration. We model this as the influx into the focal cell where an edge with a neighbor has an influx rate of $$\,1/2\,{K}_{out,neighbor}+1/2\,{K}_{in}$$. The first term represents the effect of the gradient produced by efflux from the neighboring cell with some loss to the environment and the second term represents passive influx that may occur. The second term sets a lower bound so that $$\,1/2\,{K}_{out,neighbor}+1/2\,{K}_{in}\ge {K}_{in}$$.

For the effect of antibiotics on change in biomass, we fit experimental data to a Hill function. Parameters for the toxicity term, hc and Kc, were fit to ΔacrB toxicity curves for chloramphenicol and ciprofloxacin (Fig. S1). For modeling cell growth under ciprofloxacin, we decreased Kout by using fits to experimental data. All model fits were conducted by minimizing least-squares error. All model parameters are listed in Table S2.