### Consistent quantification of persister fractions

A critical issue when studying bacterial persistence is the precise definition of the persister fraction. Previous studies have defined persister cells as the surviving fraction after antibiotic exposure for an arbitrary amount of time, ranging from hours [4, 8, 10, 11, 19, 23–25] up to several days [15]. In addition, these fractions have been assessed at different growth states: mid-exponential [8, 10, 11, 19, 25], late exponential [24] and in rare cases, stationary phase [4, 24, 25]. Most often, these studies are performed in liquid cultures of rich media. However, some studies have assayed persisters on agar [6, 12, 13], by plating samples of logarithmically growing cultures on LB agar with ampicillin, incubating overnight, spraying the plates with penicillinase, and again incubating for 24 hours to count the number of surviving cells. These different methods tremendously complicate comparisons across studies.

To quantify the fraction of persisters in a consistent manner, we use a model motivated by observations of persister cell dynamics first reported by Balaban et al. [6], who observed two types of persister cells, which they proposed arose through two different mechanisms. Type I persisters occurred through unspecified events that occur during stationary phase, and remained fully dormant until switching to a normal growth state. These have been associated with a specific genotype, the *hipA7* allele. Type II persisters arise through an infrequent stochastic switch to a slow-growth state, and remain so until switching to a normal growth state. These were associated with a mutation at a second locus, *hipQ*. A similar model of persister formation has been proposed by Wiuff et al. [23].

Here we apply this simple two-state model assuming simplified type II persister dynamics. In this model, cells exist in two states, normal and persister. During antibiotic treatment, normal cells die at a rate μ and switch to a persister state at rate α. Persister cells do not die or grow, and switch to a normal state at rate β (see Additional file 1). The advantage of using a this model is that the parameters that we infer, such as the fraction of persister cells, do not depend on experimental idiosyncrasies, for example, the time at which cell numbers are measured. It has been difficult to compare the results of many previous experiments on persisters for this reason.

### Persister fractions differ between environmental isolates

We selected 11 *E. coli* isolates from a collection of more than 450 environmental isolates sampled over a period of 12 months from two sites approximately 2m apart near a watershed of Lake Superior (46°42'04'N, and 92°12'26'W) [26]. Despite the nearly identical geographical provenance of these isolates, partial genomic sequencing of a subset of these 450 strains has shown that while all are *Escherichia* species, they encompass a genetic diversity greater than the standard panel of *E. coli* strain diversity, the ECOR collection. This initial genomic data show that isolates from this location are spread across the *E. coli* phylogeny, with members in clades A, B1, B2, D, E, F, and C-V [27] (Bertels et al., in prep). Although the strains in this collection harbor considerable genetic diversity, for the most part, they are not pathogenic, typing negatively for most common virulence loci (M. Sadowsky, personal communication).

We selected the subset of 11 environmental isolates on the basis of their differential levels of survival in ampicillin after 24 hours of treatment (using CFU counts; see Methods). In doing so, we aimed to find strains that differed to the greatest extent in the fraction of persisters that were formed in ampicillin, such that we would have the greatest power to discern whether these differences were paralleled in other antibiotics. In addition to these isolates, we used the standard laboratory strain *E. coli* K12 MG1655, for a total of 12 strains in which we quantified persister fractions.

For each of these strains, we first determined the MIC for ampicillin (see Methods), and found that the MICs for these strains differed by less than two-fold (Additional file 2: Table S1). This suggested that the differences in survival did not arise simply from differences in growth and killing dynamics, and may instead have resulted from differences in persister formation.

We then quantified, for each strain, survival curves over 48 hours during treatment with 100 mg/ml of ampicillin (Figure 1). In the vast majority of cases, the curves that we observed were clearly not characterized by a single exponential decrease, as would be expected if all individuals in the population had equal susceptibility to the antibiotic. This suggested that at least two distinct populations of cells were present. We denote these subpopulations as normal and persister cells. We used these survival curves in conjunction with a mathematical model of persistence to quantify the persister fraction for each strain. In this model we fit four independent parameters (see Additional file 1) to infer the rate of death of normal cells, the rates of switching between normal and persister states, and the fraction of persisters. For each strain, we used at least five biological replicates for model fitting.

Using this method, we found that the fraction of persisters differed significantly between strains, from less than 0.001% to more than 10% (Figures 1 and 2; Additional file 3: Table S2), a range of over four orders of magnitude.

### Persister fractions in different antibiotics are uncorrelated

To infer persister fractions, we also measured kill curves for each strain in two additional antibiotics, ciprofloxacin and nalidixic acid, both belonging to the quinolone class of antibiotics [28]. By selecting two antibiotics in the same class, we aimed to test whether persister fractions were similar and consistent for drugs with comparable modes of action. We first measured the MICs of these 12 strains in both antibiotics, and found that the MIC values showed little variation (differing by 2.5-fold and 3.5-fold for ciprofloxacin and nalidixic acid, respectively; Additional file 2: Table S1). We used the same method outlined above to quantify the persister fractions in these antibiotics. We again found substantial variation in the persister fractions, ranging from 0.001% to 0.15% in ciprofloxacin, and from less than 0.001% to more than 1% in nalidixic acid (Additional file 3: Tables S2).

Our hypothesis is that for each strain, persisters are generated through a single general mechanism, such as cell dormancy, and that this mechanism confers a multi-drug tolerance. If this is true, then strains should exhibit characteristic persister fractions: we expect that for some isolates this subset of cells will be large, and thus these isolates will have high fractions of persisters across all antibiotics, while for other isolates, this subset of cells will be small, resulting in a small fraction of persisters across all antibiotics. This pattern has been shown previously for the *hipA7* mutant of *E. coli* K12, after *relE* overexpression in K12, or after deletion of TA-pairs [11, 29, 30]. In all of these cases, these genetic changes caused a general increase in the fraction of persisters across several classes of antibiotics.

We tested this hypothesis by looking for positive correlations in the fraction of persisters in the three antibiotics (ampicillin, ciprofloxacin, and nalidixic acid). However, despite the considerable variation in the persister fractions found among isolates (Figure 2), no consistent positive correlations were found (rho = -0.49, p = 0.46, N = 12 for ampicillin versus ciprofloxacin, rho = 0.55, p = 0.07, N = 12 for ampicillin versus nalidixic acid, rho = −0.30, p = 0.34, N = 12 for ciprofloxacin versus nalidixic acid, Spearman correlation; Figure 3). Importantly, we found no positive correlation between the persister fractions in ciprofloxacin and nalidixic acid, although these two antibiotics have very similar mechanisms of action, with both targeting the DNA gyrase subunits *gyrA* and *gyrB* and the topoisomerase IV subunits *parC* and *parE*[31, 32]. It is unlikely that this result is due to an inability to accurately measure the persister fractions, as independent measurements yielded highly consistent values (Figures 1 and 2). Thus, this result suggests that different types of persister cells exist within populations, some of which are persistent to one antibiotic, while others are persistent to other antibiotics. In addition, this shows that *E. coli* persister cells are not necessarily characterized by multidrug tolerance. Although this contrasts with previous observations for mutants of *E. coli* K12, it is in concordance with observations in *M. tuberculosis*[15].

### Evidence that a subset of persister cells is multidrug tolerant

We selected two strains on the basis of the persister fractions that they exhibited in single antibiotics, requiring that the strains exhibit a high level of persistence in at least one antibiotic. For these two strains we re-measured the persister fractions in single antibiotics, as well as in all pairwise combinations of the three antibiotics. We found that the killing dynamics were qualitatively similar to those when using a single antibiotic: all kill curves exhibited biphasic behavior, indicating that at least two subpopulations of cells were present (Figure 4).

The precise dynamics of this killing in combinations of antibiotics may yield additional insight into how persisters are formed. We briefly outline three general possibilities. (1) No cells persist when a population is simultaneously treated with antibiotics. This implies that the mechanisms underlying persistence to the two antibiotics are exclusive, and cannot occur within the same cell. (2) The fraction of persistent cells under the combination of antibiotics is approximately multiplicative relative to the fraction in the two single antibiotics. Although this observation would be consistent with several explanations, the simplest is that the mechanisms of persister formation are independently induced, and occur randomly within the same cell. (3) The fraction of persistent cells under a combination of antibiotics is similar to the fraction observed under treatment with the more lethal antibiotic. Again, although several explanations would be consistent with this, the simplest is that cells that are persistent to the more lethal antibiotic are also persistent to the second. We refer to these three hypotheses as exclusive, independent, and coincident, respectively.

We found that for these two strains, there were no cases in which persister fractions were exclusive. Instead, the persister populations were largely coincident, with the fraction of cells in combinations of antibiotics being similar to the fraction observed in the more lethal antibiotic (Figures 4 and 5). This is consistent with this subset of cells being multidrug tolerant. Thus, although not all persisters are multi-drug tolerant, there appears to be a subset that is.

### Toxin-antitoxin pairs are frequently gained and lost in *E. coli*isolates

One possible explanation for the differences in persister formation of environmental isolates is that the activation of different toxin-antitoxin pairs results in different antibiotic susceptibilities. To further examine this hypothesis, we looked at the presence of TA loci that are known to affect persister formation in 15 *E. coli* and *Shigella* taxa, as well as in *Escherichia fergusonii*. We found significant variation in the presence of TA modules across different *E. coli* isolates (Figure 6), suggesting that these loci are lost (and/or gained) over relatively short time scales in this clade. Such changes in the number or types of TA pairs are likely to affect the production of persister cells, as has been shown experimentally [11].

### The rate of switching from normal to persister state is the primary determinant of persister fractions

In the analyses above, we have used information from cell-killing dynamics to infer the proportion of persister cells that were present at the start of antibiotic killing. These persisters are formed during exponential growth, and the fraction that is present is determined largely by two independent parameters, the rates of switching to and from the persister cell state. To gain additional insight into the mechanistic underpinnings of persister formation, we examined the relationship between the persister fraction and these two parameters. We find strong evidence that the primary determinant of the persister fraction is the rate at which persister cells are formed from normal cells: these two variables are strongly correlated across both strains and antibiotics (Figure 7). In contrast, the rate of switching from persister to normal cell has little to no relationship with the persister fraction.