Multi-resistance evolves in both single-drug and combination treatments when mutators are present

To determine the conditions under which multi-resistance evolves, we performed experimental evolution using four mutator frequency treatments (none, low, intermediate, high) and four selection regimes (antibiotic-free, single-drug with either rifampicin or nalidixic acid, combination with both antibiotics). We employed ramping selection, where antibiotic concentrations were doubled daily over six days (from 0.625 mg/l to 20 mg/l of each drug, where 10 mg/l of either is sufficient to inhibit wild-type growth). This concentration range is physiologically relevant for these antibiotics [49, 50]. We conducted daily assays to detect resistance, which is defined as the ability for a random sample of the population to grow on selective media containing the antibiotic(s) at concentrations above the minimum inhibitory concentration (MIC) of the wild-type strain. This characterises five possible outcomes: no resistance (no growth on any selective media), single resistance (growth on only one of two single-drug selective media), mixed resistance (growth on both single-drug selective media, but not in combination media), and double resistance, i.e. multi-resistance to two antibiotics (growth in both single-drug and combination selective media).

Fig 1 shows the number of populations with resistance in each treatment. Purely wild-type populations were capable of evolving single-drug resistance in single-drug environments, but were incapable of evolving double resistance in the combination treatment. The presence of mutators, and selection for resistance, were both required to observe the evolution of double resistance. In populations where mutators were introduced, but no antibiotics applied, only single-drug and mixed resistance evolved. However, when exposed to selection for resistance, a considerable proportion these populations evolved double resistance (23.3%–61.7%).

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Fig 1. Multi-resistance evolves in populations where mutators are present in both single-drug and combination drug treatments.

A. Dynamics over the course of the experiment. B. Summary of outcomes across treatments after the final transfer. ‘Resistance type’ is characterised by growth on single-drug (‘rifampicin resistance’, ‘nalidixic acid resistance’) or combination (‘double resistance’, i.e. multi-resistance to two antibiotics) selective media; ‘mixed resistance’ refers to growth on both single-drug media, but not combination selective media. Initial mutator frequencies were 0.06 for ‘low’, 0.1 for ‘intermediate’ and 0.3 for ‘high’. MIC_WT–minimum inhibitory concentration of the wild-type.

https://doi.org/10.1371/journal.pgen.1010791.g001

Using a Bayesian mixed-effects model (see S1 Appendix), we analysed the effects of mutator frequency and treatment on resistance at the end of the experiment (incorporating only main effects, as an interaction term did not significantly improve the fit; see Table A and Fig A in S1 Appendix). There was a positive association between the initial mutator frequency and the proportion of populations with double resistance, although with overlapping 95% C.I.s [low = 5.41 (3.57, 7.39), intermediate = 5.98 (4.36, 8.26), high = 8.01 (6.35, 10.28)]. The combination treatment was most effective overall at suppressing resistance. Nonetheless, we were surprised to find that double resistance was more likely to emerge in the single-drug treatments than the combination treatment [rifampicin = 7.80 (6.21, 9.97), nalidixic acid = 5.20 (3.71, 7.36), combination = 4.22 (2.78, 6.33)].

Phenotypic and genomic characterisation of evolved multi-resistant isolates arising during ramping selection experiment

We assayed growth phenotypes of evolved multi-resistant isolates. There was a strong correlation between growth in minimum and maximum concentrations of the combination treatment (i.e. 0 mg/l and 20 mg/l) (Fig 2A, Bayesian multivariate regression: r = 0.73, 95% C.I.: (0.57, 0.84), see Fig B and Table B in S1 Appendix). There was little effect of either initial mutator frequency or the number of acquired mutations on fitness of the evolved isolates, which may potentially be explained by counterbalancing effects of acquiring both deleterious and beneficial mutations.

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Fig 2. Phenotypic and genomic changes underpinning multi-resistance evolution in mutators.

A. Relationship between growth of multi-resistant mutants under initial and final conditions of the selection experiment. Inset shows the relationship between growth and number of acquired mutations for antibiotic-free medium (solid line, open points) and 20 mg/l of the combination treatment (dashed line, filled points). Growth is measured as area under the curve of OD 600 nm growth curves taken over 22 h. B. Mutations identified in canonical drug resistance targets for rifampicin and nalidixic acid resistance. C. Number of mutations identified in each sequenced multi-resistant isolate. D. Spectrum of spontaneous SNPs is dominated by transitions. E. Number of mutations detected by whole genome sequencing is positively associated with mutation rate in multi-resistant isolates (measured by fluctuation test to streptomycin resistance on n = 8 isolates, p- value = 0.013, R² = 0.50).

https://doi.org/10.1371/journal.pgen.1010791.g002

We performed whole genome sequencing and variant calling for a subset of multi-resistant isolates that arose in the combination treatment (see S2 Appendix). We found mutations in genes related to rifampicin and nalidixic acid resistance, as well as multi-drug efflux pumps (Fig 2B, and Table A in S2 Appendix). All isolates acquired mutations in the gene encoding the target of rifampicin, RNA polymerase subunit rpoB, with one strain acquiring an additional mutation in rpoC. All isolates acquired mutations in the gene encoding the target of nalidixic acid, DNA gyrase: 23/29 isolates possessed a single mutation in the gyrA component, 3/29 possessed a single mutation in the gyrB component, and 3/29 acquired mutations in both gyrA and gyrB. Diverse SNPs were observed for rpoB and gyrA. There was a significant association between specific SNPs occurring in rpoB and gyrA (Fisher’s exact test, p = 0.04), which arose because the pair rpoB D516G and gyrA D72G occurred 5 times in total. Most strains (23/29) also acquired mutations in multi-drug efflux pump genes and/or their regulators, the most frequent being acrR (9/29), a repressor involved in the AcrAB-TolC system [51]. However, efflux pump mutations included both synonymous substitutions and putative loss-of-function mutations in structural components, which are unlikely to improve resistance.

In addition to mutations the canonical targets of both antibiotics, we detected mutations across the genome (median = 34, range = 25–162, Fig 2C). The mutational spectrum of SNPs was dominated by transitions (Fig 2D), which is characteristic of the specific ΔmutS mutator allele introduced here [52, 53]. While some of this additional variation likely affected fitness, there was little association between the number of mutations identified through whole genome sequencing and growth (Fig 2A). Many mutations observed were likely to be selectively neutral, as 283/1252 (22.6%) of all mutations detected were synonymous SNPs. There was a negative association between mutator frequency and number of mutations acquired, although the estimated 95% C.I. of the slope overlapped with zero [Bayesian linear regression slope = −49.93, 95% C.I. = (−108.78, 8.53)]. Notably, we identified exceptionally high numbers of mutations in 4/29 isolates (three isolates with 62, 99, and 162 mutations each from the ‘low’ treatment, and one isolate with 60 mutations from the ‘intermediate’ treatment). We therefore assessed whether mutation rate itself had evolved during the experiment by measuring the mutation rates of eight multi-resistant isolates (the four mentioned above and four matched isolates from the same treatments), in comparison with the original ΔmutS strain and the wild-type. There was a positive association between estimated mutation rate and number of mutations each isolate had acquired during selection (Fig 2E). While three evolved isolates had estimated mutation rates approximately equal to (or slightly lower than) ΔmutS, five had increased mutation rates, ranging from 3-fold to 51-fold greater than ΔmutS—among most of these, we detected mutations in DNA replication and repair genes (Table B in S2 Appendix).

Stochastic simulations reveal key mechanisms of multi-resistance evolution

To gain insight into the drivers of multi-resistance evolution, including the requirement for different classes of mutations observed, we used a stochastic population-dynamic simulation model. We produced a minimal model capable of predicting multi-resistance evolution, i.e. we included only a single allele for each resistance type, and excluded multi-drug resistance mechanisms, spontaneous double mutants, recombination, and mutations at non-resistance-conferring loci. Disallowing these types of variation permitted us to test hypotheses regarding the roles of selection and mutation supply on the emergence of multi-resistance. Populations initially contained only sensitive individuals, which we denote S for the wild-type (and S′ for the mutator, if present, differing only in mutation rate from the wild-type). During growth, single mutations can occur, giving rise to rifampicin-resistant type R (and R′) and nalidixic acid resistant type N (and N′). Subsequently, R and N (and R′ and N′) can each give rise to multi-resistant type D (and D′). We used a stochastic approach because it more accurately captures the dynamics of mutations that arise in a single cell, i.e. they occur as random events [54–56]. For each set of conditions, we simulated 1000 populations with a maximum population size of 5.71 × 10⁸ bacteria, equivalent to the maximum density observed in the selection experiment. Simulation parameters relating to growth were estimated empirically from growth curve data using strains that were derived from fluctuation tests and therefore independent from the selection experiment (Fig D in S3 Appendix; see S3 Appendix for full details on the curve fitting procedure). Mutation rates of our wild-type and mutator strains were estimated in previous work [24, 57].

This simulation model captured the major features of the wet-lab experiments (Fig 3, cf. Fig 1), i.e. that multi-resistance was constrained to populations treated with antibiotics, including single antibiotic treatments, and that the presence of mutators facilitated multi-resistance evolution. A Bayesian categorical model fitted to these simulations produced parameter estimates that closely matched those from the experimental data, demonstrating that the simulations quantitatively recapitulate the experiments (Fig H in S3 Appendix). For the nalidixic acid treatment, one notable difference was a higher probability of mixed resistance in the experiment than the simulation [experiment = 2.84 (2.18, 3.53) vs. simulation = −2.58 (−4.21, −1.21)]. This can be explained by the simulation overestimating transitions from mixed resistance to double resistance if there were additional costs of double resistance in the nalidixic acid environment that were not captured by our model (e.g. differences in lag time).

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Fig 3. Simulated resistance evolution allowing only sequential acquisition of resistance recapitulated the emergence of resistance in experiments, suggesting elevated single-drug resistance mutation rates are sufficient to explain multi-resistance evolution.

Resistance type was determined in an equivalent manner to experimental data in Fig 1 (i.e. if at least on individual of each type was detected in a random sample of 1/200 of each population, see Methods). The schematic depicts the the simulation approach, where λ_i refers to the reproduction rate of Type i, and μ_j refers to the mutation rate to resist antibiotic j (see S3 Appendix for full details). Parameters used in simulations are shown in Fig D in S3 Appendix.

https://doi.org/10.1371/journal.pgen.1010791.g003

Note that a small fraction of simulated populations consisting only of wild-type individuals evolved multi-resistance (between 0/1000 and 15/1000, depending on treatment); this is consistent with expectations from our experimental results (< 1/60 per treatment). As the simulation excludes the possibility of multi-resistance emerging through a single reproductive event, this suggests that multi-resistance can emerge without invoking multi-drug resistance mechanisms (e.g. efflux pumps), simultaneous acquisition of two resistance mutations, or recombination.

Simulations enabled us to observe the dynamics of multi-resistance evolution. Fig 4A and S1 Fig demonstrate that, while selective sweeps for single-resistance were observed in all antibiotic treatments, multi-resistance only swept to fixation in the combination treatment. Moreover, although the combination treatment was more effective at preventing the emergence of multi-resistance, once it had emerged, it facilitated the sweep of multi-resistance toward fixation. Within populations, Fig 4B shows the most commonly observed evolutionary trajectory to multi-resistance, S′ → R′ → D′ (examples of other trajectories can be found in S2 Fig). In general, single resistance arose early in the mutator genetic background, but remained at low frequency until it conferred a fitness benefit over the sensitive type. Once the single-resistant lineage began to increase in frequency, a subsequent mutation producing the multi-resistant type emerged. In some cases, resistant types can be lost due to population bottlenecks (as is the case for N′ in Fig 4B and R′ and D′ in S2 Fig); these may re-emerge and go on to found a D′ type lineage, or ultimately go extinct. R′ and N′ types can sometimes emerge and co-exit without going extinct, ultimately leading to two independent lineages resulting in D′ type individuals.

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Fig 4. Population dynamics of simulated resistance evolution.

A. Number of bacteria of each resistant type for the four simulated treatments (interquartile range, IQR, over n = 1000 replicate simulations). Results shown from the ‘intermediate’ initial mutator frequency (u = 0.1; other frequencies are shown in S1 Fig). B. Muller diagram showing typical progression from sensitive to multi-resistant in the combination treatment within a single population. In the combination treatment, multi-resistance most commonly emerged via S′ → R′ → D′ in the mutator genetic background (examples of other paths are shown in S2 Fig). Height of each area corresponds to the population size of each type. Example shown is a single replicate from the ‘intermediate’ initial mutator frequency (u = 0.1) treatment.

https://doi.org/10.1371/journal.pgen.1010791.g004

Simulating other conditions

To evaluate the generality of these findings with regard to mutators, we ran further simulations with different parameter values. We first explored different dose escalation schemes, varying the amount of time until inhibition is achieved. We found that the presence of mutators facilitates multi-resistance evolution across a range of dose-escalation schemes (Fig I in S3 Appendix).

We next assessed whether our findings are specific to the particular empirical parameters we estimated (Fig D in S3 Appendix). We used parameter values that produce logistic growth with an imposed ‘cost of resistance’ under the antibiotic-free condition [58]. Even with these parameter values, we observed the evolution and spread of multi-resistance under the same conditions as occurred using our empirical estimates (Fig J in S3 Appendix).

Considerable attention has been given to how interactions between pairs of antibiotic can improve (‘synergistic’) or worsen (‘antagonistic’) their efficacy when used in combination [3, 13, 17–19, 59]. Synergistic combinations have been found to enhance resistance evolution, and antagonistic pairs to suppress it [13, 19]; our simulations concur with these findings, and also suggest that mutators may allow populations to overcome the ability for antagonistic combinations to suppress resistance evolution, to some extent (Fig K in S3 Appendix).

Finally, we explored whether large population sizes could allow multi-resistance evolution in the absence of mutators. We found that, in the combination treatment, population sizes > 5.71 × 10¹⁰ evolve multi-resistance in the absence of mutators at an appreciable rate (Fig L in S3 Appendix), although this represents a population size much larger than most typical infections [60–63].

Strains and media

Selection experiments involved ‘wild-type’ E. coli str. K-12 substr. BW25113 [F-, Δ(araD-araB)567, ΔlacZ4787(::rrnB-3), λ-, rph-1, Δ(rhaD-rhaB)568, hsdR514] [103], and a ‘mutator’ strain ΔmutS (as above, but with ΔmutS738::kan, indicating ΔmutS replacement with kanamycin resistance). The kanamycin resistance cassette has not previously been observed to affect resistance to the antibiotics we have considered here [24, 57]. Both strains were obtained from Dharmacon, Horizon Discovery Group, UK. Relative to the published reference genome [104], whole genome resequencing revealed no pre-existing mutations in the wild-type BW25113 background, and a single point mutation in the ΔmutS strain (1,985,889 G>A, resulting in an amino acid substitution in pgsA A137V), which does not have a known association with resistance.

Routine culturing was performed in lysogeny broth [LB, 10 g/l tryptone (Fisher Scientific, UK), 5 g/l Bacto yeast extract (BD Biosciences, UK), 10 g/l NaCl (Fisher Scientific, UK)]. Selection experiments in the presence of antibiotic(s) were performed in Müller-Hinton broth (MH broth, 23 g/l, Sigma-Aldrich, UK). MH is a preferred medium for use with antibiotics [105]. Solid media were made by adding 12 g/l agar (BD Biosciences, UK) to either broth prior to autoclaving. Stock antibiotic solutions were prepared at 10 mg/ml. Rifampicin (Fisher Scientific, UK) was dissolved in methanol (Fisher Scientific, UK), and nalidixic acid (Fisher Scientific, UK) was dissolved in double distilled water, with 1N NaOH (Fisher Scientific, UK) added drop-wise until the antibiotic was solubilised. Strains were stored in LB with 40% glycerol at −80°C.

Experimental evolution under single-drug and combination treatments

Growth parameters of single- and multi-resistant clones

To determine the effects of single and multi-resistance on growth parameters, we selected five nalidixic acid resistant and five rifampicin resistant clones arising from the wild-type BW25113 genetic background via fluctuation tests [114], using an established protocol [115]. Briefly, 1 ml LB cultures of E. coli K-12 BW25113 were grown overnight in 96-well deep-well plates. The entire volume of each culture was plated on MH agar supplemented with rifampicin (50 mg/l) or nalidixic acid (30 mg/l) in the wells of a 6-well plate (each well approximately 35 mm in diameter). These 6-well plates were incubated for 48 h. To select multi-resistant clones, we performed a second fluctuation test using resistant strains from the first, plating on the antibiotic to which they were not already resistant. Colonies were isolated from selective plates, grown overnight in LB medium, and then stored at −80°C.

Growth curves were generated by measuring optical density (OD) at 600 nm every 30 min for 45 h using a BMG FLUOstar OMEGA with Microplate Stacker (BMG Labtech, Ortenberg, Germany). Each clone was grown in duplicate at 37°C under each of the antibiotic concentrations experienced during the selection experiments (i.e. 0.625, 1.25, 2.5, 5, 10, 20 mg/l each of rifampicin and/or nalidixic acid). Cultures were initiated by first growing clones overnight in 200 μL MH broth, then diluted 1/200 into a total volume of 200 μL MH broth containing one or both antibiotic(s). The growth curves were used to estimate growth rate and carrying capacity parameters for the stochastic simulation model using a custom MATLAB script (see ‘Data availability’ statement). The fitting procedure is described in full in S3 Appendix. We estimate r_i and k_i for resistant strains, rather than a simple growth threshold (e.g. MIC) because it directly relates to the population growth, mutation and selection occurring in this system. Moreover, we estimated growth parameters for each concentration, instead of imposing mechanistic constrains across environments and concentrations, because it allows for a more generalisable result.

In addition to fitting growth curves, we also summarised growth curves into a single metric, area under the curve (AUC, Fig A in S3 Appendix), as the empirical growth curves did not follow a standard logistic shape (which we also account for in the simulations below). We calculated AUC using the SummarizeGrowth function from the R package growthcurver [116]. AUC incorporates all of lag phase, growth rate, and density, and highly repeatable. Comparing the effect of the single-drug and combination concentrations on AUC, the effects of the antibiotics appears to be additive. To determine whether multi-resistance conferred a benefit under single-drug treatments, we fit a Bayesian multivariate linear regression model of AUC of different strains in the presence of each treatment over all concentrations (described in full in the S1 Appendix).

Using the same protocol as above, growth curves for the multi-resistant clones that evolved during the selection experiment (all in the mutator genetic background) were measured in antibiotic-free medium, and in 20 mg/l of the combination treatment. The association between AUC, initial mutator frequency and treatment was analysed using a Bayesian multivariate regression model (described in full in S1 Appendix).

Mutation rate estimates and the probability of spontaneous double mutants

Mutation rates to rifampicin resistance (μ_R = 6.7 × 10⁻⁹ per cell division) and nalidixic acid resistance (μ_N = 7.4 × 10⁻¹⁰ per cell division), were obtained for the these strains in a previous publication [57], as was the mutator effect of ΔmutS (80-fold increase relative to wild type) [24]. Given that each antibiotic has independent targets, we assume that mutation rates to rifampicin resistance and nalidixic acid resistance are equal for wild-type and single-resistant strains, and constant across environments.

As each resistance arises independently, we can estimate the probability of simultaneously acquiring both resistance mutations during a single replication event (i.e. a ‘spontaneous double mutant’) for the wild-type as the product of their mutation rates to resistance [1, 25], i.e. μ_Rμ_N = 5.0 × 10⁻¹⁸, and for mutators as μ_Rμ_N × 80² = 3.2 × 10⁻¹⁴. We can use these probabilities to obtain a rough estimate for the probability of observing a spontaneous double mutant by simulating a fluctuation test using rflan() from the R package ‘flan’ [117]. We performed 10⁶ simulations using the same parameters as the selection experiment (i.e. 60 independent populations, days 1–4 permitting wild-type growth, maximum population size of 5.71 × 10⁸). For populations comprising only wild-type individuals, no spontaneous double mutants were observed in 10⁶ simulations. For populations comprising solely mutators, a spontaneous double mutant was observed in 4210 out of 10⁶ simulations. Hence, the probability of having observed a spontaneous double mutant in the experimental setup seems likely to be very low.

Whole genome sequencing and mutation identification

Whole genome sequencing was performed as described in S2 Appendix. Briefly, sequencing was performed on thirty multi-resistant isolates from the combination treatment. Genome sequencing was performed by MicrobesNG (http://www.microbesng.com, Birmingham, UK) according to their protocols (provided in S2 Appendix). Trimmed reads were then aligned to a reference genome and variants called using the breseq 0.36.1 pipeline [118, also see https://github.com/barricklab/breseq/]. The reference genome used was the E. coli K-12 BW25113 genome [104, NCBI accession CP009273.1], with additional annotations for insertion (IS) element regions to improve the calling of mutations related to IS insertion (modified Genbank format file, S1 File). One genome sequence did not correspond to E. coli K-12 BW25113 and was therefore discarded, leaving n = 9 genomes for the ‘low’ mutator treatment and n = 10 genomes for the ‘intermediate’ and ‘high’ mutator treatments. Genes relating to drug efflux, drug uptake, and DNA replication and repair were identified using the Ecocyc database (https://ecocyc.org [119]).

Fluctuation tests on evolved multi-resistant isolates

Fluctuation tests were performed as previously described in ref. [115]. Briefly, ancestral BW25113, ΔmutS and eight evolved multi-resistant strains (four with ≥ 60 mutations identified by whole genome sequencing, and four randomly selected) were streaked from −80°C stocks onto LB agar and incubated overnight at 37°C. One colony each was inoculated into 5 ml of MH broth and grown overnight at 37°C and 250 rpm shaking. Cultures were diluted to an OD of approximately 0.3, and subsequently diluted 1000-fold into MH broth. For each strain, 16 parallel cultures of 300 μL were pipetted into deep-well 96-well plates and grown for 24 h. Each parallel culture was then pipetted onto selective media, i.e. TA agar with 25 μg/L streptomycin. Resistant mutants (m counts) were counted after 48 h growth. For each isolate, final population sizes (N_t counts) were estimated from n = 3 randomly-selected parallel cultures by serial dilution (to 10⁻⁶) and plating on TA agar. Mutation rates were estimated from m and N_t counts using mutestim() from the R package ‘flan’ [117].

Stochastic population dynamics model

We numerically simulated resistance evolution using a stochastic population dynamic model according to the schematic in Fig 3. Model variables and parameters are described in full in Table A in S3 Appendix. The model describes four types of resistance i ∈ {S, R, N, D}, where S is antibiotic sensitive, R is rifampicin resistant, N is nalidixic acid resistant, and D is multi-resistant. We write i′ to refer to a type i with a mutator background (Fig 3). Here we consider a mutator that only differs in mutation rate from the wild-type, hence all growth parameters for types i and i′ are equal. Simulated populations were initiated with 5.71 × 10⁶ sensitive individuals; this is our estimate of the starting population size in the experiments obtained by serial dilution plating. Of the initial population of sensitive individuals, a fraction u were designated mutators, Type S′ (u = 0, 0.05, 0.1, or 0.3, approximating the observed frequencies in the ‘none’, ‘low’, ‘medium’ and ‘high’ mutator treatments) and the remaining 1 − u were designated wild-type, Type S (i.e. non-mutators). Bacterial growth was modelled as a Yule-Furry process, which has been used in many studies to describe resistance evolution [120–123] (see S3 Appendix). Note that this is a pure-birth process; the model makes the assumption that death, e.g. due to senescence or antibiotics, is negligible relative to the effect of periodic population bottlenecks (see below). We additionally allowed the reproduction rate to depend on population density (which provides equivalent results to continuous-time Gillespie simulations, but with reduced computational time; see Fig F in S3 Appendix).

At the start of the simulation, there were no Type R/R′, N/N′, or D/D′ individuals. Single-resistant Types R/R′ and N/N′, individuals must initially arise by mutation in reproduction events of Type S/S′ individuals. Once single resistant types exist in the population, they may produce further such individuals by reproduction. In reproduction events of individuals of Types R/R′ or N/N′, a subsequent mutation can occur, producing Type D/D′ individuals. Type D/D′ individuals may also reproduce, but we do not include further mutations in the model. We write μ_R/μ_R′ for the probability with which an offspring acquires resistance to rifampicin by mutation, and μ_N/μ_N′ for the probability that the offspring acquires resistance to nalidixic acid. We exclude the possibility that both resistance mutations can be newly acquired in the same reproduction event (i.e. no multi-drug resistance mechanisms, and no double-mutation events, which we have shown in the preceding section to be rare).

As the experiment involved a serial transfer protocol, population bottlenecks of 1/200 every 22 h were also simulated. Other parameter values were set to match the experimental procedure (initial frequency of mutators, dilution, duration of experiment; see Table E in S3 Appendix). Parameter values for growth rates and carrying capacities were estimated from OD growth curves using strains that were derived in an experiment independent of the selection experiments (see Figs B and C in S3 Appendix). The relationship between optical density and colony forming units was used to convert between OD units and numbers of bacteria (see Fig E and Table D in S3 Appendix).