Strains

E. coli K-12 strains KX1102 (luxS+lsrK+ Ara+ ΔlacZYA::Cm), KX1200(ΔluxS::Cm lsrK+ Ara+) and KX1228 (ΔluxSlsrK+ Ara+) were derived from the wild-type K-12MG1665 (luxS+lsrK+ Ara+)37. The lsrK::Cm deletion in the parent of KX1448 (luxS+ΔlsrK Ara+) was constructed by Karina Xavier using the red swap protocol described by Datsenko and Wanner38. To eliminate the Cm-resistance cassette, the FLP recombinase expressing plasmid pCP20 was introduced in the parent yielding KX1448 (ref. 38). E. coli B strain REL606 (luxS+ΔlsrKAra−) is the ancestor of all B strains used in this study. REL607 (luxS+ ΔlsrKAra+) is a spontaneous Ara+ revertant from REL606 (ref. 17). REL8593A Ara-1 (luxS+ΔlsrK Ara−) was derived from REL606 after 20,000 generations of batch culture in a glucose-limited environment17,39. During experimental evolution the fitness of REL8593A increased by ~70% relative to REL606 and REL607 via several beneficial mutations39. REL8593A retains the ancestral mutation rate40. Strains in cocultures are distinguished by a visible arabinose (Ara) marker or Cm-resistance marker. B and K-12 strains used in this study possess an rpoB gene with an identical DNA sequence and it is located on the same position within the genome.

Media

We used Milli-Q water for all media. Tetrazolium arabinose agar (TA) and Davis minimal medium (DM) were prepared according to Lenski et al.17 (on TA agar Ara− strains are red, and Ara+ strains are white or pinkish). Magnesium, thiamine, carbon source (3 g l−1 L-arabinose or various concentrations of D-glucose), tetrazolium red (Sigma T8877) and 0.5 mM aspartate dipeptide (BACHEM) were sterile filtered and added to a cooled medium as necessary. Selective TA medium is TA supplemented with freshly prepared antibiotic 50 μg ml−1 rifampicin. For KX1102, selective TA was supplemented with both 50 μg ml−1 of rifampicin (Rif) and 25 μg ml−1 of Cm. For all cell dilutions, sterile saline (8.5 g l−1 NaCl) was used. Media were solidified as necessary with 15 g l−1 of agar (Difco).

Fluctuation tests

We used fluctuation tests designed by Luria and Delbrück15. Specifically, strains were first inoculated from frozen stock and grown in 10 ml liquid LB medium at 37 °C (shaken at 120 r.p.m.) to OD 600 =~1 (~7 h). As a preconditioning step, each strain was transferred (via a 2,000-fold dilution) to 10 ml of non-selective liquid DM medium supplemented with a particular concentration (80–1,500 mg l−1) of glucose and allowed to grow overnight at 37 °C (120 r.p.m.). Cells were again diluted into fresh medium giving N 0 (the initial number of viable cells, containing no rifampicin resistant, RifR, mutants) of ~7,000. The same medium was used as in the preconditioning step. Where N 0 included two strains, they were distinguished by alternative Ara- or Cm-resistance markers. Three volumes of cultures were used: 1 and 1.5 ml cultures were grown in 96 deep-well plates, and 10 ml cultures in glass universal tubes. Cultures were then grown to saturation (24–28 h at 37 °C at 250 r.p.m.). To minimize spatial effects, we positioned each independent culture on the plate randomly. The final number of viable cells, N t , was determined by plating an appropriate dilution on solid non-selective TA medium. N t was calculated with 3–6 cultures per mutation rate estimate. Evaporation (routinely monitored by weighing plate before and after incubation) was accounted for in the N t value. For 1 ml cultures, this was on average 12% of the population density, calculated per millilitre of the medium. We obtained the observed number of RifR mutants, r, by plating the entirety of remaining cultures (at least 12 per estimate) onto solid selective TA medium that allows spontaneous RifR mutants to produce colonies. Plates were incubated at 37 °C and mutants were counted at the earliest possible time after plating. For Rif plates, this was 44–48 h, when both Rif and Cm were used the incubation time was 68–72 h.

For Figs 1a,b and 2a,b and Fig. 3 we used 10, 18, 13, 7 and 6 independent experimental blocks, respectively. Across Fig. 1a,b, the number of plates per estimation is at least 12 (median=17, interquartile range 13–21), across Fig. 2a,b is at least 17 (median=21, interquartile range 20–21) and across Fig. 3 is at least 21 (median=21, interquartile range 21–23).

Estimation of mutation rates

For calculating the number of mutational events m, we used the Ma–Sandri–Sarkar maximum-likelihood method41,42. This method is valid over the entire range of values of m43,44 and is implemented by the FALCOR web tool45 that uses Stewart’s Equation 1 to calculate s.d. of m46. The mutation rate per cell per generation, μ, is calculated as m divided by the number of cells at risk, N t . Only values of m >0.3 were considered to be valid44 and were analysed further.

Fitness assay

In two-strain fluctuation tests, the neutral Ara marker or Cm resistance allowed us to assess the initial and final number of viable cells (N 0 and N t respectively) of the two strains. From these values we calculated each strain's realized Malthusian parameter log(N t /N 0 ). Relative fitness (w rel ) was then calculated as the ratio of the realized Malthusian parameters17, averaged across 3–6 replicates. When we used one strain in a fluctuation test w rel was designated as 1. Absolute fitness (w abs ) was measured as number of generations (G) per 24 h, calculated as G=log 2 (N t /N 0 )/t, where t is time in days.

In vitro synthesis of AI-2

In vitro synthesis of (S)-DPD (AI-2) was carried out as previously described47. We supplemented DM medium with 1, 10, 100, 400 and 1,000 μM of synthetic AI-2.

Bioluminescence assay

Standard bioluminescence assay was performed according to Surette and Bassler48. Bioluminescence were integrated across a 16-h culture of Vibrio harveyi BB170, ATCC number BAA-1117, at 30 °C with aeration in AB medium, with the given concentration of DPD. Overnight cultures were diluted to an OD 600 of 0.2 and then further diluted to 1:5,000 in fresh AB medium. Cultures (180 μl) were then aliquotted in a 96-well plate. Bioluminescence was recorded every 30 min using a Biotek Synergy-2 luminometer.

Quantitative real-time PCR

Primers were designed using the tool available at Invitrogen (http://tools.lifetechnologies.com/content.cfm?pageid=9716) to give a product between 70 and 200 bp. Primer sequences are the following: lsrB forward (F): (5′-CCCAGTGTTTCTGGTCAGGT-3′) and reverse (R): (5′-AACCGCAGAAACGATAATGG-3′), lsrK F:(5′-TCGACACCTATACGCTGCTG-3′) and R:(5′-CGCAGGTGATACCAGGTTTT-3′), dinB F:(5′-ACGCCTACAAAGAAGCCTCA-3′) and R:(5′-TTGCAGCTCGTTGAAGATTG-3′), umuC F:(5′-TGGGGGATTTCTTCAGTCAG-3′) and R:(5′-TTCCTCTGCCCTCTTTAGCA-3′). The duration of the reverse transcription reaction was 60 min at 45 °C, the reaction was stopped at 95 °C for 15 min. Reverse transcription products were subjected to 50 cycles of PCR amplification (1 min at 95 °C for denaturation, 1 min at 62 °C for annealing and 30 s at 72 °C for extension). At the end, we run a dissociation curve by gradually increasing temperature from 55 to 95 °C (0.2 °C per second). The iScript One-Step RT-PCR Kit with SYBR Green was used. All reactions were performed with Bio-Rad (M J Research) Chromo4 real-time PCR machine, and we used Opticon Monitor 3 for analysis.

Analysis of published expression data

Data were taken from the Colombos transcription database version 2 (20131118), containing 131 different studies covering a wide range of environmental and genetic perturbations in E. coli23. For all combinations of genes of interest, rank correlations of expression and associated P values were calculated across samples within a single study. In each case, the median value of the correlation and P value was calculated across studies, weighted by –log 10 (P) (that is, a weighting from 0 to 16, the limit of numerical accuracy, in favour of studies where strong correlations were found or that were powerful enough to find weaker correlations). We included all studies where there was sufficient data to calculate both full and partial correlations. For partial correlations this requires that, when controlling for correlations with N other genes, there are at least N+3 samples with data for all N+2 genes. Ninety-six studies met these criteria for all genes of interest and were included. Only two example of genes of interest were taken for each subgroup, as increasing the number of genes reduces the number of studies in which there are sufficient data available to calculate correlations. However, similar results are found using different representative genes.

Statistical analysis

All statistical models were fitted using the nlme package in R49. This enabled the inclusion within the same model of experimental factors (fixed effects), blocking effects (random effects) and factors affecting variance (giving heteroscedasticity). Note that many of the models are heteroscedastic and accounting for this involves fitting one or more parameters. Therefore, the P values used in model simplification (comparing two models one with and one without an effect of interest, where heteroscedasticity parameter(s) may be fitted differently in each case) will not be identical to the P values given in the ANOVA tables for effects within a single model (Supplementary Tables 1–10). To see how we tested model assumptions, see Supplementary Note 1, Supplementary Figs 12 and 13 and Supplementary Table 11. Box–Cox power transformations50 of mutation rate in models with mutation rate as the response consistently gave a maximum likelihood for a power (λ) significantly <1 (untransformed mutation rate), and not significantly different from zero (log-transformed mutation rate); see Supplementary Fig. 14. Therefore, log 2 -transformed mutation rate was considered in all the models below. The same was true of modelling bioluminescence (Model 5 below). Details of models and their fitting are given below and diagnostic plots in Supplementary Figs 15–24. ANOVA tables for each model are given in Supplementary Tables 1–10. Where relevant in those tables, the level of a factor is given in parentheses next to an effect (for example, ‘Intercept (wild-type)’ implies that the intercept is the value for the wild-type, and a subsequent ‘Strain’ effect will be the difference of another strain considered from that).

Model 1

The model giving the fitted line in Fig. 1a is the log 2 mutation rate as a function of absolute fitness (w abs ). A random effect of experimental block explained only a tiny proportion of the variance (6.0 × 10−8) and was, therefore, not included in the final model (the same applies to each of the models below). Various experimental effects could in principle affect the variability of results (heteroscedasticity), specifically: experimental blocks again and their order, the number of plates used to estimate the final population size and the number of mutation events (m), the estimated value and coefficient of variation of m, the estimated density of the culture (D) and fitted value of the mutation rate, the estimated inoculum size, the proportion of the culture remaining following evaporation and glucose concentration ([glc] treated as either a continuous or discrete variable). Models including each of these effects were fitted and compared, plus models containing combinations of effects that individually improved the model. The best model (lowest Akaike information criterion, AIC) was achieved allowing the variance to change as [number of plates used to estimate the final population size]–1.6. See Supplementary Table 1, Fig. 1a and Supplementary Fig. 15.

Model 2

Glucose concentration ([glc]), absolute fitness (w abs ), final culture density (log 2 (D)) and relative fitness (w rel ), plus all interactions, were considered as explanatory variables for mutation rate measured for strains in cocultures including both ancestral and evolved strains (20,000 generations in minimal glucose). To minimize any issues with error in these explanatory variables (Supplementary Note 1), the median (for example, D med ) of each of these values was used within each strain–environment combination (where environment includes nutrient, competitor strain, culture volume and growth period; for D med there were 2 (median) 1.25–3 (interquartile range) measurements for each of 30 unique strain–environment combinations). There is also potential for pseudoreplication in the cases where mutation rate estimates for both strains in a culture were available (Fig. 1b). This was accounted for by including a random effect of culture (nested within experimental block) in the model (giving s.d.=0.56 and 0.45 at block and culture level respectively, with residual s.d.=81). This model was simplified, sequentially removing non-significant effects not required in higher-level interactions until any further removal resulted in a significantly worse model (LR test P<0.05, that is, finding the minimal adequate model). Heteroscedasticity relating to experimental variables was tested for as above, including the effect of strain (either the strain for which the mutation estimate was made or the cocultured strain, either separating the alternatively marked versions of the ancestral B strain or not) and competition time (in hours). The resulting model contained only the effect of final culture density (log 2 (D)), with variance increasing as [number of plates used for estimating the number of mutational events]–2.0. See Supplementary Table 2, Fig. 1b and Supplementary Fig. 16.

Model 3

Mutation rate was considered as a response to strain (wild-type K-12 or ΔluxS), cocultured strain (in monocultures this was the strain itself and in cocultures the wild-type B strain REL606) and density (log 2 (D), centred on the average density: log 2 (D) centred ) and their interactions. Testing the experimental variables as above, significant heteroscedasticity among strains was identified in the final model with the ΔluxS mutant strain having 1.4 times the variance of the other strains and variance increasing as [number of plates used to estimate the final population size]–1.0. This model was simplified by sequentially removing non-significant effects not required in higher-level interactions until any further removal resulted in a significantly worse model (LR test P<0.05, that is, finding the minimal adequate model). The resulting model contained no effect of cocultured strain, only the effect of strain, final culture density (log 2 (D) centred ) and their interaction. See Supplementary Table 3, Fig. 2a and Supplementary Fig. 17.

Model 4

The difference in mutation rate between two strains in coculture was considered as function of final population density (log 2 (D), centred on the average density: log 2 (D) centred ), strain pairing (wild-type K-12, ΔluxS or ancestral B Ara+, each paired with ancestral B Ara−) and their interaction. Heteroscedasticity associated with experimental variables was tested for as above, although where appropriate, variables were tested for each cocultured strain separately (either the ‘winning’ or ‘losing’ strain) and together (for example, when asking whether the number of mutational events estimated had an effect on variance, the numbers for each strain separately and the total number of events for both strains were all tested). Variance was found to increase with [fitted value]1.3 and to be 2.7-fold greater in competitions where the B Ara+ strain was out-competed. The fitted lines for K-12 wild-type and ancestral B Ara+ were very similar, giving non-significant treatment contrasts between them (P=0.11 for both the main effect and interaction with density) and with higher P values than contrasts between other pairs of strains. Therefore, these two strains were combined, which improved the model (lower AIC, LR 7,9 =4.4, P=0.11). See Supplementary Table 4 and Supplementary Figs 4 and 18.

Model 5

log 2 (Bioluminescence), where Bioluminescence is integrated over the course of the experiment, was considered as a response to the concentration of DPD added ([DPD]), the batch of DPD used and their interaction. The interaction was non-significant (LR 8,7 =2.3, P=0.13) but both main effects were significant. Heteroscedasticity relating to experimental variables was tested for as above, variance increasing significantly as [fitted value]42 and with decreasing DPD concentration (relative variance of 1 for 6.25 μM DPD, 0.2 for concentrations of 12.5–50 μM and 0.066 for 100 μM). See Supplementary Table 5, and Supplementary Figs 5 and 19.

Model 6

Mutation rate was considered as a response to strain (wild-type (K-12) or ΔluxS), DPD concentration and their interaction. As the shape of any DPD concentration response was unknown, power transformation was used (Box–Cox as above), which gave a maximum likelihood for a transformation close to logarithmic (λ=0.099). This model was simplified, sequentially removing non-significant effects (not required in the interaction) until any further removal resulted in a significantly worse model (LR test P<0.05; that is, finding the minimal adequate model). Heteroscedasticity associated with experimental variables was tested for as above. Variance was found change as [number of plates used to estimate the mutation rate]−2.6. The resulting model contained only the effect of DPD concentration. See Supplementary Table 6 and Supplementary Fig. 20.

Model 7

Mutation rate in the ΔluxS CM-marked mutant was considered as a response to culture density (D), competitor (wild-type K-12 or ΔluxS), aspartate (presence/absence) and all possible interactions. This model was simplified, sequentially removing non-significant effects not required in higher-level interactions until any further removal resulted in a significantly worse model (LR test P<0.05, that is, finding the minimal adequate model). Heteroscedasticity relating to experimental variables was tested for as above, variance increasing significantly as [inoculum size]–1.7 in the final model. The final model contained only the effect of final culture density (D), the effect of aspartate and their interaction. See Supplementary Table 7, Fig. 2b and Supplementary Fig. 21.

Model 8

The final culture density (log 2 (D)), the identity of the cocultured strain (wild-type or the ΔluxS mutant) and their interaction were considered as explanatory variables for mutation rate measured in the Cm-marked wild-type strain. This model was simplified, sequentially removing non-significant effects, not required in the interaction, until any further removal resulted in a significantly worse model (LR test P<0.05, that is, finding the minimal adequate model). Heteroscedasticity relating to experimental variables was tested for as above. The resulting model contained only the effect of cocultured strain, allowing the variance to increase as [coefficient of variation of m]0.81. See Fig. 3, Supplementary Table 8 and Supplementary Figs 8 and 22.

Model 9

Mutation rate was considered in response to strain (CM-marked wild-type or ΔluxS mutant), competitor (wild-type (K-12) or ΔluxS) and aspartate (presence/absence) and all possible interactions. Removal of the three-way interaction made the model significantly worse (LR 10,9 =4.3 P=0.037 despite its marginally non-significant P value by ANOVA, see Supplementary Table 8, AIC was also lower for the complete model than any simplification of it), therefore no simplification was possible. Heteroscedasticity relating to experimental variables was tested for as above, variance increasing as [m]0.25. See Supplementary Table 9, and Supplementary Figs 9 and 23.

Model 10

Expression (measured as C t , the time taken in minutes to reach a threshold of amplification) was considered as a response to the particular genes assayed (dinB, umuC, lsrB and lsrK), the strain (wild-type or ΔluxS) and their interaction, including an effect of experimental block. Both the interaction and the experimental block effect were significant (P<0.05 comparing a reduced model to the full model). However, the results for dinB and umuC were very similar; considering these genes together improved the model (lower AIC, LR 11,13 =3.6 P=0.17). Heteroscedasticity relating to experimental variables was tested for as above, variance increasing significantly as [fitted value]2.7. Variance also differed among strains (relative variance for wild-type=1, for ΔluxS=1.7) and experimental blocks (block A=1 and block B=2.5) See Supplementary Table 10, and Supplementary Figs 10 and 24.

The data and R code used to construct Figs 1, 2, 3 and their associated models are available as Supplementary Data set 1 and Supplementary Methods, respectively.