Initial computational model of nucleotide metabolism in a growing microbial population fails to reproduce mutation rate plasticity

To generate hypotheses for the mechanisms of DAMP, we constructed a system of ordinary differential equations (ODEs) that recapitulates the dynamics of metabolism, growth, and mutagenesis in a 1-ml batch culture of E. coli (Fig 1). The enzyme MutT, responsible for degrading mutagenic oxidised deoxy GTP [20], is essential in DAMP [3]; the ODE model is therefore focussed on guanine bases. In the model external glucose (eGlc) is taken up by a small initial E. coli population (wtCell). Internal glucose (iGlc) is then metabolised to produce dGTP, ROS [21–24] and, largely, “other” molecules (“Sink” in Fig 1). dGTP is then either integrated into a newly synthesised DNA molecule (DNA) or it reacts with ROS to produce 8-oxo-2′-deoxyguanosine triphosphate (odGTP). In this model, non-oxidised dGTP always pairs correctly with cytosine, producing non-mutant DNA (DNA). In a second round of DNA replication, the guanine base is now on the template strand, cytosine is correctly inserted opposite producing new chromosomes (wtCell). odGTP, if it is not dephosphorylated by MutT into dGMP (Sink), can either pair correctly with cytosine (becoming DNA) or mis-pair with adenine (becoming mDNA). When odGTP is inserted opposite adenine into DNA (mDNA), it may be repaired by the MutS or MutY proteins, converting the mDNA back to DNA. As with DNA, mDNA undergoes a second round of DNA replication to be fixed in the genome as mCell. Because these mutant base-pairs do not replicate, mCell measures the number of mutational events, referred to as “m” in mutation rate estimation [25]. The key output of interest is the mutation rate, which is defined as the number of mutant base pairs (mCell) divided by the total number of base pairs (wtCell + mCell). The model comprises 10 ODEs, one for each substance variable in Fig 1 (excluding “Sink”), plus cytVol, the total population cytoplasmic volume within which all the reactions occur (Table 1, Eqs 1–10, Methods). These equations require 14 parameters (some of them composite, Table 2); the structure and parameter values are largely taken from the existing literature (for details, see Methods). Un-measurable parameters (notably the rate of dGTP oxidation to odGTP by ROS, “O2”) were set to give the observed mutation rate (2 × 10^-10 mutations per base pair per generation, [26]) at a final population density of 3 × 10⁸ CFU ml^-1, typical of 250 mg L^-1 glucose in minimal media. As with most experiments demonstrating DAMP [3,27], final population density is controlled by varying initial external glucose. We initiated approximately 28 h simulations of 1 ml cultures with 2,175 cells (a small number, typical of fluctuation assays estimating mutation rate, S1 Fig), no internal metabolites and external glucose concentrations relevant to wet-lab experiments—across a log scale from 55 to 1,100 mg L^-1 (Table 1). The dynamics of external glucose, ROS, population size, and mutation rate for these simulations are shown in Fig 1B–1E, dynamics of all variables are included as Fig A2 in S1 Appendix.

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Fig 1. Dynamical computational model of growth, metabolism, and mutagenesis in E. coli.

(A) Model structure connecting variables. Red variables indicate the pathway to mutagenesis; green numbered arrows indicate pathways targeted by model variants. This structure was represented in ODEs (Eqs 1–10, Methods), parameterised from the literature (Table 2), and simulated from appropriate starting values (Table 1) to give output shown in B–E. (B) Kinetics of eGlc, (C) molar concentration of ROS in the cytoplasm, (D) population density calculated as the number of genomes in the 1 ml culture (wtCell/GCperGen), and (E) mutation rate calculated as the ratio of mutated to total base pairs therefore representing the chance of a single base-pair mutating in a single division (generation); this is a cumulative measure of mutation rate in the sense that it considers all the mutations that have accumulated up to the given time, making it directly comparable to experimental measures of mutation rate. Panels B–E are plotted for 5 initial glucose concentrations (range 55 – 1,100 mg L^-1 as shown in legend), initial glucose concentration indicated by line colour. Raw data for panels A–E can be found in S1 Data. eGlc, external glucose concentration; ODE, ordinary differential equation; ROS reactive oxygen species.

https://doi.org/10.1371/journal.pbio.3002711.g001

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Table 1. Definitions and starting values for the 10 variables in ODE model A (Fig 1A).

For variables measured as a concentration, the volume within which this is calculated is given in the “region” column. wtCell and cytVol starting values equate to 2,175 cells (assuming 2357528 GC bp in the E. coli genome (strain MG1655, EBI Accession U00096.3)) and cell volume of 1.03 × 10^-12 ml [83]).

https://doi.org/10.1371/journal.pbio.3002711.t001

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Table 2. Parameter values and descriptions for all parameters used in model A.

https://doi.org/10.1371/journal.pbio.3002711.t002

This initial model (Fig 1, referred to as model A) creates an approximately linear log-log slope of 0.09 ± 0.016 (95% CI, Regression 1 (SI)) between final population and mutation rate (red line, Fig 2A, Regression 1 (SI)). We can compare the slope directly to in culture estimates of mutation rates in E. coli, which show strong DAMP, with a slope of −0.83 ± 0.13 (95% CI, grey dots and dashed line, Fig 2A, Regression 2 (SI)). Model A is therefore not describing the processes causing DAMP—the structure and/or the parameters used are either incomplete or fail to replicate biology for some other reason. To test whether inappropriate parameter values could be responsible for the lack of DAMP in model A, we simulated 50,000 parameter sets simultaneously varying all parameters randomly across 10% to 1,000% of their original value. These results were filtered as described in Methods and are plotted in Fig 2B (far left). This global sensitivity analysis showed the mutation rate plasticity, i.e., slope of model A to be very robust, with an interquartile range of 0.02 to 0.13 as shown by error bars in Fig 2B. All tested parameter sets gave a log-log linear slope of > - 0.06, suggesting that DAMP requires processes not represented in this initial model.

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Fig 2. Mutation rates in model variants.

(A) Solid coloured lines show fitted log-log linear relationship between final population density and mutation rate for models A to K (Regression 1 (SI)); numbers 1–4 in legend indicate the pathway targeted from Fig 1A. Black points and dashed line show lab data for E. coli wild-type BW25113 in glucose minimal media with a log-log linear regression fitted (Regression 2 (SI)). (B) Global sensitivity analysis; coloured points show slopes from baseline parameters (as in Fig 2A), and crosses and error bars show median and interquartile range of slope across 5 × 10⁵ randomly perturbed parameter sets, models are coloured as in Fig 2A. Dashed line shows slope of lab data in Fig 2A (Regression 2), and grey area shows 95% CI on this slope. Raw data for panel A can be found in S2 Data, raw data for panel B (prior to filtering) can be found in S3 Data, and summary statistics as plotted can be found in S4 Data. eGlc, external glucose concentration; ODE, ordinary differential equation.

https://doi.org/10.1371/journal.pbio.3002711.g002

ROS production and degradation are central to density-associated mutation rate (DAMP) plasticity in silico

While there was only limited variation in the relationship between mutation rate and population density, defining the slope of DAMP, in model A (Fig 2B), we can ask which model parameters are associated either with this slope variation or with variation in mutation rate itself across the set of models with all parameters simultaneously perturbed in the global sensitivity analysis (S2 Fig). The affinity of importers for glucose (Ks, part of reaction 1 in Fig 1A) had by far the closest association with the DAMP slope (Spearman’s Rho _{(DF = 3583)} = 0.91, P < 2.2 × 10^-16, S2 Fig), whereas a group of parameters, including parameters controlling the rates of both ROS production (r, reaction 2 in Fig 1A) and ROS degradation (parameters O2 and O3, corresponding to reaction 3 in Fig 1A) had the closest association with the mutation rate (Spearman’s Rho _{(DF = 3583)} = 0.22, 0.21, and −0.21, respectively, all P < 2.2 × 10^-16, S2 Fig). The parameter representing MutT activity (parameter C1, reaction 4, Fig 1A), found to be relevant in previous work on DAMP [3], was also in this group of parameters controlling mutation rate and so was also considered as candidate processes for further exploration. We hypothesise that the additional processes required to reproduce DAMP as observed in the lab are associated with these reactions (numbered 1 to 4 in Fig 1A). We systematically tested each of these processes using structural variants to the model, explicitly modifying density dependence in biologically plausible ways. We thus use these models as a method of hypothesis generation, to determine which mechanisms may plausibly cause DAMP, with a view to testing these candidate mechanisms in the lab.

The slight increase in mutation rates seen as density increases in model A (a reversal of the negative association seen in the DAMP phenotype, therefore, referred to as “reverse DAMP”) is the result of increased external glucose leading to increased internal glucose concentrations (S3 Fig). Since ROS production in model A is linearly related to internal glucose (Eq 7), this higher internal glucose results in higher mutation rates. It is therefore plausible that if glucose importer proteins are more expressed under low external glucose conditions, increasing the rate of reaction 1 (Fig 1A) at low glucose concentrations may increase mutation rates at low density. Introducing this model variant (model B, using Eq 1_B) does indeed remove model A’s positive association between mutation rate and density but does not give the negative association observed in culture (model B slope = −0.01 ± 0.016 (95% CI), Fig 2, Regression 1 (SI)).

In model A, ROS are produced only by cellular metabolism (at a rate linearly related, with slope ‘r×M1’, to glucose metabolism); however, lab media also accumulates significant concentrations of H₂O₂ through photochemistry [28]. This is represented in model C by replacing reaction 2 (Fig 1A) with a constant ROS concentration in the system (using Eq 8_c rather than Eq 8 and Eq 3_c rather than Eq 3) and in model D by a constant rate of ROS production (using Eqs 7_DA and 7_DB rather than Eq 7). Both models abolish model A’s positive slope. However, while model C removes DAMP (slope = −0.001 ± 0.03 (95% CI), Regression 1 (SI)), model D introduces a strong negative slope similar to the laboratory data (slope = −0.91 ± 0.016 (95% CI), Regression 1 (SI)). As model D introduces ROS to the environment (representing the photochemical production of H₂O₂ in lab media [28]), we model both internal (Eq 7_DA) and external ROS (Eq 7_DB) with passive diffusion across the membrane as in [29]. Interestingly, the DAMP produced by this model is dependent on membrane permeability with decreased permeability reducing the slope of DAMP (Fig A5 in S1 Appendix).

Decreasing mutation rates at higher population densities could also be the result of changes in cellular ROS degradation rates (reaction 3). We therefore created models where degradation is determined by the internal glucose concentration (model E) and by the population density (model F), replacing Eq 7 with Eqs 7_E and 7_F, respectively. Of these 2, the first had very little effect (model E, slope = 0.09 ± 0.016 (95% CI), Regression 1 (SI)), whereas the second had a large effect, giving a strong slope similar to in culture measurements (model F, slope = −0.89 ± 0.016 (95% CI), Regression 1 (SI)).

Given that previous work has shown the action of MutT in degrading ROS-damaged dGTP (odGTP, Fig 1A) to be essential to DAMP [3], we explored models in which the rate of odGTP degradation by MutT (reaction 4, Fig 1A) is determined by the internal glucose (model G, using Eq 8_G rather than Eq 8), odGTP (model H, using Eq 8_H rather than Eq 8) or ROS concentration (model I, using Eq 8_I rather than Eq 8). None of these models consistently resulted in DAMP (Fig 2B): making MutT activity dependent on odGTP had very little effect at all (model H, slope = 0.08 ± 0.03 (95% CI), Regression 1 (SI)), whereas making MutT activity directly responsive to internal glucose or ROS concentration did reproduce some degree of DAMP slope (models G and I slopes −0.28 ± 0.016 and −0.62 ± 0.016, respectively (95% CI), Regression 1 (SI)). However, the DAMP slopes of models G and I are highly parameter dependent with the majority of parameter combinations in the global sensitivity analysis giving very little slope at all (Fig 2B).

Finally, we replaced model A’s mass action dynamics with saturating Michaelis Menten kinetics for MutT activity (reaction 4, model J using Eq 7_J rather than Eq 7 [20]) and enzymatic degradation of H₂O₂ (reaction 3, model K using Eq 7_KA and Eq 7_KB rather than Eq 7, [29]). Neither of these modifications greatly affected the mutation rate response of the model to population density (slope = 0.10 ± 0.016 and 0.096 ± 0.016, respectively, (95% CI), Regression 1 (SI), Fig 2). Thus, across 11 biologically plausible model structures chosen as those most likely to affect mutation rate plasticity, only 2, D and F, affecting reactions 2 and 3, respectively, in specific ways, produced DAMP comparable to that observed in the laboratory (Fig 2A) and robust to parameter variations (Fig 2B). Further details of the behaviour of all ODE model variants are included in S1 Appendix.

We can use these model findings for hypothesis generation: Model A (without DAMP) only describes ROS production from metabolism, whereas Model D (with DAMP) modifies the initial model to have a constant rate of ROS generation, independent of the cell density. Model D is consistent with ROS production in the system being dominated by environmental sources at a constant rate. If DAMP is a result of such environmental ROS production, we would expect this phenotype to be absent under anaerobic conditions where external H₂O₂ production is negligible [28].

Model F, which gains DAMP relative to model A, describes an increased rate of ROS detoxification dependent on the population density. This reflects a system in which ROS detoxification is primarily occurring within cells. Here, ROS diffusion into cells from the environment is significant and therefore the environment is more efficiently detoxified by larger populations. If DAMP is a result of an increased environmental detoxification capacity in dense populations in this way, we expect strains deficient in ROS degradation not to show DAMP. We would further expect dense populations to show greater removal of environmental ROS than low-density populations.

We therefore go on to test these predictions in culture using fluctuation assays to estimate the mutation rate in batch cultures of E. coli.

Environmental oxygen is necessary for DAMP in culture

To test the hypothesis (from model D) that DAMP is dependent on external oxygen, we estimated mutation rates of E. coli under anaerobiosis across a range of nutrient-determined final population densities, analysing the results using a linear mixed effects model (Regression 4 (SI)). We find that anaerobic growth results in a loss of the negative relationship between density and mutation rate, indeed mutation rates significantly increased with density (slope = 0.65 ± 0.41 (95% CI), Fig 3B, statistical tests in S1 Table, Regression 4 (SI)). We further test this relationship using a second wild-type strain (E. coli MG1655). Again, we see a loss of DAMP under anaerobiosis (slope = 0.14 ± 0.7 (95% CI), cf. slope = −0.43 ± 0.25 (95%CI), anaerobic and aerobic, respectively, Regression 4 (SI), S4 Fig). This supports the hypothesis arising from model D that when external ROS production is substantial (model D/aerobiosis), mutation rates fall with increasing final population size, while when external ROS production is not included (model A/anaerobiosis) mutation rates remain similar or increase slightly with higher cell densities.

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Fig 3. Mutation rate responses to population density in culture under environmental and genetic manipulations.

Points show the slope of a log-log relationship between final population size and mutation rate (raw data shown in S5 Fig, Regression 4 (SI)), error bars show 95% CI on slope. Treatments shown are BW25113 ancestor (1,122 parallel cultures (pc) across 70 fluctuation assays (fa)); ancestor minimal media (974 pc, 61 fa); ΔahpF (266 pc, 17 fa); Hpx^- (546 pc, 35 fa); ancestor anaerobic (168 pc, 11 fa); ancestor 10mM H₂O₂ (243 pc, 16 fa); ancestor 70U ml^-1 catalase (231 pc, 15 fa); Hpx^- anaerobic (105 pc, 7 fa); ancestor + chelator 2,2,Bipyridyl 100 μm (382 pc, 24 fa); ancestor + FeCl₂ 100 μm (210 pc, 13 fa); ΔfeoB (210 pc, 13 fa); Δfur (504 pc, 31 fa); ΔtonB (113 pc, 7 fa); ΔsodA (134 pc, 9 fa); ΔsodB (151 pc, 10 fa): ΔsodC (150 pc, 10 fa). Dashed line shows a slope of 0 (no DAMP); solid blue line shows the slope of BW25113 ancestor in rich media with dashed blue lines showing 95% CI on this estimate (Regression 4 (SI)). All experiments were conducted in dilute LB media unless stated “Minimal,” in which case glucose minimal media was used. Raw data can be found in S5 data and summary statistics as plotted are in S1 Table. DAMP, density-associated mutation rate plasticity.

https://doi.org/10.1371/journal.pbio.3002711.g003

As well as losing DAMP, cultures grown under anaerobic conditions show significantly reduced mutation rates (LR = 15.83, P = 1 × 10^-4, Regression 4, S1 Table). This raises the question of whether high-density cultures display reduced mutation rates because of increased oxygen consumption compared with low-density cultures, resulting in a more anaerobic environment [30,31]. To address the hypothesis that the level of anaerobiosis depends on cell density, we measured dissolved oxygen concentrations in high- and low-density populations over the course of the growth cycle (S6 Fig). Although oxygen concentrations vary significantly between time points (F = 22.5, df = 17, P = 3.7 × 10^-6), with an expected decrease during exponential growth, there is no difference in oxygenation between low- and high-density cultures in our system (F = 1.2, df = 17, P = 0.29). Furthermore, even where others have found a relationship between population density and oxygenation [31], this is highly nonlinear. Therefore, if DAMP were driven by oxygen availability we would expect differing DAMP slopes in subsamples of the data at high and low density. We find DAMP in wild-type BW25113 below and above a density of 1 × 10⁸ CFU mL^-1 to show indistinguishable slopes (−0.89 ± 0.72 (N = 11) and −0.70 ± 0.82 (N = 59) (±SD), respectively; comparison t = −0.80, DF = 467, P = 0.42). Thus, while environmental oxygen is necessary for DAMP, its differential utilisation by high- and low-density cultures is unlikely to be its cause.

Endogenous ROS degradation is necessary for DAMP in culture

The second ODE model able to reproduce DAMP (model F) introduces increased rates of ROS degradation with increasing population density. If DAMP is the result of active cellular ROS degradation, we would expect strains deficient in this trait to lack DAMP. The 2 alkyl hydroperoxide reductase subunits AhpC and AhpF are together responsible for the majority of H₂O₂ scavenging in aerobically growing E. coli [32]. The remaining H₂O₂ is degraded by the catalase enzymes HPI (katG) and HPII (katE) [33]. The role of catalases in H₂O₂ scavenging is much more significant at high H₂O₂ concentrations due to the higher Michaelis constants of these enzymes, whereas AhpCF is saturated at approximately 20 μm [33]. We therefore estimated DAMP in a version of the E. coli MG1655 strain lacking ahpC, ahpF, katG, and katE (Hpx^-, [21]). This quadruple deletion results in a complete loss of DAMP with no significant change in the mutation rate across densities (slope = 0.41 ± 0.2 (95% CI), Fig 3C, Regression 4 (SI)). Enzymatic degradation of H₂O₂ is thus essential to the DAMP phenotype, consistent with model F. Deleting only ahpF gives an intermediate DAMP phenotype (slope = −0.23 ± 0.44 (95% CI), Fig 3C, Regression 4 (SI)) with significantly weaker DAMP than the wild-type (LR = 4.8, P = 0.028, Regression 4 (SI)), but still retaining stronger DAMP than Hpx^- (LR = 7.4, P = 0.0064, Regression 4 (SI)), indicating that DAMP requires both catalase and alkyl-hydroperoxide reductase activity. In contrast, individual knockouts affecting superoxide rather than H₂O₂ (the superoxide dismutase genes sodA, sodB, and sodC, slope = −0.62 ± 0.23, −0.58 ± 0.24, and −0.44 ± 0.34, respectively (95% CI), Fig 3C, Regression 4 (SI)), or adding environmental H₂O₂ or catalase (slope = −0.6 ± 0.2, −0.57 ± 0.2, respectively (95% CI), Fig 3B, Regression 4 (SI)) do not significantly disrupt the wild-type negative relationship between population density and mutation rate (S1 Table). It seems likely that the addition of extracellular catalase does not impact DAMP because in low H₂O₂ concentrations, such as those in lab media, it is alkyl hydroperoxide reductase (AhpCF) which plays a larger role than catalase in H₂O₂ degradation [33].

If the DAMP reproduced by model F is biologically realistic in this way, it requires that high-density populations, exhibiting reduced mutation rates, show greater efficiency at removing H₂O₂ from their environment than low-density populations. We measured external H₂O₂ in cultures after 24 h of growth in rich or minimal media and found high-density populations to achieve significantly lower H₂O₂ concentrations (F₂₈ = 24.3, P = 3.3 × 10^-5, Regression 7B (SI), S7A Fig); there was no significant effect of rich versus minimal media (F₂₆ = 0.77, P = 0.39, Regression 7A (SI)). The log-log relationship between H₂O₂ and population density (−0.33 ± 0.1, 95% CI, Regression 7B) is of a similar magnitude to the log-log relationship between mutation rate and population density (−0.43 ± 0.25 and −0.58 ± 0.24 in rich and minimal media respectively, 95% CI, Regression 4). The reverse pattern is seen in sterile media where increasing nutrient provision leads to increased H₂O₂ concentration (F₄₆ = 9.8, P = 3 × 10^-3, Regression 6 (SI), S7B Fig). This supports the hypothesis that, as embodied in model F, high-density populations detoxify external H₂O₂ better than low-density populations. Testing the expression dynamics of H₂O₂ degrading enzymes at high and low population density could clarify whether this greater H₂O₂ degradation capacity is purely the result of an increased population size (as in model D) or also reflects changed expression of enzymes such as AhpCF (as in model F).

Cellular iron regulation is required for DAMP

Our model-guided hypothesis testing has shown that DAMP requires H₂O₂. Our models involve the direct effect of ROS on DNA; however, it is the reaction of free Fe(II) with H₂O₂ to produce mutagenic OH^. radicals, Fenton chemistry, which is a major source of oxidative stress in E. coli [34,35]. These radicals are far more reactive and damaging to DNA than H₂O₂ itself, making iron critical to determining the amount of damage H₂O₂ causes [36]. If DAMP’s dependence on H₂O_2, is the result of variable oxidative damage to DNA and nucleotides, we would expect this mutation rate plasticity to be perturbed by changes in cellular iron homeostasis. We first tested this using environmental manipulations of iron. However, the provision of FeCl₂ or starving cells of iron with a chelator (2,2-bipyridyl) has little effect on DAMP (Fig 3D and S1 Table). Nonetheless, we find that a deletant of fur, the master regulator of intracellular iron, results in an almost constant mutation rate across cell densities, with a significant reduction in DAMP compared to the BW25113 wild-type (slope = −0.16 ± 0.16 (95% CI); wild-type slope comparison: LR = 29.8, P = 4.9 × 10^-8, Regression 4 (SI), S1 Table). Although Fur is a regulator of many genes including ROS detoxification genes katE/G and sodB/C, it is Fur’s central role as a negative regulator of multiple iron importers [37], which causes Δfur strains to have an elevated internal redox-active iron pool [38] leading to increased oxidative stress and DNA damage ([39,40], S5 Fig). Knockouts of the iron importer genes feoB and tonB, which, if anything, reduce intracellular iron [41,42], do not lead to any change in mutation rate plasticity (Fig 3D and S1 Table), likely because regulators such as Fur may maintain iron homeostasis in the absence of these individual importers.

The critical contribution of iron to H₂O₂ stress is further demonstrated through whole genome sequencing of the Hpx^- LC106 strain used here. We find a 190-bp loss-of-function mutation in the iron importer fecD (all mutations listed in S2 Table). This may have allowed this Hpx^- strain to escape the positive feedback cycle that Hpx^- cells experience, in which higher H₂O₂ concentrations prevent Fur from effectively limiting iron uptake. More intracellular free iron then further exacerbates the damage done by the excess H₂O₂ [43,44]. It is likely that this loss-of-function mutation is an adaptation, during laboratory culture, to the loss of Fur functionality caused by the oxidation of intracellular iron. This raises the question of whether the lack of DAMP in Hpx^- arises not from the katE/G ahpCF knockout, but from this secondary mutation. To address this, we show that the independently derived Hpx^- strain BE007, without mutations in the fecD gene (S2 Table), also lacks DAMP (X² = 0.808, df = 1, P = 0.369) (S8 Fig).

Wild-type cells restore DAMP in cells deficient in peroxide degradation

We have identified DAMP as requiring environmental H₂O₂ and endogenous H₂O₂ degradation, so that, with wild-type iron regulation, increased detoxification of environmental H₂O₂ leads to lower mutation rates at higher final cell densities. This understanding leads us to predict that the presence of wild-type cells should restore DAMP in the peroxidase and catalase-deficient Hpx^- strain. It has previously been shown that a wild-type population can provide protection against environmental H₂O₂ to cocultured Hpx^- cells, or similarly H₂O₂ sensitive ΔoxyR cells, through decreasing the peroxide concentration of the external environment [32,45]. To better distinguish Hpx^- and wild-type strains in a coculture, 2 nalidixic acid (Nal)-resistant strains of Hpx^- were independently created with the resistance conferred by point mutations in gyrA (D87G and D87Y). Coculturing these Hpx^- _nalR strains with wild-type BW25113 cells, the loss of DAMP via the Hpx^- mutation (Fig 3C) is phenotypically complemented by the wild-type cells. That is, Hpx^- _nalR mutation rate is significantly decreased in coculture with increasing population density either of the Hpx^- strain (Figs 4, S9, slope = −0.93 ± 0.5 (95% CI), Χ² _(DF=1) = 11.7, P = 6.4 × 10^-4, Regression 4 (SI)), or total population density (S10 Fig, Slope = −1.4 ± 1.06 (95% CI), t₂₉ = −3.79, P = 7 × 10^-4, Regression 8 (SI)). This supports the hypothesis that DAMP is the result of reduced environmental H₂O₂ concentrations achieved by the local wild-type population. These results are also replicated by introducing an Hpx^- population to the ODE model D, highlighting the ability of this simple model to explain the DAMP phenotype (see Methods and S11 Fig).

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Fig 4. Coculture with wild-type cells restores DAMP in cells deficient in peroxide degradation.

Points show log-log relationship between final population density of the focal strain and mutation rate fitted by Regression 4 (SI) (raw data shown in S9 Fig), error bars show 95% CI on slope. We found no significant differences between independent Hpx^-_nalR strains; therefore, Hpx^- strains D87Y and D87G are combined in Hpx^-_nalR. Treatments shown are: BW25113 ancestor (1,122 pc, 70 fa); BW25113 in coculture with Hpx^- (498 pc, 31 fa); Hpx^-_nalR (388 pc, 24 fa); Hpx^-_nalR in coculture with BW25113 (319 pc, 20 fa). Raw data can be found in S5 Data and summary statistics as plotted are in S1 Table. DAMP, density-associated mutation rate plasticity.

https://doi.org/10.1371/journal.pbio.3002711.g004

Such mutation rate estimates in coculture could potentially be confounded by differential survival of rifampicin-resistant (RifR) mutants of Hpx^-_nalR when plated in a monoculture or a coculture. In order to test for any differences in mutant survival, we conducted a “reconstruction test” (as in S13 Fig of [27]); plating a predetermined number of Hpx^-_nalR&rifR cells with a population of rifampicin susceptible Hpx^- or wild-type cells on the selective rifampicin agar. No significant difference in plating efficiency was seen between plating with Hpx^- versus low, medium, or high density of wild-type cells (S12 Fig; LR_df=6 = 11.7, P = 0.07, Regression 9 (SI)). Some difference in plating efficiency between the 2 Hpx^-_nalR&rifR strains was observed (S12 Fig), this is likely due to the pleiotropic effects of different RifR resistance mutations in the rpoB gene [46,47]. The rifampicin resistance mutations in these strains were identified with Sanger sequencing of the rpoB rifampicin-resistance determining region and are given in S12 Fig. The specific protein sequence changes caused by these mutations have different known pleiotropic effects, as characterised in [47].

Although the wild-type strain reintroduces DAMP in Hpx^-_nalR it also causes an increase in total Hpx^-_nalR mutation rates (S10 Fig and S1 Table). This is potentially the result of out-competition by the wild-type strain leading Hpx^-_nalR growth to stop earlier in the culture cycle where, consistent with previous fluctuation assay results ([48], Chapter 5.4.3), our modelling leads us to expect higher mutation rates (Fig 1E and Fig A3 in S1 Appendix).

Ordinary differential equations and Model A

Models were created as coupled sets of ODEs for the change over time of relevant variables. These equations were largely parameterised from the literature, given appropriate starting values and simulated over time by integration with a solver, as described below.

All variables (Fig 1A and Table 1) are measured in molar concentration within the cytoplasm, aside from the volume of that cytoplasm (cytVol), measured in ml, and external glucose (eGlc) and number of growing cells (wtCell and mCell) which are measured as molar concentrations within the 1 ml batch culture. It is possible to convert between cytoplasmic and total metabolite concentrations through scaling by the cytoplasmic volume; this is calculated as the number of cells multiplied by a volume of 1.03 × 10^-9 μl per cell [83]. The reaction of dGTP with ROS creates oxidised dGTP (odGTP) which is then incorporated into DNA, creating AT > CG base pair substitution transversion mutations [26]. Mutations caused by odGTP may be avoided or repaired by the action of MutT, MutY, and MutS enzymes [84]. By dividing the number of mutant cells (mCell) by the total cell number (mCell + wtCell) at any point during the simulation, a mutation rate (bp^-1 generation^-1) across the simulation up to that point, can be calculated. Final population density is here manipulated by changing nutrient input, this also modifies a range of other timings and features of the culture cycle. We model growth with no death; though in practice death does occur in laboratory media, mortality rates are generally low [85]. Although DAMP is measured at approximately 28 h during the stationary phase where all metabolites are drained (Figs 1C, S3, and Fig A2 in S1 Appendix), we show that these slopes are also representative of DAMP during the exponential phase (16 h) (Fig A4 in S1 Appendix). This recapitulates in culture findings that DAMP slope is constant across growth phases in E. coli ([48], Chapter 5.4.3).

The uptake of glucose is described by saturating Michaelis Menten kinetics while the oxidation of dGTP is described as a bimolecular reaction dependent on the cytoplasmic concentrations of dGTP and ROS. All other steps are described by first-order mass action kinetics in which the rate equals the concentration of the reactant multiplied by a rate constant (Eqs 1–10). The model is parameterised from published enzymatic and culture data alongside our own wet lab data (Table 1).

R code to recreate all figures, models, and analysis relating to the ODE models is available as S1 Code. All models were simulated in R (V4.3.1) [86] using package deSolve (V1.36) [87]; logarithmic sequences were produced with emdbook (V1.3.13) [88]; data handling and plotting was done using the tidyverse (V2.0.0) [89] and magrittr (V2.0.3); and parallel computing was done using parallel (V4.3.0), doParallel (V1.0.17), and foreach (V1.5.2). Linear mixed models were fitted to lab data with nlme (V3.1-162) [90], and plots formatted and coloured using cowplot (V1.1.1), gridExtra (V2.3), ggeffects (V1.3.1) [91], and RColorBrewer (V1.1-3). Fig 1A was made using R package DiagrammeR (V1.0.10).

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Equations 1–10: ODE equations for initial model (A).

Model B—Glucose uptake increases at low eGlc

Original Michaelis Menten kinetics are removed as this reverses the intended effect.

(1_B)

Both U2 and K2 are in Molar units.

6.7 × 10^-3 is chosen as a value slightly higher than maximum eGlc so that the value of can cover almost a full range of 0 to 1. This means that glucose uptake rate will increase from almost 0 to 100% of the measured uptake rate as the external glucose concentration falls. K2 is given as 1.82 × 10^-4 as this value produces the most negative DAMP slope achievable within the structure; values were tested from 1.82 × 10^-6 to 1.82 × 10^-2 (S1 Code).

Model C—Constant dGTP oxidation, regardless of ROS concentration

By decoupling ROS concentration from dGTP oxidation there is no extra odGTP in cells grown to higher density, we expect this to prevent a positive DAMP slope. ROS no longer alters odGTP formation and therefore Eq 7 is removed from model C.

(3_c)

(8_c)

ROSC in Molar units.

ROS is removed as a variable and replaced with a constant concentration of 1.8 × 10^-7, this is within the known internal ROS concentration of 1.3 × 10^-7 - 2.5 × 10^-7 M [23] and produces mutation rate of 1.93 × 10^-10 based on lab data and [26].

Model D—Constant ROS production regardless of population density

By creating a situation in which ROS is produced in the media at a constant rate (e.g., [28]) and then diffuses into all present cells, higher density populations will expose each individual cell to less ROS. We expect this to create a negative DAMP slope as high-density populations will be able to maintain external, and therefore also internal, peroxide concentrations at lower levels.

(7_DA)

(7_DB)

ROSC2 in Molar units.

ROSC2 defines the number of millimoles of hydrogen peroxide produced in the media each second, this can then diffuse into the cells. The chosen value of 6 × 10^-11 creates an H₂O₂ production rate at 78% of that expected from [32] and an altering O2 to 40 restores the mutation rate to 95.5% of that expected from [26].

Permeability coefficient, diffusion coefficient, and cell surface area are taken from [29] to calculate the diffusion coefficient as follows:

kdiff is in is in Sec^-1 units.

Model E—ROS removal dependent on internal glucose

We expect greater rates of ROS removal to lead to lower rates of GTP oxidation, and therefore, lower mutation rates. If ROS is more able to be degraded when resources are abundant this may produce DAMP.

(7_E)

C3 is in Molar units.

C3 is adjusted to produce known mutation rate of 1.98 × 10^-10 base pair substitutions per nucleotide in 0.2% glucose minimal media [26].

Model F—ROS removal dependent on population density

We expect direct control of ROS degradation by population density to allow cells in higher density populations to avoid mutations more efficiently. The expression calculates the population density. The rate of AhpCF+KatEG catalysed ROS degradation is calculated in this model as this population density multiplied by numeric constant “C3a,” replacing “O3.” (7_F)

C3a is in Sec^-1 units.

C3a of 3.5 × 10^-6 is chosen to reproduce the mutation rate of 2.05 × 10^-10 base pair substitutions per nucleotide.

Model G—MutT activity up-regulated by internal glucose

MutT activity is known to be essential to DAMP and so density-dependent MutT activity is a candidate DAMP mechanism. iGlc accumulates at higher levels in cells growing to high density, we expect high MutT activity in these cells to lead to a reduced mutation rate due to MutT cleaning of odGTP.

(8_G)

C3G is in Molar units.

2.6 × 10^-3 is selected as a number slightly higher than the maximum iGlc achieved (approximately 0.0023), this prevents MutT activity levels from falling below 0. O2 is refitted to 70 to restore desired mutation rate.

Model H—MutT activity up-regulated by odGTP

If MutT activity is actively up-regulated to degrade odGTP at a higher rate upon exposure to higher odGTP concentrations, then we expect cells grown in higher glucose, with higher internal metabolite concentrations, to have a greater ability to evade mutations caused by odGTP.

(8_H)

C3b is in Molar units.

8 × 10^-10 is selected as a number slightly higher than the maximum odGTP achieved, this prevents MutT activity levels from falling below 0.

Model I—MutT activity up-regulated by ROS

Reasoning and value selection as in Models G/H.

(8_I)

C3c is in Molar units.

Model J—Michaelis Menten MutT kinetics

Michaelis Menten kinetics describe saturating, enzyme catalysed reactions. In this situation, reaction rates proceed slower at low substrate concentrations rising to an asymptote at maximum reaction rate. As with models G/H/I, we expect this to reduce mutation rates by increasing MutT activity in high-density populations with greater internal metabolite concentrations.

(8_J)

Kt is in Molar units and is the Michaelis Menten Km value.

Kt value given by [20], O2 is then titrated to restore mutation rate as in [26].

Model K—Separated activity of ahpCF and katEG genes + limited diffusion of ROS across the plasma membrane

(7_KA)

(7_KB)

As in [29], the activity of alkylhyrdoperoxidase and catalase proteins are separated to allow for their specialisations to low and high H₂O₂ concentrations, respectively. Michaelis Menten and Vmax constants are as follows:

Km in Molar units and [Conc]k_cat in M.sec^-1units.

All diffusion parameters shared with model D are defined in the same way. H₂O₂ production rate and standing concentration are restored to expected values by altering the value of r:

Model D Hpx^- coculture

To assess the expected DAMP of an Hpx^- population cocultured with wild-type E. coli, we add a second population to model D which differs from the wild type only in that the rate of ROS degradation by AhpCF/KatEG, “O3,” is set to 0. In this model, the populations of Hpx^- and wt cells interact only through shared eGlc and a shared pool of ROS_external. The starting values of all variables are as in Table 1 and the starting population of both cell populations are set as in Table 1. As in model D, ROS originates from an exogenous source and can then diffuse into cells. When ROS diffuses into the Hpx^- cells it is not degraded, it is only when it diffuses into wt cells that ROS can be removed from the system. Eq 11 describes eGlc (external glucose), Eqs 12–20 describe wt cell metabolism, Eq 21 describes the external ROS pool, and Eqs 22–30 describe the Hpx cell metabolism. All equations are included below: (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) (30)

Global sensitivity analysis

For each parameter within each model, 50,000 values between 10% and 1,000% of the baseline value (Table 2), spaced evenly along a log scale were tested. The set of values for each individual parameter were then independently shuffled so that no parameters were correlated with one another, allowing for substantial exploration of the available parameter space. Of these 50,000 parameter sets, some encountered fatal errors in the ODE solver and so did not produce a DAMP slope estimate, the number of parameter sets run without fatal error is shown in Table 3 as “complete.” Results were filtered for the following criteria: (1) Stationary phase is reached in all glucose conditions (defined as an average increase of less than 1 cell per 10 s time step across the last 1,000 time steps (2.7 h) of the simulation); (2) final population size >1 × 10⁷ and <1 × 10¹⁰ at every glucose condition; (3) final population size increases with each increase in glucose concentration; (4) mutation rate >2 × 10^-12 and <2 × 10^-8 at all glucose conditions; and (5) log-log relationship between mutation rate and final population size is substantially linear (defined by R-squared >0.5). After this filtering, the following number of parameter sets was retained for each model (Table 3).

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Table 3. Counts of completed and filtered simulations from 50,000 parameter sets produced for global sensitivity analysis for each model variant.

“Complete” column lists the number of these parameter sets that were able to be simulated without fatal error from the ODE solver. “Filter” columns list how many parameter sets remained after filtering as described and numbered above.

https://doi.org/10.1371/journal.pbio.3002711.t003

Strains used in this study

The parent of the Keio collection is E. coli strain BW25113 (F-, Δ(araD-araB)567, ΔlacZ4787 (::rrnB-3), λ-, rph-1, Δ(rhaD-rhaB)568, hsdR514). E. coli Hpx^- LC106 mutant is ΔahpCF’ kan:: ΔahpF Δ (katG17::Tn10)1 Δ (katE12::Tn10)1 [21]. E. coli Hpx^- strain BE007 is from Benjamin Ezraty as described in [99]. E. coli single-gene knockouts Δfur, ΔfeoB, ΔtonB, and ΔahpF are sourced from the Keio collection [100]. E. coli K-12 strain MG1655 is from Karina B. Xavier. Nalidixic acid-resistant strains Hpx^- (gyrA D87Y) and Hpx^- (gyrA D87G) were isolated from independent fluctuation assays of the original Hpx^- strains on 30 mg L^-1 nalidixic acid selective plating.

Strains Δfur, ΔfeoB, ΔtonB, ΔahpF, Hpx^-, Hpx^-_nalR(D87Y), and Hpx^-_nalR(D87G) were sequenced to 30× depth by MicrobesNG to verify gene deletions. Lack of KatE activity in Hpx^- was verified by covering a colony on TA agar with 30% H₂O₂ with no bubbles of oxygen observed (as in [33]); the MG1655 wild-type was used as a positive control. Mutations were identified using breseq version 0.36.0 [101,102] with bowtie2 version 2.4.1 and R version 4.2.0 and are listed in S2 Table. For Hpx^- strains, the reference genome used was the E. coli K-12 MG1655 genome [[103], NCBI accession U00096.3]. For Keio knockout strains, 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 as file S1 in [1]).

Media

We used Milli-Q water for all media, all chemicals are supplied by Sigma-Aldrich unless stated otherwise. LB medium contained: 10 g of NaCl (Thermo Fisher Scientific), 5 g of yeast extract (Thermo Fisher Scientific) and 10 g of tryptone (Thermo Fisher Scientific) per litre. DM medium contained 0.5 g of C₆H₅Na₃O₇ ·2H₂O, 1 g of (NH₄)2SO₄ (Thermo Fisher Scientific), 2 g of H₂KO₄P and 7 g of HK₂O₄P· 3H₂O per litre; 100 mg L^-1 MgSO₄ ·7H₂O (406 μmol) and 4.4 μg L^-1 thiamine hydrochloride were added to DM after autoclaving. Selective tetrazolium arabinose agar (TA) medium contained 10 g of tryptone, 1 g of yeast extract, 3.75 g of NaCl, and 15 g bacto agar per litre; after autoclaving 3 g of arabinose and 0.05 g of 2,3,5-triphenyl-tetrazolium chloride were added per litre, this was supplemented with freshly prepared rifampicin (50 μg ml⁻¹) or nalidixic acid (30 μg ml⁻¹) dissolved in 1 ml of methanol or 1 M NaOH, respectively, when required. For all cell dilutions, sterile saline (8.5 g L^-1 NaCl) was used.

Fluctuation assays

Fluctuation assays were conducted as described in [105]. Briefly, initial growth of glycerol stocks in LB was carried out for 4 h for all strains aside from Hpx^- which was grown for 7 h due to its reduced growth rate. A dilution factor of 1,000× was then used for transfer to overnight cultures. Overnight acclimatisation was carried out in DM supplemented with 3.5% LB or 250 mg L^-1 glucose with nutrient type matching that of the fluctuation assay. The density achieved in the assay was manipulated by growth in varying nutrient conditions, either 2% to 5% LB diluted in DM or 80 to 1,000 mg glucose L^-1. Manipulation of density via nutrient provision potentially confounds density with both nutrient environment and growth rate; the effects of these factors have been shown to be separable with a distinct effect of density ([106], Chapter 4). Selective plates were prepared 48 h before use and stored for 24 h at room temperature followed by 24 h at 4°C. All strains were plated on rifampicin selective media.

Anaerobic conditions were produced by incubating the 96 deep well plates in an airtight 2.6 L container with 1 Anaerogen 2.5 L sachet (Thermo Scientific). The Anaerogen sachet rapidly absorbs oxygen and releases CO₂ creating anaerobic conditions. Aerobic plates of matching design were grown in an identical container ventilated with 8 × 4 mm diameter holes without an Anaerogen sachet. In these plates, 2 to 4 wells in each 96-well plate contained DM supplemented with 2.5% LB, resazurin, and E. coli MG1655, leaving space for fluctuation assays of 15 to 16 parallel cultures. On removing the 96-well plates from incubation the resazurin absorbance at 670 nm was measured; this quantifies the change from pink resorufin (aerobic cell growth) to clear dihydro resorufin (anaerobic cell growth), thus providing an objective measure of anaerobiosis (S15 Fig).

During coculture fluctuation assays between BW25113 wild-type and Hpx^- both strains were grown up in LB for 4 to 7 h, then in 3.5% diluted LB with DM overnight and then diluted into cultures of approximately 1 × 10³ CFU ml^-1 as above. Some combination of these 2 initial cultures was then mixed in each parallel culture ranging from an Hpx^-:wild-type ratio of 1:1 to 124:1 (recorded in S1 Data file as “Mut_to_WT_ratio”). Plating of these cultures on TA or TA+Rif agar enabled the Ara+ (white) Hpx^- colonies and the Ara- (red) wind-type colonies to be distinguished. For assays using NalR Hpx^- strains, selective plating was done on TA+Rif+Nal plates and so only Hpx^- mutants and not wild-type mutants were counted, Nt was determined for both strains using plating on both TA+Nal and TA. Due to amino acid synthesis defects, Hpx^- cells cannot be cultured in glucose minimal media and so all cocultures were conducted in dilute LB media [34].

In order to test for any differences in survival of Hpx^- (NalR) grown in monoculture VS with differing densities of BW25113 wild-type cells, we conducted a reconstruction test (S12 Fig). A known quantity of Hpx^- (NalR + RifR) cells were plated with one of the following treatments: sterile DM, Hpx^- (5%LB overnight growth), wild-type (2.5%LB overnight growth), wild-type (3.5%LB overnight growth), and wild-type (5% overnight growth). Raw data from the reconstruction test is available as S11_data.xlsx.

Though fluctuation assays allow for high-throughput and low-cost estimates of mutation rate, they classically come with some important assumptions to consider [25]. For example, the assumption that resistance markers will be selectively neutral is not reasonable in practice [47]. Fortunately, this can be accounted for with the estimation of fitness cost which can then be accounted for in the estimation of mutational events using R package flan (V0.9). We find estimations of DAMP with the co-estimation of the individual fitness cost in each assay or with the application of the median mutant:wild-type fitness ratio estimation (median = 0.59; fitness cost estimates shown in S16 Fig, regression 3) to have no effect on our conclusions. Specifically, in regression 4 (SI), re-running the model using either of these approaches to account for genotypes having different competitive fitness makes no difference to whether DAMP is inferred (i.e., categorising each treatment as DAMP, no DAMP, or reverse DAMP; S1 Table) for all treatments. In this study, we allow flan to co-estimate fitness along with mutational events (m) for each assay. Occasionally, this model failed to converge on estimates, in these cases average fitness effects were estimated from a model fitted to all successful estimates (Regression 3 (SI)) and then used to estimate m from the data with this predetermined fitness effect of mutation. It is also possible to avoid issues of mutant fitness effects by using the p₀ method of estimation [25,107] in which parallel cultures are simply divided into those with or without any viable mutants. However, this method is more restrictive as only in assays in which parallel cultures both with and without growth have been observed can the method be applied; it is also subject to more error on estimates than maximum-likelihood methods [25,108]. Reanalysing our data with the p₀ method shows DAMP to exist in almost all of the same treatments as in the original analysis (S17 Fig), discounting any effect of mutant fitness costs on our conclusions. Another potentially unrealistic assumption of the fluctuation assay is that there will be no death; this too is possible to account for using the tools provided in R package flan. We find that introducing a death rate of 25%, beyond what would be expected under our conditions which lack added stressors [85], cause no consistent or substantial changes in DAMP slope (S18 Fig).

Sanger sequencing of rpoB mutations

PCR amplification of the rifampicin-resistance determining region (bp 1328–2235) of rpoB in rifR mutants (S12 Fig) was carried out as described in [15]. Rifampicin-resistant mutants isolated from a fluctuation assay were grown in LB to exponential phase and stored in 18% glycerol at −80°C. Mutants were revived by streaking of 1 μl of this glycerol stock onto LB agar plates. DNA was diluted by touching a colony with a pipette tip, submerging this pipette tip in 25 μl nuclease-free water, and diluting 1 μl of that solution in a further 9 μl of nuclease-free water. Approximately 1 μl of diluted DNA was added to 24 μl of master mix containing 1.25 μl of both forward and reverse 100 μm primer stock, 5 μl buffer, 5 μl MgCl₂, 0.25 μl high-fidelity DNA polymerase, and 11.25 μl nuclease-free water.

Polymerase chain reactions (PCRs) were carried out to amplify the rifampicin-resistance determining region of the rpoB gene for Sanger sequencing, using forward primer 5′-ATGATATCGACCACCTCGG-3′ and reverse primer 3′-TTCACCCGGATACATCTCG-5′ [15]. PCR was run with the following protocol: (i) initial denaturation (98°C for 5 min); (ii) denaturation (98°C for 10 s); (iii) annealing (55°C for 30 s); (iv) extension (72°C for 1 min); (v) repeat steps 2 to 4 for 35 cycles; (vi) final extension (72°C for 5 min); and (vii) hold at 4°C. PCR product verification was performed by gel electrophoresis carried out on 1% agarose TAE gel with 0.1% SybrSafe stain. PCR products were submitted to Source BioScience for PCR Product clean-up and sequencing (Source BioScience, Cheshire). Both reverse and forward primers were submitted for each sample as sequencing primers.

Using Unipro UGENE v49.0, downloaded from https://ugene.net/, sequences of the rpoB gene of the mutants were aligned to a reference rpoB genome nucleotide sequence, of the strain E. coli K-12 substr. MG1655, obtained from EcoCyc version 27.5 to identify point mutations. BLAST was used to identify amino acid changes created by the mutations [109].

Hydrogen peroxide measurement

External hydrogen peroxide is measured using the Amplex UltraRed (AUR)/Peroxidase assay as described in [28]. All reagents were dissolved in 50 mM dibasic potassium phosphate. Diethylenetetraaminepentaacetic acid (DTPA) and AUR solutions were corrected to pH 7.8 with HCl or NaOH. Reactions containing 660 μl 1 mM DTPA, 80 μl filter sterilised sample solution, and 20 μl 0.25 mM AUR were mixed by vortexing before transferring 141 μl to 3 wells of a clear bottomed black 96-well plate. Fluorescence was measured at 580 nm excitation, 610 nm emission before and after the injection of 7.5 μl horseradish peroxidase (0.25 mg ml^-1) to each well, net fluorescence was calculated as initial fluorescence subtracted from final fluorescence. H₂O₂ concentration was estimated by calibration to standard solutions of 5 and 20 μm H₂O₂ (Regression 5 (SI)). Because of background levels of fluorescence, some predicted concentrations were negative, this was accounted for by taking the absolute value of the lowest prediction and adding this to all predictions. The range of H₂O₂ concentrations we observed is in good agreement with similar measurements in the literature (e.g., Fig 6B in [28]).

Dissolved oxygen (DO) measurement

Dissolved oxygen was measured in 10-ml cultures grown in 50-ml falcon tubes; DAMP has been shown to be present in E. coli grown under these conditions (see E. coli cultures plated on nalidixic acid in the second figure of [3]). Tubes were either loosened ½ turn with the lid secured with a small piece of tape or screwed on fully though no difference was evident between these treatments. Each starting culture of 40 ml was split between 4 tubes of 10 ml sampled at 0, 5, 7, and 24 h (sampling is destructive as the head of the DO probe cannot be confirmed to be sterile). DO was measured by submerging the probe in the given sample for 45 s to allow the measurement to stabilise. Following DO measurement, each culture was appropriately diluted and plated to determine population density by CFU. Dissolved oxygen analyser DO9100 was purchased from BuyWeek.

Statistical analysis

All statistical analysis was executed in R (V4.3.1) [86] using the nlme (V3.1-162) package for linear mixed effects modelling [90]. This enabled the inclusion within the same regression of experimental factors (fixed effects), blocking effects (random effects), and factors affecting variance (giving heteroscedasticity). R package car (V3.1.2) [110] was used to carry out Chi-squared tests comparing slope to a null-hypothesis of 1 (S1 Table). In all cases, log₂ mutation rates were used. Details of all regression models are given S1 supplementary statistics along with diagnostic plots and ANOVA tables for each model. The code and data to reproduce the main text figures are given in the accompanying R scripts S1 and S2 Code files, and supplementary data files S1–S14 data, respectively. Column header definitions for S1–S14 data are given in S3 Table. Standard deviation on estimates of m is calculated as in [108]. The same R packages were used for parallel computing, data handling, and plotting as for the ODE modelling, with the addition of plyr (V1.8.8), ggbeeswarm (V0.7.2), and gridExtra (V2.3).