Opposing effects of population density and stress on Escherichia coli mutation rate

Evolution depends on mutations. For an individual genotype, the rate at which mutations arise is known to increase with various stressors (stress-induced mutagenesis – SIM) and decrease at high population density (density-associated mutation-rate plasticity – DAMP). We hypothesised that these two forms of mutation rate plasticity would have opposing effects across a nutrient gradient. Here we test this hypothesis, culturing Escherichia coli bacteria in increasingly rich media. We distinguish an increase in mutation rate with added nutrients through SIM (dependent on error-prone polymerases Pol IV and Pol V) and an opposing effect of DAMP (dependent on MutT, which removes oxidised G nucleotides). The combination of DAMP and SIM result in a mutation rate minimum at intermediate nutrient levels (which can support 7×108 cells ml−1). These findings demonstrate a strikingly close and nuanced relationship of ecological factors – stress and population density – with mutation, the fuel of all evolution.

Introduction: How and why the rate of spontaneous genetic mutation varies is a fundamental and enduring biological issue (Lynch et al 2016). Mutation rate can vary both among species (Sung et al 2012) and within a genotype (Maharjan and Ferenci 2017b). Intra-genotypic variation can depend upon stressful environmental conditions such as nutrient limitation, growth-rate reduction, high osmotic pressure, low pH, extreme shifts in temperature or various DNA damaging agents (Foster 2007, Galhardo et al 2007, MacLean et al 2013. In these environments cells induce stress responses that can increase mutation rates, typically via up-regulation of error-prone polymerases Recently, we found that across microbes, the mutation rate of a particular genotype critically depends on the density to which the population grows (that is, the carrying capacity of the environment divided by its volume) (Krašovec et al 2017). In this socalled Density-Associated Mutation-rate Plasticity (DAMP), bacterial and yeast populations show a power law (log-log linear) reduction in mutation rate with D when grown in a defined minimal medium with glucose as the sole carbon source (Krašovec et al 2014, Krašovec et al 2017. DAMP and SIM modify mutation rates in Escherichia coli via different genetic pathways. DAMP requires a Nudix hydrolase protein, whose primary role is degrading highly mutagenic 8-oxo-dGTP (Michaels and Miller 1992), while error-prone polymerases such as Pol IV is not involved in DAMP (Krašovec et al 2017). Differences in the underlying mechanism and the fact that the most dense populations, experiencing the highest stress, show the lowest mutation rates, suggest that DAMP is not obviously associated with stress.
Growth in minimal medium on a single carbon source does not, however, reflect the environmental complexity or range of population densities experienced by many species. E. coli population density in host environments varies over 5 orders of magnitude among host species, and can be higher than 10 9 colony forming units per gram of faeces (reviewed in (Tenaillon et al 2010)). As the highest population densities, with the greatest competition, rely on high nutrient availability, we reasoned that the addition of nutrients to minimal nutrient environments could indirectly increase both population densities and the level of stress. We therefore hypothesised that effects of density and stress on mutation rates, DAMP and SIM respectively, will act in opposition to one another across such a nutrient gradient -DAMP decreasing mutation rate and SIM increasing it as nutrients and population density increase.
Here we test this hypothesis by determining E. coli mutation rates across a nutrient gradient, while genetically manipulating DAMP and SIM independently. As hypothesised, we identify genetically separable and opposed associations of mutation rate with nutrient availabilitya negative association requiring mutT (DAMP) and a positive association requiring polymerases IV and V (dinB and umuC respectively; SIM).
We find that these associations combine to minimise average mutation rates in environments with intermediate nutrient availability and population density.

Results:
We assayed mutation rates to rifampicin resistance using fluctuation tests in E.
coli K-12 MG1655 grown across a gradient of nutrient availability: a range of concentrations (1-90% v/v) of lysogeny broth (LB) mixed with Davis minimal (DM) medium (LB/DM). We find that the relationship of mutation rate to LB concentration is non-linear ( Fig. 1, likelihood ratio test of a quadratic effect of log nutrient availability on log mutation rate: N=97, LR 8,7 =105, P=1.2×10 -24 , model S-I in Supplementary Information). Mutation rate to rifampicin resistance decreases as LB/DM is increased from 1% to 10% LB (increasing final population density, D, from 1×10 8 to 7×10 8 cells ml -1 Fig. S2-S3). This is comparable to DAMP in DM with glucose (Krašovec et al 2014, Krašovec et al 2017. However, mutation rate starts to increase in richer media, with 90% LB reaching similar or higher mutation rates than in 1% LB. We next asked whether the increase in mutation rate at higher nutrient availability is genetically separable from the decrease in mutation rate due to DAMP. DAMP in E. coli requires the 8-oxo-dGTP diphosphatase MutT protein, meaning that, in minimal medium with glucose, the mutation rate in a ΔmutT mutant does not decrease with increased nutrient concentration (Krašovec et al 2017). We therefore performed fluctuation tests to nalidixic acid resistance in LB/DM with a ΔmutT mutant. We find that in LB/DM, as in DM with glucose, mutation rate in ΔmutT shows no relationship with increased nutrients or population density below 10% LB (Fig. 2, Model S-II in Supplementary Information).
However, even more clearly than in the wild-types (both MG1655 [ Fig. 1] and the immediate parent of the ΔmutT mutant [ Fig. S6]), mutation rate of the ΔmutT mutant increases with the nutrient availability above 10% LB (population density of ~1×10 9 cells ml -1 ). The only other E. coli mutant reported not to exhibit DAMP is E. coli K-12 MG1655 ΔluxS (Krašovec et al 2014). However, this mutant's deficiency in DAMP is functionally complemented by added aspartate (Krašovec et al 2014), and LB is a medium rich in amino acids (Sezonov et al 2007). If variation in mutation rate at 10% LB/DM and below is the same phenomenon as DAMP, we expect this mutant strain to behave more similarly to wild-type than the ΔmutT mutant. We find that the ΔluxS mutant's mutation rate is indistinguishable from the wild-type MG1655 across LB/DM environments ( The fact that mutation rate increases at high LB concentrations in a ΔmutT mutant ( Fig. 2), where DAMP is absent, suggests that high nutrient availability increases mutation rate via a DAMP-independent mechanism. We hypothesised that higher nutrient concentrations increase the level of stress (e.g. by promoting competition), thereby causing error-prone polymerases Pol IV and Pol V (coded by dinB and umuC respectively) to increase the mutation rate at very high LB concentrations. We tested this hypothesis by estimating mutation rates to rifampicin resistance in E. coli ΔdinB and ΔumuC growing in LB/DM. We find that, unlike E. coli MG1655 (Fig. 1) and ΔmutT ( Fig. 2), mutation rates of the ΔdinB and ΔumuC deletants (Fig. 3

, Model S-III in
Supplementary Information) decrease with increasing nutrients above 10% LB (above population densities of 7×10 8 cells ml -1 , Fig. S7). This continued decrease indicates that these polymerases are required for the rise in mutation rates as nutrients increase, and that DAMP continues to affect mutation rates at high nutrient levels.
The fitness effects of resistance mutations are known to be variable among nonselective environments, particularly for rifampicin (Maharjan and Ferenci 2017a). This variation has the potential to give artefactual differences in mutation rates among environments. We therefore estimated the fitness effects of resistance mutations in the fluctuation tests reported in Figs Discussion: Our previous work on density associated mutation rate plasticity (Krašovec et al 2017) contained a paradox. In the laboratory, E. coli displays a substantial and highly significant decrease in mutation rate with population density (DAMP, much more so than related bacteria -Pseudomonas aeruginosa PAO1); yet, in the published literature, of all 56 species with appropriate data (including P. aeruginosa), the one with least negative association was E. coli. Here we have resolved that paradox. We have shown how two mechanistically independent plastic processes act on the mutation rate: DAMPapparent at lower population densities (< 7×10 8 cells ml -1 ), causing mutation rate to decrease with nutrient concentration; SIMapparent at higher population densities (> 1×10 9 cells ml -1 ), causing mutation rate to increase with nutrient concentration. E. coli is the organism whose mutation rate has, across the last 75 years of literature, been measured across the broadest range of population densities (7.50×10 6 to 8.85×10 9 cells ml -1 ) (Krašovec et al 2017). This means that, like coli's mutation rate at around 7×10 8 cells ml -1 (Fig. 4). This explains why attempting to fit a linear trend to this data does not yield a steep negative relationship (Krašovec et al 2017). It is also consistent with DAMP acting at low population densities and SIM at high densities across diverse published studies (144 individual estimates across 18 studies), as we find here in a single, controlled study.
It seems likely a priori that the dynamics of population growth and cell division, which differ among nutrient environments, are involved in the mutation rate changes observed here. For instance, environmental differences that affect growth rate will in turn affect ploidy (Pecoraro et al 2011), which can affect mutation rate estimates (Sun et al 2017).
Therefore, we cannot exclude the possibility that the effects of either DAMP or SIM on mutation rate considered here are mediated by some aspect(s) of the culture cycle that differ across different nutrient environments. Such dynamics are largely inaccessible to fluctuation tests, as used here, or indeed other standard methods of assaying mutation rate (Foster 2006) that consider at least one full population growth cycle. It may become possible to assay such changes in the future with single-cell mutation monitoring approaches (Elez et al 2010, Uphoff et al 2016. Variation in mutation rate among members of a population can itself provide evolutionary advantages , and modulating mutation rate in response to the environment could hypothetically allow organisms to optimise their rate of adaptation (Belavkin et al 2016). Such 'optimal' variation involves minimising mutation rates at high fitness, but allowing them to increase away from fitness peaks.
For all cell dilutions sterile saline (8.5 g l -1 NaCl) was used. All media were solidified as necessary with 15 g l -1 of agar (Difco).

Fluctuation tests.
We did fluctuation tests with Escherichia coli as already explained (Krašovec et al 2014, Krašovec et al 2017. In short, strains were first inoculated from frozen stock and grown in liquid LB medium at 37°C and then transferred to nonselective liquid media (LB or DM with glucose) and allowed to grow overnight shaking at 37°C. E. coli cells were again diluted into fresh LB/DM, giving the initial population size (N 0 ) of 2,373 (range 1.5×10 2 -1.3×10 4 ). Various volumes (0.35-1 ml) of parallel cultures were grown to saturation for 24 hours at 37°C in 96 deep-well plates. The position of each culture on a 96-deep-well polypropylene plate was chosen randomly.
Final population size (N t ) was determined by colony forming units (CFU) where appropriate dilution was plated on solid non-selective TA medium. Population density (D) was estimated was determined by two independent techniques using CFU and an ATP based assay: luminescence (LUM) was measured using a Promega GloMax luminometer and the Promega Bac-Titer Glo kit, according to manufacturer's instructions. We measured luminescence of each culture 0.5 and 510 seconds after adding the Bac-Titer Glo reagent and calculated net luminescence as LUM = luminescence 510sluminescence 0.5s . Each estimate of D and N t was averaged across 3 independent cultures. Evaporation (routinely monitored by weighing plate before and after 24h incubation) was accounted for in the N t value determined by CFU and was also used in statistical modelling as a variance covariate. We obtained the observed number of mutants resistant to rifampicin or nalidixic acid, r, by plating the entirety of remaining cultures onto solid selective TA medium (4.5cm plates in Figs. 1-2 and 9cm plates in Fig. 3) that allows spontaneous mutants to form colonies. Plates were incubated at 37°C and mutants were counted at the earliest possible time after plating.
For rifampicin plates this was 44-48 hours, when nalidixic acid was used the incubation time was 68-72 hours. This issue can be corrected for by co-estimating the average fitness effect of resistance mutations with the mutation number of mutational events (Zheng 2005). In addition, variation in N t may also affect estimates and may also be accounted for (Ycart and Veziris 2014). We therefore co-estimated mutation rates and fitness effects, accounting for variability in N t using the flan package in R (Adrien et al 2017), also setting the Winsorization parameter to remove the effects of 'jackpots' with un-countably large numbers of mutants (greater than 150 on 4.5cm plates and greater than 1000 on 9cm plates). Since the estimated fitnesses (Fig. S8) tend to reinforce the patterns seen in Fig. 1-3, we report the results of the simpler and more widely used calculations in the main text as being more conservative.   Supplementary Information N=97). Cells were grown in Davis minimal medium mixed with 1% to 90% of lysogeny broth (LB) medium. Colours represent a range of population densities from 4.5×10 7 (dark blue) to 3.3×10 9 (dark red, see Fig. S1 for details of the scale). See Figure S3 for a plot of mutation rate directly against population density and S9 for mutation rates co-estimated with the relative fitness of resistant mutants. Note the non-linear axes.

Figure 2.
Effect of nutrient availability on mutation rate to nalidixic acid resistance in cells without DAMP (ΔmutT, N=30). Cells were grown in Davis minimal medium mixed with 1% to 90% of lysogeny broth (LB) medium. Colours represent a range of population densities from 4.5×10 7 to 4.5×10 9 (see Fig. S1 for details of the colour scale). See Fig.   S5 for a plot of mutation rate directly against population density and S10 for mutation rates co-estimated with the relative fitness of resistant mutants. Note the non-linear axes. There is no evidence of a non-linear relationship of log mutation rate with nutrient availability (likelihood ratio test of a quadratic effect [N=36,LR 8,7 =0.15,P=0.70]), but there is a highly significant linear effect of nutrient availability (likelihood ratio test of linear effect [N=36, LR 7,6 =45, P=1.6×10 -11 ], see model S-IV in Supplementary   Information). Colours represent a range of ΔdinB and ΔumuC population densities, 4.8×10 7 -3.5×10 9 and 5.6×10 7 -3.2×10 9 , respectively (see also Fig. S1). See Figure S7 for an equivalent plot using population density and S11 for mutation rates co-estimated with the relative fitness of resistant mutants. Note the non-linear axes.