Abstract Rates of random, spontaneous mutation can vary plastically, dependent upon the environment. Such plasticity affects evolutionary trajectories and may be adaptive. We recently identified an inverse plastic association between mutation rate and population density at 1 locus in 1 species of bacterium. It is unknown how widespread this association is, whether it varies among organisms, and what molecular mechanisms of mutagenesis or repair are required for this mutation-rate plasticity. Here, we address all 3 questions. We identify a strong negative association between mutation rate and population density across 70 years of published literature, comprising hundreds of mutation rates estimated using phenotypic markers of mutation (fluctuation tests) from all domains of life and viruses. We test this relationship experimentally, determining that there is indeed density-associated mutation-rate plasticity (DAMP) at multiple loci in both eukaryotes and bacteria, with up to 23-fold lower mutation rates at higher population densities. We find that the degree of plasticity varies, even among closely related organisms. Nonetheless, in each domain tested, DAMP requires proteins scavenging the mutagenic oxidised nucleotide 8-oxo-dGTP. This implies that phenotypic markers give a more precise view of mutation rate than previously believed: having accounted for other known factors affecting mutation rate, controlling for population density can reduce variation in mutation-rate estimates by 93%. Widespread DAMP, which we manipulate genetically in disparate organisms, also provides a novel trait to use in the fight against the evolution of antimicrobial resistance. Such a prevalent environmental association and conserved mechanism suggest that mutation has varied plastically with population density since the early origins of life.

Author summary Spontaneous mutations fuel evolution, but the rate at which they occur can vary for a particular organism depending on its environment—a phenomenon known as mutation-rate plasticity. For microbes growing in liquid, the density to which a population can grow is a key feature of the environment. We find that organisms’ mutation rates are associated with the density to which they grow, such that higher population densities are associated with lower mutation rates. Initially we identify this density-associated mutation-rate plasticity (DAMP) in data culled from the published literature: beyond well-known patterns of mutation-rate variation among organisms, we see substantial variation within diverse organisms, the large majority of which is associated with population densities. We test this association in the laboratory, finding DAMP at different sites in the genomes of both bacteria (Escherichia coli) and eukaryotes (the yeast, Saccharomyces cerevisiae). In each case, DAMP requires a protein that avoids mutation by cleaning cells of oxidatively damaged guanine nucleotides (MutT in E. coli and Pcd1 in yeast). In our assays, DAMP results in a lower probability of seeing the evolution of antibiotic resistance at higher population densities. We anticipate that DAMP affects the course of evolution more generally and that understanding its causes and effects will help us to understand and control evolutionary trajectories.

Citation: Krašovec R, Richards H, Gifford DR, Hatcher C, Faulkner KJ, Belavkin RV, et al. (2017) Spontaneous mutation rate is a plastic trait associated with population density across domains of life. PLoS Biol 15(8): e2002731. https://doi.org/10.1371/journal.pbio.2002731 Academic Editor: Jeff Gore, Massachusetts Institute of Technology, United States of America Received: April 12, 2017; Accepted: July 21, 2017; Published: August 24, 2017 Copyright: © 2017 Krašovec et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: All relevant data are within the paper and its Supporting Information files, except the genome sequence data underlying S3 Table, which is available from the European Nucleotide Archive (accession number ERP024110, http://www.ebi.ac.uk/ena/data/view/ERP024110). Funding: Biotechnology and Biological Sciences Research Council www.bbsrc.ac.uk. This project was supported by BB/L009579/1, BB/M021157/1 and BB/M021106/1, HR was supported by BB/M011208/1, DG and EA were supported by BB/M020975/1. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. School of Biological Sciences, Faculty of Biology Medicine and Health, The University of Manchester https://www.bmh.manchester.ac.uk. Additional support to RK. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Wellcome Trust https://wellcome.ac.uk/. Additional support to CK (082453/Z/07/Z) and RK (105610/Z/14/Z). The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. European Molecular Biology Organization http://www.embo.org/ (grant number ASTF 642—2014). Fellowship support to RK. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. Abbreviations: 5-FOA, 5-Fluoro-orotic acid; CC, Cell Counts; CFU, Colony-Forming Units; D, The final population density; DAMP, Density-associated mutation-rate plasticity; GO, 8-Hydroxyguanine; m, Number of mutational events; MMR, Methyl-directed DNA mismatch repair; N 0 , The initial population size; N t , The final population size; N e , The effective population size

Introduction The probability of spontaneous genetic mutations occurring during replication evolves among organisms [1]. This mutation rate can also vary at a particular site in a particular genotype, dependent upon the environment [2]. Specifically, mutation rate can increase with endogenous and exogenous factors [3]. Indeed, any factor that affects the balance between mutagenesis and DNA repair can modify the mutation rate. These include intracellular nucleotide pools [4], organism age [5], and factors affecting the expression [6] and stochastic presence or absence [7] of low copy number repair proteins. Where such mutation/repair-balance factors depend on the environment, the result is mutation-rate plasticity. Plastic mutation rates have been most thoroughly addressed for stress-induced mutagenesis. This may involve the induction of error-prone polymerases, for instance, in the E. coli SOS response [8]. We have recently identified a novel mode of mutation-rate plasticity in response to population density in E. coli. This plasticity does not have any very obvious association with stress—the densest populations, experiencing the most competition, show the lowest mutation rates [9]. Understanding mutation-rate plasticity is hampered by the difficulty of accurately measuring any mutation rate. Spontaneous mutation rates have long been estimated in microbes using counts of cells gaining a phenotypic marker of mutation in environments lacking selection for that marker: the “fluctuation test” created by Luria and Delbrück in 1943 [10]. Alternative approaches to measuring rates of mutation in the absence of selection, such as accumulation of mutations through many population bottlenecks [11], directly comparing genome sequences of parents and offspring [12], or targeted population sequencing [13], are much more laborious and thus poorly suited to potentially dynamic responses. Therefore, well-conducted fluctuation tests [14], remain the most appropriate tool to assay environmental dependence in mutation rates. Population density affects many traits, particularly in microbes [15]. Its association with mutation rate has great potential to affect evolutionary trajectories [16] in ways relevant to the evolution of antimicrobial resistance [9]. However, thus far, this plasticity associated with population density is poorly understood: Its prevalence across domains of life is unknown. Whether it varies among organisms, enabling its evolution, remains to be tested. A little is known about the relationship of mutation rate with density perception in 1 organism [17], but the required downstream mechanisms of mutation or repair remain uncharacterised. Here, we address each of these issues. We demonstrate that there is indeed density-associated mutation-rate plasticity (DAMP) across domains of life: high population density is associated with low mutation rates. DAMP differs between closely related organisms, indicating that this trait does indeed evolve. Strikingly, the same mutation avoidance mechanism is required to modulate mutation rate in response to population density in both prokaryotes and eukaryotes.

Discussion The negative association between published mutation rates and population density (D, Fig 1) is remarkably tight. Much of the between-organism variation in microbial mutation rate is associated with variation in genome size, in which larger genomes tend to have smaller per-base-pair mutation rates [28]. We account for this in our analysis of the data in Fig 1 by allowing mutation rates to vary among organisms and accounting for their phylogeny (explicitly including a typical genome size for each organism makes little difference to this analysis, Model S-I in S1 Text). However, the within-organism variation in mutation rate associated with D is strong enough to explain radical differences in mutation-rate estimates for the same organism within and between laboratories, without assuming any inconsistency in the fluctuation test itself. For instance, the estimates for Salmonella at the bottom of Fig 1 vary by over an order of magnitude but diverge little from a negatively sloping straight line. This suggests that, once population density is taken into account, fluctuation tests can give a more precise estimate of mutation rate than previously believed. Fluctuation tests, however, have drawbacks, such as the possibility of unanticipated selection on mutant cells in a supposedly nonselective environment [19]. We avoided that specific issue here by using short incubation times and making estimates at multiple loci. The more general drawback of using fluctuation tests for considering environmental correlates (shared with most other methods for estimating mutation rates) is that they average across the time-varying environment of batch culture. Thus almost any environmental variable, including population density, has no fixed value and is itself associated with many other characteristics of the culture, both environmental and organismal (e.g., times spent in different phases of the culture cycle). Thus, while we have demonstrated an association of mutation rate with final population density D (Fig 2) and the dependence of that association on a downstream mechanism (Fig 4), the link between 8-oxo-dGTPase and D remains unclear. Nonetheless, 2 important things can be said about this link. First, DAMP is observed across a wide range of environmental conditions and organisms (Fig 1 and Fig 2), which argues that features of particular environments, such as the starting nutrient concentration, as manipulated here, are unlikely to provide a general link between D and mutation rate. Second, we have previously demonstrated that in 1 organism, E. coli, cell–cell interactions are involved in DAMP and deletion of a quorum-sensing gene (luxS) breaks the association between D and mutation rate [9], demonstrating that population interactions can be important for DAMP. Such quorum-sensing mechanisms occur widely (even in some phages [29]). Future work, therefore, needs to focus on asking whether DAMP is associated with particular environmental molecules. Mutation rate is a central population genetic parameter. Across organisms, it is negatively associated with the other central population genetic parameter, effective population size (N e ) [1]. In our experiments, despite 2 orders of magnitude variation in each measure, we find no consistent association between mutation rate and N e (S9 Fig). This is unsurprising because the proposed reason for the negative association across organisms is that selection for replication fidelity is more efficient at higher N e , meaning that, over the long term, average mutation rates evolve to be lower at higher N e [1]. In our short-term experiments, there is little opportunity for such evolutionary change to occur, so we do not see this association. Nonetheless, this reinforces the clear distinction between within-organism plasticity and among-organism variation in mutation rate. Both have shaped mutation rates in the published literature (Fig 1), and we are able to separate the 2, both statistically and by focused experiments (Fig 2). There may be links between the causes of among-organism variation and within-organism plasticity in mutation rate, for instance, in the differing opportunities for selection on replication fidelity in polymerases expressed in common or rare environmental conditions [30]. However, the evolutionary causes and effects of within-organism plasticity in mutation rate in general, and DAMP in particular, need further investigation. The evolutionary causes of plasticity in mutation rates need not be adaptive [30]. Nonetheless, mutation is an evolutionary mechanism, so any plastic variation in mutation rates will have consequences for evolutionary trajectories [31]. What the evolutionary consequences might be depend on how mutation rate associates with the environment. For evolutionary computing, in which mutation rate is controlled, understanding the effect of that control is an important area of research [32]. In biology, constitutively high mutation rates can evolve under specific circumstances [33,34], but incur the costs of many, typically deleterious, mutations. If plasticity is such that mutation rate is inversely related to absolute organismal fitness, then organisms may benefit from a high mutation-supply rate without paying the full evolutionary cost of a constitutively raised mutation rate, as seen in mathematical studies of evolutionary systems [16] and population genetic models [35]. In some circumstances, DAMP can result in such a negative association of mutation rate with fitness [9], but the evolutionary effects of this remain to be tested. The probability of a particular mutational event occurring (e.g., the emergence of spontaneous antibiotic resistance) might be expected to increase with D, as denser populations, containing more cells, will have had more opportunity for mutation. But for the DAMP described here, this increase is offset by a reduction in the mutation rate. This offsetting means that for organisms with DAMP, numbers of mutational events per space and time vary much less with N t than expected from a fixed mutation rate per generation (S10 Fig). Population genetic models typically consider mutations per replication to be constant for an organism. However, we find that the approximate constant is the number of mutational events per space and time (S10 Fig). This is consistent with observations of invariant numbers of mutations per time in Mycobacterium infections [36] and, indeed, in human somatic [37] and germ cells [6]. Both the occurrence across domains of life (Fig 2) and the conserved mutation avoidance mechanism required (Fig 4) point to an ancient evolutionary origin for DAMP. Furthermore, Fig 1 suggests that DAMP also occurs in viruses and bacteriophage. Any variation in mutation rates in viruses and phage lacking mutation-avoidance or -correction mechanisms must be mediated by the host environment. Consistent with this, we see different mutation rates, but similar DAMP, for the same RNA virus in different host cells (S11 Fig reanalysed from [38]). DAMP itself, therefore, seems closely related to basic processes of replication common to all organisms. Nonetheless, our findings are limited to organisms in which it is possible to assay mutation rate by fluctuation tests. This excludes multicellular eukaryotes, so how our findings might apply to them is unclear. Recent findings of variation in mitochondrial mutation rates at different population sizes and densities of the nematode Caenorhabditis elegans highlight the challenge of separating out what population density could mean at the organism, tissue, cellular, and subcellular (e.g., mitochondrial) levels [39]. Even so, if it were possible to manipulate microbial DAMP clinically as well as genetically (Fig 4), for instance as a strategy to slow the rate at which antibiotic resistance arises [40], that could be applicable across the breadth of microbes, including pathogenic viruses.

Materials and methods Strains used in this study See S2 Table. Media We used MilliQ water for all media. Tetrazolium arabinose agar (TA), Davis minimal medium (DM), and M9 minimal medium were prepared according to [41]. Luria-Bertani medium (LB), yeast extract peptone medium (YP), and yeast nitrogen base (YNB) were prepared according to manufacturers’ instructions. Magnesium sulphate heptahydrate, thiamine hydrochloride, carbon source (3 g/l L-arabinose or various concentrations of D-glucose), and 2,3,5-triphenyltetrazolium chloride (Sigma T8877) were sterile filtered and added to a cooled medium. Selective TA medium was supplemented with freshly prepared rifampicin (50 μg/ml) or nalidixic acid (30 μg/ml). Selective YP medium was supplemented with freshly prepared 5-FOA (1,000 μg/ml) or hygromycin B (300 μg/ml). For all cell dilutions, sterile saline (8.5 g/l NaCl) was used. All media were solidified as necessary with 15 g/l of agar (Difco). Fluctuation tests with bacteria We did fluctuation tests with E. coli and P. aeruginosa as explained in [9]. In short, strains were first inoculated from frozen stock and grown in liquid LB medium at 37°C and then transferred to nonselective liquid DM (for E. coli) or M9 (for P. aeruginosa), supplemented with a particular concentration of glucose (25–300 mgl−1), and allowed to grow overnight shaking at 37°C. E. coli and P. aeruginosa were again diluted into fresh DM or M9 medium, respectively, giving the initial population size (N 0 ) of around 10,000 (range 2.5×102 to 1.3×105) and 5,000 (range 2.5×103 to 1.2×104), respectively. Various volumes (0.5–10 ml) of parallel cultures were grown to saturation for 24 hours at 37°C in 96-deep-well plates or 50 ml falcon tubes. The position of each culture on a 96-well plate was chosen randomly. N t of each culture was determined by 2 independent techniques. N t was determined by CFU in which appropriate dilution was plated on a solid nonselective TA medium. Estimates of N t using net luminescence were determined using a Promega GloMax luminometer and the Promega Bac-Titer Glo kit, according to manufacturer's instructions. We measured the luminescence of each culture 0.5 seconds and 510 seconds after adding the Bac-Titer Glo reagent and calculated net luminescence as LUM = LUM 510s − LUM 0.5s . Each estimate of N t is an average of 3 cultures. Evaporation (routinely monitored by weighing the plate before and after 24 hours of 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 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. Fluctuation tests with yeast We did fluctuation tests with yeast in a similar way to fluctuation tests with bacteria (see above). Strains were inoculated from frozen stock in liquid YP medium with 20 mg/ml of glucose at 30°C (200 rpm) and then transferred to nonselective liquid YNB medium supplemented with a particular percentage of YP (v/v) and glucose, except for S288C in which YP was not added. We then allowed cultures to grow overnight at 30°C (200 rpm). Overnight cultures were again diluted into fresh medium giving N 0 of around 5,000 per parallel culture (range 5×102 to 5.1×104). Various volumes of parallel cultures (0.35–10 ml) were grown in yeast nitrogen base with 25–8,000 mgl−1 glucose and 0%–7% v/v YP in 96-deep-well plates or in 50 ml falcon tubes to saturation for 48 or 72 hours at 30°C (200 rpm). We positioned each culture on the plate randomly. N t was determined by CFU, in which an appropriate dilution was plated on solid nonselective YP medium. N t determined with haemocytometer (Cellometer Auto M10 –Nexcelom) (CC) was done according to manufacturer’s instructions. N t was calculated with 3 cultures per mutation-rate estimate, in which for each culture, CFU and CC were determined. Evaporation was accounted for in the N t value determined by CFU and also used in statistical modelling as a variance covariate. We obtained the observed number of mutants resistant to 5-FOA or hygromycin B, r, by plating the entirety of remaining cultures onto solid selective YP medium. Plates were incubated at 30°C, and mutants were counted at the earliest possible time after plating, for both markers that was 68–72 hours. For Figs 2A, 2B, 3, 4A, 4B, 4C and 4D, we used 21, 14, 14, 8, 5, 5, and 3 independent experimental blocks, respectively, carried out on different days. Within an experimental block, multiple 96-well plates, or groups of falcon tubes, were used. Any individual mutation-rate estimate requires multiple parallel cultures, which were all carried out on a particular plate, or group of falcon tubes. For Figs 2A, 2B, 3, 4A, 4B, 4C and 4D, the median number of parallel cultures used (with interquartile range) was 16 (15–16), 16 (16–16), 16 (16–16), 16 (16–16), 16 (16–16), 16 (16–16), and 16 (15–16), respectively. Estimation of mutation rates To calculate m from the observed number of mutants, we employed the Ma-Sandri-Sarkar maximum-likelihood method implemented by the FALCOR web tool [42] or rSalvador [43,44]. The mutation rate per cell per generation is calculated as m divided by N t . The median (with interquartile range) of the coefficient of variation for N t estimated with CFU and ATP-based luminescence assay is 15.9% (9.6%–24.8%) and 10.9% (6.9%–18.4%), respectively. N e is calculated as the harmonic mean of the population size across generations. Statistical analysis All statistical analysis was executed in R v3.2.4 and v3.3.1, respectively, when using spaMM v 1.7.2 (Model S-I, S1 Text) and nlme v3.1 (Model S-II to S-XVIII, S1 Text) packages for linear mixed effects modelling [45, 46]. This enabled the inclusion within the same model of experimental factors (fixed effects), blocking effects (random effects), and factors affecting variance (heteroscedasticity) as described in S1 Text. In all cases, the log 2 mutation rate was used. Raw data (S1 Data, described in S4 Table) and R code (S1 Code) are provided, sufficient to reproduce Figs 1–4, S1, S3 and S4 Figs, S6 Fig and S8–S11 Figs. Whole genome sequencing E. coli genomes were sequenced with the Illumina HiSeq2500 platform using 2 x 250 bp paired-end reads. Sequencing and initial read quality checking were provided by MicrobesNG (http://www.microbesng.uk) and deposited at the European Nucleotide Archive (accession number ERP024110, http://www.ebi.ac.uk/ena/data/view/ERP024110). Strains derived from MG1655 and from the Keio collection were aligned to the E. coli str. K-12 substr. MG1655 (NC_000913.3) and E. coli BW25113 (NZ_CP009273.1) genomes, respectively. Mutations (i.e., single nucleotide substitutions, small and large indels, and copy number variants) were predicted using breseq-0.27.2 using the default settings [47]. Published mutation rate search criteria We identified studies that used Luria-Delbrück fluctuation tests for estimating mutation rates. We considered all papers citing the original reference [10] and further searched the Google Scholar and Web of Science databases with keywords “mutation rate”, “Luria Delbruck”, “fluctuation test”, and “fluctuation assay”; we also considered papers cited by papers identified in this way. We collected mutation rate estimations from studies spanning over 70 years, starting with Luria and Delbrück’s pioneering paper in 1943 outlining the fluctuation test [10]. In all, we collected 474 mutation rate estimations from 68 separate studies, covering 26 different organisms from across domains of life (Archaea, Bacteria, Eukaryota) and viruses. From these studies, we recorded the mutation rate estimation, the estimator used for calculating mutation rate, the D of parallel cultures, identity of the nonselective medium, the organism studied, the selective marker used and its concentration, and the study the estimate came from. We excluded estimates that (i) involved microorganisms cultured in intentionally selective conditions, (ii) used genetically manipulated or mutator strains, or (iii) did not plate the entire culture volume onto the selective media. Any of this information that was not included in the published article was collected via a direct communication with the corresponding author. Where the number of observed mutants per plate was available and the estimator was not the Ma-Sandri-Sarkar maximum-likelihood method, we recalculated the mutation rate using this method implemented by the FALCOR web tool [42]. When only the proportion of plates without mutants was available, we recalculated the mutation rate using the P 0 method [14], implemented by equation −ln(P 0 )/N t in which P 0 is the proportion of plates containing no mutant colonies. For viral mutation rates, we recorded the mutation rate as substitutions per strand copying. Where the published mutation rates were not in this format, these were converted using equation 10 in [48]. All these points are highlighted in the column ‘recalculation’ as ‘yes’ in S1 Data (see S4 Table). Phylogeny used in analysing published mutation rates To take account of the fact that organisms may show similarity (including in mutation rates) through common ancestry, we accounted for phylogenetic relatedness using a correlation matrix within our Model S-I (S1 Text). This matrix was derived from a phylogeny (S1 Fig) constructed from a combination of 3 published phylogenies. All the bacteria and archaea came from the ‘All-Species Living Tree’ Project (LTP) [49] version LTPs123, and this phylogeny was used to add other organisms. S. cerevisiae was taken from [50], and viruses were taken from [51]. Branch lengths for S. cerevisiae and the viruses were scaled to correspond to those in the LTP tree as follows. For S. cerevisiae, average branch lengths from the tips to the last common ancestor of the archaea Halobacterium and Sulfolobus were compared for the LTP and Lane and Darst [50] trees. The ratio between them was applied to the branch length of S. cerevisiae in Lane and Darst phylogeny [50] before adding it to the LTP tree at the branch point of the bacteria and archaea. For the viruses, 4 common tips from both trees (P. aeruginosa, Thermus thermophilus, S. cerevisiae, and Halobacterium) were selected, and the distance of each to a shared common ancestor (P. aeruginosa with T. thermophilus and S. cerevisiae with Halobacterium) were plotted against each other. A straight line was then fitted through the origin, and the gradient of that line was used to correct the branch length of the viruses in the Nasir and Caetano-Anollés tree [51] before being added to the combined LTP/S. cerevisiae tree at the branch point of the 3 domains. Some organisms in our analysis were not present in these phylogenies. These were as follows: separate serovars of Salmonella enterica (serovars Typhimurium and Enteritidis), which we treated as subspecies of S. enterica (indica and enterica, present in the tree); Vesicular stomatitis virus and Measles virus, which were combined into their common order of Mononegavirales; and Bacteriophage ΦX174, which was positioned at Bacteriophage M13.

Acknowledgments We thank Johanna M. Schwingel for P. aeruginosa PAO1, Karina B. Xavier for E. coli MG1655, Richard E. Lenski for E. coli B, and Daniela Delneri for all yeast strains. We thank César Aguilar, Sutirth Dey, Jaroslaw Dziadek, Bhavna Gordhan, Alina Górna, Dennis Grogan, Gregory Lang, Sasha Levy, Christina Moon, Shinichi Oide, Marianoel Pereira-Gómez, Colin Russell, Rafael Sanjuán, Gavin James Sherlock, Clara Torres-Barceló, Arjan de Visser, Sebastian Wielgoss, and Clifford Zeyl for providing data. We thank Mark Foster and John Parfitt for technical assistance. Genome sequencing was provided by MicrobesNG (http://www.microbesng.uk), which is supported by the BBSRC (grant number BB/L024209/1). We thank David Robertson, James McInerney, John Fitzpatrick, and Chris Thompson for critical readings of the manuscript.