article: Understanding how beneficial mutations affect fitness is crucial to our understanding of adaptation by natural selection. Here, using adaptation to the antibiotic rifampicin in the opportunistic pathogen Pseudomonas aeruginosa as a model system, we investigate the underlying distribution of fitness effects of beneficial mutations on which natural selection acts. Consistent with theory, the effects of beneficial mutations are exponentially distributed where the fitness of the wild type is moderate to high. However, when the fitness of the wild type is low, the data no longer follow an exponential distribution, because many beneficial mutations have large effects on fitness. There is no existing population genetic theory to explain this bias towards mutations of large effects, but it can be readily explained by the underlying biochemistry of rifampicin–RNA polymerase interactions. These results demonstrate the limitations of current population genetic theory for predicting adaptation to severe sources of stress, such as antibiotics, and they highlight the utility of integrating statistical and biophysical approaches to adaptation.
  Adaptation by natural selection ultimately depends on the spread of novel beneficial mutations that increase fitness. Can we predict the fitness effects of beneficial mutations? Gillespie[1], [2] argued that extreme value theory (EVT) provides a simple answer to this question: the tails of all-Gumbel type distributions (a very flexible type of distribution that includes many familiar distributions, including the normal) are exponential. As such, the fitness effects of beneficial mutations will be exponentially distributed provided that the fitness of the wild-type is high enough so that beneficial mutations are drawn from the extreme tail of the distribution of fitness effects of mutations. It is however unclear how robust this theory is with respect to the fitness of the population prior to selection. As the absolute fitness of the wild-type decreases (for example, because of environmental change), a larger proportion of single mutations will increase fitness. Beneficial mutations will therefore no longer be drawn exclusively from the tail of the distribution, hence the exponential distribution may no longer apply (Figure 1). In this paper, we investigate how the distribution of fitness effects of beneficial mutations changes with the fitness of the wildtype population using the evolution of antibiotic resistance in the opportunistic pathogen Pseudomonas aeruginosa as a model system. Experimental studies of the underlying distribution of fitness effects of beneficial mutations[3], [4], [5], [6] have lagged behind the theory, both because beneficial mutations are exceedingly rare and because beneficial mutations of small effect are less likely to reach appreciable frequencies in populations because of the combined effects of drift[7] and competition between independent mutations[8]. To overcome these limitations, we used a fluctuation test to isolate clones of the bacterium Pseudomonas aeruginosa with mutations in the β-subunit of RNA polymerase (rpoB) that are beneficial in the presence of the drug rifampicin [9], [10], [11]. Our experimental design ensured that we obtained an unbiased sample of all beneficial mutations. First, we isolated mutants from populations that were propagated in culture media lacking rifampicin, implying that we isolated beneficial mutations prior to any selection for rifampicin resistance. Second, we experimentally prevented competition (ie clonal interference[8]) among independently derived beneficial mutations by randomly choosing independent mutants. Third, we ensured all mutations included in the analyses were unique by sequencing rpoB of the mutants. To test the hypothesis that the fitness effects of beneficial mutations are exponentially distributed, we used log-likelihood tests that have been specifically developed to test this hypothesis using this experimental design[12]. Using this approach, we show that the distribution of fitness effects of beneficial mutations is variable: under conditions where the fitness of the wild-type is high, the fitness effects of beneficial mutations are exponentially distributed, as predicted by theory. However, when the fitness of the wildtype is low, the data may no longer fit an exponential distribution because many beneficial mutations have large effects on fitness. We show that this non-exponential distribution of fitness effects emerges as a direct consequence of the molecular interactions that are under selection in this system and we argue that existing theory on the fitness effects of beneficial mutations cannot be applied to understand adaptation to novel stressful environments, such as those provided by antibiotics.
  The variability in the distribution of fitness effects of beneficial mutations in this study is consistent with population genetic theory. When the fitness of the wild-type is high, beneficial mutations can be viewed from a statistical perspective as representing draws from the extreme tail of the distribution of fitness effects of mutations, hence the fitness effects of beneficial mutations will be exponentially distributed. However, EVT does not specify how high fitness has to be in order for this theory to apply. In our experimental system, this distribution held over a wide range of parameter space: we failed to detect significant deviations from the exponential distribution when the fitness of the wild-type was reduced by 20–30%. When the fitness of the wild-type is low, statistical theory does not make any predictions regarding the form of the distribution of fitness effects of beneficial mutations and hence there is no reason to expect an exponential distribution. Comparable experimental studies in viral systems are in agreement with this idea: Sanjuan and colleagues [4] found that the fitness effects of beneficial mutations are exponentially distributed in VSV under conditions where the fitness of the wild-type is high, while Rokyta et al. [3] found that the fitness effects of beneficial mutations that allow phage to attack novel hosts (ie hosts that are inaccessible to a WT virus) are not exponentially distributed. Note that in these and our experiments, the data may stop fitting the exponential distribution under conditions of low wildtype fitness not only because EVT, by definition, no longer applies, but also because the underlying mutational distributions may vary with environmental conditions. Despite our lack of certainty of the statistical explanation for the observed distribution when the fitness of the wild-type is low, we have a good molecular mechanistic explanation (in retrospect we may have been able to predict this distribution a priori). Specifically, the distribution is biased towards mutations of large effect as a result of the high specificity of interactions between rifampicin and RNA polymerase that arises from the low conformational flexibility of rifampicin. Antibacterial and antiviral drugs are usually involved in highly specific interactions with their target proteins [17], suggesting that a bias towards mutations of large effect may be a general feature of adaptation to antibiotics [17], [18] and other situations when high-specificity protein-ligand interactions are under strong selection, for example during host-parasite interactions[19] or when enzymes are selected to recognize novel substrates[20], [21]. Recently, there has been considerable interest among population geneticists in developing general models of adaptation based on the statistical properties of extreme events. Our work highlights both the strengths and limitations of this approach and we suggest that the development of a complete theory of adaptation will require integrating molecular biology, in order to be able to predict the impact of mutations on fitness, and statistical approaches to adaptation, to be able to understand how natural selection samples the distribution of fitness effects of beneficial mutations during adaptive walks.
  A single clone of Pseudomonas aeruginosa PAO1 was inoculated into 5 ml of M9KB medium that was incubated overnight at 37 C with constant shaking (150 rpm). This overnight culture was diluted down 10−6 into fresh M9KB and 120 uL aliquots of this diluted culture were used to setup 480 cultures on 5 96 well microplates. These cultures were incubated overnight at 37 C without shaking. To isolate beneficial mutations, 5 uL of each of the 480 overnight cultures was plated out on M9KB supplemented with 62. 11 ug/mL of rifampicin, the minimal concentration required for complete inhibition of growth of the wildtype strain. To isolate beneficial mutations, we isolated a single colony from each of the first 80 cultures that gave samples containing exactly 1 colony on agar plate containing rifampicin. To determine the mutations underlying adaptation, we sequenced the rpoB gene in each of the 80 colonies that we isolated in our fluctuation test. Genomic DNA was isolated from each colony using a Wizard Genomic DNA extraction kit (Promega, UK) as per the manufacturer' s instructions. Our sequencing strategy was to first sequence a highly-conserved domain of rpoB that is known to be important for rifampicin resistance in all 80 clones. This region was amplified with primers rpoB_fwd (5′-GTTCTTCAGCGCCGAGCG-3′) and rpoB_rev (5′-GCGATGACGTGGTCGGC-3′) that amplify the region of the rpoB gene between nucleotides 1178 and 1864. Reaction mixtures consisted of BIOTAQ polymerase (Bioline, UK), 1 mM dNTPs, 16 nM (NH4) 2SO4,62. 5 mM Tris-HCL (pH 8. 8), . 01% Tween 20,2 mM MgCl2, and each primer at a concentration of. 2pM. Amplification reactions were carried out as follows: 94 C for 5 minutes, followed by 35 cycles of 94 C for 30 seconds, 60 C for 30 seconds, and 72 C for 1 minute, followed by a final incubation at 72 C for 10 minutes. PCR products were purified using a MultiScreen PCR96 filter plate (Millipore, UK) as per the manufacturer' s instructions. Purified PCR products were sequenced with both forward and reverse primers using BigDye 3. 1 sequencing (Applied Biosystems International) followed by ethanol/EDTA precipitation of sequencing products. In all cases, this strategy identified either a single mutation in this region of rpoB or no mutations. Clones that lacked a mutation in the highly conserved domain of rpoB were subsequently sequenced for a second region that has previously been implicated in rifampicin resistance spanning nucleotides 1 to 1012 of the rpoB gene. This region was amplified and sequenced with primers rpoB_up (5′–ATGGCTTACTCATACACTGAG-3′) and rpo_B1 (5′-CTCGATGCG CACGACCTG-3′). The protocol was the same as described above, except that the annealing temperature used in the PCR reactions was 54 C instead of 60 C. We idenfied a single mutation in this region in all of the clones that did not contain a mutation in the highly conserved domain of rpoB. As a further control, we sequenced the entire rpoB gene in six randomly chosen clones. We failed to detect any second site mutations in rpoB using this approach. To assay fitness, we estimated the growth rate, r, of each beneficial mutation and wildtype PAO1 at 4 different concentrations of rifampicin (0,1, 2,8, and 64 mg/L). Pre-assay overnight cultures of each mutant were prepared by growth in M9KB. These cultures were then diluted 100 fold into fresh culture medium and we measured the growth rate of each culture using an automated microplate reader by taking hourly measurements of optical density at 600 nm (OD600) over a period of approximately 12 hours. All incubations were carried out at 37 C. Assays at low concentrations of rifampicin (0,1, 2,8 mg/L) were carried out with 12 fold replication and assays at high concentrations of rifampicin (64 mg/L) were carried out with 18 fold replication. A further assay was carried out using the same method to measure fitness in the presence of sorangicin (20 ug/mL). OD600 is proportional to the log of cell density, and the slope of OD600 against time (mOD/min) in exponential growth phase therefore provides an estimate of r, the growth rate of the bacterial clone, such that ri, j is the growth rate to the ith genotype at the jth concentration of rifampicin. To test the hypothesis that the fitness effects of beneficial mutations are exponentially distributed, we used a likelihood ratio test developed by Beisel and colleagues [12]. According to EVT, there are three limiting tail distributions, the Fréchet (which has a heavier-than-exponential tail), the Gumbel (which has an exponential tail), and the Weibull (right-truncated). The tails of all three of EVT domains can be described by the generalized Pareto distribution (GPD), which has a cumulative distribution function given by: with shape parameter κ and scale parameter τ. One very interesting property of the GPD is that the shape parameter is threshold-independent. This property of the GPD is critical, because it implies that it is possible to account for any potential bias against detecting mutations of small beneficial effect by simply re-scaling fitness data so that the fitness of beneficial mutations is expressed relative to the least-fit beneficial mutation instead of the wild-type. To take advantage of this property, we estimated the fitness of each beneficial mutation as as wi, j = ri, j−r1, j where wi, j is the fitness of the ith beneficial mutation in the jth environment, ri, j is the growth rate of the ith beneficial mutation in the jth environment, and r1, j is the growth rate of the least fit beneficial mutation in the the jth environment (ie the beneficial mutation that has the smallest increase in growth rate relative to the rifampicin sensitive clone in the jth environment). The likelihood ratio test developed by Beisel and colleagues calculates −2logΛ, negative twice the difference in log-likelihood between two statistical models, one model in which the shape parameter of the GPD is set to 0 and the other in which the scale parameter of the GPD is free to vary (ie H0: κ = 0, HA: κ≠0). P values were calculated by performing 10000 parametric bootstrap replicates using a software package (EVDA) developed for R (software available at http: //www. webpages. uidaho. edu/~joyce/Lab%20Page/Computer-Programs. html). This test is potentially sensitive to measurement error, but the accuracy of our fitness measurements was high enough (Average CV = 19. 8%) that measurement error should not inflate the probability of making a type I error [12]. To measure the resistance conferred by rpoB mutations, we assayed growth in media containing rifampicin at different concentrations. Pre-assay cultures of rpoB mutants and PAO1 were prepared by overnight growth of freezer cultures in M9KB at 37 C. These cultures were then diluted 2. 5×10−5 into M9KB, or M9KB supplemented with rifampicin at the following concentrations (all in ug/mL): 0,3. 9,7. 8,15. 6,31. 3,62. 5,125,250,500, and 1000. Assay cultures were incubated at 37 C and we measured the optical density of cultures after exactly 24 hours of incubation (+/−10 minutes) at 600 nM using an automated microplate reader. We assayed the resistance of 12 cultures of each of the rpoB mutants that we identified and 12 replicates of PAO1. Resistance was calculated as IC50, the concentration of rifampicin necessary to cause a 50% reduction in optical density, using the following regression model: , where y is optical density, measured in absorbance units, x is the concentration of rifampicin, measured in ug/mL, and H is parameter that estimates the rate of decay in optical density with increasing rifampicin concentration.
summary: Adaptation by natural selection depends on the spread of novel beneficial mutations, and one of the most important challenges in our understanding of adaptation is to be able to predict how beneficial mutations impact fitness. Here, we investigate the underlying distribution of fitness effects of beneficial mutations that natural selection acts on during the evolution of antibiotic resistance in the opportunistic human pathogen P. aeruginosa. When the fitness of the wild type is high, most beneficial mutations have small effects. This finding is consistent with existing population genetic models of adaptation based on statistical theory. When the fitness of the wild type is low, most beneficial mutations have large effects. This distribution cannot be explained by population genetic theory, but it can be readily understood by considering the biochemical basis of resistance. This study confirms an important prediction of population genetic theory, and it highlights the need to integrate statistical and biochemical approaches to adaptation in order to understand evolution in stressful environments, such as those provided by antibiotics.
keywords: evolutionary biology
  evolutionary biology/microbial evolution and genomics
  genetics and genomics/population genetics
title: The Distribution of Fitness Effects of Beneficial Mutations in Pseudomonas aeruginosa