Evolution of human immunodeficiency virus type 1 cytotoxic T-lymphocyte epitopes: fitness-balanced escape

CD8(+) cytotoxic T lymphocytes (CTL) are strong mediators of human immunodeficiency virus type 1 (HIV-1) control, yet HIV-1 frequently mutates to escape CTL recognition. In an analysis of sequences in the Los Alamos HIV-1 database, we show that emerging CTL escape mutations were more often present at lower frequencies than the amino acid(s) that they replaced. Furthermore, epitopes that underwent escape contained amino acid sites of high variability, whereas epitopes persisting at high frequencies lacked highly variable sites. We therefore infer that escape mutations are likely to be associated with weak functional constraints on the viral protein. This was supported by an extensive analysis of one subject for whom all escape mutations within defined CTL epitopes were studied and by an analysis of all reported escape mutations of defined CTL epitopes in the HIV Immunology Database. In one of these defined epitopes, escape mutations involving the substitution of amino acids with lower database frequencies occurred, and the epitope soon reverted back to the sensitive form. We further show that this escape mutation substantially diminished viral fitness in in vitro competition assays. Coincident with the reversion in vivo, we observed the fixation of a mutation 3 amino acids C terminal to the epitope, coincident with the ablation of the corresponding CTL response. The C-terminal mutation did not restore replication fitness reduced by the escape mutation in the epitope and by itself had little effect on replication fitness. Therefore, this C-terminal mutation presumably impaired the processing and presentation of the epitope. Finally, for one persistent epitope, CTL cross-reactivity to a mutant form may have suppressed the mutant to undetected levels, whereas for two other persistent epitopes, each of two mutants showed poor cross-reactivity and appeared in the subject at later time points. Thus, a viral dynamic exists between the advantage of immune escape, peptide cross-reactivity, and the disadvantage of lost replication fitness, with the balance playing an important role in determining whether a CTL epitope will persist or decline during infection.     

The rate of adaptation in asexuals

I study the population genetics of adaptation in asexuals. I show that the rate of adaptive substitution in an asexual species or nonrecombining chromosome region is a bell-shaped function of the mutation rate: at some point, increasing the mutation rate decreases the rate of substitution. Curiously, the mutation rate that maximizes the rate of adaptation depends solely on the strength of selection against deleterious mutations. In particular, adaptation is fastest when the genomic rate of mutation, U, equals the harmonic mean of selection coefficients against deleterious mutations, where we assume that selection for favorable alleles is milder than that against deleterious ones. This simple result is independent of the shape of the distribution of effects among favorable and deleterious mutations, population size, and the action of clonal interference. In the course of this work, I derive an approximation to the probability of fixation of a favorable mutation in an asexual genome or nonrecombining chromosome region in which both favorable and deleterious mutations occur.     

AN ADAPTIVE WALK BY HUMAN IMMUNODEFICIENCY VIRUS TYPE 1 THROUGH A FLUCTUATING FITNESS LANDSCAPE

The mutational landscape model of adaptive sequence evolution has been used to explain an unexpected strong positive linear relationship between marginal fitness and mean site‐specific amino acid frequency in the functionally important HIV‐1 gp120 V3 protein region. The model predicts a positive linear relationship between the probability that a particular beneficial allele, among several, is the next to spread to fixation during an adaptive walk, its transition probability, and the allele's selection coefficient. Here, stochastic simulation is used to confirm the intuition that the linear relationship between transition probabilities and selection coefficients, predicted by the model, should, under fluctuating selection, produce a linear relationship between allele frequency, averaged across populations, and fitness. In addition, these relationships hold for the effective population size and mutation rate of HIV‐1 and for the moderately strong selection observed for V3. A survey of the strength of mutation for diverse organisms suggests that these relationships may be widely applicable.     

Fitness costs limit viral escape from cytotoxic T lymphocytes at a structurally constrained epitope

The intense selection pressure exerted by virus-specific cytotoxic T lymphocytes (CTL) on replicating human immunodeficiency virus and simian immunodeficiency virus results in the accumulation of CTL epitope mutations. It has been assumed that fitness costs can limit the evolution of CTL epitope mutations. However, only a limited number of studies have carefully examined this possibility. To explore the fitness costs associated with viral escape from p11C, C-M-specific CTL, we constructed a panel of viruses encoding point mutations at each position of the entire p11C, C-M epitope. Amino acid substitutions at positions 3, 4, 5, 6, 7, and 9 of the epitope significantly impaired virus replication by altering virus production and Gag protein expression as well as by destabilizing mature cores. Amino acid substitutions at position 2 of the epitope were tolerated but required reversion or additional compensatory mutations to generate replication-competent viruses. Finally, while amino acid substitutions at positions 1 and 8 of the p11C, C-M epitope were functionally tolerated, these substitutions were recognized by p11C, C-M-specific CTL and therefore provided no selection advantage for the virus. Together, these data suggest that limited sequence variation is tolerated by the region of the capsid encoding the p11C, C-M epitope and therefore that only a very limited number of mutations can allow successful viral escape from the p11C, C-M-specific CTL response.     

Selection, transmission, and reversion of an antigen-processing cytotoxic T-lymphocyte escape mutation in human immunodeficiency virus type 1 infection

Numerous studies now support that human immunodeficiency virus type 1 (HIV-1) evolution is influenced by immune selection pressure, with population studies showing an association between specific HLA alleles and mutations within defined cytotoxic T-lymphocyte epitopes. Here we combine sequence data and functional studies of CD8 T-cell responses to demonstrate that allele-specific immune pressures also select for mutations flanking CD8 epitopes that impair antigen processing. In persons expressing HLA-A3, we demonstrate consistent selection for a mutation in a C-terminal flanking residue of the normally immunodominant Gag KK9 epitope that prevents its processing and presentation, resulting in a rapid decline in the CD8 T-cell response. This single amino acid substitution also lies within a second HLA-A3-restricted epitope, with the mutation directly impairing recognition by CD8 T cells. Transmission of the mutation to subjects expressing HLA-A3 was shown to prevent the induction of normally immunodominant acute-phase responses to both epitopes. However, subsequent in vivo reversion of the mutation was coincident with delayed induction of new CD8 T-cell responses to both epitopes. These data demonstrate that mutations within the flanking region of an HIV-1 epitope can impair recognition by an established CD8 T-cell response and that transmission of these mutations alters the acute-phase CD8(+) T-cell response. Moreover, reversion of these mutations in the absence of the original immune pressure reveals the potential plasticity of immunologically selected evolutionary changes.     

Cytotoxic T-lymphocyte escape mutations identified by HLA association favor those which escape and revert rapidly

Identifying human immunodeficiency virus (HIV) immune escape mutations has implications for understanding the impact of host immunity on pathogen evolution and guiding the choice of vaccine antigens. One means of identifying cytotoxic-T-lymphocyte (CTL) escape mutations is to search for statistical associations between mutations and host human leukocyte antigen (HLA) class I alleles at the population level. The impact of evolutionary rates on the strength of such associations is not well defined. Here, we address this topic using a mathematical model of within-host evolution and between-host transmission of CTL escape mutants that predicts the prevalence of escape mutants at the population level. We ask how the rates at which an escape mutation emerges in a host who bears the restricting HLA and reverts when transmitted to a host who does not bear the HLA affect the strength of an association. We consider the impact of these factors when using a standard statistical method to test for an association and when using an adaptation of that method that corrects for phylogenetic relationships. We show that with both methods, the average sample size required to identify an escape mutation is smaller if the mutation escapes and reverts quickly. Thus, escape mutations identified as HLA associated systematically favor those that escape and revert rapidly. We also present expressions that can be used to infer escape and reversion rates from cross-sectional escape prevalence data.     

Escape from HLA-B*08-restricted CD8 T cells by hepatitis C virus is associated with fitness costs

The inherent sequence diversity of the hepatitis C virus (HCV) represents a major hurdle for the adaptive immune system to control viral replication. Mutational escape within targeted CD8 epitopes during acute HCV infection has been well documented and is one possible mechanism for T-cell failure. HLA-B*08 was recently identified as one HLA class I allele associated with spontaneous clearance of HCV replication. Selection of escape mutations in the immunodominant HLA-B*08-restricted epitope HSKKKCDEL(1395-1403) was observed during acute infection. However, little is known about the impact of escape mutations in this epitope on viral replication capacity. Their previously reported reversion back toward the consensus residue in patients who do not possess the B*08 allele suggests that the consensus sequence in this epitope is advantageous for viral replication in the absence of immune pressure. The aim of this study was to determine the impact of mutational escape from this immunodominant epitope on viral replication. We analyzed it with a patient cohort with chronic HCV genotype 1b infection and in a single-source outbreak (genotype 1b). Sequence changes in this highly conserved region are rare and selected almost exclusively in the presence of the HLA-B*08 allele. When tested in the subgenomic replicon (Con1), the observed mutations reduce viral replication compared with the prototype sequence. The results provide direct evidence that escape mutations in this epitope are associated with fitness costs and that the antiviral effect of HLA-B*08-restricted T cells is sufficiently strong to force the virus to adopt a relatively unfavorable sequence.     

Fixation probability of rare nonmutator and evolution of mutation rates

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation‐selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift‐barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.     

Adaptive evolution of asexual populations under Muller's ratchet

We study the population genetics of adaptation in nonequilibrium haploid asexual populations. We find that the accumulation of deleterious mutations, due to the operation of Muller's ratchet, can considerably reduce the rate of fixation of advantageous alleles. Such reduction can be approximated reasonably well by a reduction in the effective population size. In the absence of Muller's ratchet, a beneficial mutation can only become fixed if it creates the best possible genotype; if Muller's ratchet operates, however, mutations initially arising in a nonoptimal genotype can also become fixed in the population, since the loss of the least-loaded class implies that an initially nonoptimal background can become optimal. We show that, while the rate at which adaptive mutations become fixed is reduced, the rate of fixation of deleterious mutations due to the ratchet is not changed by the presence of beneficial mutations as long as the rate of their occurrence is low and the deleterious effects of mutations (s(d)) are higher than the beneficial effects (s(a)). When s(a) > s(d), the advantage of a beneficial mutation can outweigh the deleterious effects of associated mutations. Under these conditions, a beneficial allele can drag to fixation deleterious mutations initially associated with it at a higher rate than in the absence of advantageous alleles. We propose analytical approximations for the rates of accumulation of deleterious and beneficial mutations. Furthermore, when allowing for the possible occurrence of interference between beneficial alleles, we find that the presence of deleterious mutations of either very weak or very strong effect can marginally increase the rate of accumulation of beneficial mutations over that observed in the absence of such deleterious mutations.     

HLA-Associated Immune Pressure on Gag Protein in CRF01_AE-Infected Individuals and Its Association with Plasma Viral Load

Background

The human leukocyte antigen (HLA)-restricted cytotoxic T-lymphocyte (CTL) immune response is one of the major factors determining the genetic diversity of human immunodeficiency virus (HIV). There are few population-based analyses of the amino acid variations associated with the host HLA type and their clinical relevance for the Asian population. Here, we identified HLA-associated polymorphisms in the HIV-1 CRF01_AE Gag protein in infected married couples, and examined the consequences of these HLA-selected mutations after transmission to HLA-unmatched recipients.

Methodology/Principal Findings

One hundred sixteen HIV-1-infected couples were recruited at a government hospital in northern Thailand. The 1.7-kb gag gene was amplified and directly sequenced. We identified 56 associations between amino acid variations in Gag and HLA alleles. Of those amino acid variations, 35 (62.5%) were located within or adjacent to regions reported to be HIV-specific CTL epitopes restricted by the relevant HLA. Interestingly, a significant number of HLA-associated amino acid variations appear to be unique to the CRF01_AE-infected Thai population. Variations in the capsid protein (p24) had the strongest associations with the viral load and CD4 cell count. The mutation and reversion rates after transmission to a host with a different HLA environment varied considerably. The p24 T242N variant escape from B57/58 CTL had a significant impact on the HIV-1 viral load of CRF01_AE-infected patients.

Conclusions/Significance

HLA-associated amino acid mutations and the CTL selection pressures on the p24 antigen appear to have the most significant impact on HIV replication in a CRF01_AE-infected Asian population. HLA-associated mutations with a low reversion rate accumulated as a footprint in this Thai population. The novel HLA-associated mutations identified in this study encourage us to acquire more extensive information about the viral dynamics of HLA-associated amino acid polymorphisms in a given population as effective CTL vaccine targets.     

Impact of V2 mutations on escape from a potent neutralizing anti-V3 monoclonal antibody during in vitro selection of a primary human immunodeficiency virus type 1 isolate

KD-247, a humanized monoclonal antibody to an epitope of gp120-V3 tip, has potent cross-neutralizing activity against subtype B primary human immunodeficiency virus type 1 (HIV-1) isolates. To assess how KD-247 escape mutants can be generated, we induced escape variants by exposing bulked primary R5 virus, MOKW, to increasing concentrations of KD-247 in vitro. In the presence of relatively low concentrations of KD-247, viruses with two amino acid mutations (R166K/D167N) in V2 expanded, and under high KD-247 pressure, a V3 tip substitution (P313L) emerged in addition to the V2 mutations. However, a virus with a V2 175P mutation dominated during passaging in the absence of KD-247. Using domain swapping analysis, we demonstrated that the V2 mutations and the P313L mutation in V3 contribute to partial and complete resistance phenotypes against KD-247, respectively. To identify the V2 mutation responsible for the resistance to KD-247, we constructed pseudoviruses with single or double amino acid mutations in V2 and measured their sensitivity to neutralization. Interestingly, the neutralization phenotypes were switched, so that amino acid residue 175 (Pro or Leu) located in the center of V2 was exchanged, indicating that the amino acid at position 175 has a crucial role, dramatically changing the Env oligomeric state on the membrane surface and affecting the neutralization phenotype against not only anti-V3 antibody but also recombinant soluble CD4. These data suggested that HIV-1 can escape from anti-V3 antibody attack by changing the conformation of the functional envelope oligomer by acquiring mutations in the V2 region in environments with relatively low antibody concentrations.     

Fitness evolution and the rise of mutator alleles in experimental Escherichia coli populations

We studied the evolution of high mutation rates and the evolution of fitness in three experimental populations of Escherichia coli adapting to a glucose-limited environment. We identified the mutations responsible for the high mutation rates and show that their rate of substitution in all three populations was too rapid to be accounted for simply by genetic drift. In two of the populations, large gains in fitness relative to the ancestor occurred as the mutator alleles rose to fixation, strongly supporting the conclusion that mutator alleles fixed by hitchhiking with beneficial mutations at other loci. In one population, no significant gain in fitness relative to the ancestor occurred in the population as a whole while the mutator allele rose to fixation, but a substantial and significant gain in fitness occurred in the mutator subpopulation as the mutator neared fixation. The spread of the mutator allele from rarity to fixation took >1000 generations in each population. We show that simultaneous adaptive gains in both the mutator and wild-type subpopulations (clonal interference) retarded the mutator fixation in at least one of the populations. We found little evidence that the evolution of high mutation rates accelerated adaptation in these populations.     

Mutational neighbourhood and mutation supply rate constrain adaptation in Pseudomonas aeruginosa

Understanding adaptation by natural selection requires understanding the genetic factors that determine which beneficial mutations are available for selection. Here, using experimental evolution of rifampicin-resistant Pseudomonas aeruginosa, we show that different genotypes vary in their capacity for adaptation to the cost of antibiotic resistance. We then use sequence data to show that the beneficial mutations associated with fitness recovery were specific to particular genetic backgrounds, suggesting that genotypes had access to different sets of beneficial mutations. When we manipulated the supply rate of beneficial mutations, by altering effective population size during evolution, we found that it constrained adaptation in some selection lines by restricting access to rare beneficial mutations, but that the effect varied among the genotypes in our experiment. These results suggest that mutational neighbourhood varies even among genotypes that differ by a single amino acid change, and this determines their capacity for adaptation as well as the influence of population biology processes that alter mutation supply rate.     

The effect of deleterious alleles on adaptation in asexual populations

We calculate the fixation probability of a beneficial allele that arises as the result of a unique mutation in an asexual population that is subject to recurrent deleterious mutation at rate U. Our analysis is an extension of previous works, which make a biologically restrictive assumption that selection against deleterious alleles is stronger than that on the beneficial allele of interest. We show that when selection against deleterious alleles is weak, beneficial alleles that confer a selective advantage that is small relative to U have greatly reduced probabilities of fixation. We discuss the consequences of this effect for the distribution of effects of alleles fixed during adaptation. We show that a selective sweep will increase the fixation probabilities of other beneficial mutations arising during some short interval afterward. We use the calculated fixation probabilities to estimate the expected rate of fitness improvement in an asexual population when beneficial alleles arise continually at some low rate proportional to U. We estimate the rate of mutation that is optimal in the sense that it maximizes this rate of fitness improvement. Again, this analysis relaxes the assumption made previously that selection against deleterious alleles is stronger than on beneficial alleles.     

HIV evolution: CTL escape mutation and reversion after transmission

Within-patient HIV evolution reflects the strong selection pressure driving viral escape from cytotoxic T-lymphocyte (CTL) recognition. Whether this intrapatient accumulation of escape mutations translates into HIV evolution at the population level has not been evaluated. We studied over 300 patients drawn from the B- and C-clade epidemics, focusing on human leukocyte antigen (HLA) alleles HLA-B57 and HLA-B5801, which are associated with long-term HIV control and are therefore likely to exert strong selection pressure on the virus. The CTL response dominating acute infection in HLA-B57/5801-positive subjects drove positive selection of an escape mutation that reverted to wild-type after transmission to HLA-B57/5801-negative individuals. A second escape mutation within the epitope, by contrast, was maintained after transmission. These data show that the process of accumulation of escape mutations within HIV is not inevitable. Complex epitope- and residue-specific selection forces, including CTL-mediated positive selection pressure and virus-mediated purifying selection, operate in tandem to shape HIV evolution at the population level.     

From bad to good: Fitness reversals and the ascent of deleterious mutations

Deleterious mutations are considered a major impediment to adaptation, and there are straightforward expectations for the rate at which they accumulate as a function of population size and mutation rate. In a simulation model of an evolving population of asexually replicating RNA molecules, initially deleterious mutations accumulated at rates nearly equal to that of initially beneficial mutations, without impeding evolutionary progress. As the mutation rate was increased within a moderate range, deleterious mutation accumulation and mean fitness improvement both increased. The fixation rates were higher than predicted by many population-genetic models. This seemingly paradoxical result was resolved in part by the observation that, during the time to fixation, the selection coefficient (s) of initially deleterious mutations reversed to confer a selective advantage. Significantly, more than half of the fixations of initially deleterious mutations involved fitness reversals. These fitness reversals had a substantial effect on the total fitness of the genome and thus contributed to its success in the population. Despite the relative importance of fitness reversals, however, the probabilities of fixation for both initially beneficial and initially deleterious mutations were exceedingly small (on the order of 10⁻⁵ of all mutations).     

Cytotoxic T lymphocytes do not appear to select for mutations in an immunodominant epitope of simian immunodeficiency virus gag.

Studies to date assessing HIV escape from CTL in vivo have yielded conflicting results. Previous studies have demonstrated that simian immunodeficiency virus of macaques (SIVmac)-infected rhesus monkeys expressing the MHC class I allele Mamu-A*01 reproducibly develop a gag-specific CTL response limited to a 9-amino acid epitope of the SIVmac gag protein (residues 182-190 within peptide 11C). To determine whether CTL have a role in selecting for AIDS virus mutants, we examined mutations in SIVmac proviral DNA encoding this gag CTL epitope in PBL of infected rhesus monkeys. Three Mamu-A*01+ rhesus monkeys were infected with SIVmac and assessed for gag- and peptide 11C-specific CTL responses. This specific CTL response was maintained in two monkeys, but lost in the third animal 2 yr after infection. The generation of proviral gag mutations was then determined by sequencing 500-bp proviral fragments amplified from fresh PBL obtained from the monkeys more than 2.5 yr after infection. Although numerous point mutations were characterized in 131 polymerase chain reaction-generated clones of SIVmac gag, only four mutations within the gag CTL epitope-coding region of the genome were identified. Comparison of synonymous and nonsynonymous nucleotide substitutions in the regions encoding peptide 11C (p11C) and the flanking gag protein indicated a lack of selective pressure for viral mutations in the CTL epitope coding region. Interestingly, a predominant gag mutant encoding a single amino acid change in p11C was found in a monkey which lost its CTL activity. However, even in this setting there was no evidence for selection of mutations in the CTL epitope coding region when compared with the flanking region. Furthermore, synthetic peptides corresponding to all naturally occurring variants in the gag epitope-coding region were recognized by cloned and bulk cultured effector cells of the infected monkeys with persistent CTL. These results indicate that SIVmac gag- and p11C-specific CTL do not select for mutations in the immunodominant epitope-coding region and that the naturally occurring mutants do not appear to escape CTL recognition.     

Adaptation to human populations is revealed by within-host polymorphisms in HIV-1 and hepatitis C virus

CD8(+) cytotoxic T-lymphocytes (CTLs) perform a critical role in the immune control of viral infections, including those caused by human immunodeficiency virus type 1 (HIV-1) and hepatitis C virus (HCV). As a result, genetic variation at CTL epitopes is strongly influenced by host-specific selection for either escape from the immune response, or reversion due to the replicative costs of escape mutations in the absence of CTL recognition. Under strong CTL-mediated selection, codon positions within epitopes may immediately "toggle" in response to each host, such that genetic variation in the circulating virus population is shaped by rapid adaptation to immune variation in the host population. However, this hypothesis neglects the substantial genetic variation that accumulates in virus populations within hosts. Here, we evaluate this quantity for a large number of HIV-1- (n > or = 3,000) and HCV-infected patients (n > or = 2,600) by screening bulk RT-PCR sequences for sequencing "mixtures" (i.e., ambiguous nucleotides), which act as site-specific markers of genetic variation within each host. We find that nonsynonymous mixtures are abundant and significantly associated with codon positions under host-specific CTL selection, which should deplete within-host variation by driving the fixation of the favored variant. Using a simple model, we demonstrate that this apparently contradictory outcome can be explained by the transmission of unfavorable variants to new hosts before they are removed by selection, which occurs more frequently when selection and transmission occur on similar time scales. Consequently, the circulating virus population is shaped by the transmission rate and the disparity in selection intensities for escape or reversion as much as it is shaped by the immune diversity of the host population, with potentially serious implications for vaccine design.     

Marked epitope- and allele-specific differences in rates of mutation in human immunodeficiency type 1 (HIV-1) Gag, Pol, and Nef cytotoxic T-lymphocyte epitopes in acute/early HIV-1 infection

During acute human immunodeficiency virus type 1 (HIV-1) infection, early host cellular immune responses drive viral evolution. The rates and extent of these mutations, however, remain incompletely characterized. In a cohort of 98 individuals newly infected with HIV-1 subtype B, we longitudinally characterized the rates and extent of HLA-mediated escape and reversion in Gag, Pol, and Nef using a rational definition of HLA-attributable mutation based on the analysis of a large independent subtype B data set. We demonstrate rapid and dramatic HIV evolution in response to immune pressures that in general reflect established cytotoxic T-lymphocyte (CTL) response hierarchies in early infection. On a population level, HLA-driven evolution was observed in approximately 80% of published CTL epitopes. Five of the 10 most rapidly evolving epitopes were restricted by protective HLA alleles (HLA-B*13/B*51/B*57/B*5801; P = 0.01), supporting the importance of a strong early CTL response in HIV control. Consistent with known fitness costs of escape, B*57-associated mutations in Gag were among the most rapidly reverting positions upon transmission to non-B*57-expressing individuals, whereas many other HLA-associated polymorphisms displayed slow or negligible reversion. Overall, an estimated minimum of 30% of observed substitutions in Gag/Pol and 60% in Nef were attributable to HLA-associated escape and reversion events. Results underscore the dominant role of immune pressures in driving early within-host HIV evolution. Dramatic differences in escape and reversion rates across codons, genes, and HLA restrictions are observed, highlighting the complexity of viral adaptation to the host immune response.     

Mutators, population size, adaptive landscape and the adaptation of asexual populations of bacteria.

Selection of mutator alleles, increasing the mutation rate up to 10, 000-fold, has been observed during in vitro experimental evolution. This spread is ascribed to the hitchhiking of mutator alleles with favorable mutations, as demonstrated by a theoretical model using selective parameters corresponding to such experiments. Observations of unexpectedly high frequencies of mutators in natural isolates suggest that the same phenomenon could occur in the wild. But it remains questionable whether realistic in natura parameter values could also result in selection of mutators. In particular, the main parameters of adaptation, the size of the adapting population and the height and steepness of the adaptive peak characterizing adaptation, are very variable in nature. By simulation approach, we studied the effect of these parameters on the selection of mutators in asexual populations, assuming additive fitness. We show that the larger the population size, the more likely the fixation of mutator alleles. At a large population size, at least four adaptive mutations are needed for mutator fixation; moreover, under stronger selection stronger mutators are selected. We propose a model based on multiple mutations to illustrate how second-order selection can optimize population fitness when few favorable mutations are required for adaptation.