The rate of compensatory mutation in the DNA bacteriophage phiX174

A compensatory mutation occurs when the fitness loss caused by one mutation is remedied by its epistatic interaction with a second mutation at a different site in the genome. This poorly understood biological phenomenon has important implications, not only for the evolutionary consequences of mutation, but also for the genetic complexity of adaptation. We have carried out the first direct experimental measurement of the average rate of compensatory mutation. An arbitrary selection of 21 missense substitutions with deleterious effects on fitness was introduced by site-directed mutagenesis into the bacteriophage phiX174. For each deleterious mutation, we evolved 8-16 replicate populations to determine the frequency at which a compensatory mutation, instead of the back mutation, was acquired to recover fitness. The overall frequency of compensatory mutation was approximately 70%. Deleterious mutations that were more severe were significantly more likely to be compensated for. Furthermore, experimental reversion of deleterious mutations revealed that compensatory mutations have deleterious effects in a wild-type background. A large diversity of intragenic compensatory mutations was identified from sequencing fitness-recovering genotypes. Subsequent analyses of intragenic mutation diversity revealed a significant degree of clustering around the deleterious mutation in the linear sequence and also within folded protein structures. Moreover, a likelihood analysis of mutation diversity predicts that, on average, a deleterious mutation can be compensated by about nine different intragenic compensatory mutations. We estimate that about half of all compensatory mutations are located extragenically in this organism.     

Functional origins of fitness effect-sizes of compensatory mutations in the DNA bacteriophage phiX174

Abstract Epistasis is an important and poorly understood aspect of mutations and strongly influences the evolutionary impact of genetic variation on adaptation and fitness. Although recent studies have begun to characterize the distribution of epistatic effects between mutations affecting fitness, there is currently a lack of empirical information on the underlying biological causes of these epistatic interactions. What are the functional constraints that determine the effectiveness of a compensatory mutation at restoring fitness? We have measured the effect‐sizes of 52 compensatory mutations affecting nine different deleterious mutations in the major capsid and spike proteins of the DNA bacteriophage X174. On average, an experimentally detectable compensatory mutation recovers about two‐thirds of the fitness cost of the preceding deleterious mutation. Variation in fitness effect‐sizes is only weakly associated with measures of the distance separating the deleterious and compensatory mutations in the amino acid sequence or the folded protein structure. However, there is a strong association of fitness effect‐size with the correlation in the effects of the mutations on the biochemical properties of amino acids. A compensatory mutation has the largest effect‐size, on average, when both the compensatory and deleterious mutations have radical effects on the overall biochemical make‐up of the amino acids. By examining the relative contributions of specific biochemical properties to variation in fitness effect‐size, we find that the area and charge of amino acids have a major influence, which suggests that the complexity of the amino acid phenotype is simplified by selection into a reduced number of phenotypic components.     

Characterization of compensated mutations in terms of structural and physico-chemical properties

The study of the evolution of compensatory mechanisms among amino acids is paramount to our understanding of intramolecular epistatic interactions. It has been addressed from different points of view, for example much effort has been devoted to establish the number of compensatory mutations required per deleterious mutation. However, we still do not know how the nature of the compensated mutation determines the existence of compensatory mutations. Within this context, recent studies have produced several instances of an interesting phenomenon: human disease-associated residues may sometimes appear as wild-type residues in non-human proteins. This can be explained in terms of compensatory mutations, present in the non-human protein, which would neutralize the damage caused by the disease-associated residue. Therefore, comparison between these compensated mutations and non-compensated pathological mutations provides a simple approach to understand how the nature of the compensated deleterious mutation determines the existence of compensatory mutations. To address this issue, we have obtained a large set of compensated mutations and characterised them with a series of different properties. When comparing the resulting distributions with those from pathological mutations we find that in general compensated mutations are milder than pathological mutations. More precisely, we find that the probability that a compensatory mutation will evolve is directly related (i) to the location in the protein structure and (ii) to changes in physico-chemical properties (e.g. amino acid volume or hydrophobicity) of the compensated mutation.     

QUANTITATIVE VARIATION IN FINITE PARTHENOGENETIC POPULATIONS: WHAT STOPS MULLER'S RATCHET IN THE ABSENCE OF RECOMBINATION?

Finite parthenogenetic populations with high genomic mutation rates accumulate deleterious mutations if back mutations are rare. This mechanism, known as Muller's ratchet, can explain the rarity of parthenogenetic species among so called higher organisms. However, estimates of genomic mutation rates for deleterious alleles and their average effect in the diploid condition in Drosophila suggest that Muller's ratchet should eliminate parthenogenetic insect populations within several hundred generations, provided all mutations are unconditionally deleterious. This fact is inconsistent with the existence of obligatory parthenogenetic insect species. In this paper an analysis of the extent to which compensatory mutations can counter Muller's ratchet is presented. Compensatory mutations are defined as all mutations that compensate for the phenotypic effects of a deleterious mutation. In the case of quantitative traits under stabilizing selection, the rate of compensatory mutations is easily predicted. It is shown that there is a strong analogy between the Muller's ratchet model of Felsenstein (1974) and the quantitative genetic model considered here, except for the frequency of compensatory mutations. If the intensity of stabilizing selection is too small or the mutation rate too high, the optimal genotype becomes extinct and the population mean drifts from the optimum but still reaches a stationary distribution. This distance is essentially the same as predicted for sexually reproducing populations under the same circumstances. Hence, at least in the short run, compensatory mutations for quantitative characters are as effective as recombination in halting the decline of mean fitness otherwise caused by Muller's ratchet. However, it is questionable whether compensatory mutations can prevent Muller's ratchet in the long run because there might be a limit to the capacity of the genome to provide compensatory mutations without eliminating deleterious mutations at least during occasional episodes of sex.     

Evolutionary rescue by compensatory mutations is constrained by genomic and environmental backgrounds

Since deleterious mutations may be rescued by secondary mutations during evolution, compensatory evolution could identify genetic solutions leading to therapeutic targets. Here, we tested this hypothesis and examined whether these solutions would be universal or would need to be adapted to one's genetic and environmental makeups. We performed experimental evolutionary rescue in a yeast disease model for the Wiskott–Aldrich syndrome in two genetic backgrounds and carbon sources. We found that multiple aspects of the evolutionary rescue outcome depend on the genotype, the environment, or a combination thereof. Specifically, the compensatory mutation rate and type, the molecular rescue mechanism, the genetic target, and the associated fitness cost varied across contexts. The course of compensatory evolution is therefore highly contingent on the initial conditions in which the deleterious mutation occurs. In addition, these results reveal biologically favored therapeutic targets for the Wiskott–Aldrich syndrome, including the target of an unrelated clinically approved drug. Our results experimentally illustrate the importance of epistasis and environmental evolutionary constraints that shape the adaptive landscape and evolutionary rate of molecular networks.     

Experimental estimate of the abundance and effects of nearly neutral mutations in the RNA virus phi 6

Although the frequency and effects of neutral and nearly neutral mutations are critical to evolutionary patterns and processes governed by genetic drift, the small effects of such mutations make them difficult to study empirically. Here we present the results of a mutation-accumulation experiment designed to assess the frequencies of deleterious mutations with undetectable effects. We promoted the accumulation of spontaneous mutations by subjecting independent lineages of the RNA virus 6 to repeated population bottlenecks of a single individual. We measured fitness following every bottleneck to obtain a complete picture of the timing and effects of the accumulated mutations with detectable effects and sequenced complete genomes to determine the number of mutations that were undetected by the fitness assays. To estimate the effects of the undetected mutations, we implemented a likelihood model developed for quantitative trait locus (QTL) data (Otto and Jones 2000) to estimate the number and effects of the undetected mutations from the measured number and effects of the detected mutations. Using this method we estimated a deleterious mutation rate of U = 0.03 and a gamma effects distribution with mean s=0.093 and coefficient of variation = 0.204. Although our estimates of U and s fall within the range of recent mutation rate and effect estimates in eukaryotes, the fraction of mutations with detectable effects on laboratory fitness (39%) appears to be far higher in 6 than in eukaryotes.     

Human germline mutation in the factor IX gene

The molecular epidemiology of factor IX germline mutations in patients with hemophilia B has been studied in detail because it is an advantageous model for analyzing recent germline mutations in humans. It is estimated that mutations have been defined in the majority of nucleotides that are the target for mutation. The likelihood that a factor IX missense mutation will cause disease correlates with the degree of evolutionary conservation of the amino acid. Mutation rates per base-pair have been estimated after careful consideration and correction for biases, predicting about 76 de novo mutations per generation per individual resulting in 0.3 deleterious changes. The male-to-female sex ratio of mutation varies with the type of mutation. There is evidence for a maternal age effect and an excess of non-CpG G:C to A:T transitions. The factor IX mutation pattern is similar among geographically, racially and ethnically diverse human populations. The data support primarily endogenous mechanisms of germline mutation in the factor IX gene. Mutations at splice junctions are compatible with simple rules for predicting disease causing mutations.     

Lethal mutagenesis and evolutionary epidemiology

The lethal mutagenesis hypothesis states that within-host populations of pathogens can be driven to extinction when the load of deleterious mutations is artificially increased with a mutagen, and becomes too high for the population to be maintained. Although chemical mutagens have been shown to lead to important reductions in viral titres for a wide variety of RNA viruses, the theoretical underpinnings of this process are still not clearly established. A few recent models sought to describe lethal mutagenesis but they often relied on restrictive assumptions. We extend this earlier work in two novel directions. First, we derive the dynamics of the genetic load in a multivariate Gaussian fitness landscape akin to classical quantitative genetics models. This fitness landscape yields a continuous distribution of mutation effects on fitness, ranging from deleterious to beneficial (i.e. compensatory) mutations. We also include an additional class of lethal mutations. Second, we couple this evolutionary model with an epidemiological model accounting for the within-host dynamics of the pathogen. We derive the epidemiological and evolutionary equilibrium of the system. At this equilibrium, the density of the pathogen is expected to decrease linearly with the genomic mutation rate U. We also provide a simple expression for the critical mutation rate leading to extinction. Stochastic simulations show that these predictions are accurate for a broad range of parameter values. As they depend on a small set of measurable epidemiological and evolutionary parameters, we used available information on several viruses to make quantitative and testable predictions on critical mutation rates. In the light of this model, we discuss the feasibility of lethal mutagenesis as an efficient therapeutic strategy.     

Inferring the distribution of mutational effects on fitness in Drosophila

The properties of the distribution of deleterious mutational effects on fitness (DDME) are of fundamental importance for evolutionary genetics. Since it is extremely difficult to determine the nature of this distribution, several methods using various assumptions about the DDME have been developed, for the purpose of parameter estimation. We apply a newly developed method to DNA sequence polymorphism data from two Drosophila species and compare estimates of the parameters of the distribution of the heterozygous fitness effects of amino acid mutations for several different distribution functions. The results exclude normal and gamma distributions, since these predict too few effectively lethal mutations and power-law distributions as a result of predicting too many lethals. Only the lognormal distribution appears to fit both the diversity data and the frequency of lethals. This DDME arises naturally in complex systems when independent factors contribute multiplicatively to an increase in fitness-reducing damage. Several important parameters, such as the fraction of effectively neutral non-synonymous mutations and the harmonic mean of non-neutral selection coefficients, are robust to the form of the DDME. Our results suggest that the majority of non-synonymous mutations in Drosophila are under effective purifying selection.     

Patterns of epistasis in RNA viruses: a review of the evidence from vaccine design

Epistasis results when the fitness effects of a mutation change depending on the presence or absence of other mutations in the genome. The predictions of many influential evolutionary hypotheses are determined by the existence and form of epistasis. One rich source of data on the interactions among deleterious mutations that has gone untapped by evolutionary biologists is the literature on the design of live, attenuated vaccine viruses. Rational vaccine design depends upon the measurement of individual and combined effects of deleterious mutations. In the current study, we have reviewed data from 29 vaccine-oriented studies using 14 different RNA viruses. Our analyses indicate that (1) no consistent tendency towards a particular form of epistasis exists across RNA viruses and (2) significant interactions among groups of mutations within individual viruses occur but are not common. RNA viruses are significant pathogens of human disease, and are tractable model systems for evolutionary studies--we discuss the relevance of our findings in both contexts.     

Accumulation of Spontaneous Mutations in the Ciliate Tetrahymena thermophila

Knowledge of the rate and fitness effects of mutations is essential for understanding the process of evolution. Mutations are inherently difficult to study because they are rare and are frequently eliminated by natural selection. In the ciliate Tetrahymena thermophila, mutations can accumulate in the germline genome without being exposed to selection. We have conducted a mutation accumulation (MA) experiment in this species. Assuming that all mutations are deleterious and have the same effect, we estimate that the deleterious mutation rate per haploid germline genome per generation is U = 0.0047 (95% credible interval: 0.0015, 0.0125), and that germline mutations decrease fitness by s = 11% when expressed in a homozygous state (95% CI: 4.4%, 27%). We also estimate that deleterious mutations are partially recessive on average (h = 0.26; 95% CI: –0.022, 0.62) and that the rate of lethal mutations is <10% of the deleterious mutation rate. Comparisons between the observed evolutionary responses in the germline and somatic genomes and the results from individual-based simulations of MA suggest that the two genomes have similar mutational parameters. These are the first estimates of the deleterious mutation rate and fitness effects from the eukaryotic supergroup Chromalveolata and are within the range of those of other eukaryotes.     

Rate of deleterious mutation and the distribution of its effects on fitness in vesicular stomatitis virus

Despite their importance, the parameters describing the spontaneous deleterious mutation process have not been well described in many organisms. If mutations are important for the evolution of every living organism, their importance becomes critical in the case of RNA-based viruses, in which the frequency of mutation is orders of magnitude larger than in DNA-based organisms. The present work reports minimum estimates of the deleterious mutation rate, as well as the characterization of the distribution of deleterious mutational effects on the total fitness of the vesicular stomatitis virus (VSV). The estimates are based on mutation-accumulation experiments in which selection against deleterious mutations was minimized by recurrently imposing genetic bottlenecks of size one. The estimated deleterious mutation rate was 1.2 mutations per genome and generation, with a mean fitness effect of –0.39% per generation. At the end of the mutation-accumulation experiment, the average reduction in fitness was 38% and the distribution of accumulated deleterious effects was, on average, left-skewed. The magnitude of the skewness depends on the initial fitness of the clone analysed. The implications of our findings for the evolutionary biology of RNA viruses are discussed.     

Compensatory evolution in diploid populations

Compensatory mutations are individually deleterious but harmless in appropriate combinations either at more than two sites within a gene or on separate genes. Considering that dominance effects of selection and heterodimer formation of gene products may affect the rate of compensatory evolution, we investigate compensatory neutral mutation models for diploid populations. Our theoretical analysis on the average time until fixation of compensatory mutations shows that these factors play an important role in reducing the fixation time of compensatory mutations if mutation rates are not low. Compensatory evolution of heterodimers is shown to occur more easily if the deleterious effects of single mutants are recessive.     

Compensatory mutations are repeatable and clustered within proteins

Compensatory mutations improve fitness in genotypes that contain deleterious mutations but have no beneficial effects otherwise. As such, compensatory mutations represent a very specific form of epistasis. We show that intragenic compensatory mutations occur non-randomly over gene sequence. Compensatory mutations are more likely to appear at some sites than others. Moreover, the sites of compensatory mutations are more likely than expected by chance to be near the site of the original deleterious mutation. Furthermore, compensatory mutations tend to occur more commonly in certain regions of the protein even when controlling for clustering around the site of the deleterious mutation. These results suggest that compensatory evolution at the protein level is partially predictable and may be convergent.     

Mutation-selection balance in mixed mating populations

An approximation to the average number of deleterious mutations per gamete, Q, is derived from a model allowing selection on both zygotes and male gametes. Progeny are produced by either outcrossing or self-fertilization with fixed probabilities. The genetic model is a standard in evolutionary biology: mutations occur at unlinked loci, have equivalent effects, and combine multiplicatively to determine fitness. The approximation developed here treats individual mutation counts with a generalized Poisson model conditioned on the distribution of selfing histories in the population. The approximation is accurate across the range of parameter sets considered and provides both analytical insights and greatly increased computational speed. Model predictions are discussed in relation to several outstanding problems, including the estimation of the genomic deleterious mutation rates (U), the generality of "selective interference" among loci, and the consequences of gametic selection for the joint distribution of inbreeding depression and mating system across species. Finally, conflicting results from previous analytical treatments of mutation-selection balance are resolved to assumptions about the life-cycle and the initial fate of mutations.     

PERSPECTIVE: SPONTANEOUS DELETERIOUS MUTATION

Mildly deleterious mutation has been invoked as a leading explanation for a diverse array of observations in evolutionary genetics and molecular evolution and is thought to be a significant risk of extinction for small populations. However, much of the empirical evidence for the deleterious-mutation process derives from studies of Drosophila melanogaster, some of which have been called into question. We review a broad array of data that collectively support the hypothesis that deleterious mutations arise in flies at rate of about one per individual per generation, with the average mutation decreasing fitness by about only 2% in the heterozygous state. Empirical evidence from microbes, plants, and several other animal species provide further support for the idea that most mutations have only mildly deleterious effects on fitness, and several other species appear to have genomic mutation rates that are of the order of magnitude observed in Drosophila. However, there is mounting evidence that some organisms have genomic deleterious mutation rates that are substantially lower than one per individual per generation. These lower rates may be at least partially reconciled with the Drosophila data by taking into consideration the number of germline cell divisions per generation. To fully resolve the existing controversy over the properties of spontaneous mutations, a number of issues need to be clarified. These include the form of the distribution of mutational effects and the extent to which this is modified by the environmental and genetic background and the contribution of basic biological features such as generation length and genome size to interspecific differences in the genomic mutation rate. Once such information is available, it should be possible to make a refined statement about the long-term impact of mutation on the genetic integrity of human populations subject to relaxed selection resulting from modern medical procedures.     

A review on the origin and spread of deleterious mutants of the β-globin gene in Indian populations

Deleterious mutations of the human beta-globin gene are responsible for beta-thalassaemia and other haemoglobinopathies, which are the most common genetic diseases in Indian populations. A highly heterogeneous distribution of those mutations is observed in India and certain mutations are restricted to some extent to particular groups only. The reasons behind the geographical clustering and origin of the mutations in India is a highly debated issue and the evidence is conflicting. Our present article aims at tracing the origin of the deleterious beta-globin mutation and evaluates the role of different evolutionary forces responsible for the spread and present distribution of those mutations in Indian populations, using data from molecular biology and statistical methods. Mutations are generated essentially randomly, but "hot-spot" sites for mutation are reported for the beta-globin gene cluster, indicating sequence dependency of mutation. A single origin of a deleterious beta-globin mutation, followed by recombination (in a hot spot region) and/or interallelic gene conversion (within beta-globin gene) through time is the most plausible hypothesis to explain the association of those mutations with multiple haplotype backgrounds and frameworks. It is suggested that India is the place of origin of HbE and HbD mutations and that they dispersed to other parts of the would by migration. HbS mutants present in Indian populations are not of Middle East origin but rather a fresh mutation is the probable explanation for the prevalence among tribal groups. beta-thalassaemia represents a heterogeneous group of mutant alleles in India. Five common and twelve rare mutations have been reported in variable frequencies among different Indian populations. Gene flow of those mutant alleles from different populations of the world by political, military and commercial interactions possibly accounts for the heterogenous nature of beta-thalassaemia among Indians. A multiple allelic polymorphic system of the beta-globin gene exists in different populations. Dynamic interaction of the mutant alleles in the presence of different selective forces including falciparum malaria and biosocial patterns of Indian populations is discussed in order to explain the variable distribution and maintenance of those mutant alleles.     

AMELIORATION OF THE DELETERIOUS PLEIOTROPIC EFFECTS OF AN ADAPTIVE MUTATION IN BACILLUS SUBTILIS

The deleterious pleiotropic effects of an adaptive mutation may be ameliorated by one of two modes of evolution: (1) by replacement, in which an adaptive mutation with harmful pleiotropic effects is replaced by one that confers an equal benefit but at less cost; or (2) by compensatory evolution, in which natural selection favors modifiers at other loci that compensate for the deleterious effects of the mutant allele. In this study, we have measured the potential of these two modes of evolution to ameliorate the deleterious pleiotropic effects of resistance to the antibiotic rifampicin in the soil bacterium Bacillus subtilis. One approach was to measure the fitness cost of a series of spontaneous rifampicin-resistance mutations from each of several strains. The potential for amelioration by the replacement mode was estimated by the variation in fitness cost among the mutants of a single strain. Another approach was to introduce a series of different rifampicin-resistance alleles into a diversity of strains, and to measure the fitness cost of rifampicin resistance for each allele-by-strain combination. The potential for amelioration by the replacement mode was estimated by the variation in fitness costs among rifampicin-resistance alleles; the potential for compensatory evolution was estimated by variation in the fitness cost of rifampicin resistance among strains. This study has shown that the cost of rifampicin resistance may be ameliorated by both the compensatory and replacement modes.     

Deleterious Mutations, Apparent Stabilizing Selection and the Maintenance of Quantitative Variation

Apparent stabilizing selection on a quantitative trait that is not causally connected to fitness can result from the pleiotropic effects of unconditionally deleterious mutations, because as N. Barton noted, "...individuals with extreme values of the trait will tend to carry more deleterious alleles...." We use a simple model to investigate the dependence of this apparent selection on the genomic deleterious mutation rate, U; the equilibrium distribution of K, the number of deleterious mutations per genome; and the parameters describing directional selection against deleterious mutations. Unlike previous analyses, we allow for epistatic selection against deleterious alleles. For various selection functions and realistic parameter values, the distribution of K, the distribution of breeding values for a pleiotropically affected trait, and the apparent stabilizing selection function are all nearly Gaussian. The additive genetic variance for the quantitative trait is kQa2, where k is the average number of deleterious mutations per genome, Q is the proportion of deleterious mutations that affect the trait, and a2 is the variance of pleiotropic effects for individual mutations that do affect the trait. In contrast, when the trait is measured in units of its additive standard deviation, the apparent fitness function is essentially independent of Q and a2; and beta, the intensity of selection, measured as the ratio of additive genetic variance to the "variance" of the fitness curve, is very close to s = U/k, the selection coefficient against individual deleterious mutations at equilibrium. Therefore, this model predicts appreciable apparent stabilizing selection if s exceeds about 0.03, which is consistent with various data. However, the model also predicts that beta must equal Vm/VG, the ratio of new additive variance for the trait introduced each generation by mutation to the standing additive variance. Most, although not all, estimates of this ratio imply apparent stabilizing selection weaker than generally observed. A qualitative argument suggests that even when direct selection is responsible for most of the selection observed on a character, it may be essentially irrelevant to the maintenance of variation for the character by mutation-selection balance. Simple experiments can indicate the fraction of observed stabilizing selection attributable to the pleiotropic effects of deleterious mutations.