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Instituto de Biología Molecular y Celular de Plantas, CSIC-UPV, 46022 Valencia, Spain
Correspondence
Rafael Sanjuán
rafsaver{at}ibmcp.upv.es
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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). Epistatic selection can be demonstrated by testing whether mutations act multiplicatively on fitness-related traits (Elena & Lenski, 1997; Whitlock & Bourguet, 2000; Sanjuán et al., 2004b). For deleterious mutations, if the observed fitness is above the expected multiplicative value, i.e. if mutations lessen their impact as they accumulate, epistasis is antagonistic. On the contrary, if mutations are more harmful as they accumulate, epistasis is synergistic. Genetic interactions are believed to play a central role in evolution, for they should be involved in basic processes as the genesis of genetic diversity (Wright, 1931, 1982), speciation (Dobzhansky, 1936; Muller, 1939), the origin and maintenance of recombination (Crow, 1970; Kondrashov, 1988), or the accumulation of deleterious mutations through genetic drift (Kondrashov, 1994; Butcher, 1995).
In contrast to the number of theoretical studies, there are still relatively few data on the nature of epistasis in real populations. Many experimental studies have sought to detect epistatic selection in eukaryotes and prokaryotes and, alongside some cases of synergistic epistasis (Mukai, 1969; de Visser et al., 1996; Whitlock & Bourguet, 2000), no deviation from multiplicative effects has been observed in other cases (Elena & Lenski, 1997; de Visser & Hoekstra, 1998; Elena, 1999; Elena & Lenski, 2001; Burch et al., 2003). Recent studies have provided new insights that antagonistic epistasis might be the norm among RNA viruses, in contrast to other biological systems (Burch & Chao, 2004; Sanjuán et al., 2004b; Bonhoeffer et al., 2004). First, after carrying out a mutation accumulation experiment, Burch & Chao (2004) reported that, in bacteriophage 
6, mutations are less harmful in low fitness genetic backgrounds than in high fitness backgrounds. Second, after performing a site-directed mutagenesis study in the vesicular stomatitis virus (VSV), Sanjuán et al. (2004b) concluded that, on average, the fitness of genotypes carrying two random mutations was above the multiplicatively expected value. Finally, Bonhoeffer et al. (2004) measured the productivity of nearly 10 000 human immunodeficiency type 1 virus genotypes carrying mutations that had accumulated in patients, predominately on drug therapy, in the reverse transcriptase and protease genes, concluding that, on average, fitness was higher than expected in the absence of epistasis.
The success in finding epistasis among RNA viruses, in contrast to more complex genomes, might stem from technical reasons, namely the ability to perform a higher number of replicates and to manipulate genomes more finely, but it could also reflect some specific genetic features. First, RNA viruses have extremely compact genomes, with little redundancy, few non-essential regions and frequent gene overlapping. Hence, most mutations are likely to affect a large portion of the whole set of viral functions and as a consequence, single mutations can be strongly deleterious (Domingo et al., 1996, 2001; Novella, 2003; Sanjuán et al., 2004a). Conversely, multiple mutations are likely to hit repeatedly the same functions. In this latter case, mutational effects can overlap with a higher chance than if non-related genes are hit, thus producing antagonistic epistasis (Wilke et al., 2003; Elena et al., 2006). Second, RNA frequently adopts secondary structures, with hairpin stems formed by base-pairing stretches. Single mutations can destabilize these structures, but there exists the possibility that subsequent mutations, despite their standalone deleterious effects, restore base-pairing, thereby compensating the effects of previous mutations. Here, I focus on the U5-IR region of the Rous sarcoma virus (RSV), which is adjacent to the primer binding site and adopts a conserved stem and loop structure. The region is multifunctional and essential for virus survival, since it is needed for efficient initiation of reverse transcription, encodes the integrase recognition site at the end of the U5 viral DNA and, may have a role in RNA packaging. Taking advantage of a previously published random library dataset (Johnson et al., 2004), I developed a simple method for estimating the intensity of selection and quantifying epistasis in this region of RSV. As expected, the data are consistent with strong mutational effects and antagonistic epistasis.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Model.
Given that for each target site, initially all four nucleotides have the same frequency, the probability of finding a nucleotide other than that of the wild-type is 0.75 for each site. Hence, in the target sequence, the number of differences to the wild-type, i, follows a binomial distribution,
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| (1) |
In the absence of selection, this initial distribution will remain unchanged if newly arising mutations are neglected (this assumption is reasonable in the short term, because the mutant frequency is high enough not to be noticeably affected by de novo mutation). Similarly, genetic recombination can be neglected provided that the target stretch is short enough to ensure a quasi-complete linkage between nucleotide positions during the time scale in which the experiment takes place. Here, the target is no more than 9 nt long, and less than 10 generations elapse during the evolution experiment. The model is deterministic since selection is the only factor assumed to modify the initial mutant frequency distribution. Under the multiplicative effects model, the expected fitness, E(W), associated to genotypes carrying i mutations is
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| (2) |
s1), here assumed to be constant for simplicity. After g generations, the frequency of genotypes carrying i mutations will be reduced relative to the wild-type sequence by a factor of (1–s)gi. The frequency of genotypes carrying i mutations after g generations will be
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| (3) |
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In the presence of epistasis, the expected fitness of genotypes carrying i mutations can be written as
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| (4) |
), where e stands for a mean epistasis coefficient. Epistasis is predominantly synergistic if e<0, effects are multiplicative if e=0 and, if 0<e1, epistasis is antagonistic. After g generations, the frequency of genotypes carrying i mutations will be reduced relative to the wild-type by a factor of (1–s)gi(1–e). The frequency of genotypes carrying i mutations after g generations will be
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| (5) |
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Parameter estimation.
The likelihood of observing i mutations is given by equation 1 for the neutral model, equation 3 for the multiplicative model and equation 5 for the epistatic model, where parameters L and g are experimentally given. For the multiplicative model, parameter s can be estimated, given the data, by maximum-likelihood (ML), assuming that all observations are independent and that hence the overall likelihood is the product of individual likelihoods. For the epistatic model, the parameter vector (s, e) can be estimated in the same manner. Numerical calculations can be done as follows: N, L, g, the number of possible alleles per site (here, four), plus initial values for the selection coefficient (s0) and the epistasis coefficient (e0), when necessary, are set as input parameters. A precision parameter, p, is also defined. In the first round, all combinations in the range s0±10p0 and e0±10p0 are explored in a discrete manner with step size p0. In all cases, I have used s0=0.5, e0=0 and p0=0.05. The output consists of a maximum-likelihood (ML) s1 value (multiplicative model) or a (s1, e1) vector (epistatic model) and its associated log-likelihood. After this first round, s1 or (s1, e1) can be used as new input and p can be set to a lower value to obtain more precise ML estimators.
Model test and confidence intervals.
The neutral, multiplicative and epistatic models are nested and therefore can be compared using a likelihood ratio test (LRT) (Sokal & Rohlf, 2000). If Ln, Lm and Le are the ML values corresponding to the neutral, multiplicative and epistatic model, respectively, quantities 2(logLm–logLn) and 2(log Le–log Lm) follow a 
2 distribution with one degree of freedom under the null hypotheses s=0 and e=0, respectively. More sophisticated methods for model selection (Johnson & Omland, 2004) always led to the same conclusions. The bounds of 95 % confidence intervals can be estimated as the parameter values for which the likelihood of the model drops two log-units. This ‘two logs' rule has indeed the same basis as the LRT, since two is approximately half the percentile 95 % of a 2 distribution with one degree of freedom. Confidence intervals are approximately symmetrical and thus they are given in the form of a simple error through the text.
RSV dataset.
Fig. 1 shows the RSV U5-IR wild-type primary and secondary structure according to Johnson et al. (2004). In this work, the stem and loop were subjected to random mutagenesis in separate experiments. The U5-IR stem library included positions 83–86 and 96–99, hence 48 combinations were possible. The U5-IR loop library included positions 87–95, thus 49 combinations were possible. At each step of the library construction, transfection and in vivo culture, at least 106 clones were sampled and therefore, both libraries should include all possible sequences. Johnson et al. (2004) explored the possibility of a bias in the sequence composition by sequencing 37 individual clones from the U5-IR loop library and no deviations from randomness were observed.
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2x106 cells at an m.o.i. of 0.2 particles per cell. Given that host cells are transformed by RSV, the initially infected cells remain virus-productive until the end of an infection passage, here lasting 72 h. Approximately 3–4 viral particles are released per h per cell (J. Leis, personal communication), yielding approximately 108 particles at the end of each passage. Given that viral absorption takes 1 h, when particles from the second infection cycle are released, all cells should be already infected with viruses released from the first cycle, thus preventing additional infection cycles. This means that 20 % of particles produced after an infection passage came from the primarily infected cells, whereas the remaining 80 % came from the second cycle. Therefore, on average, 1.8 infection cycles took place per passage. Although the definition of a generation in viruses is not straightforward, here, I follow the convention that a generation matches an infection cycle. This convention is based on the fact that synthesis of new viral particles from progenitor particles is concomitant to the release of daughter particles from the host cell. The possibility that more than a single replication round could occur within a cell is ignored.
Two infection passages were carried out by Johnson et al. (2004) for the U5-IR stem experiment, that is, g 3.6 viral generations were completed, whereas for the case of U5-IR loop, five passages were done, thus g 9 generations were completed. For the U5-IR stem, of 50 clones sequenced, 31 had a wild-type genotype, whereas 19 retained one to eight mutations. For the U5-IR loop, of 37 viral clones, five clones had a wild-type sequence, whereas 32 retained one to nine mutations.
Accounting for heterogeneity in the number of generations.
The above model assumes that all individuals have undergone the same number of generations. This would be true for m.o.i.=1 particle per cell, since a single infection could take place per infection passage. Provided that no more than two generations are completed in each infection, in general, for m.o.i.=m and after n passages, the fraction of the population undergoing g generations can be calculated as
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| (6) |
Equation 3 is thus modified as follows:
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| (7) |
Analogously, equation 5 becomes
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| (8) |
For a given m-value, ML estimation of parameters s and e, confidence intervals and LRT were done in the same manner as for the model that assumed no heterogeneity in the number of generations.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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(a) shows the expected frequency of each mutational class under the assumption of neutrality, superposed to the observed frequencies for the U5-IR stem. The log-likelihood for the neutral model (equation 1) is logLn=–402.085. The multiplicative model (equation 3; Fig. 2b) provides a substantially better fit, with a log-likelihood of logLm=–140.556. This improvement is highly significant according to an LRT (2=523.058, P<0.001). The estimated selection coefficient associated to single-nucleotide substitutions is s=0.494±0.035. In turn, the fit is largely improved by introducing epistasis in the model (equation 5; Fig. 2c), yielding logLe=–73.084 (2=134.944, P<0.001). This improvement seems to be due to the ability of the latter model to account for the high frequency of wild-type sequences in the population and the bimodal shape of the observed mutant frequency. For this model, the estimated mean selection coefficient associated to single-nucleotide substitutions is s=0.838±0.002, significantly larger than for the multiplicative effects model, and the mean epistatic coefficient is highly positive (e=0.651±0.033).
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(a) shows the expected frequency of each mutational class under the assumption of neutrality and the observed frequencies for the U5-IR loop. The log-likelihood for the neutral model is logLn=–141.058. The multiplicative model (Fig. 3b) fits the data significantly better (logLm=–101.061, 2=79.994, P<0.001) and the estimated selection coefficient associated to single-nucleotide substitutions in this region is s=0.106±0.019. Nonetheless, the fit to the multiplicative model is improved by the epistatic model (logLe=–77.878, 2=46.366, P<0.001; Fig. 3c). As was the case for the stem region, this better fit seems related to the ability to account for the high wild-type frequency and the bimodal shape of the observed mutant frequency. For the epistatic model, the estimated selection coefficient associated to single-nucleotide substitutions is s=0.477±0.027 and the epistatic coefficient is e=0.666±0.051.
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). Indeed, the estimated selection coefficients are even larger than those obtained with models that do not account for heterogeneity in the number of generations. The epistatic model gives an estimate of s=0.871±0.019 and e=0.552±0.044 for the U5-IR stem, whereas s=0.488±0.036 and e=0.644±0.050 for the U5-IR loop. In both cases, the fit is significantly better than for the multiplicative model (Table 1). In sum, the results are fully consistent with the simpler models that do not account for heterogeneity in the number of generations.
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). Analogous results could be obtained by letting the parameter g vary in the models that do not account for heterogeneity in the number of generations (not shown).
Inferred evolutionary dynamics
The mean population fitness, the variance in the number of mutations and the frequency of the wild-type sequence provide an overview of the population dynamics viruses would follow according to the models considered above. In doing that, I have focused on the experimentally ideal situation where the m.o.i. is one particle per cell. In this particular case, models that do not account for heterogeneity in the number of generations and models that do account for this heterogeneity are equivalent. The mean fitness of the population can be calculated from the expected fitness (equations 2 and 4) and frequency (equations 3 and 5) of each mutant class. The variance in the number of mutations per genotype is 
, 
being the mean number of mutations per genotype in the entire population. Finally, the frequency of the wild-type in the population is directly given by equations 3 and 5. I have explored the expected dynamics of adaptation under the multiplicative and epistatic models, setting both s and e to their corresponding ML estimates. Fig. 4 shows changes in mean population fitness and variance in mutation number for the U5-IR stem and loop. Although the rate of adaptation is initially faster for the multiplicative model, the situation is reversed after few generations and the time to reaching the maximal fitness is shorter for the epistatic model. The effect of including epistasis has two effects on the model. First, it inflates the estimated selection coefficient favouring the fittest sequence. Second, the maximal diversity in the number of mutations reached by the population is larger for positive epistatic coefficients, because genotypes carrying relatively large numbers of mutations are transiently more abundant due to their milder selective disadvantage.
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). Similar results are obtained for the fixation rate of the wild-type (not shown). In contrast, the maximum variance in the number of mutations along the selective sweep is more strongly influenced by the epistasis coefficient than by the selection coefficient (Fig. 5).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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). In mutation accumulation studies, drastic fitness losses, ranging from 22 % in bacteriophage 6 (Chao, 1990) to 82 % in Human immunodeficiency virus 1 (Yuste et al., 1999), have been observed. Burch & Chao (2004) estimated selection coefficients ranging from s=0.054 in phage 6 to s=0.230 in poliovirus 1, well above values reported for more complex systems (Keightley, 1994; Kibota & Lynch, 1996; Elena et al., 1998; Bruggeman et al., 2003). These differences are supported by a site-directed mutagenesis study (Sanjuán et al., 2004a), where a selection coefficient of s=0.514 was estimated for single-nucleotide substitutions in VSV. High sensitivity to mutation is further supported by the lack of neutrality associated to synonymous changes (Novella et al., 2004). In general, the genetic basis for this reduced robustness might lie on the compactness of RNA virus genomes and the abundance of secondary structures displaying a regulatory function (Novella, 2003). Here, selection coefficients of s=0.838 and s=0.477 have been estimated for the U5-IR stem and loop of RSV, respectively. These are non-translated regions, but carry out essential functions for virus survival. The larger value obtained for the U5-IR stem is in accordance with the stronger constraints imposed by the necessity of maintaining a tight secondary structure. On one hand, these results are a good example of low genetic robustness in RNA viruses. On the other hand, it must be acknowledged that they are based on a single region and thus might not be representative of the entire RSV genome.
Three recent studies have reported antagonistic epistasis in RNA viruses (Burch & Chao, 2004; Sanjuán et al., 2004b; Bonhoeffer et al., 2004). Given the heterogeneity of the viral models employed, it seems very plausible that antagonistic epistasis among deleterious mutations is a general feature of RNA viruses. Although fitness is defined in a relative scale in which there is room for accumulating unlimited deleterious effects, in genomes with relatively few functions as those of RNA viruses, mutations are likely to hit repeatedly the same function. When this occurs, the deleterious effects caused by different mutations can partially overlap, hence producing antagonistic epistasis. Interestingly, low genetic robustness and antagonistic epistasis might be related genome properties. In RNA viruses, single mutations can cause significant fitness losses but, after the initial loss, further mutations may have a comparatively lesser impact. Supporting this possibility, theoretical work, RNA folding (Wilke & Adami, 2001) and bacteriophage T7 (You & Yin, 2002) simulations have shown that selection coefficients associated to single mutations are highly correlated to epistasis coefficients. Antagonistic epistasis can be a consequence of abundant RNA secondary structures as well. The latter play a key role in the regulation of gene expression (Hofacker et al., 2004). Indeed, compensatory mutations have been proven to cause an excess of antagonistic epistasis in computer simulations with RNA secondary structures (Wilke et al., 2003). Johnson et al. (2004) showed that some nucleotides in the U5-IR region influence selection of nucleotides at nearby positions, mainly leading to the re-establishment of base pairing after mutagenesis. The results obtained here support these conclusions.
The epistatic model has been designed to describe the adaptive dynamics of a randomized sequence. When populations face new environments, for instance when a virus is challenged by the immunological system or invades a new host, the alleles at some loci (as for example a region encoding an epitope) can become a pool of highly unadapted variants. Hence, the picture of an initially random sequence stretch seems biologically relevant. However, the generality of the model is limited by the assumptions of no genetic drift, no recombination and constant selection coefficients. The first of these assumptions is reasonable in the U5-IR experimental setting, where population sizes were kept high enough to ensure that the effect of drift is negligible. The same is true for recombination, since the mutated loci are tightly linked and the number of experimental passages is low. Finally, mutational effects are obviously variable and hence, the assumption of constant selection and epistasis coefficients is not realistic. Though assessing how variation in selection coefficients might affect the reliability of the analysis would require a more extensive mathematical analysis, some verbal arguments can be made. In the first approach, the model assumed that all viruses at the end of the experiment had undergone a constant number of generations. However, for m.o.i. lower than one particle per cell, after several passages, the population conforms to a pool of lineages that have gone through different numbers of generations and consequently, have experienced variable amounts of selection. For example, for the U5-IR loop library, five discrete classes can be distinguished. Presumably, the effect of introducing variable selection coefficients could be similar to that of introducing variable numbers of generations, since analogously, the model would allow for classes of genotypes under different selection intensities. Regarding epistasis, the present analysis can only measure its overall direction and hence, the results do not preclude the existence of synergistic interactions. Though from a molecular standpoint, it is straightforward that both synergistic and antagonistic interactions must be common, from an evolutionary standpoint, the question of whether mean deviations from multiplicative effects occur is more relevant.
Keeping the limitations of the model in mind, it is predicted that large selection coefficients and strong antagonistic epistasis facilitate fast adaptation, while retaining a transiently high genetic variance. These predictions are in agreement with RNA virus high diversity and rapid adaptation to changing environments (Holland et al., 1982; Novella et al., 1995; Domingo & Holland, 1997). So-called ‘memory genomes’, defined as variants that were formerly fitter but are now maintained at a low frequency in the population (but still higher than expected under a simple mutation-selection balance), have been reported in RNA viruses (Ruiz-Jarabo et al., 2000). According to Figs 2 and 3, some genotypes genetically distant from the wild-type, probably located on the top of neighbouring adaptive peaks, can be transiently maintained in the population at relatively high frequencies, hence creating a multimodal mutant frequency distribution and potentially facilitating re-adaptation to former environments. In contrast, experiments carried out with bacteria have shown that mutations conferring adaptation to specific niches are costly in terms of adaptability (Buckling et al., 2003). Whether differences in genomic organization and epistasis are responsible for differences between RNA virus and DNA organism adaptability is an important issue that still remains to be elucidated. I suggest that after episodes of genetic drift, intense mutagenesis or environmental changes, RNA virus populations could reach suboptimal fitness peaks and that, due to antagonistic epistasis, these suboptimal variants could be maintained in the population, increasing its diversity and, together with high selection coefficients, accelerating adaptation to novel environments.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Received 4 October 2005;
accepted 2 February 2006.
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