Recombination Rate and Selection Strength in HIV Intra-patient Evolution

The evolutionary dynamics of HIV during the chronic phase of infection is driven by the host immune response and by selective pressures exerted through drug treatment. To understand and model the evolution of HIV quantitatively, the parameters governing genetic diversification and the strength of selection need to be known. While mutation rates can be measured in single replication cycles, the relevant effective recombination rate depends on the probability of coinfection of a cell with more than one virus and can only be inferred from population data. However, most population genetic estimators for recombination rates assume absence of selection and are hence of limited applicability to HIV, since positive and purifying selection are important in HIV evolution. Yet, little is known about the distribution of selection differentials between individual viruses and the impact of single polymorphisms on viral fitness. Here, we estimate the rate of recombination and the distribution of selection coefficients from time series sequence data tracking the evolution of HIV within single patients. By examining temporal changes in the genetic composition of the population, we estimate the effective recombination to be ρ = 1.4±0.6×10⁻⁵ recombinations per site and generation. Furthermore, we provide evidence that the selection coefficients of at least 15% of the observed non-synonymous polymorphisms exceed 0.8% per generation. These results provide a basis for a more detailed understanding of the evolution of HIV. A particularly interesting case is evolution in response to drug treatment, where recombination can facilitate the rapid acquisition of multiple resistance mutations. With the methods developed here, more precise and more detailed studies will be possible as soon as data with higher time resolution and greater sample sizes are available.     

Recombination in HIV and the evolution of drug resistance: for better or for worse?

The rapid evolution of drug resistance remains a major obstacle for HIV therapy. The capacity of the virus for recombination is widely believed to facilitate the evolution of drug resistance. Here, we challenge this intuitive view. We develop a population genetic model of HIV replication that incorporates the processes of mutation, cellular superinfection, and recombination. We show that cellular superinfection increases the abundance of low fitness viruses at the expense of the fittest strains due to the mixing of viral proteins during virion assembly. Moreover, we argue that whether recombination facilitates the evolution of drug resistance depends critically on how resistance mutations interact to determine viral fitness. Contrary to the commonly held belief, we find that, under the most plausible biological assumptions, recombination is expected to slow down the rate of evolution of multi-drug-resistant virus during therapy.     

Stochastic interplay between mutation and recombination during the acquisition of drug resistance mutations in human immunodeficiency virus type 1

The emergence of drug resistance mutations in human immunodeficiency virus (HIV) has been a major setback in the treatment of infected patients. Besides the high mutation rate, recombination has been conjectured to have an important impact on the emergence of drug resistance. Population genetic theory suggests that in populations limited in size recombination may facilitate the acquisition of beneficial mutations. The viral population in an infected patient may indeed represent such a population limited in size, since current estimates of the effective population size range from 500 to 10(5). To address the effects of limited population size, we therefore expand a previously described deterministic population genetic model of HIV replication by incorporating the stochastic processes that occur in finite populations of infected cells. Using parameter estimates from the literature, we simulate the evolution of drug-resistant viral strains. The simulations show that recombination has only a minor effect on the rate of acquisition of drug resistance mutations in populations with effective population sizes as small as 1,000, since in these populations, viral strains typically fix beneficial mutations sequentially. However, for intermediate effective population sizes (10(4) to 10(5)), recombination can accelerate the evolution of drug resistance by up to 25%. Furthermore, a reduction in population size caused by drug therapy can be overcome by a higher viral mutation rate, leading to a faster evolution of drug resistance.     

The clarifying role of time series data in the population genetics of HIV

HIV can evolve remarkably quickly in response to antiretroviral therapies and the immune system. This evolution stymies treatment effectiveness and prevents the development of an HIV vaccine. Consequently, there has been a great interest in using population genetics to disentangle the forces that govern the HIV adaptive landscape (selection, drift, mutation, and recombination). Traditional population genetics approaches look at the current state of genetic variation and infer the processes that can generate it. However, because HIV evolves rapidly, we can also sample populations repeatedly over time and watch evolution in action. In this paper, we demonstrate how time series data can bound evolutionary parameters in a way that complements and informs traditional population genetic approaches. Specifically, we focus on our recent paper (Feder et al., 2016, eLife), in which we show that, as improved HIV drugs have led to fewer patients failing therapy due to resistance evolution, less genetic diversity has been maintained following the fixation of drug resistance mutations. Because soft sweeps of multiple drug resistance mutations spreading simultaneously have been previously documented in response to the less effective HIV therapies used early in the epidemic, we interpret the maintenance of post-sweep diversity in response to poor therapies as further evidence of soft sweeps and therefore a high population mutation rate (θ) in these intra-patient HIV populations. Because improved drugs resulted in rarer resistance evolution accompanied by lower post-sweep diversity, we suggest that both observations can be explained by decreased population mutation rates and a resultant transition to hard selective sweeps. A recent paper (Harris et al., 2018, PLOS Genetics) proposed an alternative interpretation: Diversity maintenance following drug resistance evolution in response to poor therapies may have been driven by recombination during slow, hard selective sweeps of single mutations. Then, if better drugs have led to faster hard selective sweeps of resistance, recombination will have less time to rescue diversity during the sweep, recapitulating the decrease in post-sweep diversity as drugs have improved. In this paper, we use time series data to show that drug resistance evolution during ineffective treatment is very fast, providing new evidence that soft sweeps drove early HIV treatment failure.     

The Optimum Recombination Rate That Realizes the Fastest Evolution of a Novel Functional Combination of Many Genes

The effect of genetic recombination (or crossover) by sexual reproduction on the time until a novel set of genes performing a combined function appears, spreads, and becomes fixed is studied. First, we study a haploid finite population with many binary loci, in which only one sequence (called a functional gene set) is significantly advantageous over the others. The time for evolution of the function (T_d) is defined as the mean number of generations until the advantageous sequence dominates in an initially random population. When the sequence diversity is initially stored sufficiently, the evolution timeT_dis roughly the product of the waiting time until the appearance of the advantageous sequence (creation timeT_c) and the average number of appearances of the advantageous sequence from its absence until its fixation (destruction numberN_d). Mutation and crossover reduce the former but enlarge the latter. If the mutation rate is low, there is an intermediate optimal rate of crossover that achieves the minimumT_d. In contrast, if the mutation rate is sufficiently high,T_dis smallest without crossover. Second, the breakdown of established functions by recurrent deleterious mutation in an infinite population is examined. The number of functional genes maintained decreases monotonically with the recurrent deleterious mutation rate. Thus in higher organisms having many functional sets of genes in the genome, the mutation rate must be kept very low to preserve them, and hence a high crossover rate made possible by sexual reproduction is important in accelerating the evolution of novel functional sets of genes. Implications of this long-term advantage of recombination in the maintenance of sexual reproduction in higher organisms are discussed.     

Inference of population genetic parameters from an irregular time series of seasonal influenza virus sequences

Basic summary statistics that quantify the population genetic structure of influenza virus are important for understanding and inferring the evolutionary and epidemiological processes. However, the sampling dates of global virus sequences in the last several decades are scattered nonuniformly throughout the calendar. Such temporal structure of samples and the small effective size of viral population hampers the use of conventional methods to calculate summary statistics. Here, we define statistics that overcome this problem by correcting for the sampling-time difference in quantifying a pairwise sequence difference. A simple linear regression method jointly estimates the mutation rate and the level of sequence polymorphism, thus providing an estimate of the effective population size. It also leads to the definition of Wright’s F_ST for arbitrary time-series data. Furthermore, as an alternative to Tajima’s D statistic or the site-frequency spectrum, a mismatch distribution corrected for sampling-time differences can be obtained and compared between actual and simulated data. Application of these methods to seasonal influenza A/H3N2 viruses sampled between 1980 and 2017 and sequences simulated under the model of recurrent positive selection with metapopulation dynamics allowed us to estimate the synonymous mutation rate and find parameter values for selection and demographic structure that fit the observation. We found that the mutation rates of HA and PB1 segments before 2007 were particularly high and that including recurrent positive selection in our model was essential for the genealogical structure of the HA segment. Methods developed here can be generally applied to population genetic inferences using serially sampled genetic data.     

Critical Mutation Rate Has an Exponential Dependence on Population Size in Haploid and Diploid Populations

Understanding the effect of population size on the key parameters of evolution is particularly important for populations nearing extinction. There are evolutionary pressures to evolve sequences that are both fit and robust. At high mutation rates, individuals with greater mutational robustness can outcompete those with higher fitness. This is survival-of-the-flattest, and has been observed in digital organisms, theoretically, in simulated RNA evolution, and in RNA viruses. We introduce an algorithmic method capable of determining the relationship between population size, the critical mutation rate at which individuals with greater robustness to mutation are favoured over individuals with greater fitness, and the error threshold. Verification for this method is provided against analytical models for the error threshold. We show that the critical mutation rate for increasing haploid population sizes can be approximated by an exponential function, with much lower mutation rates tolerated by small populations. This is in contrast to previous studies which identified that critical mutation rate was independent of population size. The algorithm is extended to diploid populations in a system modelled on the biological process of meiosis. The results confirm that the relationship remains exponential, but show that both the critical mutation rate and error threshold are lower for diploids, rather than higher as might have been expected. Analyzing the transition from critical mutation rate to error threshold provides an improved definition of critical mutation rate. Natural populations with their numbers in decline can be expected to lose genetic material in line with the exponential model, accelerating and potentially irreversibly advancing their decline, and this could potentially affect extinction, recovery and population management strategy. The effect of population size is particularly strong in small populations with 100 individuals or less; the exponential model has significant potential in aiding population management to prevent local (and global) extinction events.     

Serial evolutionary networks of within-patient HIV-1 sequences reveal patterns of evolution of X4 strains

Background  

The HIV virus is known for its ability to exploit numerous genetic and evolutionary mechanisms to ensure its proliferation, among them, high replication, mutation and recombination rates. Sliding MinPD, a recently introduced computational method [1], was used to investigate the patterns of evolution of serially-sampled HIV-1 sequence data from eight patients with a special focus on the emergence of X4 strains. Unlike other phylogenetic methods, Sliding MinPD combines distance-based inference with a nonparametric bootstrap procedure and automated recombination detection to reconstruct the evolutionary history of longitudinal sequence data. We present serial evolutionary networks as a longitudinal representation of the mutational pathways of a viral population in a within-host environment. The longitudinal representation of the evolutionary networks was complemented with charts of clinical markers to facilitate correlation analysis between pertinent clinical information and the evolutionary relationships.     

Misconceptions and false expectations in neutral evolution

Neutral evolution results from random recurrent mutation and genetic drift. A small part of random evolution, that which is related to protein or DNA polymorphisms, is the subject of the Neutral Theory of Evolution. One of the foundations of this theory is the demonstration that the mutation rate (m) is equal to the substitution rate. Since both rates are independent of population size, they are independent of drift, which is dependent upon population size. Neutralists have erroneously equated the substitution rate with the fixation rate, despite the fact that they are antithetical conceptions. The neutralists then applied the random walk stochastic model to justify alleles or bases that were fixated or eliminated. In this model, once the allele or base frequencies reach the monomorphic states (values of 1.0 or 0.0), the absorbing barriers, they can no longer return to the polymorphic state. This operates in a pure mathematical model. If recurrent mutation occurs (as in biotic real systems) fixation and elimination are impossible. A population of bacteria in which m = 10(-8) base mutation (or substitution)/site/generation and the reproduction rate is 1000 cell cycle/year should replace all its genome bases in approximately 100,000 years. The expected situation for all sites is polymorphism for the four bases rather than monomorphism at 1.0 or 0.0 frequencies. If fixation and elimination of a base for more than 500,000 years are impossible, then most of the neutral theory is untenable. A new complete neutral model, which allows for recurrent substitutions, is proposed here based on recurrent mutation or substitution and drift alone. The model fits a binomial or Poisson distribution and not a geometric one, as does neutral theory.     

Evolutionary implications of the frequent horizontal transfer of mismatch repair genes

Mutation and subsequent recombination events create genetic diversity, which is subjected to natural selection. Bacterial mismatch repair (MMR) deficient mutants, exhibiting high mutation and homologous recombination rates, are frequently found in natural populations. Therefore, we have explored the possibility that MMR deficiency emerging in nature has left some "imprint" in the sequence of bacterial genomes. Comparative molecular phylogeny of MMR genes from natural Escherichia coli isolates shows that, compared to housekeeping genes, individual functional MMR genes exhibit high sequence mosaicism derived from diverse phylogenetic lineages. This apparent horizontal gene transfer correlates with hyperrecombination phenotype of MMR-deficient mutators. The sequence mosaicism of MMR genes may be a hallmark of a mechanism of adaptive evolution that involves modulation of mutation and recombination rates by recurrent losses and reacquisitions of MMR gene functions.     

Immunoglobulin diversification in DT40: a model for vertebrate DNA damage tolerance

Studies of recombination in vertebrates have rather lagged behind those in yeast and bacteria in large part due to the relative genetic intractability of vertebrate model systems. Immunoglobulin diversification in the chicken cell line DT40 provides a powerful combination of a physiological recombination process coupled with facile genetic modification. The immunoglobulin variable regions of DT40 constitutively diversify by a combination of gene conversion, in which sequence changes are templated from one of a number of upstream pseudogenes or by non-templated point mutation. Both of these events are initiated by abasic sites in the variable region DNA generated following the targeted deamination of cytidine by activation induced deaminase. Recent work has shown that the two outcomes, gene conversion and somatic mutation, are likely to reflect alternate pathways for the processing of these abasic sites. In this review I will discuss the current data on avian Ig gene diversification and examine how the immunoglobulin loci of DT40 may provide a useful model system for studying the mechanisms and interactions of vertebrate recombination and pathways of DNA damage tolerance.     

Increasing sequence correlation limits the efficiency of recombination in a multisite evolution model

The accumulation of preexisting beneficial alleles in a haploid population, under selection and infrequent recombination, and in the absence of new mutation events is studied numerically by means of detailed Monte Carlo simulations. On the one hand, we confirm our previous work, in that the accumulation rate follows modified single-site kinetics, with a timescale set by an effective selection coefficient s(eff) as shown in a previous work, and we confirm the qualitative features of the dependence of s(eff) on the population size and the recombination rate reported therein. In particular, we confirm the existence of a threshold population size below which evolution stops before the emergence of best-fit individuals. On the other hand, our simulations reveal that the population dynamics is essentially shaped by the steady accumulation of pairwise sequence correlation, causing sequence congruence in excess of what one would expect from a uniformly random distribution of alleles. By sequence congruence, we understand here the opposite of genetic distance, that is, the fraction of monomorphic sites of specified allele type in a pair of genomes (individual sequences). The effective selection coefficient changes more rapidly with the recombination rate and has a higher threshold in this parameter than found in the previous work, which neglected correlation effects. We examine this phenomenon by monitoring the time dependence of sequence correlation based on a set of sequence congruence measures and verify that it is not associated with the development of linkage disequilibrium. We also discuss applications to HIV evolution in infected individuals and potential implications for drug therapy.     

RNA recombination in animal and plant viruses.

An increasing number of animal and plant viruses have been shown to undergo RNA-RNA recombination, which is defined as the exchange of genetic information between nonsegmented RNAs. Only some of these viruses have been shown to undergo recombination in experimental infection of tissue culture, animals, and plants. However, a survey of viral RNA structure and sequences suggests that many RNA viruses were derived form homologous or nonhomologous recombination between viruses or between viruses and cellular genes during natural viral evolution. The high frequency and widespread nature of RNA recombination indicate that this phenomenon plays a more significant role in the biology of RNA viruses than was previously recognized. Three types of RNA recombination are defined: homologous recombination; aberrant homologous recombination, which results in sequence duplication, insertion, or deletion during recombination; and nonhomologous (illegitimate) recombination, which does not involve sequence homology. RNA recombination has been shown to occur by a copy choice mechanism in some viruses. A model for this recombination mechanism is presented.     

Adapt globally, act locally: the effect of selective sweeps on bacterial sequence diversity.

Previous studies have shown that genetic exchange in bacteria is too rare to prevent neutral sequence divergence between ecological populations. That is, despite genetic exchange, each population should diverge into its own DNA sequence-similarity cluster. In those studies, each selective sweep was limited to acting within a single ecological population. Here we postulate the existence of globally adaptive mutations, which may confer a selective advantage to all ecological populations constituting a metapopulation. Such adaptations cause global selective sweeps, which purge the divergence both within and between populations. We found that the effect of recurrent global selective sweeps on neutral sequence divergence is highly dependent on the mechanism of genetic exchange. Global selective sweeps can prevent populations from reaching high levels of neutral sequence divergence, but they cannot cause two populations to become identical in neutral sequence characters. The model supports the earlier conclusion that each ecological population of bacteria should form its own distinct DNA sequence-similarity cluster.     

Lethal mutagenesis of bacteria

Lethal mutagenesis, the killing of a microbial pathogen with a chemical mutagen, is a potential broad-spectrum antiviral treatment. It operates by raising the genomic mutation rate to the point that the deleterious load causes the population to decline. Its use has been limited to RNA viruses because of their high intrinsic mutation rates. Microbes with DNA genomes, which include many viruses and bacteria, have not been considered for this type of treatment because their low intrinsic mutation rates seem difficult to elevate enough to cause extinction. Surprisingly, models of lethal mutagenesis indicate that bacteria may be candidates for lethal mutagenesis. In contrast to viruses, bacteria reproduce by binary fission, and this property ensures their extinction if subjected to a mutation rate >0.69 deleterious mutations per generation. The extinction threshold is further lowered when bacteria die from environmental causes, such as washout or host clearance. In practice, mutagenesis can require many generations before extinction is achieved, allowing the bacterial population to grow to large absolute numbers before the load of deleterious mutations causes the decline. Therefore, if effective treatment requires rapid population decline, mutation rates 0.69 may be necessary to achieve treatment success. Implications for the treatment of bacteria with mutagens, for the evolution of mutator strains in bacterial populations, and also for the evolution of mutation rate in cancer are discussed.     

A simple and robust statistical test for detecting the presence of recombination

Recombination is a powerful evolutionary force that merges historically distinct genotypes. But the extent of recombination within many organisms is unknown, and even determining its presence within a set of homologous sequences is a difficult question. Here we develop a new statistic, phi(w), that can be used to test for recombination. We show through simulation that our test can discriminate effectively between the presence and absence of recombination, even in diverse situations such as exponential growth (star-like topologies) and patterns of substitution rate correlation. A number of other tests, Max chi2, NSS, a coalescent-based likelihood permutation test (from LDHat), and correlation of linkage disequilibrium (both r2 and /D'/) with distance, all tend to underestimate the presence of recombination under strong population growth. Moreover, both Max chi2 and NSS falsely infer the presence of recombination under a simple model of mutation rate correlation. Results on empirical data show that our test can be used to detect recombination between closely as well as distantly related samples, regardless of the suspected rate of recombination. The results suggest that phi(w) is one of the best approaches to distinguish recurrent mutation from recombination in a wide variety of circumstances.     

Genetic relationship between cocirculating Human enteroviruses species C

Recombination events between human enteroviruses (HEV) are known to occur frequently and to participate in the evolution of these viruses. In a previous study, we reported the isolation of a panel of viruses belonging to the Human enterovirus species C (HEV-C) that had been cocirculating in a small geographic area of Madagascar in 2002. This panel included type 2 vaccine-derived polioviruses (PV) that had caused several cases of acute flaccid paralysis in humans. Previous partial sequencing of the genome of these HEV-C isolates revealed considerable genetic diversity, mostly due to recombination. In the work presented herein, we carried out a more detailed characterization of the genomes of viruses from this collection. First, we determined the full VP1 sequence of 41 of these isolates of different types. These sequences were compared with those of HEV-C isolates obtained from other countries or in other contexts. The sequences of the Madagascan isolates of a given type formed specific clusters clearly differentiated from those formed by other strains of the same type isolated elsewhere. Second, we sequenced the entire genome of 10 viruses representing most of the lineages present in this panel. All but one of the genomes appeared to be mosaic assemblies of different genomic fragments generated by intra- and intertypic recombination. The location of the breakpoints suggested potential preferred genomic regions for recombination. Our results also suggest that recombination between type HEV-99 and other HEV-C may be quite rare. This first exhaustive genomic analysis of a panel of non-PV HEV-C cocirculating in a small human population highlights the high frequency of inter and intra-typic genetic recombination, constituting a widespread mechanism of genetic plasticity and continually shifting the HEV-C biodiversity.     

A statistical characterization of consistent patterns of human immunodeficiency virus evolution within infected patients

Within-patient HIV populations evolve rapidly because of a high mutation rate, short generation time, and strong positive selection pressures. Previous studies have identified "consistent patterns" of viral sequence evolution. Just before HIV infection progresses to AIDS, evolution seems to slow markedly, and the genetic diversity of the viral population drops. This evolutionary slowdown could be caused either by a reduction in the average viral replication rate or because selection pressures weaken with the collapse of the immune system. The former hypothesis (which we denote "cellular exhaustion") predicts a simultaneous reduction in both synonymous and nonsynonymous evolution, whereas the latter hypothesis (denoted "immune relaxation") predicts that only nonsynonymous evolution will slow. In this paper, we present a set of statistical procedures for distinguishing between these alternative hypotheses using DNA sequences sampled over the course of infection. The first component is a new method for estimating evolutionary rates that takes advantage of the temporal information in longitudinal DNA sequence samples. Second, we develop a set of probability models for the analysis of evolutionary rates in HIV populations in vivo. Application of these models to both synonymous and nonsynonymous evolution affords a comparison of the cellular-exhaustion and immune-relaxation hypotheses. We apply the procedures to longitudinal data sets in which sequences of the env gene were sampled over the entire course of infection. Our analyses (1) statistically confirm that an evolutionary slowdown occurs late in infection, (2) strongly support the immune-relaxation hypothesis, and (3) indicate that the cessation of nonsynonymous evolution is associated with disease progression.     

Quasispecies Theory and the Behavior of RNA Viruses

A large number of medically important viruses, including HIV, hepatitis C virus, and influenza, have RNA genomes. These viruses replicate with extremely high mutation rates and exhibit significant genetic diversity. This diversity allows a viral population to rapidly adapt to dynamic environments and evolve resistance to vaccines and antiviral drugs. For the last 30 years, quasispecies theory has provided a population-based framework for understanding RNA viral evolution. A quasispecies is a cloud of diverse variants that are genetically linked through mutation, interact cooperatively on a functional level, and collectively contribute to the characteristics of the population. Many predictions of quasispecies theory run counter to traditional views of microbial behavior and evolution and have profound implications for our understanding of viral disease. Here, we discuss basic principles of quasispecies theory and describe its relevance for our understanding of viral fitness, virulence, and antiviral therapeutic strategy.