Genetic instability and the quasispecies model

Genetic instability is a defining characteristic of cancers. Microsatellite instability (MIN) leads to by elevated point mutation rates, whereas chromosomal instability (CIN) refers to increased rates of losing or gaining whole chromosomes or parts of chromosomes during cell division. CIN and MIN are, in general, mutually exclusive. The quasispecies model is a very successful theoretical framework for the study of evolution at high mutation rates. It predicts the existence of an experimentally verified error catastrophe. This catastrophe occurs when the mutation rates exceed a threshold value, the error threshold, above which replicative infidelity is incompatible with cell survival. We analyse the semiconservative quasispecies model of both MIN and CIN tumors. We consider the role of post-methylation DNA repair in tumor cells and demonstrate that DNA repair is fundamental to the nature of the error catastrophe in both types of tumors. We find that CIN introduces a plateau in the maximum viable mutation rate for a repair-free model, which does not exist in the case of MIN. This provides a plausible explanation for the mutual exclusivity of CIN and MIN.     

In silico identification of functional divergence between the multiple groEL gene paralogs in Chlamydiae

Background

RNA molecules, through their dual appearance as sequence and structure, represent a suitable model to study evolutionary properties of quasispecies. The essential ingredient in this model is the differentiation between genotype (molecular sequences which are affected by mutation) and phenotype (molecular structure, affected by selection). This framework allows a quantitative analysis of organizational properties of quasispecies as they adapt to different environments, such as their robustness, the effect of the degeneration of the sequence space, or the adaptation under different mutation rates and the error threshold associated.

Results

We describe and analyze the structural properties of molecular quasispecies adapting to different environments both during the transient time before adaptation takes place and in the asymptotic state, once optimization has occurred. We observe a minimum in the adaptation time at values of the mutation rate relatively far from the phenotypic error threshold. Through the definition of a consensus structure, it is shown that the quasispecies retains relevant structural information in a distributed fashion even above the error threshold. This structural robustness depends on the precise shape of the secondary structure used as target of selection. Experimental results available for natural RNA populations are in qualitative agreement with our observations.

Conclusion

Adaptation time of molecular quasispecies to a given environment is optimized at values of the mutation rate well below the phenotypic error threshold. The optimal value results from a trade-off between diversity generation and fixation of advantageous mutants. The critical value of the mutation rate is a function not only of the sequence length, but also of the specific properties of the environment, in this case the selection pressure and the shape of the secondary structure used as target phenotype. Certain functional motifs of RNA secondary structure that withstand high mutation rates (as the ubiquitous hairpin motif) might appear early in evolution and be actually frozen evolutionary accidents.     

Stochastic Simulations Suggest that HIV-1 Survives Close to Its Error Threshold

The use of mutagenic drugs to drive HIV-1 past its error threshold presents a novel intervention strategy, as suggested by the quasispecies theory, that may be less susceptible to failure via viral mutation-induced emergence of drug resistance than current strategies. The error threshold of HIV-1, , however, is not known. Application of the quasispecies theory to determine poses significant challenges: Whereas the quasispecies theory considers the asexual reproduction of an infinitely large population of haploid individuals, HIV-1 is diploid, undergoes recombination, and is estimated to have a small effective population size in vivo. We performed population genetics-based stochastic simulations of the within-host evolution of HIV-1 and estimated the structure of the HIV-1 quasispecies and . We found that with small mutation rates, the quasispecies was dominated by genomes with few mutations. Upon increasing the mutation rate, a sharp error catastrophe occurred where the quasispecies became delocalized in sequence space. Using parameter values that quantitatively captured data of viral diversification in HIV-1 patients, we estimated to be substitutions/site/replication, ∼2–6 fold higher than the natural mutation rate of HIV-1, suggesting that HIV-1 survives close to its error threshold and may be readily susceptible to mutagenic drugs. The latter estimate was weakly dependent on the within-host effective population size of HIV-1. With large population sizes and in the absence of recombination, our simulations converged to the quasispecies theory, bridging the gap between quasispecies theory and population genetics-based approaches to describing HIV-1 evolution. Further, increased with the recombination rate, rendering HIV-1 less susceptible to error catastrophe, thus elucidating an added benefit of recombination to HIV-1. Our estimate of may serve as a quantitative guideline for the use of mutagenic drugs against HIV-1.     

Validating viral quasispecies with digital organisms: a re-examination of the critical mutation rate

Background  

In this report we re-examine some recent experiments with digital organisms to test some predictions of quasispecies theory. These experiments revealed that under high mutation rates populations of less fit organisms previously adapted to such high mutation rates were able to outcompete organisms with higher average fitness but adapted to low mutation rates.     

The fittest versus the flattest: experimental confirmation of the quasispecies effect with subviral pathogens

The "survival of the fittest" is the paradigm of Darwinian evolution in which the best-adapted replicators are favored by natural selection. However, at high mutation rates, the fittest organisms are not necessarily the fastest replicators but rather are those that show the greatest robustness against deleterious mutational effects, even at the cost of a low replication rate. This scenario, dubbed the "survival of the flattest", has so far only been shown to operate in digital organisms. We show that "survival of the flattest" can also occur in biological entities by analyzing the outcome of competition between two viroid species coinfecting the same plant. Under optimal growth conditions, a viroid species characterized by fast population growth and genetic homogeneity outcompeted a viroid species with slow population growth and a high degree of variation. In contrast, the slow-growth species was able to outcompete the fast species when the mutation rate was increased. These experimental results were supported by an in silico model of competing viroid quasispecies.     

Sexual selection does not influence minisatellite mutation rate

Background  

Moller and Cuervo report a significant trend between minisatellite mutation rate and the frequency of extra-pair copulations in birds. This is interpreted as evidence that the high rate of evolution demanded by sexual selection has itself selected for a higher mutation rate in species where selection is strongest. However, there are good a priori reasons for believing that their method of calculating minisatellite mutation rates will be highly error prone and a poor surrogate measure of the evolutionary rate of genes. I therefore attempted to replicate their results using both their data and an independent data set based on papers they failed to locate.     

Effect of lethality on the extinction and on the error threshold of quasispecies

In this paper the effect of lethality on error threshold and extinction has been studied in a population of error-prone self-replicating molecules. For given lethality and a simple fitness landscape, three dynamic regimes can be obtained: quasispecies, error catastrophe, and extinction. Using a simple model in which molecules are classified as master, lethal and non-lethal mutants, it is possible to obtain the mutation rates of the transitions between the three regimes analytically. The numerical resolution of the extended model, in which molecules are classified depending on their Hamming distance to the master sequence, confirms the results obtained in the simple model and shows how an error catastrophe regime changes when lethality is taken in account.     

Phenotypic effect of mutations in evolving populations of RNA molecules

Background  

The secondary structure of folded RNA sequences is a good model to map phenotype onto genotype, as represented by the RNA sequence. Computational studies of the evolution of ensembles of RNA molecules towards target secondary structures yield valuable clues to the mechanisms behind adaptation of complex populations. The relationship between the space of sequences and structures, the organization of RNA ensembles at mutation-selection equilibrium, the time of adaptation as a function of the population parameters, the presence of collective effects in quasispecies, or the optimal mutation rates to promote adaptation all are issues that can be explored within this framework.     

Viral quasispecies profiles as the result of the interplay of competition and cooperation

Background  

Viral quasispecies can be regarded as a swarm of genetically related mutants. A common approach employed to describe viral quasispecies is by means of the quasispecies equation (QE). However, a main criticism of QE is its lack of frequency-dependent selection. This can be overcome by an alternative formulation for the evolutionary dynamics: the replicator-mutator equation (RME). In turn, a problem with the RME is how to quantify the interaction coefficients between viral variants. Here, this is addressed by adopting an ecological perspective and resorting to the niche theory of competing communities, which assumes that the utilization of resources primarily determines ecological segregation between competing individuals (the different viral variants that constitute the quasispecies). This provides a theoretical framework to estimate quantitatively the fitness landscape.     

Quasispecies theory in the context of population genetics

Background  

A number of recent papers have cast doubt on the applicability of the quasispecies concept to virus evolution, and have argued that population genetics is a more appropriate framework to describe virus evolution than quasispecies theory.     

Error threshold in RNA quasispecies models with complementation

A general assumption of quasispecies models of replicons dynamics is that the fitness of a genotype is entirely determined by its sequence. However, a more biologically plausible situation is that fitness depends on the proteins that catalyze metabolic reactions, including replication. In a stirred population of replicons, such as viruses replicating and accumulating within the same cell, the association between a given genome and the proteins it encodes is not tight as it can be replicated by proteins translated from other genomes. We have investigated how this complementation phenomenon affects the error threshold in simple quasispecies mean field models. We first studied a model in which the master and the mutant genomes code for wild-type and mutant replicases, respectively. We assume that the mutant replicase has a reduced activity and that the wild-type replicase does not have increased affinity for the master genome. The whole pool of replicases can bind and replicate both genomes. We then analyze a different model considering a more extreme case of mutant genomes, the defective interfering particles (DIPs) described in many cases of viral infection. DIPs, with a higher replication rate owed to their shorter genomes, do not code for replicase, but they are able of using the replicase translated from the master genome. Our models allow to study how the probability of interaction between the genomes and the whole pool of replicases affects the error threshold. In both systems we characterize the scenario of coexistence between master and mutant genomes, providing the critical values of mutation rate, μ_c, and the critical interaction rate between master genomes and replicases, γ_c, at which the quasispecies enters into error catastrophe, a situation in which the mutant genomes dominate the population. In both cases, we showed that the error-threshold transition is given by transcritical-like bifurcations, suggesting a continuous phase transition. We have also found that the region in the parameter space (μ,γ) in which the master sequence survives is reduced when DIPs are introduced into the system.     

Quasispecies made simple

Quasispecies are clouds of genotypes that appear in a population at mutation–selection balance. This concept has recently attracted the attention of virologists, because many RNA viruses appear to generate high levels of genetic variation that may enhance the evolution of drug resistance and immune escape. The literature on these important evolutionary processes is, however, quite challenging. Here we use simple models to link mutation–selection balance theory to the most novel property of quasispecies: the error threshold—a mutation rate below which populations equilibrate in a traditional mutation–selection balance and above which the population experiences an error catastrophe, that is, the loss of the favored genotype through frequent deleterious mutations. These models show that a single fitness landscape may contain multiple, hierarchically organized error thresholds and that an error threshold is affected by the extent of back mutation and redundancy in the genotype-to-phenotype map. Importantly, an error threshold is distinct from an extinction threshold, which is the complete loss of the population through lethal mutations. Based on this framework, we argue that the lethal mutagenesis of a viral infection by mutation-inducing drugs is not a true error catastophe, but is an extinction catastrophe.     

Information catastrophe in RNA viruses through replication thresholds

RNA viruses are known to replicate at very high mutation rates. These rates are actually known to be close to their so-called error threshold. This threshold is in fact a critical point beyond which genetic information is lost through a so-called error catastrophe. However, the transition from a stable quasispecies to genetic drift and loss of information can also occur by crossing replication thresholds, below some replication rates, the viral population is suddenly unable to survive. Available data from hepatitis C virus population analysis [Mas, A., Ulloa, E., Bruguera, M., Furci?, I., Garriga, D., Fábregas, S., Andreu, D., Saiz, J.C., Díez, J., 2004. Hepatitis C virus population analysis of a single-source nosocomial outbreak reveals an inverse correlation between viral load and quasispecies complexity. J. Gen. Virol. 85, 3619-3626] can be interpreted through this theoretical view, providing evidence for such a replication threshold. Here a simple model is used in order to provide evidence for such a phenomenon, consistent with available data.     

Pathways to extinction: beyond the error threshold

Since the introduction of the quasispecies and the error catastrophe concepts for molecular evolution by Eigen and their subsequent application to viral populations, increased mutagenesis has become a common strategy to cause the extinction of viral infectivity. Nevertheless, the high complexity of virus populations has shown that viral extinction can occur through several other pathways apart from crossing an error threshold. Increases in the mutation rate enhance the appearance of defective forms and promote the selection of mechanisms that are able to counteract the accelerated appearance of mutations. Current models of viral evolution take into account more realistic scenarios that consider compensatory and lethal mutations, a highly redundant genotype-to-phenotype map, rough fitness landscapes relating phenotype and fitness, and where phenotype is described as a set of interdependent traits. Further, viral populations cannot be understood without specifying the characteristics of the environment where they evolve and adapt. Altogether, it turns out that the pathways through which viral quasispecies go extinct are multiple and diverse.     

Simple quasispecies models for the survival-of-the-flattest effect: The role of space

The survival-of-the-flattest effect postulates that under high mutation rates natural selection does not necessarily favor the faster replicators. Under such conditions, genotypes which are robust against deleterious mutational effects may be favored instead, even at the cost of a slower replication. This tantalizing hypothesis has been recently proved using digital organisms, subviral RNA plant pathogens (viroids), and an animal RNA virus. In this work we study a simple theoretical system composed by two competing quasispecies which are located at two widely different fitness landscapes that represent, respectively, a fit and a flat quasispecies. The fit quasispecies is characterized by high replication rate and low mutational robustness, whereas the flat quasispecies is characterized by low replication rate but high mutational robustness. By using a mean field model, in silico simulations with digital replicons and a two-dimensional spatial model given by a stochastic cellular automata (CA), we predict the presence of an absorbing first-order phase transition with critical slowing down between selection for replication speed and selection for mutational robustness, where the surpassing of a critical mutation rate involves the outcompetition of the fit quasispecies by the flat one. Furthermore, it is shown that space, which involves a lower critical mutation rate, broadens the conditions at which the survival-of-the-flattest may occur.     

Combinatorial analysis and algorithms for quasispecies reconstruction using next-generation sequencing

Background  

Next-generation sequencing (NGS) offers a unique opportunity for high-throughput genomics and has potential to replace Sanger sequencing in many fields, including de-novo sequencing, re-sequencing, meta-genomics, and characterisation of infectious pathogens, such as viral quasispecies. Although methodologies and software for whole genome assembly and genome variation analysis have been developed and refined for NGS data, reconstructing a viral quasispecies using NGS data remains a challenge. This application would be useful for analysing intra-host evolutionary pathways in relation to immune responses and antiretroviral therapy exposures. Here we introduce a set of formulae for the combinatorial analysis of a quasispecies, given a NGS re-sequencing experiment and an algorithm for quasispecies reconstruction. We require that sequenced fragments are aligned against a reference genome, and that the reference genome is partitioned into a set of sliding windows (amplicons). The reconstruction algorithm is based on combinations of multinomial distributions and is designed to minimise the reconstruction of false variants, called in-silico recombinants.     

Viral RNA mutations are region specific and increased by ribavirin in a full-length hepatitis C virus replication system

High rates of genetic variation ensure the survival of RNA viruses. Although this variation is thought to result from error-prone replication, RNA viruses must also maintain highly conserved genomic segments. A balance between conserved and variable viral elements is especially important in order for viruses to avoid "error catastrophe." Ribavirin has been shown to induce error catastrophe in other RNA viruses. We therefore used a novel hepatitis C virus (HCV) replication system to determine relative mutation frequencies in variable and conserved regions of the HCV genome, and we further evaluated these frequencies in response to ribavirin. We sequenced the 5' untranslated region (5' UTR) and the core, E2 HVR-1, NS5A, and NS5B regions of replicating HCV RNA isolated from cells transfected with a T7 polymerase-driven full-length HCV cDNA plasmid containing a cis-acting hepatitis delta virus ribozyme to control 3' cleavage. We found quasispecies in the E2 HVR-1 and NS5B regions of untreated replicating viral RNAs but not in conserved 5' UTR, core, or NS5A regions, demonstrating that important cis elements regulate mutation rates within specific viral segments. Neither T7-driven replication nor sequencing artifacts produced these nucleotide substitutions in control experiments. Ribavirin broadly increased error generation, especially in otherwise invariant regions, indicating that it acts as an HCV RNA mutagen in vivo. Similar results were obtained in hepatocyte-derived cell lines. These results demonstrate the potential utility of our system for the study of intrinsic factors regulating genetic variation in HCV. Our results further suggest that ribavirin acts clinically by promoting nonviable HCV RNA mutation rates. Finally, the latter result suggests that our replication model may be useful for identifying agents capable of driving replicating virus into error catastrophe.     

Analysis of the genetic diversity of influenza A viruses using next-generation DNA sequencing

Background

Influenza viruses exist as a large group of closely related viral genomes, also called quasispecies. The composition of this influenza viral quasispecies can be determined by an accurate and sensitive sequencing technique and data analysis pipeline. We compared the suitability of two benchtop next-generation sequencers for whole genome influenza A quasispecies analysis: the Illumina MiSeq sequencing-by-synthesis and the Ion Torrent PGM semiconductor sequencing technique.

Results

We first compared the accuracy and sensitivity of both sequencers using plasmid DNA and different ratios of wild type and mutant plasmid. Illumina MiSeq sequencing reads were one and a half times more accurate than those of the Ion Torrent PGM. The majority of sequencing errors were substitutions on the Illumina MiSeq and insertions and deletions, mostly in homopolymer regions, on the Ion Torrent PGM. To evaluate the suitability of the two techniques for determining the genome diversity of influenza A virus, we generated plasmid-derived PR8 virus and grew this virus in vitro. We also optimized an RT-PCR protocol to obtain uniform coverage of all eight genomic RNA segments. The sequencing reads obtained with both sequencers could successfully be assembled de novo into the segmented influenza virus genome. After mapping of the reads to the reference genome, we found that the detection limit for reliable recognition of variants in the viral genome required a frequency of 0.5% or higher. This threshold exceeds the background error rate resulting from the RT-PCR reaction and the sequencing method. Most of the variants in the PR8 virus genome were present in hemagglutinin, and these mutations were detected by both sequencers.

Conclusions

Our approach underlines the power and limitations of two commonly used next-generation sequencers for the analysis of influenza virus gene diversity. We conclude that the Illumina MiSeq platform is better suited for detecting variant sequences whereas the Ion Torrent PGM platform has a shorter turnaround time. The data analysis pipeline that we propose here will also help to standardize variant calling in small RNA genomes based on next-generation sequencing data.     

Environmental stress and reproduction in Drosophila melanogaster : starvation resistance, ovariole numbers and early age egg production

Background  

The Y model of resource allocation predicts a tradeoff between reproduction and survival. Environmental stress could affect a tradeoff between reproduction and survival, but the physiological mechanisms underlying environmental mediation of the tradeoff are largely unknown. One example is the tradeoff between starvation resistance and early fecundity. One goal of the present study was to determine if reduced early age fecundity was indeed a robust indirect response to selection for starvation resistance, by investigation of a set of D. melanogaster starvation selected lines which had not previously been characterized for age specific egg production. Another goal of the present study was to investigate a possible relationship between ovariole number and starvation resistance. Ovariole number is correlated with maximum daily fecundity in outbred D. melanogaster. Thus, one might expect that a negative genetic correlation between starvation resistance and early fecundity would be accompanied by a decrease in ovariole number.     

Substitution rate variation at human CpG sites correlates with non-CpG divergence,methylation level and GC content

Background  

A major goal in the study of molecular evolution is to unravel the mechanisms that induce variation in the germ line mutation rate and in the genome-wide mutation profile. The rate of germ line mutation is considerably higher for cytosines at CpG sites than for any other nucleotide in the human genome, an increase commonly attributed to cytosine methylation at CpG sites. The CpG mutation rate, however, is not uniform across the genome and, as methylation levels have recently been shown to vary throughout the genome, it has been hypothesized that methylation status may govern variation in the rate of CpG mutation.