Error threshold in RNA quasispecies models with complementation

Phase transitions in evolutionary dynamics

Sharp changes in state, such as transitions from survival to extinction, are hallmarks of evolutionary dynamics in biological systems. These transitions can be explored using the techniques of statistical physics and the physics of nonlinear and complex systems. For example, a survival-to-extinction transition can be characterized as a non-equilibrium phase transition to an absorbing state. Here, we review the literature on phase transitions in evolutionary dynamics. We discuss directed percolation transitions in cellular automata and evolutionary models, and models that diverge from the directed percolation universality class. We explore in detail an example of an absorbing phase transition in an agent-based model of evolutionary dynamics, including previously unpublished data demonstrating similarity to, but also divergence from, directed percolation, as well as evidence for phase transition behavior at multiple levels of the model system's evolutionary structure. We discuss phase transition models of the error catastrophe in RNA virus dynamics and phase transition models for transition from chemistry to biochemistry, i.e., the origin of life. We conclude with a review of phase transition dynamics in models of natural selection, discuss the possible role of phase transitions in unraveling fundamental unresolved questions regarding multilevel selection and the major evolutionary transitions, and assess the future outlook for phase transitions in the investigation of evolutionary dynamics.

Next-Generation Sequencing for Confronting Virus Pandemics

Virus pandemics have happened, are happening and will happen again. In recent decades, the rate of zoonotic viral spillover into humans has accelerated, mirroring the expansion of our global footprint and travel network, including the expansion of viral vectors and the destruction of natural spaces, bringing humans closer to wild animals. Once viral cross-species transmission to humans occurs, transmission cannot be stopped by cement walls but by developing barriers based on knowledge that can prevent or reduce the effects of any pandemic. Controlling a local transmission affecting few individuals is more efficient that confronting a community outbreak in which infections cannot be traced. Genetic detection, identification, and characterization of infectious agents using next-generation sequencing (NGS) has been proven to be a powerful tool allowing for the development of fast PCR-based molecular assays, the rapid development of vaccines based on mRNA and DNA, the identification of outbreaks, transmission dynamics and spill-over events, the detection of new variants and treatment of vaccine resistance mutations, the development of direct-acting antiviral drugs, the discovery of relevant minority variants to improve knowledge of the viral life cycle, strengths and weaknesses, the potential for becoming dominant to take appropriate preventive measures, and the discovery of new routes of viral transmission.

The Social Life of Viruses

Despite their simplicity, viruses exhibit certain types of social interactions. Situations in which a given virus achieves higher fitness in combination with other members of the viral population have been described at the level of transmission, replication, suppression of host immune responses, and host killing, enabling the evolution of viral cooperation. Although cellular coinfection with multiple viral particles is the typical playground for these interactions, cooperation between viruses infecting different cells is also established through cellular and viral-encoded communication systems. In general, the stability of cooperation is compromised by cheater genotypes, as best exemplified by defective interfering particles. As predicted by social evolution theory, cheater invasion can be avoided when cooperators interact preferentially with other cooperators, a situation that is promoted in spatially structured populations. Processes such as transmission bottlenecks, organ compartmentalization, localized spread of infection foci, superinfection exclusion, and even discrete intracellular replication centers promote multilevel spatial structuring in viruses. Expected final online publication date for the Annual Review of Virology, Volume 8 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Why are viral genomes so fragile? The bottleneck hypothesis

If they undergo new mutations at each replication cycle, why are RNA viral genomes so fragile, with most mutations being either strongly deleterious or lethal? Here we provide theoretical and numerical evidence for the hypothesis that genetic fragility is partly an evolutionary response to the multiple population bottlenecks experienced by viral populations at various stages of their life cycles. Modelling within-host viral populations as multi-type branching processes, we show that mutational fragility lowers the rate at which Muller’s ratchet clicks and increases the survival probability through multiple bottlenecks. In the context of a susceptible-exposed-infectious-recovered epidemiological model, we find that the attack rate of fragile viral strains can exceed that of more robust strains, particularly at low infectivities and high mutation rates. Our findings highlight the importance of demographic events such as transmission bottlenecks in shaping the genetic architecture of viral pathogens.

Given that most mutations are deleterious, high mutation rates carry a significant evolutionary cost. To reduce this burden, an obvious evolutionary solution would be to reduce the fitness cost of mutations by becoming more robust; this solution is indeed selected in populations of constantly large size. Here, we show that when populations regularly experience bottlenecks, as viruses do upon transmission to a new host, a less obvious solution becomes more viable: namely, to increase the fitness cost of mutations so that unfit mutants are less likely to fix at each passage. This could explain why viruses—especially RNA viruses—do in fact have very fragile genomes.

Quasispecies characteristic in "a" determinant region is a potential predictor for the risk of immunoprophylaxis failure of mother-to-child-transmission of sub-genotype C2 hepatitis B virus: a prospective nested case-control study

OBJECTIVE

This study was performed to explore the correlation between the characteristics of hepatitis B virus (HBV) quasispecies in HBV-infected pregnant women and the risk of immunoprophylaxis failure for their infants.

DESIGN

In this prospective nested case-control study, the characteristics of HBV quasispecies in mothers whose infants were immunoprophylaxis success (control group) and those whose infants were immunoprophylaxis failure (case group) were analysed by the clone-based sequencing of full-length HBV genome and next-generation sequencing (NGS) of "a" determinant region, and were compared between the two groups.

RESULTS

The quasispecies characteristics including mutant frequency, Shannon entropy and mean genetic distance at amino acid level of "a" determinant region were significantly lower in case group than that in control group, using the full-length HBV genome clone-based sequencing assay. These results were confirmed by NGS assay. Notably, we discovered that the differences were also significant at nucleotide level by NGS assay. Furthermore, the risk of immunoprophylaxis failure could be predicted by analysing the three HBV quasispecies characteristics either at nucleotide level or at amino acid level of "a" determinant region, and the corresponding predictive values were tentatively set up.

CONCLUSIONS

HBV quasispecies with a more complex mutant spectrum in "a" determinant region might be more vulnerable to extinct through mother-to-child-transmission (MTCT). More importantly, analysing HBV quasispecies characteristics in pregnant women with high HBV DNA load might be helpful to predict the high-risk population of immunoprophylaxis failure, and consequently provide accurate intervention against MTCT of HBV.

Collective Viral Spread Mediated by Virion Aggregates Promotes the Evolution of Defective Interfering Particles

Recent insights have revealed that viruses use a highly diverse set of strategies to release multiple viral genomes into the same target cells, allowing the emergence of beneficial, but also detrimental, interactions among viruses inside infected cells. This has prompted interest among microbial ecologists and evolutionary biologists in studying how collective dispersal impacts the outcome of viral infections. Here, we have used vesicular stomatitis virus as a model system to study the evolutionary implications of collective dissemination mediated by viral aggregates, since this virus can spontaneously aggregate in the presence of saliva. We find that saliva-driven aggregation has a dual effect on viral fitness; whereas aggregation tends to increase infectivity in the very short term, virion aggregates are highly susceptible to invasion by noncooperative defective variants after a few viral generations.

A growing number of studies report that viruses can spread in groups in so-called collective infectious units. By increasing the cellular multiplicity of infection, collective dispersal may allow for social-like interactions, such as cooperation or cheating. Yet, little is known about how such interactions evolve. In previous work with vesicular stomatitis virus, we showed that virion aggregation accelerates early infection stages in most cell types, providing a short-term fitness benefit to the virus. Here, we examine the effects of virion aggregation over several infection cycles. Flow cytometry, deep sequencing, infectivity assays, reverse transcription-quantitative PCR, and electron microscopy revealed that virion aggregation rapidly promotes the emergence of defective interfering particles. Therefore, virion aggregation provides immediate fitness benefits to the virus but incurs fitness costs after a few viral generations. This suggests that an optimal strategy for the virus is to undergo virion aggregation only episodically, for instance, during interhost transmission.

The effect of genetic complementation on the fitness and diversity of viruses spreading as collective infectious units

Viruses can spread collectively using different types of structures such as extracellular vesicles, virion aggregates, polyploid capsids, occlusion bodies, and even cells that accumulate virions at their surface, such as bacteria and dendritic cells. Despite the mounting evidence for collective spread, its implications for viral fitness and diversity remain poorly understood. It has been postulated that, by increasing the cellular multiplicity of infection, collective spread could enable mutually beneficial interactions among different viral genetic variants. One such interaction is genetic complementation, whereby deleterious mutations carried by different genomes are compensated. Here, we used simulations to evaluate whether complementation is likely to increase the fitness of viruses spreading collectively. We show that complementation among co-spreading viruses initially buffers the deleterious effects of mutations, but has no positive effect on mean population fitness over the long term, and even promotes error catastrophe at high mutation rates. Additionally, we found that collective spread increases the risk of invasion by social cheaters such as defective interfering particles. We also show that mutation accumulation depends on the type of collective infectious units considered. Co-spreading viral genomes produced in the same cell (e.g. extracellular vesicles, polyploid capsids, occlusion bodies) should exhibit higher genetic relatedness than groups formed extracellularly by viruses released from different cells (aggregates, binding to bacterial or dendritic cell surfaces), and we found that increased relatedness limits the adverse effects of complementation as well cheater invasion risk. Finally, we found that the costs of complementation can be offset by recombination. Based on our results, we suggest that alternative factors promoting collective spread should be considered.

Emergency Services of Viral RNAs: Repair and Remodeling

Reproduction of RNA viruses is typically error-prone due to the infidelity of their replicative machinery and the usual lack of proofreading mechanisms. The error rates may be close to those that kill the virus. Consequently, populations of RNA viruses are represented by heterogeneous sets of genomes with various levels of fitness. This is especially consequential when viruses encounter various bottlenecks and new infections are initiated by a single or few deviating genomes. Nevertheless, RNA viruses are able to maintain their identity by conservation of major functional elements. This conservatism stems from genetic robustness or mutational tolerance, which is largely due to the functional degeneracy of many protein and RNA elements as well as to negative selection. Another relevant mechanism is the capacity to restore fitness after genetic damages, also based on replicative infidelity. Conversely, error-prone replication is a major tool that ensures viral evolvability. The potential for changes in debilitated genomes is much higher in small populations, because in the absence of stronger competitors low-fit genomes have a choice of various trajectories to wander along fitness landscapes. Thus, low-fit populations are inherently unstable, and it may be said that to run ahead it is useful to stumble. In this report, focusing on picornaviruses and also considering data from other RNA viruses, we review the biological relevance and mechanisms of various alterations of viral RNA genomes as well as pathways and mechanisms of rehabilitation after loss of fitness. The relationships among mutational robustness, resilience, and evolvability of viral RNA genomes are discussed.

High virulence does not necessarily impede viral adaptation to a new host: a case study using a plant RNA virus

BACKGROUND

Theory suggests that high virulence could hinder between-host transmission of microparasites, and that virulence therefore will evolve to lower levels. Alternatively, highly virulent microparasites could also curtail host development, thereby limiting both the host resources available to them and their own within-host effective population size. In this case, high virulence might restrain the mutation supply rate and increase the strength with which genetic drift acts on microparasite populations. Thereby, this alternative explanation limits the microparasites' potential to adapt to the host and ultimately the ability to evolve lower virulence. As a first exploration of this hypothesis, we evolved Tobacco etch virus carrying an eGFP fluorescent marker in two semi-permissive host species, Nicotiana benthamiana and Datura stramonium, for which it has a large difference in virulence. We compared the results to those previously obtained in the natural host, Nicotiana tabacum, where we have shown that carriage of eGFP has a high fitness cost and its loss serves as a real-time indicator of adaptation.

RESULTS

After over half a year of evolution, we sequenced the genomes of the evolved lineages and measured their fitness. During the evolution experiment, marker loss leading to viable virus variants was only observed in one lineage of the host for which the virus has low virulence, D. stramonium. This result was consistent with the observation that there was a fitness cost of eGFP in this host, while surprisingly no fitness cost was observed in the host for which the virus has high virulence, N. benthamiana. Furthermore, in both hosts we observed increases in viral fitness in few lineages, and host-specific convergent evolution at the genomic level was only found in N. benthamiana.

CONCLUSIONS

The results of this study do not lend support to the hypothesis that high virulence impedes microparasites' evolution. Rather, they exemplify that jumps between host species can be game changers for evolutionary dynamics. When considering the evolution of genome architecture, host species jumps might play a very important role, by allowing evolutionary intermediates to be competitive.

Abrupt transitions to tumor extinction: a phenotypic quasispecies model

The dynamics of heterogeneous tumor cell populations competing with healthy cells is an important topic in cancer research with deep implications in biomedicine. Multitude of theoretical and computational models have addressed this issue, especially focusing on the nature of the transitions governing tumor clearance as some relevant model parameters are tuned. In this contribution, we analyze a mathematical model of unstable tumor progression using the quasispecies framework. Our aim is to define a minimal model incorporating the dynamics of competition between healthy cells and a heterogeneous population of cancer cell phenotypes involving changes in replication-related genes (i.e., proto-oncogenes and tumor suppressor genes), in genes responsible for genomic stability, and in house-keeping genes. Such mutations or loss of genes result into different phenotypes with increased proliferation rates and/or increased genomic instabilities. Despite bifurcations in the classical deterministic quasispecies model are typically given by smooth, continuous shifts (i.e., transcritical bifurcations), we here identify a novel type of bifurcation causing an abrupt transition to tumor extinction. Such a bifurcation, named as trans-heteroclinic, is characterized by the exchange of stability between two distant fixed points (that do not collide) involving tumor persistence and tumor clearance. The increase of mutation and/or the decrease of the replication rate of tumor cells involves this catastrophic shift of tumor cell populations. The transient times near bifurcation thresholds are also characterized, showing a power law dependence of exponent [Formula: see text] of the transients as mutation is changed near the bifurcation value. These results are discussed in the context of targeted cancer therapy as a possible therapeutic strategy to force a catastrophic shift by simultaneously delivering mutagenic and cytotoxic drugs inside tumor cells.

Statistical properties and error threshold of quasispecies on single-peak Gaussian-distributed fitness landscapes

The stochastic Eigen model proposed by Feng et al. (2007) (Journal of Theoretical Biology, 246, 28) showed that error threshold is no longer a phase transition point but a crossover region whose width depends on the strength of the random fluctuation in an environment. The underlying cause of this phenomenon has not yet been well examined. In this article, we adopt a single peak Gaussian distributed fitness landscape instead of a constant one to investigate and analyze the change of the error threshold and the statistical property of the quasi-species population. We find a roughly linear relation between the width of the error threshold and the fitness fluctuation strength. For a given quasi-species, the fluctuation of the relative concentration has a minimum with a normal distribution of the relative concentration at the maximum of the averaged relative concentration, it has however a largest value with a bimodal distribution of the relative concentration near the error threshold. The above results deepen our understanding of the quasispecies and error threshold and are heuristic for exploring practicable antiviral strategies.

Theories of Lethal Mutagenesis: From Error Catastrophe to Lethal Defection

RNA viruses get extinct in a process called lethal mutagenesis when subjected to an increase in their mutation rate, for instance, by the action of mutagenic drugs. Several approaches have been proposed to understand this phenomenon. The extinction of RNA viruses by increased mutational pressure was inspired by the concept of the error threshold. The now classic quasispecies model predicts the existence of a limit to the mutation rate beyond which the genetic information of the wild type could not be efficiently transmitted to the next generation. This limit was called the error threshold, and for mutation rates larger than this threshold, the quasispecies was said to enter into error catastrophe. This transition has been assumed to foster the extinction of the whole population. Alternative explanations of lethal mutagenesis have been proposed recently. In the first place, a distinction is made between the error threshold and the extinction threshold, the mutation rate beyond which a population gets extinct. Extinction is explained from the effect the mutation rate has, throughout the mutational load, on the reproductive ability of the whole population. Secondly, lethal defection takes also into account the effect of interactions within mutant spectra, which have been shown to be determinant for the understanding the extinction of RNA virus due to an augmented mutational pressure. Nonetheless, some relevant issues concerning lethal mutagenesis are not completely understood yet, as so survival of the flattest, i.e. the development of resistance to lethal mutagenesis by evolving towards mutationally more robust regions of sequence space, or sublethal mutagenesis, i.e., the increase of the mutation rate below the extinction threshold which may boost the adaptability of RNA virus, increasing their ability to develop resistance to drugs (including mutagens). A better design of antiviral therapies will still require an improvement of our knowledge about lethal mutagenesis.

Variability in mutational fitness effects prevents full lethal transitions in large quasispecies populations

The distribution of mutational fitness effects (DMFE) is crucial to the evolutionary fate of quasispecies. In this article we analyze the effect of the DMFE on the dynamics of a large quasispecies by means of a phenotypic version of the classic Eigen's model that incorporates beneficial, neutral, deleterious, and lethal mutations. By parameterizing the model with available experimental data on the DMFE of Vesicular stomatitis virus (VSV) and Tobacco etch virus (TEV), we found that increasing mutation does not totally push the entire viral quasispecies towards deleterious or lethal regions of the phenotypic sequence space. The probability of finding regions in the parameter space of the general model that results in a quasispecies only composed by lethal phenotypes is extremely small at equilibrium and in transient times. The implications of our findings can be extended to other scenarios, such as lethal mutagenesis or genomically unstable cancer, where increased mutagenesis has been suggested as a potential therapy.

Shrinkage of genome size in a plant RNA virus upon transfer of an essential viral gene into the host genome

Nonretroviral integrated RNA viruses (NIRVs) are genes of nonretroviral RNA viruses found in the genomes of many eukaryotic organisms. NIRVs are thought to sometimes confer virus resistance, meaning that they could impact spread of the virus in the host population. However, a NIRV that is expressed may also impact the evolution of virus populations within host organisms. Here, we experimentally addressed the evolution of a virus in a host expressing a NIRV using Tobacco etch virus (TEV), a plant RNA virus, and transgenic tobacco plants expressing its replicase, NIb. We found that a virus missing the NIb gene, TEV-ΔNIb, which is incapable of autonomous replication in wild-type plants, had a higher fitness than the full-length TEV in the transgenic plants. Moreover, when the full-length TEV was evolved by serial passages in transgenic plants, we observed genomic deletions within NIb--and in some cases the adjacent cistrons--starting from the first passage. When we passaged TEV and TEV-ΔNIb in transgenic plants, we found mutations in proteolytic sites, but these only occurred in TEV-ΔNIb lineages, suggesting the adaptation of polyprotein processing to altered NIb expression. These results raise the possibility that NIRV expression can indeed induce the deletion of the corresponding genes in the viral genome, resulting in the formation of viruses that are replication defective in hosts that do not express the same NIRV. Moreover, virus genome evolution was contingent upon the deletion of the viral replicase, suggesting NIRV expression could also alter patterns of virus evolution.

Genomic mutation rates that neutralize adaptive evolution and natural selection

When mutation rates are low, natural selection remains effective, and increasing the mutation rate can give rise to an increase in adaptation rate. When mutation rates are high to begin with, however, increasing the mutation rate may have a detrimental effect because of the overwhelming presence of deleterious mutations. Indeed, if mutation rates are high enough: (i) adaptive evolution may be neutralized, resulting in a zero (or negative) adaptation rate despite the continued availability of adaptive and/or compensatory mutations, or (ii) natural selection may be neutralized, because the fitness of lineages bearing adaptive and/or compensatory mutations--whether established or newly arising--is eroded by excessive mutation, causing such lineages to decline in frequency. We apply these two criteria to a standard model of asexual adaptive evolution and derive mathematical expressions--some new, some old in new guise--delineating the mutation rates under which either adaptive evolution or natural selection is neutralized. The expressions are simple and require no a priori knowledge of organism- and/or environment-specific parameters. Our discussion connects these results to each other and to previous theory, showing convergence or equivalence of the different results in most cases.

Viral population dynamics and virulence thresholds

Viral factors and host barriers influence virally induced disease, and asymptomatic versus symptomatic infection is governed by a 'virulence threshold'. Understanding modulation of virulence thresholds could lend insight into disease outcome and aid in rational therapeutic and vaccine design. RNA viruses are an excellent system to study virulence thresholds in the context of quasispecies population dynamics. RNA viruses have high error frequencies and our understanding of viral population dynamics has been shaped by quasispecies evolutionary theory. In turn, research using RNA viruses as replicons with short generation times and high mutation rates has been an invaluable tool to test models of quasispecies theory. The challenge and new frontier of RNA virus population dynamics research is to combine multiple theoretical models and experimental data to describe viral population behavior as it changes, moving within and between hosts, to predict disease and pathogen emergence. Several excellent studies have begun to undertake this challenge using novel approaches.

Viral quasispecies evolution

Evolution of RNA viruses occurs through disequilibria of collections of closely related mutant spectra or mutant clouds termed viral quasispecies. Here we review the origin of the quasispecies concept and some biological implications of quasispecies dynamics. Two main aspects are addressed: (i) mutant clouds as reservoirs of phenotypic variants for virus adaptability and (ii) the internal interactions that are established within mutant spectra that render a virus ensemble the unit of selection. The understanding of viruses as quasispecies has led to new antiviral designs, such as lethal mutagenesis, whose aim is to drive viruses toward low fitness values with limited chances of fitness recovery. The impact of quasispecies for three salient human pathogens, human immunodeficiency virus and the hepatitis B and C viruses, is reviewed, with emphasis on antiviral treatment strategies. Finally, extensions of quasispecies to nonviral systems are briefly mentioned to emphasize the broad applicability of quasispecies theory.

Dynamics of alternative modes of RNA replication for positive-sense RNA viruses

We propose and study nonlinear mathematical models describing the intracellular time dynamics of viral RNA accumulation for positive-sense single-stranded RNA viruses. Our models consider different replication modes ranging between two extremes represented by the geometric replication (GR) and the linear stamping machine replication (SMR). We first analyse a model that quantitatively reproduced experimental data for the accumulation dynamics of both polarities of turnip mosaic potyvirus RNAs. We identify a non-degenerate transcritical bifurcation governing the extinction of both strands depending on three key parameters: the mode of replication (α), the replication rate (r) and the degradation rate (δ) of viral strands. Our results indicate that the bifurcation associated with α generically takes place when the replication mode is closer to the SMR, thus suggesting that GR may provide viral strands with an increased robustness against degradation. This transcritical bifurcation, which is responsible for the switching from an active to an absorbing regime, suggests a smooth (i.e. second-order), absorbing-state phase transition. Finally, we also analyse a simplified model that only incorporates asymmetry in replication tied to differential replication modes.