A trade-off between neutrality and adaptability limits the optimization of viral quasispecies

Redundancy-selection trade-off in phenotype-structured populations

Realistic fitness landscapes generally display a redundancy-fitness trade-off: highly fit trait configurations are inevitably rare, while less fit trait configurations are expected to be more redundant. The resulting sub-optimal patterns in the fitness distribution are typically described by means of effective formulations, where redundancy provided by the presence of neutral contributions is modelled implicitly, e.g. with a bias of the mutation process. However, the extent to which effective formulations are compatible with explicitly redundant landscapes is yet to be understood, as well as the consequences of a potential miss-match. Here we investigate the effects of such trade-off on the evolution of phenotype-structured populations, characterised by continuous quantitative traits. We consider a typical replication-mutation dynamics, and we model redundancy by means of two dimensional landscapes displaying both selective and neutral traits. We show that asymmetries of the landscapes will generate neutral contributions to the marginalised fitness-level description, that cannot be described by effective formulations, nor disentangled by the full trait distribution. Rather, they appear as effective sources, whose magnitude depends on the geometry of the landscape. Our results highlight new important aspects on the nature of sub-optimality. We discuss practical implications for rapidly mutant populations such as pathogens and cancer cells, where the qualitative knowledge of their trait and fitness distributions can drive disease management and intervention policies.

Gauging genetic diversity of generalists: A test of genetic and ecological generalism with RNA virus experimental evolution

Generalist viruses, those with a comparatively larger host range, are considered more likely to emerge on new hosts. The potential to emerge in new hosts has been linked to viral genetic diversity, a measure of evolvability. However, there is no consensus on whether infecting a larger number of hosts leads to higher genetic diversity, or whether diversity is better maintained in a homogeneous environment, similar to the lifestyle of a specialist virus. Using experimental evolution with the RNA bacteriophage phi6, we directly tested whether genetic generalism (carrying an expanded host range mutation) or environmental generalism (growing on heterogeneous hosts) leads to viral populations with more genetic variation. Sixteen evolved viral lineages were deep sequenced to provide genetic evidence for population diversity. When evolved on a single host, specialist and generalist genotypes both maintained the same level of diversity (measured by the number of single nucleotide polymorphisms (SNPs) above 1%, P = 0.81). However, the generalist genotype evolved on a single host had higher SNP levels than generalist lineages under two heterogeneous host passaging schemes (P = 0.001, P < 0.001). RNA viruses’ response to selection in alternating hosts reduces standing genetic diversity compared to those evolving in a single host to which the virus is already well-adapted.

Differences in adaptive dynamics determine the success of virus variants that propagate together

Virus fitness is a complex parameter that results from the interaction of virus-specific characters (e.g. intracellular growth rate, adsorption rate, virion extracellular stability, and tolerance to mutations) with others that depend on the underlying fitness landscape and the internal structure of the whole population. Individual mutants usually have lower fitness values than the complex population from which they come from. When they are propagated and allowed to attain large population sizes for a sufficiently long time, they approach mutation-selection equilibrium with the concomitant fitness gains. The optimization process follows dynamics that vary among viruses, likely due to differences in any of the parameters that determine fitness values. As a consequence, when different mutants spread together, the number of generations experienced by each of them prior to co-propagation may determine its particular fate. In this work we attempt a clarification of the effect of different levels of population diversity in the outcome of competition dynamics. To this end, we analyze the behavior of two mutants of the RNA bacteriophage Qβ that co-propagate with the wild-type virus. When both competitor viruses are clonal, the mutants rapidly outcompete the wild type. However, the outcome in competitions performed with partially optimized virus populations depends on the distance of the competitors to their clonal origin. We also implement a theoretical population dynamics model that describes the evolution of a heterogeneous population of individuals, each characterized by a fitness value, subjected to subsequent cycles of replication and mutation. The experimental results are explained in the framework of our theoretical model under two non-excluding, likely complementary assumptions: (1) The relative advantage of both competitors changes as populations approach mutation-selection equilibrium, as a consequence of differences in their growth rates and (2) one of the competitors is more robust to mutations than the other. The main conclusion is that the nearness of an RNA virus population to mutation-selection equilibrium is a key factor determining the fate of particular mutants arising during replication.

Antigenic diversification is correlated with increased thermostability in a mammalian virus

The theory of plastogenetic congruence posits that ultimately, the pressure to maintain function in the face of biomolecular destabilization produces robustness. As temperature goes up so does destabilization. Thus, genetic robustness, defined as phenotypic constancy despite mutation, should correlate with survival during thermal challenge. We tested this hypothesis using vesicular stomatitis virus (VSV). We produced two sets of evolved strains after selection for higher thermostability by either preincubation at 37°C or by incubation at 40°C during infection. These VSV populations became more thermostable and also more fit in the absence of thermal selection, demonstrating an absence of tradeoffs. Eleven out of 12 evolved populations had a fixed, nonsynonymous substitution in the nucleocapsid (N) open reading frame. There was a partial correlation between thermostability and mutational robustness that was observed when the former was measured at 42°C, but not at 37°C. These results are consistent with our earlier work and suggest that the relationship between robustness and thermostability is complex. Surprisingly, many of the thermostable strains also showed increased resistance to monoclonal antibody and polyclonal sera, including sera from natural hosts. These data suggest that evolved thermostability may lead to antigenic diversification and an increased ability to escape immune surveillance in febrile hosts, and potentially to an improved robustness. These relationships have important implications not only in terms of viral pathogenesis, but also for the development of vaccine vectors and oncolytic agents.

Identification and characterization of influenza variants resistant to a viral endonuclease inhibitor

The influenza endonuclease is an essential subdomain of the viral RNA polymerase. It processes host pre-mRNAs to serve as primers for viral mRNA and is an attractive target for antiinfluenza drug discovery. Compound L-742,001 is a prototypical endonuclease inhibitor, and we found that repeated passaging of influenza virus in the presence of this drug did not lead to the development of resistant mutant strains. Reduced sensitivity to L-742,001 could only be induced by creating point mutations via a random mutagenesis strategy. These mutations mapped to the endonuclease active site where they can directly impact inhibitor binding. Engineered viruses containing the mutations showed resistance to L-742,001 both in vitro and in vivo, with only a modest reduction in fitness. Introduction of the mutations into a second virus also increased its resistance to the inhibitor. Using the isolated wild-type and mutant endonuclease domains, we used kinetics, inhibitor binding and crystallography to characterize how the two most significant mutations elicit resistance to L-742,001. These studies lay the foundation for the development of a new class of influenza therapeutics with reduced potential for the development of clinical endonuclease inhibitor-resistant influenza strains.

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.

The advantage of arriving first: characteristic times in finite size populations of error-prone replicators

We study the evolution of a finite size population formed by mutationally isolated lineages of error-prone replicators in a two-peak fitness landscape. Computer simulations are performed to gain a stochastic description of the system dynamics. More specifically, for different population sizes, we compute the probability of each lineage being selected in terms of their mutation rates and the amplification factors of the fittest phenotypes. We interpret the results as the compromise between the characteristic time a lineage takes to reach its fittest phenotype by crossing the neutral valley and the selective value of the sequences that form the lineages. A main conclusion is drawn: for finite population sizes, the survival probability of the lineage that arrives first to the fittest phenotype rises significantly.

Virus replication as a phenotypic version of polynucleotide evolution

In this paper, we revisit and adapt to viral evolution an approach based on the theory of branching process advanced by Demetrius et al. (Bull. Math. Biol. 46:239-262, 1985), in their study of polynucleotide evolution. By taking into account beneficial effects, we obtain a non-trivial multivariate generalization of their single-type branching process model. Perturbative techniques allows us to obtain analytical asymptotic expressions for the main global parameters of the model, which lead to the following rigorous results: (i) a new criterion for "no sure extinction", (ii) a generalization and proof, for this particular class of models, of the lethal mutagenesis criterion proposed by Bull et al. (J. Virol. 18:2930-2939, 2007), (iii) a new proposal for the notion of relaxation time with a quantitative prescription for its evaluation, (iv) the quantitative description of the evolution of the expected values in four distinct "stages": extinction threshold, lethal mutagenesis, stationary "equilibrium", and transient. Finally, based on these quantitative results, we are able to draw some qualitative conclusions.

Congruent evolution of fitness and genetic robustness in vesicular stomatitis virus

Quasispecies theory is a case of mutation-selection balance for evolution at high mutation rates, such as those observed in RNA viruses. One of the main predictions of this model is the selection for robustness, defined as the ability of an organism to remain phenotypically unchanged in the face of mutation. We have used a collection of vesicular stomatitis virus strains that had been evolving either under positive selection or under random drift. We had previously shown that the former increase in fitness while the latter have overall fitness decreases (I. S. Novella, J. B. Presloid, T. Zhou, S. D. Smith-Tsurkan, B. E. Ebendick-Corpus, R. N. Dutta, K. L. Lust, and C. O. Wilke, J. Virol. 84:4960-4968, 2010). Here, we determined the robustness of these strains and demonstrated that strains under positive selection not only increase in fitness but also increase in robustness. In contrast, strains under drift not only decreased in fitness but also decreased in robustness. There was a good overall correlation between fitness and robustness. We also tested whether there was a correlation between fitness and thermostability, and we observed that the correlation was imperfect, indicating that the fitness effects of mutations are exerted in part at a level other than changing the resistance of the protein to temperature.

Severe hindrance of viral infection propagation in spatially extended hosts

The production of large progeny numbers affected by high mutation rates is a ubiquitous strategy of viruses, as it promotes quick adaptation and survival to changing environments. However, this situation often ushers in an arms race between the virus and the host cells. In this paper we investigate in depth a model for the dynamics of a phenotypically heterogeneous population of viruses whose propagation is limited to two-dimensional geometries, and where host cells are able to develop defenses against infection. Our analytical and numerical analyses are developed in close connection to directed percolation models. In fact, we show that making the space explicit in the model, which in turn amounts to reducing viral mobility and hindering the infective ability of the virus, connects our work with similar dynamical models that lie in the universality class of directed percolation. In addition, we use the fact that our model is a multicomponent generalization of the Domany-Kinzel probabilistic cellular automaton to employ several techniques developed in the past in that context, such as the two-site approximation to the extinction transition line. Our aim is to better understand propagation of viral infections with mobility restrictions, e.g., in crops or in plant leaves, in order to inspire new strategies for effective viral control.

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.

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.

Results

We investigate the effect of microscopic mutations on the phenotype of RNA molecules during their in silico evolution and adaptation. We calculate the distribution of the effects of mutations on fitness, the relative fractions of beneficial and deleterious mutations and the corresponding selection coefficients for populations evolving under different mutation rates. Three different situations are explored: the mutation-selection equilibrium (optimized population) in three different fitness landscapes, the dynamics during adaptation towards a goal structure (adapting population), and the behavior under periodic population bottlenecks (perturbed population).

Conclusions

The ratio between the number of beneficial and deleterious mutations experienced by a population of RNA sequences increases with the value of the mutation rate μ at which evolution proceeds. In contrast, the selective value of mutations remains almost constant, independent of μ, indicating that adaptation occurs through an increase in the amount of beneficial mutations, with little variations in the average effect they have on fitness. Statistical analyses of the distribution of fitness effects reveal that small effects, either beneficial or deleterious, are well described by a Pareto distribution. These results are robust under changes in the fitness landscape, remarkably when, in addition to selecting a target secondary structure, specific subsequences or low-energy folds are required. A population perturbed by bottlenecks behaves similarly to an adapting population, struggling to return to the optimized state. Whether it can survive in the long run or whether it goes extinct depends critically on the length of the time interval between bottlenecks.

Evolutionary dynamics on networks of selectively neutral genotypes: effects of topology and sequence stability

Networks of selectively neutral genotypes underlie the evolution of populations of replicators in constant environments. Previous theoretical analysis predicted that such populations will evolve toward highly connected regions of the genome space. We first study the evolution of populations of replicators on simple networks and quantify how the transient time to equilibrium depends on the initial distribution of sequences on the neutral network, on the topological properties of the latter, and on the mutation rate. Second, network neutrality is broken through the introduction of an energy for each sequence. This allows to study the competition between two features (neutrality and energetic stability) relevant for survival and subjected to different selective pressures. In cases where the two features are negatively correlated, the population experiences sudden migrations in the genome space for values of the relevant parameters that we calculate. The numerical study of larger networks indicates that the qualitative behavior to be expected in more realistic cases is already seen in representative examples of small networks.