Effects of spatial competition on the diversity of a quasispecies

Phase transitions in virology

Viruses have established relationships with almost every other living organism on Earth and at all levels of biological organization: from other viruses up to entire ecosystems. In most cases, they peacefully coexist with their hosts, but in most relevant cases, they parasitize them and induce diseases and pandemics, such as the AIDS and the most recent avian influenza and COVID-19 pandemic events, causing a huge impact on health, society, and economy. Viruses play an essential role in shaping the eco-evolutionary dynamics of their hosts, and have been also involved in some of the major evolutionary innovations either by working as vectors of genetic information or by being themselves coopted by the host into their genomes. Viruses can be studied at different levels of biological organization, from the molecular mechanisms of genome replication, gene expression and encapsidation, to global pandemics. All these levels are different and yet connected through the presence of threshold conditions allowing for the formation of a capsid, the loss of genetic information or epidemic spreading. These thresholds, as occurs with temperature separating phases in a liquid, define sharp qualitative types of behaviour. Thesephase transitionsare very well known in physics. They have been studied by means of simple, but powerful models able to capture their essential properties, allowing us to better understand them. Can the physics of phase transitions be an inspiration for our understanding of viral dynamics at different scales? Here we review well-known mathematical models of transition phenomena in virology. We suggest that the advantages of abstract, simplified pictures used in physics are also the key to properly understanding the origins and evolution of complexity in viruses. By means of several examples, we explore this multilevel landscape and how minimal models provide deep insights into a diverse array of problems. The relevance of these transitions in connecting dynamical patterns across scales and their evolutionary and clinical implications are outlined.

Composition and Dynamics of H1N1 and H7N9 Influenza A Virus Quasispecies in a Co-infected Patient Analyzed by Single Molecule Sequencing Technology

A human co-infected with H1N1 and H7N9 subtypes influenza A virus (IAV) causes a complex infectious disease. The identification of molecular-level variations in composition and dynamics of IAV quasispecies will help to understand the pathogenesis and provide guidance for precision medicine treatment. In this study, using single-molecule real-time sequencing (SMRT) technology, we successfully acquired full-length IAV genomic sequences and quantified their genotypes abundance in serial samples from an 81-year-old male co-infected with H1N1 and H7N9 subtypes IAV. A total of 26 high diversity nucleotide loci was detected, in which the A-G base transversion was the most abundant substitution type (67 and 64%, in H1N1 and H7N9, respectively). Seven significant amino acid variations were detected, such as NA:H275Y and HA: R222K in H1N1 as well as PB2:E627K and NA: K432E in H7N9, which are related to viral drug-resistance or mammalian adaptation. Furtherly, we retrieved 25 H1N1 and 22 H7N9 genomic segment haplotypes from the eight samples based on combining high-diversity nucleotide loci, which provided a more concise overview of viral quasispecies composition and dynamics. Our approach promotes the popularization of viral quasispecies analysis in a complex infectious disease, which will boost the understanding of viral infections, pathogenesis, evolution, and precision medicine.

Mutagenesis Scanning Uncovers Evolutionary Constraints on Tobacco Etch Potyvirus Membrane-Associated 6K2 Protein

RNA virus high mutation rate is a double-edged sword. At the one side, most mutations jeopardize proteins functions; at the other side, mutations are needed to fuel adaptation. The relevant question then is the ratio between beneficial and deleterious mutations. To evaluate this ratio, we created a mutant library of the 6K2 gene of tobacco etch potyvirus that contains every possible single-nucleotide substitution. 6K2 protein anchors the virus replication complex to the network of endoplasmic reticulum membranes. The library was inoculated into the natural host Nicotiana tabacum, allowing competition among all these mutants and selection of those that are potentially viable. We identified 11 nonsynonymous mutations that remain in the viral population at measurable frequencies and evaluated their fitness. Some had fitness values higher than the wild-type and some were deleterious. The effect of these mutations in the structure, transmembrane properties, and function of 6K2 was evaluated in silico. In parallel, the effect of these mutations in infectivity, virus accumulation, symptoms development, and subcellular localization was evaluated in the natural host. The α-helix H1 in the N-terminal part of 6K2 turned out to be under purifying selection, while most observed mutations affect the link between transmembrane α-helices H2 and H3, fusing them into a longer helix and increasing its rigidity. In general, these changes are associated with higher within-host fitness and development of milder or no symptoms. This finding suggests that in nature selection upon 6K2 may result from a tradeoff between within-host accumulation and severity of symptoms.

Limited role of spatial self-structuring in emergent trade-offs during pathogen evolution

Pathogen transmission and virulence are main evolutionary variables broadly assumed to be linked through trade-offs. In well-mixed populations, these trade-offs are often ascribed to physiological restrictions, while populations with spatial self-structuring might evolve emergent trade-offs. Here, we reexamine a spatially-explicit, SIR model of the latter kind proposed by Ballegooijen and Boerlijst with the aim of characterising the mechanisms causing the emergence of the trade-off and its structural robustness. Using invadability criteria, we establish the conditions under which an evolutionary feedback between transmission and virulence mediated by pattern formation can poise the system to a critical boundary separating a disordered state (without emergent trade-off) from a self-structured phase (where the trade-off emerges), and analytically calculate the functional shape of the boundary in a certain approximation. Beyond evolutionary parameters, the success of an invasion depends on the size and spatial structure of the invading and invaded populations. Spatial self-structuring is often destroyed when hosts are mobile, changing the evolutionary dynamics to those of a well-mixed population. In a metapopulation scenario, the systematic extinction of the pathogen in the disordered phase may counteract the disruptive effect of host mobility, favour pattern formation and therefore recover the emergent trade-off.

Mosquito bottlenecks alter viral mutant swarm in a tissue and time-dependent manner with contraction and expansion of variant positions and diversity

Viral diversity is theorized to play a significant role during virus infections, particularly for arthropod-borne viruses (arboviruses) that must infect both vertebrate and invertebrate hosts. To determine how viral diversity influences mosquito infection and dissemination Culex taeniopus mosquitoes were infected with the Venezuelan equine encephalitis virus endemic strain 68U201. Bodies and legs/wings of the mosquitoes were collected individually and subjected to multi-parallel sequencing. Virus sequence diversity was calculated for each tissue. Greater diversity was seen in mosquitoes with successful dissemination versus those with no dissemination. Diversity across time revealed that bottlenecks influence diversity following dissemination to the legs/wings, but levels of diversity are restored by Day 12 post-dissemination. Specific minority variants were repeatedly identified across the mosquito cohort, some in nearly every tissue and time point, suggesting that certain variants are important in mosquito infection and dissemination. This study demonstrates that the interaction between the mosquito and the virus results in changes in diversity and the mutational spectrum and may be essential for successful transition of the bottlenecks associated with arbovirus infection.

Getting to Know Viral Evolutionary Strategies: Towards the Next Generation of Quasispecies Models

Viral populations are formed by complex ensembles of genomes with broad phenotypic diversity. The adaptive strategies deployed by these ensembles are multiple and often cannot be predicted a priori. Our understanding of viral dynamics is mostly based on two kinds of empirical approaches: one directed towards characterizing molecular changes underlying fitness changes and another focused on population-level responses. Simultaneously, theoretical efforts are directed towards developing a formal picture of viral evolution by means of more realistic fitness landscapes and reliable population dynamics models. New technologies, chiefly the use of next-generation sequencing and related tools, are opening avenues connecting the molecular and the population levels. In the near future, we hope to be witnesses of an integration of these still decoupled approaches, leading into more accurate and realistic quasispecies models able to capture robust generalities and endowed with a satisfactory predictive power.

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.

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.

Quasispecies spatial models for RNA viruses with different replication modes and infection strategies

Empirical observations and theoretical studies suggest that viruses may use different replication strategies to amplify their genomes, which impact the dynamics of mutation accumulation in viral populations and therefore, their fitness and virulence. Similarly, during natural infections, viruses replicate and infect cells that are rarely in suspension but spatially organized. Surprisingly, most quasispecies models of virus replication have ignored these two phenomena. In order to study these two viral characteristics, we have developed stochastic cellular automata models that simulate two different modes of replication (geometric vs stamping machine) for quasispecies replicating and spreading on a two-dimensional space. Furthermore, we explored these two replication models considering epistatic fitness landscapes (antagonistic vs synergistic) and different scenarios for cell-to-cell spread, one with free superinfection and another with superinfection inhibition. We found that the master sequences for populations replicating geometrically and with antagonistic fitness effects vanished at low critical mutation rates. By contrast, the highest critical mutation rate was observed for populations replicating geometrically but with a synergistic fitness landscape. Our simulations also showed that for stamping machine replication and antagonistic epistasis, a combination that appears to be common among plant viruses, populations further increased their robustness by inhibiting superinfection. We have also shown that the mode of replication strongly influenced the linkage between viral loci, which rapidly reached linkage equilibrium at increasing mutations for geometric replication. We also found that the strategy that minimized the time required to spread over the whole space was the stamping machine with antagonistic epistasis among mutations. Finally, our simulations revealed that the multiplicity of infection fluctuated but generically increased along time.

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.

Struggle for space: viral extinction through competition for cells

The design of protocols to suppress the propagation of viral infections is an enduring enterprise, especially hindered by limited knowledge of the mechanisms leading to viral extinction. Here we report on infection extinction due to intraspecific competition to infect susceptible hosts. Beneficial mutations increase the production of viral progeny, while the host cell may develop defenses against infection. For an unlimited number of host cells, a feedback runaway coevolution between host resistance and progeny production occurs. However, physical space limits the advantage that the virus obtains from increasing offspring numbers; thus, infection clearance may result from an increase in host defenses beyond a finite threshold. Our results might be relevant to devise improved control strategies in environments with mobility constraints or different geometrical properties.

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.