Information catastrophe in RNA viruses through replication thresholds

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.

Viral replication modes in single-peak fitness landscapes: A dynamical systems analysis

Positive-sense, single-stranded RNA viruses are important pathogens infecting almost all types of organisms. Experimental evidence from distributions of mutations and from viral RNA amplification suggest that these pathogens may follow different RNA replication modes, ranging from the stamping machine replication (SMR) to the geometric replication (GR) mode. Although previous theoretical work has focused on the evolutionary dynamics of RNA viruses amplifying their genomes with different strategies, little is known in terms of the bifurcations and transitions involving the so-called error threshold (mutation-induced dominance of mutants) and lethal mutagenesis (extinction of all sequences due to mutation accumulation and demographic stochasticity). Here we analyze a dynamical system describing the intracellular amplification of viral RNA genomes evolving on a single-peak fitness landscape focusing on three cases considering neutral, deleterious, and lethal mutants. We analytically derive the critical mutation rates causing lethal mutagenesis and error threshold, governed by transcritical bifurcations that depend on parameters α (parameter introducing the mode of replication), replicative fitness of mutants (k₁), and on the spontaneous degradation rates of the sequences (ϵ). Our results relate the error catastrophe with lethal mutagenesis in a model with continuous populations of viral genomes. The former case involves dominance of the mutant sequences, while the latter, a deterministic extinction of the viral RNAs during replication due to increased mutation. For the lethal case the critical mutation rate involving lethal mutagenesis is μ_c=1-ɛ/α. Here, the SMR involves lower critical mutation rates, being the system more robust to lethal mutagenesis replicating closer to the GR mode. This result is also found for the neutral and deleterious cases, but for these later cases lethal mutagenesis can shift to the error threshold once the replication mode surpasses a threshold given by α=ϵ/k₁.

Trans-heteroclinic bifurcation: a novel type of catastrophic shift

Global and local bifurcations are extremely important since they govern the transitions between different qualitative regimes in dynamical systems. These transitions or tipping points, which are ubiquitous in nature, can be smooth or catastrophic. Smooth transitions involve a continuous change in the steady state of the system until the bifurcation value is crossed, giving place to a second-order phase transition. Catastrophic transitions involve a discontinuity of the steady state at the bifurcation value, giving place to first-order phase transitions. Examples of catastrophic shifts can be found in ecosystems, climate, economic or social systems. Here we report a new type of global bifurcation responsible for a catastrophic shift. This bifurcation, identified in a family of quasi-species equations and named as trans-heteroclinic bifurcation, involves an exchange of stability between two distant and heteroclinically connected fixed points. Since the two fixed points interchange the stability without colliding, a catastrophic shift takes place. We provide an exhaustive description of this new bifurcation, also detailing the structure of the replication-mutation matrix of the quasi-species equation giving place to this bifurcation. A perturbation analysis is provided around the bifurcation value. At this value the heteroclinic connection is replaced by a line of fixed points in the quasi-species model. But it is shown that, if the replication-mutation matrix satisfies suitable conditions, then, under a small perturbation, the exchange of heteroclinic connections is preserved, except on a tiny range around the bifurcation value whose size is of the order of magnitude of the perturbation. The results presented here can help to understand better novel mechanisms behind catastrophic shifts and contribute to a finer identification of such transitions in theoretical models in evolutionary biology and other dynamical systems.

Enhanced cytopathic effect of Japanese encephalitis virus strain SA14-14-2: Probable association of mutation in amino acid of its envelope protein

Japanese encephalitis (JE) is a mosquito-borne viral disease. It is a global public health concern since it causes an acute encephalitis syndrome (AES). A large number of JE/AES cases are reported to occur in areas with established or developing JE vaccination program. Partial vaccine coverage and emergence of new variants of Japanese encephalitis virus (JEV) might be playing an important role. The envelope protein (E) of JEV is a major antigenic determinant and responsible for immunogenic responses as well as membrane fusion and virion assembly. In the present study, we have characterized the JEV live attenuated vaccine strain SA14-14-2 in baby hamster kidney cells (BHK-21). The vaccine strain showed enhanced replication following its passage in BHK-21 cells. Nucleotide sequence analysis of the E protein gene of the cell-culture adapted vaccine strain showed an important point mutation. The mutation in the E protein gene was identical to its wild-type parent strain SA14. This study suggests the possibility of reversion mutation and exaltation of vaccine strains following adaptation in the host cells.

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.

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.

Influence of mutagenesis and viral load on the sustained low-level replication of an RNA virus

Lethal mutagenesis is an antiviral strategy that aims to extinguish viruses as a consequence of enhanced mutation rates during virus replication. The molecular mechanisms that underlie virus extinction by mutagenic nucleoside analogues are not well understood. When mutagenic agents and antiviral inhibitors are administered sequentially or in combination, interconnected and often conflicting selective constraints can influence the fate of the virus either towards survival through selection of mutagen-escape or inhibitor-escape mutants or towards extinction. Here we report a study involving the mutagenesis of foot-and-mouth disease virus (FMDV) by the nucleoside analogue ribavirin (R) and the effect of R-mediated mutagenesis on the selection of FMDV mutants resistant to the inhibitor of RNA replication, guanidine hydrochloride (GU). The results show that under comparable (and low) viral load, an inhibitory activity by GU could not substitute for an equivalent inhibitory activity by R in driving FMDV to extinction. Both the prior history of R mutagenesis and the viral population size influenced the selection of GU-escape mutants. A sufficiently low viral load allowed continued viral replication without selection of inhibitor-escape mutants, irrespective of the history of mutagenesis. These observations imply that reductions of viral load as a result of a mutagenic treatment may provide an opportunity either for immune-mediated clearing of a virus or for an alternative antiviral intervention, even if extinction is not initially achieved.

Error catastrophe for viruses infecting cells: analysis of the phase transition in terms of error classes

RNA viruses offer a very exciting arena in which to study evolution in 'real time' owing to both their high replication rate-many generations per day are possible-and their high mutation rate, leading to a large phenotypic variety. They can be regarded as a swarm of genetically related mutants around a dominant or master genetic sequence. This system is called a 'viral quasi-species'. Thus, a common framework to describe RNA viral dynamics is by means of the quasi-species equation (QSE). The QSE is in fact a system of a very large number of nonlinear coupled equations. Here, we consider a simpler formulation in terms of 'error classes', which groups all the sequences differing from the master sequence by the same number of genomic differences into one population class. From this, based on the analogies with Bose condensation, we use thermodynamic inspired observables to analyse and characterize the 'phase transition' through the so-called 'RNA virus error catastrophe'.

Simple genomes, complex interactions: epistasis in RNA virus

Owed to their reduced size and low number of proteins encoded, RNA viruses and other subviral pathogens are often considered as being genetically too simple. However, this structural simplicity also creates the necessity for viral RNA sequences to encode for more than one protein and for proteins to carry out multiple functions, all together resulting in complex patterns of genetic interactions. In this work we will first review the experimental studies revealing that the architecture of viral genomes is dominated by antagonistic interactions among loci. Second, we will also review mathematical models and provide a description of computational tools for the study of RNA virus dynamics and evolution. As an application of these tools, we will finish this review article by analyzing a stochastic bit-string model of in silico virus replication. This model analyzes the interplay between epistasis and the mode of replication on determining the population load of deleterious mutations. The model suggests that, for a given mutation rate, the deleterious mutational load is always larger when epistasis is predominantly antagonistic than when synergism is the rule. However, the magnitude of this effect is larger if replication occurs geometrically than if it proceeds linearly.

Potential benefits of sequential inhibitor-mutagen treatments of RNA virus infections

Lethal mutagenesis is an antiviral strategy consisting of virus extinction associated with enhanced mutagenesis. The use of non-mutagenic antiviral inhibitors has faced the problem of selection of inhibitor-resistant virus mutants. Quasispecies dynamics predicts, and clinical results have confirmed, that combination therapy has an advantage over monotherapy to delay or prevent selection of inhibitor-escape mutants. Using ribavirin-mediated mutagenesis of foot-and-mouth disease virus (FMDV), here we show that, contrary to expectations, sequential administration of the antiviral inhibitor guanidine (GU) first, followed by ribavirin, is more effective than combination therapy with the two drugs, or than either drug used individually. Coelectroporation experiments suggest that limited inhibition of replication of interfering mutants by GU may contribute to the benefits of the sequential treatment. In lethal mutagenesis, a sequential inhibitor-mutagen treatment can be more effective than the corresponding combination treatment to drive a virus towards extinction. Such an advantage is also supported by a theoretical model for the evolution of a viral population under the action of increased mutagenesis in the presence of an inhibitor of viral replication. The model suggests that benefits of the sequential treatment are due to the involvement of a mutagenic agent, and to competition for susceptible cells exerted by the mutant spectrum. The results may impact lethal mutagenesis-based protocols, as well as current antiviral therapies involving ribavirin.

RNA viruses are associated with many important human and animal diseases such as AIDS, influenza, hemorrhagic fevers and several forms of hepatitis. RNA viruses mutate at very high rates and, therefore, can adapt easily to environmental changes. Viral mutants resistant to antiviral inhibitors are readily selected, resulting in treatment failure. The simultaneous administration of three or more inhibitors is a means to prevent or delay selection of resistant mutants. A new antiviral strategy termed lethal mutagenesis is presently under investigation. It consists of the administration of mutagenic agents to elevate the mutation rate of the virus above the maximum level compatible with virus infectivity, without mutagenizing the host cells. Since low amounts of virus are extinguished more easily, the combination of a mutagen and inhibitor was more efficient than a mutagen alone in driving virus to extinction. Here we show that foot-and-mouth disease virus replicating in cell culture can be extinguished more easily when the inhibitor guanidine is administered first, followed by the mutagenic agent ribavirin, than when both drugs are administered simultaneously. Interfering mutants that contribute to extinction were active in the presence of ribavirin but not in the presence of guanidine. This observation provides a mechanism for the advantage of the sequential versus the combination treatment. This unexpected effectiveness of a sequential treatment is supported by a theoretical model of virus evolution in the presence of the inhibitor and the mutagen. The results can have an application for future lethal mutagenesis protocols and for current antiviral treatments that involve the antiviral agent ribavirin when it acts as a mutagen.

Antigenic diversity, transmission mechanisms, and the evolution of pathogens

Pathogens have evolved diverse strategies to maximize their transmission fitness. Here we investigate these strategies for directly transmitted pathogens using mathematical models of disease pathogenesis and transmission, modeling fitness as a function of within- and between-host pathogen dynamics. The within-host model includes realistic constraints on pathogen replication via resource depletion and cross-immunity between pathogen strains. We find three distinct types of infection emerge as maxima in the fitness landscape, each characterized by particular within-host dynamics, host population contact network structure, and transmission mode. These three infection types are associated with distinct non-overlapping ranges of levels of antigenic diversity, and well-defined patterns of within-host dynamics and between-host transmissibility. Fitness, quantified by the basic reproduction number, also falls within distinct ranges for each infection type. Every type is optimal for certain contact structures over a range of contact rates. Sexually transmitted infections and childhood diseases are identified as exemplar types for low and high contact rates, respectively. This work generates a plausible mechanistic hypothesis for the observed tradeoff between pathogen transmissibility and antigenic diversity, and shows how different classes of pathogens arise evolutionarily as fitness optima for different contact network structures and host contact rates.

Infectious diseases vary widely in how they affect those who get infected and how they are transmitted. As an example, the duration of a single infection can range from days to years, while transmission can occur via the respiratory route, water or sexual contact. Measles and HIV are contrasting examples—both are caused by RNA viruses, but one is a genetically diverse, lethal sexually transmitted infection (STI) while the other is a relatively mild respiratory childhood disease with low antigenic diversity. We investigate why the most transmissible respiratory diseases such as measles and rubella are antigenically static, meaning immunity is lifelong, while other diseases—such as influenza, or the sexually transmitted diseases—seem to trade transmissibility for the ability to generate multiple diverse strains so as to evade host immunity. We use mathematical models of disease progression and evolution within the infected host coupled with models of transmission between hosts to explore how transmission modes, host contact rates and network structure determine antigenic diversity, infectiousness and duration of infection. In doing so, we classify infections into three types—measles-like (high transmissibility, but antigenically static), flu-like (lower transmissibility, but more antigenically diverse), and STI-like (very antigenically diverse, long lived infection, but low overall transmissibility).

Replication mode and landscape topology differentially affect RNA virus mutational load and robustness

Regardless of genome polarity, intermediaries of complementary sense must be synthesized and used as templates for the production of new genomic strands. Depending on whether these new genomic strands become themselves templates for producing extra antigenomic ones, thus giving rise to geometric growth, or only the firstly synthesized antigenomic strands can be used to this end, thus following Luria's stamping machine model, the abundances and distributions of mutant genomes will be different. Here we propose mathematical and bit string models that allow distinguishing between stamping machine and geometric replication. We have observed that, regardless the topology of the fitness landscape, the critical mutation rate at which the master sequence disappears increases as the mechanism of replication switches from purely geometric to stamping machine. We also found that, for a wide range of mutation rates, large-effect mutations do not accumulate regardless the scheme of replication. However, mild mutations accumulate more in the geometric model. Furthermore, at high mutation rates, geometric growth leads to a population collapse for intermediate values of mutational effects at which the stamping machine still produces master genomes. We observed that the critical mutation rate was weakly dependent on the strength of antagonistic epistasis but strongly dependent on synergistic epistasis. In conclusion, we have shown that RNA viruses may increase their robustness against the accumulation of deleterious mutations by replicating as stamping machines and that the magnitude of this benefit depends on the topology of the fitness landscape assumed.

Understanding the molecular epidemiology of foot-and-mouth-disease virus

The use of molecular epidemiology is an important tool in understanding and consequently controlling FMDV. In this review I will present basic information about the disease, needed to perform molecular epidemiology. I will give a short introduction to the history and impact of foot-and-mouth disease, clinical picture, infection route, subclinical and persistent infections, general aspects of the transmission of FMDV, serotype-specific epidemiological characteristics, field epidemiology of FMDV, evolution and molecular epidemiology of FMDV. This is followed by two chapters describing the molecular epidemiology of foot-and-mouth disease in global surveillance and molecular epidemiology of foot-and-mouth disease in outbreak investigation.

Quasispecies and its impact on viral hepatitis

Quasispecies dynamics mediates adaptability of RNA viruses through a number of mechanisms reviewed in the present article, with emphasis on the medical implications for the hepatitis viruses. We discuss replicative and non-replicative molecular mechanisms of genome variation, modulating effects of mutant spectra, and several modes of viral evolution that can affect viral pathogenesis. Relevant evolutionary events include the generation of minority virus variants with altered functional properties, and alterations of mutant spectrum complexity that can affect disease progression or response to treatment. The widespread occurrence of resistance to antiviral drugs encourages new strategies to control hepatic viral disease such as combination therapies and lethal mutagenesis. In particular, ribavirin may be exerting in some cases its antiviral activity with participation of its mutagenic action. Despite many unanswered questions, here we document that quasispecies dynamics has provided an interpretation of the adaptability of the hepatitis viruses, with features conceptually similar to those observed with other RNA viruses, a reflection of the common underlying Darwinian principles.