Introduction to Quasispecies Theory as it Applies to Viruses

The first mathematical treatment of replication with production of error copies was established by Manfred Eigen in a study that integrated concepts of information theory and Darwinian natural selection.Reference Eigen¹ The theory was further developed by Manfred Eigen and Peter Schuster and published in a series of papers that were compiled in a book.Reference Eigen and Schuster² The main point of the theory was to define conditions for self-organization and transmission of inheritable information in primitive replicating molecules such as those that may have been at the origin of the first life forms on Earth. A critical transition in the origin of life must have been the generation of a polymer with the capacity to act as template to produce progeny and generate sets of replicating molecules. According to quasispecies theory, a master copy of the replicating ensemble produces mutant versions that conform a mutant spectrum, distribution, clan, swarm or cloud, an essential point that renders mutation an event closely linked to replication. This is an important difference from population genetics treatments such as the Crow-Kimura model, in which mutation is treated as independent of replication (reviewed in Ref. 3).

In parallel with the theoretical development of quasispecies, Charles Weissmann and his colleagues established the experimental system that permitted the first site-directed mutagenesis experiments and the birth of what we now know as reverse genetics.Reference Flavell, Sabo, Bandle and Weissmann^4, Reference Weissmann, Taniguchi, Domingo, Sabo and Flavell⁵ They used the replicase (enzyme that catalyses genome replication) of the bacterial virus (bacteriophage) Qβ that infects the bacterium Escherichia coli. One of the extracistronic mutants (that affected a genome site that is not in a protein-coding region) of bacteriophage Qβ constructed by site-directed mutagenesis was viable (produced infectious progeny) but displayed a selective disadvantage relative to the wild-type virus.Reference Domingo, Flavell and Weissmann⁶ Multiplication of mutant clones of the virus resulted in reversion to the wild-type sequence; quantification of the reversion rate and of the competition parameters between the mutant and wild type allowed the first calculation of a mutation rate for an RNA virus. The value obtained was 10^–4 mutations incorporated per nucleotide copied,Reference Batschelet, Domingo and Weissmann⁷ a value close to values obtained later for other RNA viruses. In the course of these experiments it was observed that clonal population (those amplified from a single parental genome) of wild-type Qβ actually consisted of a heterogeneous collection of genomes in which, on average, each individual RNA differed from the others in one to two mutations.Reference Domingo, Sabo, Taniguchi and Weissmann⁸ Thus, the genome of bacteriophage Qβ consisted of a cloud of mutants, as predicted by the quasispecies theory of Eigen and Schuster.

The quasispecies features of RNA and some DNA viruses have several important consequences. Optimization of a viral quasispecies by repeated replication in the same environment does not result in a single molecular solution for high fitness (overall replicative efficacy). What is selected is a mutant cloud that may be dominated by one or several genomes, which are the equivalent to the master sequence in quasispecies theory. Commonly, the most frequent sequence is the one that displays the highest fitness, while the mutant spectrum consists of multitudes of variants whose frequency is ranked according to fitness. A consensus sequence (of nucleotides or amino acids) is defined as the one that at each position in the sequence includes the residue (nucleotide or amino acid), which is the most frequent at that position in the mutant distribution.

A critical consequence for the understanding of virus adaptability and survival is that the mutant distributions that conform viral populations are a huge reservoir of genetic and phenotypic variants. Minority genomes are ready to be selected in response to environmental demands. Most mutants are not selectively neutral: the mutations they harbour affect virus behaviour. In fact, viral evolution consists fundamentally of the replacement of genome subpopulations by others. The traditionally called ‘wild type’ virus no longer exists as a defined genome (as classic virology textbooks implied) but as sets of related mutants. Viral quasispecies are defined by virologists as collections of different but closely related genomes subjected to a continuous process of genetic variation, competition and selection, and that act as a unit of selection. (For an overview of theoretical and experimental advances in the field of quasispecies, see Ref. 3.)

In addition to providing a new understanding of RNA viruses, quasispecies theory has also inspired new approaches to the control of viral disease.

Quasispecies and Antiviral Interventions

The stability of a mutant distribution can be influenced by key parameters, with relevant consequences for antiviral strategies. Here, again, the connection between theory and experiment has been essential. The critical parameters are the amount of genetic information in the replicative system, the mutation rate, and the fitness superiority of the master sequence relative to other components of the mutant spectrum. Let us examine what these parameters are. In the case of viruses, the amount of genetic information can be equated with the genome length in nucleotides, that we denote with ι. This is because viruses generally do not encode redundant information (repeated sequences with the same function). The mutation rate during replication is termed μ. The superiority of the master or dominant sequence is represented as σ, and it means the ratio between the fitness of the master and the average fitness of the components of the mutant spectrum. A stable quasispecies requires an adequate balance between the mutation rate and the complexity of the information to be transmitted. This requirement is expressed by the following error threshold relationships: $$\mu _{{max}} \cdot \,\cong\, \cdot ln\sigma \,/\,l\,or\,t_{{max}} \cdot \,\cong\, \cdot {\rm In}s\sigma \,/\,\mu $$ (for the derivation of these equations and recent advances in the concept of error threshold, see Ref. 9). The first equation expresses the maximum mutation rate compatible with maintaining an information of complexity ι; the second equation expresses the maximum complexity of information that can be transmitted given an average mutation rate μ. Importantly, these equations hint at key parameters that can be modified to decrease quasispecies stability. The superiority of the master genome, σ, being in the numerator of the equations, is an obvious choice. Intuitively, it is understood that a high superiority of the master means a well-established quasispecies in that environment. A second choice is increasing the mutation rate above the maximum tolerable value μ _max.

John J. Holland and his colleagues were the first to test experimentally the error threshold concept with viruses.Reference Holland, Domingo, de la Torre and Steinhauer^10, Reference Lee, Gilbertson, Novella, Huerta, Domingo and Holland¹¹ They showed that, in agreement with theoretical predictions, an increase of mutation rate during virus replication decreased virus progeny production. These early studies were followed by many additional studies that established enhanced mutagenesis as a strategy to combat viral diseases. Lawrence A. Loeb and colleagues coined the term ‘lethal mutagenesis’ to refer to this new antiviral strategy.Reference Loeb, Essigmann, Kazazi, Zhang, Rose and Mullins¹² Progress in lethal mutagenesis over the last two decades has been remarkable, and the results (demonstration of virus extinction as a consequence of increased mutation rates, discovery of new virus-specific mutagenic agents, feasibility of this antiviral approach in vivo, etc.) have been recently reviewed.Reference Domingo^13, Reference Perales and Domingo¹⁴

The main lethal mutagenesis design to inhibit and extinguish viruses consists of administering base or nucleoside analogues that are converted through cellular enzymes into the corresponding nucleoside-triphosphates that are incorporated by the viral polymerase into progeny RNA. The critical molecular event is that the analogue acts as a mutagenic agent specifically for the virus because it is not incorporated by cellular DNA or RNA polymerases. The search for a new base or nucleoside analogues followed from the important discovery that the purine analogue ribavirin (1-β-D-ribofuranosyl-1-H-1,2,4-triazole-3-carboxamide) is mutagenic for the poliovirus.Reference Crotty, Maag, Arnold, Zhong, Lau, Hong, Andino and Cameron^15, Reference Crotty, Cameron and Andino¹⁶ Ribavirin has been used as an antiviral agent since the 1970s and it has become apparent that it is mutagenic for several RNA viruses. It is possible that, inadvertently, ribavirin has been curing infected patients with the participation of lethal mutagenesis. The search for new antiviral mutagens is an active field of research that has already had a first phase II clinical trial with HIV-1-infected patients.Reference Mullins, Heath, Hughes, Kicha, Styrchak, Wong, Rao, Hansen, Harris, Laurent, Li, Simpson, Essigmann, Loeb and Parkins¹⁷ The molecular basis of the mutagenic activity is that the nucleotide analogues establish ambiguous base pairs with the standard nucleotides through Watson-Crick or wobble base pairs, resulting in nucleotide misincorporations during viral RNA synthesis (reviewed in Ref. Reference Domingo13).

Increasing the mutation rate has two related consequences for a viral quasispecies: to create an unfavourable mutant environment and to diminish the superiority of the master or dominant sequences. The transition towards extinction has several steps: the generation of defector mutants that can deteriorate viral replication because they interfere with replication of the standard virus,Reference Grande-Pérez, Lázaro, Lowenstein, Domingo and Manrubia¹⁸ a decrease of fitness of the viable genomes that remain in the mutagenic environment,Reference Arias, Isabel de Avila, Sanz-Ramos, Agudo, Escarmis and Domingo¹⁹ and a final step of overt lethality with the complete collapse of the virus as a carrier of infectivity (reviews in Refs 14 and 20).

Antiviral Alternatives to Confront the Quasispecies Challenge

Lethal mutagenesis is actively investigated as a means to overcome the adaptive capacity of viral quasispecies, which means achieving reductions of viral load or viral extinction without selection of treatment-escape viral mutants, a common problem in antiviral therapy. Other antiviral strategies with the same aim are: (i) combination treatments with three or more inhibitors directed to different viral targets; this strategy has been the big success for the control of human immunodeficiency virus type 1 (HIV-1) infections, that has drastically reduced AIDS-related mortality. Despite not being an accepted procedure in classic pharmacology, the combined administration of drugs was suggested almost three decades ago as a means to control viruses that display quasispecies dynamics.Reference Domingo^21, Reference Domingo and Holland²² Antiviral combination therapies are now common, and they represent an increasing trend in general pharmacology; (ii) division of a treatment in two phases: an induction step with an antiviral inhibitor, and a maintenance step with a different inhibitor; (iii) use of drugs that target cellular functions that are required for the virus to complete its replication cycle; (iv) drugs that stimulate the innate immune response, such as some inhibitors of pyrimidine biosynthesis; (v) combined use of immunotherapy (either passive immunotherapy based on administration of antibodies or vaccination), and chemotherapy (drugs with any mechanism of activity). Each of these strategies is based on experimental observations and theoretical considerations that have been amply reviewed (as recent summaries, see Refs 13 and 20). They can be considered as a first line of response to increasing the number of voices that think new paradigms are needed to confront infectious disease in our globalized world.Reference Domingo¹³

Combination versus Sequential Treatments based on Lethal Mutagenesis

When sufficient antiviral agents are available for a viral pathogen, combination treatments are the choice to increase the genetic barrier to antiviral resistance (given by the number and types of mutations required for the virus to attain resistanceReference Domingo¹³). Initial studies showed that a combination of a mutagenic agent and a non-mutagenic antiviral inhibitor was more effective than the mutagenic agent alone to inhibit replication of high fitness viruses.Reference Pariente, Sierra, Lowenstein and Domingo^23, Reference Tapia, Fernandez, Parera, Gomez-Mariano, Clotet, Quinones-Mateu, Domingo and Martinez²⁴ Additional studies, however, showed that the expectation of the advantage of combination treatments did not necessarily apply when one of the drugs was a mutagenic agent. Two lines of evidence, one experimental, the other theoretical, showed that a sequential inhibitor-mutagen administration could have an advantage over the corresponding combination in reducing viral loads and achieving virus extinction. The key experiments were performed by C. Perales and colleagues using foot-and-mouth disease virus (FMDV) as the model system. The critical experiment was a comparison of the effects on viral production and extinction of four protocols consisting of passaging the virus in the presence of one of the following drug regimens: (i) in the presence of the non-mutagenic inhibitor guanidine alone (guanidine is an inhibitor of FMDV replication that interacts with non-structural protein 2C of the virus); (ii) in the presence of the mutagenic nucleoside ribavirin alone; (iii) in the presence of a mixture of guanidine and ribavirin; (iv) a first passage in the presence of guanidine alone, followed by passages in the presence of ribavirin alone. Determination of the yield of virus infectivity and viral RNA as a function of passage number, and application of a highly sensitive procedure to amplify small amounts of viral RNA, indicated that protocol (iv) was significantly more effective than the others to achieve virus extinction.Reference Perales, Agudo, Tejero, Manrubia and Domingo²⁵ The advantage of the sequential inhibitor-mutagen administration was more accentuated at high concentrations of the inhibitor. The same conclusions were reached with the arenavirus lymphocytic choriomeningitis virus (LCMV),Reference Moreno, Grande-Pérez, Domingo and Martín²⁶ and we are currently examining the relative effectiveness of sequential versus combination protocols for inhibition of hepatitis C virus (HCV).

A theoretical model developed by S. Manrubia and J. Iranzo also supports a potential advantage of sequential inhibitor-mutagen administration versus the corresponding combination, or the converse mutagen-inhibitor administration. The basic features of the model are presented in Ref. 25, and takes into consideration the following main parameters: the number of wild-type and defective viruses that are resistant or sensitive to the inhibitor, the viral mutation rate, the rate of generation of inhibitor-resistant individuals, the number of wild-type and defective progeny, the number of infected cells, and the number of replication cycles per cell. The model is explained in more detail in Ref. 25, and it successfully predicted the following experimental observations during serial viral infections in the presence of inhibitors and/or mutagens: (i) virus extinction by continued presence of a mutagenic activity but virus recovery upon removal of the mutagen prior to extinction; (ii) the kinetics of selection of inhibitor-escape mutants in the presence of increasing concentrations of inhibitor; and (iii) the advantage of the sequential administration of an inhibitor followed by a mutagen as compared with the corresponding combination, as observed experimentally.Reference Perales, Agudo, Tejero, Manrubia and Domingo²⁵

Despite the need of studies with animal models, and the recognized reticence of expert panels to modify treatment protocols,Reference Domingo¹³ there are additional arguments in favour of an advantage of inhibitor-mutagen sequential administration over the combination of the two components. In the investigations of lethal defection (virus extinction driven by defective genomes produced by mutagenesis) it was documented that for a defective viral genome to be able to contribute to viral extinction, its RNA had to be competent in replication.Reference Perales, Mateo, Mateu and Domingo²⁷ The simultaneous presence of a mutagen and an inhibitor in a combination protocol may have as an undesirable consequence that the presence of the inhibitor will impede the replication of the defectors that should be important actors of viral extinction. Furthermore, side effects for the patient should diminish if the number of drugs given simultaneously to the patient is lower.

The interplay between mutagens and inhibitors must be taken into consideration in antiviral protocols for the following interconnected reasons that recapitulate the points discussed in previous paragraphs: (i) the presence of an inhibitor during viral replication can prevent the replication of the defector genomes produced by the mutagenic agent, thereby delaying or hindering extinction; (ii) the presence of a mutagen can increase the frequency of inhibitor-escape mutants if both are present in the same replicative ensemble; (iii) the mutant spectrum of a viral quasispecies can have suppressive activities reflected in slowing the replication of high fitness viral genomes or genomes that are resistant to mutagens and inhibitors. The reader is referred to two recent publications for further information on underlying molecular mechanism, Refs 13 and 20.

In summary, the challenge that represents the adaptability of viral quasispecies has promising responses derived from an understanding of quasispecies dynamics that has unveiled new levels of vulnerability of viruses.Reference Domingo¹³

Summary and Concluding Remarks

One of the major conceptual departures in the understanding of RNA viruses (and DNA viruses subjected to error-prone replication) as populations was the discovery that viruses consist of collections of mutants, and that the mutant composition changes continuously as a function of time. The traditional wild-type concept used for viruses and microbes in general, which implied a defined genomic sequence, has changed its focus from being a prototypic individual to a collection of related individuals. A viral genome replicated by a low fidelity polymerase, as RNA viruses and many DNA viruses do, can only be represented by a weighted average of many different sequences, most of them present at low frequency. The nature of viral populations as mutant clouds was established by traditional methods of indirect sequence screenings (oligonucleotide fingerprinting in the pre-sequencing era), later by comparisons of nucleotide sequences of molecular and biological clones from the same viral population, and more recently confirmed by application of next generation deep sequencing methodologies.

Error-prone replication due to the biochemical properties of the viral polymerases (inherent limited fidelity of template copying and absence of proofreading-repair activities) is the reason for viral populations to produce mutant genomes in an incessant manner. Replication cannot be dissociated from mutagenesis. Most interesting and significant in support of interdisciplinary science, quasispecies theory (that originated in the field of theoretical biophysics and which is the theory that until now best provides a theoretical framework for virus evolution), suggests new means to control virus infections. Indeed, new levels of vulnerability have been discovered as a result of applications of concepts intrinsic to quasispecies theory. Such vulnerability has two main lines of action: (i) the application of classic antiviral drugs keeping in mind the Darwinian principles that fuel virus adaptability (what we may call the conservative antiviral approach), and (ii) the introduction of mutagenic agents to increase the virus mutation rate above a level that marks a limit of stability of viral functions (what we may call the rupture antiviral approach or, in more scientific terms, the error threshold-inspired approach).

This article has been devoted to explaining the rupture approach that constitutes an antiviral strategy that virologists know as lethal mutagenesis. It aims as causing lethality through an increase of mutational load in the viral genome through mutagenic agents, generally base or nucleoside analogues that are converted into mutagenic nucleotide polymerase substrates inside the cells. As discussed in previous sections, the introduction of mutagens as therapeutic agents has also opened the possibility that sequential inhibitor-mutagen treatments may have an advantage over the traditional combination treatments. If the advantage is confirmed, such sequential treatments may produce more tolerable side-effects in the patients because a lower number of drugs are administered at the same time. This is an active field of research, and soon there should be sufficient information to evaluate the possibilities of sequential treatments.

In these closing statements, it is legitimate and interesting to ask if lethal mutagenesis can ever become a viable antiviral strategy. This question has many facets. An obvious one is if any panel that decides on treatment protocols will ever accept that mutagenic agents be licensed for administration to humans. Even if a critical and accepted point is that the mutagenic agents to be used as lethal mutagens for viruses must not display any mutagenic activity for cells, it is questionable if the available evidence of mutagenesis specificity will ever be considered sufficient. Despite this big uncertainty, there are many arguments to fight for such a licensing to be accepted and mutagen use implemented. One is that ribavirin, which is a well-characterized antiviral agent and was licensed for human use four decades ago, is an effective antiviral mutagen that was being administered to thousands of humans while this manuscript was being written. In fact, as described in previous sections, new mutagens are under investigation, and there have already been clinical trials involving mutagenic agents to try to control viral disease. One would not take an antiviral mutagen to treat a common cold but one would certainly consider such treatment if one suffers from AIDS or advanced cirrhosis and the viruses involved have evolved to be resistant to the available antiviral agents. Reluctance towards lethal mutagenesis will be largely overcome if new non-toxic, effective virus-specific mutagens are identified or discovered, and a proof that licensed antiviral agents such as ribavirin indeed include mutagenesis as one of their mechanisms of action.

There are additional arguments in favour of a future application of lethal mutagenesis to clinical practice. An interesting one is that nature has already invented lethal mutagenesis as a defence mechanism. There are a number of cellular activities in many different organisms that play a role in cellular physiology, but that are converted into mutagenic agents to attack invading parasites, viruses or other. Such activities have various names with acronyms such as APOBEC, ADAR, RIP, etc, and the reader can find a summary of their origin and mechanisms of activity in previous reviews we have written about lethal mutagenesis and that are quoted in the previous sections of this text. Some scientists consider that if a mechanism operates in nature, it has a greater chance of success when used as a human intervention. We do not have strong arguments to endorse such a statement but it is somehow reassuring and instructive that epochs ago nature invented something that scientists have reinvented and keep wondering hesitantly about its efficacy.

What most scientists should agree on is that new possibilities for the prevention and treatment of viral disease are on the horizon, and that they do not necessarily fit what was predicted or anticipated just a few years ago.