Does Mutational Robustness Inhibit Extinction by Lethal Mutagenesis in Viral Populations?

Lethal mutagenesis is a promising new antiviral therapy that kills a virus by raising its mutation rate. One potential shortcoming of lethal mutagenesis is that viruses may resist the treatment by evolving genomes with increased robustness to mutations. Here, we investigate to what extent mutational robustness can inhibit extinction by lethal mutagenesis in viruses, using both simple toy models and more biophysically realistic models based on RNA secondary-structure folding. We show that although the evolution of greater robustness may be promoted by increasing the mutation rate of a viral population, such evolution is unlikely to greatly increase the mutation rate required for certain extinction. Using an analytic multi-type branching process model, we investigate whether the evolution of robustness can be relevant on the time scales on which extinction takes place. We find that the evolution of robustness matters only when initial viral population sizes are small and deleterious mutation rates are only slightly above the level at which extinction can occur. The stochastic calculations are in good agreement with simulations of self-replicating RNA sequences that have to fold into a specific secondary structure to reproduce. We conclude that the evolution of mutational robustness is in most cases unlikely to prevent the extinction of viruses by lethal mutagenesis

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

Critical mutation rate has an exponential dependence on population size for eukaryotic-length genomes with crossover

The critical mutation rate (CMR) determines the shift between survival-of-the-fittest and survival of individuals with greater mutational robustness (“flattest”). We identify an inverse relationship between CMR and sequence length in an in silico system with a two-peak fitness landscape; CMR decreases to no more than five orders of magnitude above estimates of eukaryotic per base mutation rate. We confirm the CMR reduces exponentially at low population sizes, irrespective of peak radius and distance, and increases with the number of genetic crossovers. We also identify an inverse relationship between CMR and the number of genes, confirming that, for a similar number of genes to that for the plant Arabidopsis thaliana (25,000), the CMR is close to its known wild-type mutation rate; mutation rates for additional organisms were also found to be within one order of magnitude of the CMR. This is the first time such a simulation model has been assigned input and produced output within range for a given biological organism. The decrease in CMR with population size previously observed is maintained; there is potential for the model to influence understanding of populations undergoing bottleneck, stress, and conservation strategy for populations near extinction

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

The effects of low-impact mutations in digital organisms

<p>Abstract</p> <p>Background</p> <p>Avida is a computer program that performs evolution experiments with digital organisms. Previous work has used the program to study the evolutionary origin of complex features, namely logic operations, but has consistently used extremely large mutational fitness effects. The present study uses Avida to better understand the role of low-impact mutations in evolution.</p> <p>Results</p> <p>When mutational fitness effects were approximately 0.075 or less, no new logic operations evolved, and those that had previously evolved were lost. When fitness effects were approximately 0.2, only half of the operations evolved, reflecting a threshold for selection breakdown. In contrast, when Avida's default fitness effects were used, all operations routinely evolved to high frequencies and fitness increased by an average of 20 million in only 10,000 generations.</p> <p>Conclusions</p> <p>Avidian organisms evolve new logic operations only when mutations producing them are assigned high-impact fitness effects. Furthermore, purifying selection cannot protect operations with low-impact benefits from mutational deterioration. These results suggest that selection breaks down for low-impact mutations below a certain fitness effect, the <it>selection threshold</it>. Experiments using biologically relevant parameter settings show the tendency for increasing genetic load to lead to loss of biological functionality. An understanding of such genetic deterioration is relevant to human disease, and may be applicable to the control of pathogens by use of lethal mutagenesis.</p

The relationship between the error catastrophe, survival of the flattest, and natural selection

<p>Abstract</p> <p>Background</p> <p>The quasispecies model is a general model of evolution that is generally applicable to replication up to high mutation rates. It predicts that at a sufficiently high mutation rate, quasispecies with higher mutational robustness can displace quasispecies with higher replicative capacity, a phenomenon called "survival of the flattest". In some fitness landscapes it also predicts the existence of a maximum mutation rate, called the error threshold, beyond which the quasispecies enters into error catastrophe, losing its genetic information. The aim of this paper is to study the relationship between survival of the flattest and the transition to error catastrophe, as well as the connection between these concepts and natural selection.</p> <p>Results</p> <p>By means of a very simplified model, we show that the transition to an error catastrophe corresponds to a value of zero for the selective coefficient of the mutant phenotype with respect to the master phenotype, indicating that transition to the error catastrophe is in this case similar to the selection of a more robust species. This correspondence has been confirmed by considering a single-peak landscape in which sequences are grouped with respect to their Hamming distant from the master sequence. When the robustness of a classe is changed by modification of its quality factor, the distribution of the population changes in accordance with the new value of the robustness, although an error catastrophe can be detected at the same values as in the general case. When two quasispecies of different robustness competes with one another, the entry of one of them into error catastrophe causes displacement of the other, because of the greater robustness of the former. Previous works are explicitly reinterpreted in the light of the results obtained in this paper.</p> <p>Conclusions</p> <p>The main conclusion of this paper is that the entry into error catastrophe is a specific case of survival of the flattest acting on phenotypes that differ in the trade-off between replicative ability and mutational robustness. In fact, entry into error catastrophe occurs when the mutant phenotype acquires a selective advantage over the master phenotype. As both entry into error catastrophe and survival of the flattest are caused by natural selection when mutation rate is increased, we propose differentiating between them by the level of selection at which natural selection acts. So we propose to consider the transition to error catastrophe as a phenomenon of intra-quasispecies selection, and survival of the flattest as a phenomenon of inter-quasispecies selection.</p

Natural Selection Fails to Optimize Mutation Rates for Long-Term Adaptation on Rugged Fitness Landscapes

The rate of mutation is central to evolution. Mutations are required for adaptation, yet most mutations with phenotypic effects are deleterious. As a consequence, the mutation rate that maximizes adaptation will be some intermediate value. Here, we used digital organisms to investigate the ability of natural selection to adjust and optimize mutation rates. We assessed the optimal mutation rate by empirically determining what mutation rate produced the highest rate of adaptation. Then, we allowed mutation rates to evolve, and we evaluated the proximity to the optimum. Although we chose conditions favorable for mutation rate optimization, the evolved rates were invariably far below the optimum across a wide range of experimental parameter settings. We hypothesized that the reason that mutation rates evolved to be suboptimal was the ruggedness of fitness landscapes. To test this hypothesis, we created a simplified landscape without any fitness valleys and found that, in such conditions, populations evolved near-optimal mutation rates. In contrast, when fitness valleys were added to this simple landscape, the ability of evolving populations to find the optimal mutation rate was lost. We conclude that rugged fitness landscapes can prevent the evolution of mutation rates that are optimal for long-term adaptation. This finding has important implications for applied evolutionary research in both biological and computational realms

Quasispecies Theory and the Behavior of RNA Viruses

A large number of medically important viruses, including HIV, hepatitis C virus, and influenza, have RNA genomes. These viruses replicate with extremely high mutation rates and exhibit significant genetic diversity. This diversity allows a viral population to rapidly adapt to dynamic environments and evolve resistance to vaccines and antiviral drugs. For the last 30 years, quasispecies theory has provided a population-based framework for understanding RNA viral evolution. A quasispecies is a cloud of diverse variants that are genetically linked through mutation, interact cooperatively on a functional level, and collectively contribute to the characteristics of the population. Many predictions of quasispecies theory run counter to traditional views of microbial behavior and evolution and have profound implications for our understanding of viral disease. Here, we discuss basic principles of quasispecies theory and describe its relevance for our understanding of viral fitness, virulence, and antiviral therapeutic strategy

A Developmental Systems Perspective on Epistasis: Computational Exploration of Mutational Interactions in Model Developmental Regulatory Networks

The way in which the information contained in genotypes is translated into complex phenotypic traits (i.e. embryonic expression patterns) depends on its decoding by a multilayered hierarchy of biomolecular systems (regulatory networks). Each layer of this hierarchy displays its own regulatory schemes (i.e. operational rules such as +/− feedback) and associated control parameters, resulting in characteristic variational constraints. This process can be conceptualized as a mapping issue, and in the context of highly-dimensional genotype-phenotype mappings (GPMs) epistatic events have been shown to be ubiquitous, manifested in non-linear correspondences between changes in the genotype and their phenotypic effects. In this study I concentrate on epistatic phenomena pervading levels of biological organization above the genetic material, more specifically the realm of molecular networks. At this level, systems approaches to studying GPMs are specially suitable to shed light on the mechanistic basis of epistatic phenomena. To this aim, I constructed and analyzed ensembles of highly-modular (fully interconnected) networks with distinctive topologies, each displaying dynamic behaviors that were categorized as either arbitrary or functional according to early patterning processes in the Drosophila embryo. Spatio-temporal expression trajectories in virtual syncytial embryos were simulated via reaction-diffusion models. My in silico mutational experiments show that: 1) the average fitness decay tendency to successively accumulated mutations in ensembles of functional networks indicates the prevalence of positive epistasis, whereas in ensembles of arbitrary networks negative epistasis is the dominant tendency; and 2) the evaluation of epistatic coefficients of diverse interaction orders indicates that, both positive and negative epistasis are more prevalent in functional networks than in arbitrary ones. Overall, I conclude that the phenotypic and fitness effects of multiple perturbations are strongly conditioned by both the regulatory architecture (i.e. pattern of coupled feedback structures) and the dynamic nature of the spatio-temporal expression trajectories displayed by the simulated networks

Terrain, politics, history

This article is based on the 2019 Dialogues in Human Geography plenary lecture at the Royal Geographical Society. It has four parts. The first discusses my work on territory in relation to recent work by geographers and others on the vertical, the volumetric, the voluminous, and the milieu as ways of thinking space in three-dimensions, of a fluid and dynamic earth. Second, it proposes using the concept of terrain to analyse the political materiality of territory. Third, it adds some cautions to this, through thinking about the history of the concept of terrain in geographical thought, which has tended to associate it with either physical or military geography. Finally, it suggests that this work is a way geographers might begin to respond to the challenge recently made by Bruno Latour, where he suggests that ‘belonging to a territory is the phenomenon most in need of rethinking and careful redescription; learning new ways to inhabit the Earth is our biggest challenge’. Responding to Latour continues this thinking about the relations between territory, Earth, land, and ground, and their limits