Exploring the complexity of the HIV-1 fitness landscape

Diverse mutant selection windows shape spatial heterogeneity in evolving populations

Mutant selection windows (MSWs), the range of drug concentrations that select for drug-resistant mutants, have long been used as a model for predicting drug resistance and designing optimal dosing strategies in infectious disease. The canonical MSW model offers comparisons between two subtypes at a time: drug-sensitive and drug-resistant. In contrast, the fitness landscape model with N alleles, which maps genotype to fitness, allows comparisons between N genotypes simultaneously, but does not encode continuous drug response data. In clinical settings, there may be a wide range of drug concentrations selecting for a variety of genotypes in both cancer and infectious diseases. Therefore, there is a need for a more robust model of the pathogen response to therapy to predict resistance and design new therapeutic approaches. Fitness seascapes, which model genotype-by-environment interactions, permit multiple MSW comparisons simultaneously by encoding genotype-specific dose-response data. By comparing dose-response curves, one can visualize the range of drug concentrations where one genotype is selected over another. In this work, we show how N-allele fitness seascapes allow for N * 2N-1 unique MSW comparisons. In spatial drug diffusion models, we demonstrate how fitness seascapes reveal spatially heterogeneous MSWs, extending the MSW model to more fully reflect the selection of drug resistant genotypes. Furthermore, using synthetic data and empirical dose-response data in cancer, we find that the spatial structure of MSWs shapes the evolution of drug resistance in an agent-based model. By simulating a tumor treated with cyclic drug therapy, we find that mutant selection windows introduced by drug diffusion promote the proliferation of drug resistant cells. Our work highlights the importance and utility of considering dose-dependent fitness seascapes in evolutionary medicine.

Diverse mutant selection windows shape spatial heterogeneity in evolving populations

Mutant selection windows (MSWs), the range of drug concentrations that select for drug-resistant mutants, have long been used as a model for predicting drug resistance and designing optimal dosing strategies in infectious disease. The canonical MSW model offers comparisons between two subtypes at a time: drug-sensitive and drug-resistant. In contrast, the fitness landscape model with N alleles, which maps genotype to fitness, allows comparisons between N genotypes simultaneously, but does not encode continuous drug response data. In clinical settings, there may be a wide range of drug concentrations selecting for a variety of genotypes. Therefore, there is a need for a more robust model of the pathogen response to therapy to predict resistance and design new therapeutic approaches. Fitness seascapes, which model genotype-by-environment interactions, permit multiple MSW comparisons simultaneously by encoding genotype-specific dose-response data. By comparing dose-response curves, one can visualize the range of drug concentrations where one genotype is selected over another. In this work, we show how N-allele fitness seascapes allow for N*2N-1 unique MSW comparisons. In spatial drug diffusion models, we demonstrate how fitness seascapes reveal spatially heterogeneous MSWs, extending the MSW model to more accurately reflect the selection fo drug resistant genotypes. Furthermore, we find that the spatial structure of MSWs shapes the evolution of drug resistance in an agent-based model. Our work highlights the importance and utility of considering dose-dependent fitness seascapes in evolutionary medicine.

Viral Fitness, Population Complexity, Host Interactions, and Resistance to Antiviral Agents

Fitness of viruses has become a standard parameter to quantify their adaptation to a biological environment. Fitness determinations for RNA viruses (and some highly variable DNA viruses) meet with several uncertainties. Of particular interest are those that arise from mutant spectrum complexity, absence of population equilibrium, and internal interactions among components of a mutant spectrum. Here, concepts, fitness measurements, limitations, and current views on experimental viral fitness landscapes are discussed. The effect of viral fitness on resistance to antiviral agents is covered in some detail since it constitutes a widespread problem in antiviral pharmacology, and a challenge for the design of effective antiviral treatments. Recent evidence with hepatitis C virus suggests the operation of mechanisms of antiviral resistance additional to the standard selection of drug-escape mutants. The possibility that high replicative fitness may be the driver of such alternative mechanisms is considered. New broad-spectrum antiviral designs that target viral fitness may curtail the impact of drug-escape mutants in treatment failures. We consider to what extent fitness-related concepts apply to coronaviruses and how they may affect strategies for COVID-19 prevention and treatment.

Virus Evolution on Fitness Landscapes

The landscape paradigm is revisited in the light of evolution in simple systems. A brief overview of different classes of fitness landscapes is followed by a more detailed discussion of the RNA model, which is currently the only evolutionary model that allows for a comprehensive molecular analysis of a fitness landscape. Neutral networks of genotypes are indispensable for the success of evolution. Important insights into the evolutionary mechanism are gained by considering the topology of sequence and shape spaces. The dynamic concept of molecular quasispecies is viewed in the light of the landscape paradigm. The distribution of fitness values in state space is mirrored by the population structures of mutant distributions. Two classes of thresholds for replication error or mutations are important: (i) the-conventional-genotypic error threshold, which separates ordered replication from random drift on neutral networks, and (ii) a phenotypic error threshold above which the molecular phenotype is lost. Empirical landscapes are reviewed and finally, the implications of the landscape concept for virus evolution are discussed.

Commonly Elicited Antibodies against the Base of the HIV-1 Env Trimer Guide the Population-Level Evolution of a Structure-Regulating Region in gp41

The antibody response against the HIV-1 envelope glycoproteins (Envs) guides evolution of this protein within each host. Whether antibodies with similar target specificities are elicited in different individuals and affect the population-level evolution of Env is poorly understood. To address this question, we analyzed properties of emerging variants in the gp41 fusion peptide-proximal region (FPPR) that exhibit distinct evolutionary patterns in HIV-1 clade B. For positions 534, 536, and 539 in the FPPR, alanine was the major emerging variant. However, 534A and 536A show a constant frequency in the population between 1979 and 2016, whereas 539A is gradually increasing. To understand the basis for these differences, we introduced alanine substitutions in the FPPR of primary HIV-1 strains and examined their functional and antigenic properties. Evolutionary patterns could not be explained by fusion competence or structural stability of the emerging variants. Instead, 534A and 536A exhibited modest but significant increases in sensitivity to antibodies against the membrane-proximal external region (MPER) and gp120-gp41 interface. These Envs were also more sensitive to poorly neutralizing sera from HIV-1-infected individuals than the clade ancestral form or 539A variant. Competition binding assays confirmed for all sera tested the presence of antibodies against the base of the Env trimer that compete with monoclonal antibodies targeting the MPER and gp120-gp41 interface. Our findings suggest that weakly neutralizing antibodies against the trimer base are commonly elicited; they do not exert catastrophic population size reduction effects on emerging variants but, instead, determine their set point frequencies in the population and historical patterns of change. IMPORTANCE Infection by HIV-1 elicits formation of antibodies that target the viral Env proteins and can inactivate the virus. The specific targets of these antibodies vary among infected individuals. It is unclear whether some target specificities are shared among the antibody responses of different individuals. We observed that antibodies against the base of the Env protein are commonly elicited during infection. The selective pressure applied by such antibodies is weak. As a result, they do not completely eliminate the sensitive forms of the virus from the population, but maintain their frequency at a low level that has not increased since the beginning of the AIDS pandemic. Interestingly, the changes in Env do not occur at the sites targeted by the antibodies, but at a distinct region of Env, the fusion peptide-proximal region, which regulates their exposure.

A Family of Fitness Landscapes Modeled through Gene Regulatory Networks

Fitness landscapes are a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other through mutation and related through fitness. Empirical studies of fitness landscapes have increasingly revealed conserved topographical features across diverse taxa, e.g., the accessibility of genotypes and "ruggedness". As a result, theoretical studies are needed to investigate how evolution proceeds on fitness landscapes with such conserved features. Here, we develop and study a model of evolution on fitness landscapes using the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as phenotypes. With the assumption that regulation is a binary process, we prove the existence of empirically observed, topographical features such as accessibility and connectivity. We further show that these results hold across arbitrary fitness functions and that a trade-off between accessibility and ruggedness need not exist. Then, using graph theory and a coarse-graining approach, we deduce a mesoscopic structure underlying GRN fitness landscapes where the information necessary to predict a population's evolutionary trajectory is retained with minimal complexity. Using this coarse-graining, we develop a bottom-up algorithm to construct such mesoscopic backbones, which does not require computing the genotype network and is therefore far more efficient than brute-force approaches. Altogether, this work provides mathematical results of high-dimensional fitness landscapes and a path toward connecting theory to empirical studies.

Evolutionary modeling reveals enhanced mutational flexibility of HCV subtype 1b compared with 1a

Hepatitis C virus (HCV) is a leading cause of liver-associated disease and liver cancer. Of the major HCV subtypes, patients infected with subtype 1b have been associated with having a higher risk of developing chronic infection and hepatocellular carcinoma. However, underlying reasons for this increased disease severity remain unknown. Here, we provide an evolutionary rationale, based on a comparative study of fitness landscape and in-host evolutionary models of the E2 glycoprotein of HCV subtypes 1a and 1b. Our analysis demonstrates that a higher chronicity rate of 1b may be attributed to lower fitness constraints, enabling 1b viruses to more easily escape antibody responses. More generally, our results suggest that differences in evolutionary constraints between HCV subtypes may be an important factor in mediating distinct disease outcomes. Our analysis also identifies antibodies that appear escape-resistant against both subtypes 1a and 1b, providing directions for designing HCV vaccines having cross-subtype protection.

A Two-Level, Intramutant Spectrum Haplotype Profile of Hepatitis C Virus Revealed by Self-Organized Maps

RNA viruses replicate as complex mutant spectra termed viral quasispecies. The frequency of each individual genome in a mutant spectrum depends on its rate of generation and its relative fitness in the replicating population ensemble. The advent of deep sequencing methodologies allows for the first-time quantification of haplotype abundances within mutant spectra. There is no information on the haplotype profile of the resident genomes and how the landscape evolves when a virus replicates in a controlled cell culture environment. Here, we report the construction of intramutant spectrum haplotype landscapes of three amplicons of the NS5A-NS5B coding region of hepatitis C virus (HCV). Two-dimensional (2D) neural networks were constructed for 44 related HCV populations derived from a common clonal ancestor that was passaged up to 210 times in human hepatoma Huh-7.5 cells in the absence of external selective pressures. The haplotype profiles consisted of an extended dense basal platform, from which a lower number of protruding higher peaks emerged. As HCV increased its adaptation to the cells, the number of haplotype peaks within each mutant spectrum expanded, and their distribution shifted in the 2D network. The results show that extensive HCV replication in a monotonous cell culture environment does not limit HCV exploration of sequence space through haplotype peak movements. The landscapes reflect dynamic variation in the intramutant spectrum haplotype profile and may serve as a reference to interpret the modifications produced by external selective pressures or to compare with the landscapes of mutant spectra in complex in vivo environments. IMPORTANCE The study provides for the first time the haplotype profile and its variation in the course of virus adaptation to a cell culture environment in the absence of external selective constraints. The deep sequencing-based self-organized maps document a two-layer haplotype distribution with an ample basal platform and a lower number of protruding peaks. The results suggest an inferred intramutant spectrum fitness landscape structure that offers potential benefits for virus resilience to mutational inputs.

Viral surface geometry shapes influenza and coronavirus spike evolution through antibody pressure

The evolution of circulating viruses is shaped by their need to evade antibody response, which mainly targets the viral spike. Because of the high density of spikes on the viral surface, not all antigenic sites are targeted equally by antibodies. We offer here a geometry-based approach to predict and rank the probability of surface residues of SARS spike (S protein) and influenza H1N1 spike (hemagglutinin) to acquire antibody-escaping mutations utilizing in-silico models of viral structure. We used coarse-grained MD simulations to estimate the on-rate (targeting) of an antibody model to surface residues of the spike protein. Analyzing publicly available sequences, we found that spike surface sequence diversity of the pre-pandemic seasonal influenza H1N1 and the sarbecovirus subgenus highly correlates with our model prediction of antibody targeting. In particular, we identified an antibody-targeting gradient, which matches a mutability gradient along the main axis of the spike. This identifies the role of viral surface geometry in shaping the evolution of circulating viruses. For the 2009 H1N1 and SARS-CoV-2 pandemics, a mutability gradient along the main axis of the spike was not observed. Our model further allowed us to identify key residues of the SARS-CoV-2 spike at which antibody escape mutations have now occurred. Therefore, it can inform of the likely functional role of observed mutations and predict at which residues antibody-escaping mutation might arise.

MrHAMER yields highly accurate single molecule viral sequences enabling analysis of intra-host evolution

Technical challenges remain in the sequencing of RNA viruses due to their high intra-host diversity. This bottleneck is particularly pronounced when interrogating long-range co-evolved genetic interactions given the read-length limitations of next-generation sequencing platforms. This has hampered the direct observation of these genetic interactions that code for protein-protein interfaces with relevance in both drug and vaccine development. Here we overcome these technical limitations by developing a nanopore-based long-range viral sequencing pipeline that yields accurate single molecule sequences of circulating virions from clinical samples. We demonstrate its utility in observing the evolution of individual HIV Gag-Pol genomes in response to antiviral pressure. Our pipeline, called Multi-read Hairpin Mediated Error-correction Reaction (MrHAMER), yields >1000s of viral genomes per sample at 99.9% accuracy, maintains the original proportion of sequenced virions present in a complex mixture, and allows the detection of rare viral genomes with their associated mutations present at <1% frequency. This method facilitates scalable investigation of genetic correlates of resistance to both antiviral therapy and immune pressure and enables the identification of novel host-viral and viral-viral interfaces that can be modulated for therapeutic benefit.

Predicting in vivo escape dynamics of HIV-1 from a broadly neutralizing antibody

Broadly neutralizing antibodies are promising candidates for treatment and prevention of HIV-1 infections. Such antibodies can temporarily suppress viral load in infected individuals; however, the virus often rebounds by escape mutants that have evolved resistance. In this paper, we map a fitness model of HIV-1 interacting with broadly neutralizing antibodies using in vivo data from a recent clinical trial. We identify two fitness factors, antibody dosage and viral load, that determine viral reproduction rates reproducibly across different hosts. The model successfully predicts the escape dynamics of HIV-1 in the course of an antibody treatment, including a characteristic frequency turnover between sensitive and resistant strains. This turnover is governed by a dosage-dependent fitness ranking, resulting from an evolutionary trade-off between antibody resistance and its collateral cost in drug-free growth. Our analysis suggests resistance-cost trade-off curves as a measure of antibody performance in the presence of resistance evolution.

From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics-cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.

Viral surface geometry shapes influenza and coronavirus spike evolution through antibody pressure

The evolution of circulating viruses is shaped by their need to evade antibody response, which mainly targets the glycoprotein (spike). However, not all antigenic sites are targeted equally by antibodies, leading to complex immunodominance patterns. We used 3D computational models to estimate antibody pressure on the seasonal influenza H1N1 and SARS spikes. Analyzing publically available sequences, we show that antibody pressure, through the geometrical organization of spikes on the viral surface, shaped their mutability. Studying the mutability patterns of SARS-CoV-2 and the 2009 H1N1 pandemic spikes, we find that they are not predominantly shaped by antibody pressure. However, for SARS-CoV-2, we find that over time, it acquired mutations at antibody-accessible positions, which could indicate possible escape as define by our model. We offer a geometry-based approach to predict and rank the probability of surface resides of SARS-CoV-2 spike to acquire antibody escaping mutations.

Ecology shapes epistasis in a genotype-phenotype-fitness map for stick insect colour

Genetic interactions such as epistasis are widespread in nature and can shape evolutionary dynamics. Epistasis occurs due to nonlinearity in biological systems, which can arise via cellular processes that convert genotype to phenotype and via selective processes that connect phenotype to fitness. Few studies in nature have connected genotype to phenotype to fitness for multiple potentially interacting genetic variants. Thus, the causes of epistasis in the wild remain poorly understood. Here, we show that epistasis for fitness is an emergent and predictable property of nonlinear selective processes. We do so by measuring the genetic basis of cryptic colouration and survival in a field experiment with stick insects. We find that colouration shows a largely additive genetic basis but with some effects of epistasis that enhance differentiation between colour morphs. In terms of fitness, different combinations of loci affecting colouration confer high survival in one host-plant treatment. Specifically, nonlinear correlational selection for specific combinations of colour traits in this treatment drives the emergence of pairwise and higher-order epistasis for fitness at loci underlying colour. In turn, this results in a rugged fitness landscape for genotypes. In contrast, fitness epistasis was dampened in another treatment, where selection was weaker. Patterns of epistasis that are shaped by ecologically based selection could be common and central to understanding fitness landscapes, the dynamics of evolution and potentially other complex systems.

Deconvolving mutational patterns of poliovirus outbreaks reveals its intrinsic fitness landscape

Vaccination has essentially eradicated poliovirus. Yet, its mutation rate is higher than that of viruses like HIV, for which no effective vaccine exists. To investigate this, we infer a fitness model for the poliovirus viral protein 1 (vp1), which successfully predicts in vitro fitness measurements. This is achieved by first developing a probabilistic model for the prevalence of vp1 sequences that enables us to isolate and remove data that are subject to strong vaccine-derived biases. The intrinsic fitness constraints derived for vp1, a capsid protein subject to antibody responses, are compared with those of analogous HIV proteins. We find that vp1 evolution is subject to tighter constraints, limiting its ability to evade vaccine-induced immune responses. Our analysis also indicates that circulating poliovirus strains in unimmunized populations serve as a reservoir that can seed outbreaks in spatio-temporally localized sub-optimally immunized populations.

Poliovirus has a higher mutation rate than HIV, yet has been almost eradicated by vaccination while an effective vaccine against HIV does not exist. Here, the authors develop a fitness model for poliovirus viral protein 1 to show that it is subject to stringent evolutionary constraints that limit its ability to avoid vaccine-induced immune responses.

Model genotype-phenotype mappings and the algorithmic structure of evolution

Cancers are complex dynamic systems that undergo evolution and selection. Personalized medicine approaches in the clinic increasingly rely on predictions of tumour response to one or more therapies; these predictions are complicated by the inevitable evolution of the tumour. Despite enormous amounts of data on the mutational status of cancers and numerous therapies developed in recent decades to target these mutations, many of these treatments fail after a time due to the development of resistance in the tumour. The emergence of these resistant phenotypes is not easily predicted from genomic data, since the relationship between genotypes and phenotypes, termed the genotype-phenotype (GP) mapping, is neither injective nor functional. We present a review of models of this mapping within a generalized evolutionary framework that takes into account the relation between genotype, phenotype, environment and fitness. Different modelling approaches are described and compared, and many evolutionary results are shown to be conserved across studies despite using different underlying model systems. In addition, several areas for future work that remain understudied are identified, including plasticity and bet-hedging. The GP-mapping provides a pathway for understanding the potential routes of evolution taken by cancers, which will be necessary knowledge for improving personalized therapies.

Large-effect flowering time mutations reveal conditionally adaptive paths through fitness landscapes in Arabidopsis thaliana

Mutations are often assumed to be largely detrimental to fitness, but they may also be beneficial, and mutations with large phenotypic effects can persist in nature. One explanation for these observations is that mutations may be beneficial in specific environments because these conditions shift trait expression toward higher fitness. This hypothesis is rarely tested due to the difficulty of replicating mutants in multiple natural environments and measuring their phenotypes. We did so by planting Arabidopsis thaliana genotypes with large-effect flowering time mutations in field sites across the species’ European climate range. We quantified the adaptive value of mutant traits, finding that certain mutations increased fitness in some environments but not in others.

Contrary to previous assumptions that most mutations are deleterious, there is increasing evidence for persistence of large-effect mutations in natural populations. A possible explanation for these observations is that mutant phenotypes and fitness may depend upon the specific environmental conditions to which a mutant is exposed. Here, we tested this hypothesis by growing large-effect flowering time mutants of Arabidopsis thaliana in multiple field sites and seasons to quantify their fitness effects in realistic natural conditions. By constructing environment-specific fitness landscapes based on flowering time and branching architecture, we observed that a subset of mutations increased fitness, but only in specific environments. These mutations increased fitness via different paths: through shifting flowering time, branching, or both. Branching was under stronger selection, but flowering time was more genetically variable, pointing to the importance of indirect selection on mutations through their pleiotropic effects on multiple phenotypes. Finally, mutations in hub genes with greater connectedness in their regulatory networks had greater effects on both phenotypes and fitness. Together, these findings indicate that large-effect mutations may persist in populations because they influence traits that are adaptive only under specific environmental conditions. Understanding their evolutionary dynamics therefore requires measuring their effects in multiple natural environments.

DISSEQT-DIStribution-based modeling of SEQuence space Time dynamics

Rapidly evolving microbes are a challenge to model because of the volatile, complex, and dynamic nature of their populations. We developed the DISSEQT pipeline (DIStribution-based SEQuence space Time dynamics) for analyzing, visualizing, and predicting the evolution of heterogeneous biological populations in multidimensional genetic space, suited for population-based modeling of deep sequencing and high-throughput data. The pipeline is openly available on GitHub (https://github.com/rasmushenningsson/DISSEQT.jl, accessed 23 June 2019) and Synapse (https://www.synapse.org/#!Synapse: syn11425758, accessed 23 June 2019), covering the entire workflow from read alignment to visualization of results. Our pipeline is centered around robust dimension and model reduction algorithms for analysis of genotypic data with additional capabilities for including phenotypic features to explore dynamic genotype-phenotype maps. We illustrate its utility and capacity with examples from evolving RNA virus populations, which present one of the highest degrees of genetic heterogeneity within a given population found in nature. Using our pipeline, we empirically reconstruct the evolutionary trajectories of evolving populations in sequence space and genotype-phenotype fitness landscapes. We show that while sequence space is vastly multidimensional, the relevant genetic space of evolving microbial populations is of intrinsically low dimension. In addition, evolutionary trajectories of these populations can be faithfully monitored to identify the key minority genotypes contributing most to evolution. Finally, we show that empirical fitness landscapes, when reconstructed to include minority variants, can predict phenotype from genotype with high accuracy.

Stochastic tunneling across fitness valleys can give rise to a logarithmic long-term fitness trajectory

Adaptation, where a population evolves increasing fitness in a fixed environment, is typically thought of as a hill-climbing process on a fitness landscape. With a finite genome, such a process eventually leads the population to a fitness peak, at which point fitness can no longer increase through individual beneficial mutations. Instead, the ruggedness of typical landscapes due to epistasis between genes or DNA sites suggests that the accumulation of multiple mutations (via a process known as stochastic tunneling) can allow a population to continue increasing in fitness. However, it is not clear how such a phenomenon would affect long-term fitness evolution. By using a spin-glass type model for the fitness function that takes into account microscopic epistasis, we find that hopping between metastable states can mechanistically and robustly give rise to a slow, logarithmic average fitness trajectory.

Adaptive Landscapes in the Age of Synthetic Biology

For nearly a century adaptive landscapes have provided overviews of the evolutionary process and yet they remain metaphors. We redefine adaptive landscapes in terms of biological processes rather than descriptive phenomenology. We focus on the underlying mechanisms that generate emergent properties such as epistasis, dominance, trade-offs and adaptive peaks. We illustrate the utility of landscapes in predicting the course of adaptation and the distribution of fitness effects. We abandon aged arguments concerning landscape ruggedness in favor of empirically determining landscape architecture. In so doing, we transform the landscape metaphor into a scientific framework within which causal hypotheses can be tested.

Antibiotic collateral sensitivity is contingent on the repeatability of evolution

Antibiotic resistance represents a growing health crisis that necessitates the immediate discovery of novel treatment strategies. One such strategy is the identification of collateral sensitivities, wherein evolution under a first drug induces susceptibility to a second. Here, we report that sequential drug regimens derived from in vitro evolution experiments may have overstated therapeutic benefit, predicting a collaterally sensitive response where cross-resistance ultimately occurs. We quantify the likelihood of this phenomenon by use of a mathematical model parametrised with combinatorially complete fitness landscapes for Escherichia coli. Through experimental evolution we then verify that a second drug can indeed stochastically exhibit either increased susceptibility or increased resistance when following a first. Genetic divergence is confirmed as the driver of this differential response through targeted and whole genome sequencing. Taken together, these results highlight that the success of evolutionarily-informed therapies is predicated on a rigorous probabilistic understanding of the contingencies that arise during the evolution of drug resistance.

The evolution of resistance to an antibiotic can render bacteria more susceptible, or more resistant, to a second antibiotic. Here, Nichol et al. provide evidence that the final outcome can be fairly stochastic and depends on the shape of the evolutionary fitness landscape.

Predicting mutational routes to new adaptive phenotypes

Predicting evolutionary change poses numerous challenges. Here we take advantage of the model bacterium Pseudomonas fluorescens in which the genotype-to-phenotype map determining evolution of the adaptive 'wrinkly spreader' (WS) type is known. We present mathematical descriptions of three necessary regulatory pathways and use these to predict both the rate at which each mutational route is used and the expected mutational targets. To test predictions, mutation rates and targets were determined for each pathway. Unanticipated mutational hotspots caused experimental observations to depart from predictions but additional data led to refined models. A mismatch was observed between the spectra of WS-causing mutations obtained with and without selection due to low fitness of previously undetected WS-causing mutations. Our findings contribute toward the development of mechanistic models for forecasting evolution, highlight current limitations, and draw attention to challenges in predicting locus-specific mutational biases and fitness effects.

On the networked architecture of genotype spaces and its critical effects on molecular evolution

Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at the macroevolutionary, ecological and molecular level. Actually, when the complex architecture of genotype spaces is taken into account, the evolutionary dynamics of molecular populations becomes intrinsically non-uniform, sharing deep qualitative and quantitative similarities with slowly driven physical systems: nonlinear responses analogous to critical transitions, sudden state changes or hysteresis, among others. Furthermore, the phenotypic plasticity inherent to genotypes transforms classical fitness landscapes into multiscapes where adaptation in response to an environmental change may be very fast. The quantitative nature of adaptive molecular processes is deeply dependent on a network-of-networks multilayered structure of the map from genotype to function that we begin to unveil.

Neutral Theory and Rapidly Evolving Viral Pathogens

The evolution of viral pathogens is shaped by strong selective forces that are exerted during jumps to new hosts, confrontations with host immune responses and antiviral drugs, and numerous other processes. However, while undeniably strong and frequent, adaptive evolution is largely confined to small parts of information-packed viral genomes, and the majority of observed variation is effectively neutral. The predictions and implications of the neutral theory have proven immensely useful in this context, with applications spanning understanding within-host population structure, tracing the origins and spread of viral pathogens, predicting evolutionary dynamics, and modeling the emergence of drug resistance. We highlight the multiple ways in which the neutral theory has had an impact, which has been accelerated in the age of high-throughput, high-resolution genomics.

Molecular evolution between chemistry and biology : The interplay of competition, cooperation, and mutation

Biological evolution is reduced to three fundamental processes in the spirit of a minimal model: (i) Competition caused by differential fitness, (ii) cooperation of competitors in the sense of symbiosis, and (iii) variation introduced by mutation understood as error-prone reproduction. The three combinations of two fundamental processes each, ([Formula: see text]) competition and mutation, ([Formula: see text]) cooperation and competition, and ([Formula: see text]) cooperation and mutation, are analyzed. Changes in population dynamics that are induced by bifurcations and threshold phenomena are discussed.

Mapping mutational effects along the evolutionary landscape of HIV envelope

The immediate evolutionary space accessible to HIV is largely determined by how single amino acid mutations affect fitness. These mutational effects can shift as the virus evolves. However, the prevalence of such shifts in mutational effects remains unclear. Here, we quantify the effects on viral growth of all amino acid mutations to two HIV envelope (Env) proteins that differ at >100 residues. Most mutations similarly affect both Envs, but the amino acid preferences of a minority of sites have clearly shifted. These shifted sites usually prefer a specific amino acid in one Env, but tolerate many amino acids in the other. Surprisingly, shifts are only slightly enriched at sites that have substituted between the Envs—and many occur at residues that do not even contact substitutions. Therefore, long-range epistasis can unpredictably shift Env’s mutational tolerance during HIV evolution, although the amino acid preferences of most sites are conserved between moderately diverged viral strains.

The virus that causes AIDS, or HIV, has a protein called Env on its surface, which is essential for the virus to infect cells. Env can also be recognized by the immune system, which then targets the virus for destruction or blocks it from infecting cells. Unfortunately, Env evolves very quickly, which means that HIV can evade our defenses. However, there are limits to how much this protein can change, since it still needs to perform its essential role in helping viruses enter cells.

In the century since HIV first appeared in human populations, the virus has evolved considerably. There are now many HIV strains that infect people, and they bear Env proteins with substantially different sequences. However, it is not clear if these changes in sequence have resulted in Envs from distinct strains being able to tolerate different mutations.

To examine this question, Haddox et al. compared how the Envs from two strains of HIV react to modifications in their sequences. They created all possible individual mutations in the proteins, and the resulting collections of mutated viruses were then tested for their ability to infect cells in the laboratory.

Most mutations had similar effects in both Env proteins. This allowed Haddox et al. to identify portions of the protein that easily accommodate changes, and portions that must remain unchanged for viruses to remain infectious—at least in the laboratory. Some of these mutations are under different types of pressures when the virus faces the immune system, and those were identified using computational approaches.

However, some mutations were tolerated differently by the two Env proteins. Therefore, viral strains differ in how their Env proteins can evolve. The parts of Env that showed differences in mutational tolerance between the strains were not necessarily the parts that differ in sequence. This shows that changes in sequence in one part of the protein can modify how other portions evolve.

It remains to be determined whether changes in tolerance to mutations translate into differences in how the virus can escape immunity. This is an important question given that the rapid evolution of Env is a major obstacle to creating a vaccine for HIV.

Studies on Manfred Eigen's model for the self-organization of information processing

In 1971, Manfred Eigen extended the principles of Darwinian evolution to chemical processes, from catalytic networks to the emergence of information processing at the molecular level, leading to the emergence of life. In this paper, we investigate some very general characteristics of this scenario, such as the valuation process of phenotypic traits in a high-dimensional fitness landscape, the effect of spatial compartmentation on the valuation, and the self-organized transition from structural to symbolic genetic information of replicating chain molecules. In the first part, we perform an analysis of typical dynamical properties of continuous dynamical models of evolutionary processes. In particular, we study the mapping of genotype to continuous phenotype spaces following the ideas of Wright and Conrad. We investigate typical features of a Schrödinger-like dynamics, the consequences of the high dimensionality, the leading role of saddle points, and Conrad's extra-dimensional bypass. In the last part, we discuss in brief the valuation of compartment models and the self-organized emergence of molecular symbols at the beginning of life.

Key issues review: evolution on rugged adaptive landscapes

Adaptive landscapes represent a mapping between genotype and fitness. Rugged adaptive landscapes contain two or more adaptive peaks: allele combinations with higher fitness than any of their neighbors in the genetic space. How do populations evolve on such rugged landscapes? Evolutionary biologists have struggled with this question since it was first introduced in the 1930s by Sewall Wright. Discoveries in the fields of genetics and biochemistry inspired various mathematical models of adaptive landscapes. The development of landscape models led to numerous theoretical studies analyzing evolution on rugged landscapes under different biological conditions. The large body of theoretical work suggests that adaptive landscapes are major determinants of the progress and outcome of evolutionary processes. Recent technological advances in molecular biology and microbiology allow experimenters to measure adaptive values of large sets of allele combinations and construct empirical adaptive landscapes for the first time. Such empirical landscapes have already been generated in bacteria, yeast, viruses, and fungi, and are contributing to new insights about evolution on adaptive landscapes. In this Key Issues Review we will: (i) introduce the concept of adaptive landscapes; (ii) review the major theoretical studies of evolution on rugged landscapes; (iii) review some of the recently obtained empirical adaptive landscapes; (iv) discuss recent mathematical and statistical analyses motivated by empirical adaptive landscapes, as well as provide the reader with instructions and source code to implement simulations of evolution on adaptive landscapes; and (v) discuss possible future directions for this exciting field.

Multitype infinite-allele branching processes in continuous time

We introduce extensions to an infinite-allele branching process that allows for multiple types to exist alongside labels. We consider a Markov branching process and general branching process under different assumptions, and show asymptotic results about the growth of the labels as well as the frequency spectrum. These results are motivated by two separate models. The Markov binary splitting results are motivated by a model of clonal evolution in cancer that considers the effect of both driver and passenger mutations on tumor growth. The general process has applications in viral reproduction and dynamics.

Beyond the Hypercube: Evolutionary Accessibility of Fitness Landscapes with Realistic Mutational Networks

Evolutionary pathways describe trajectories of biological evolution in the space of different variants of organisms (genotypes). The probability of existence and the number of evolutionary pathways that lead from a given genotype to a better-adapted genotype are important measures of accessibility of local fitness optima and the reproducibility of evolution. Both quantities have been studied in simple mathematical models where genotypes are represented as binary sequences of two types of basic units, and the network of permitted mutations between the genotypes is a hypercube graph. However, it is unclear how these results translate to the biologically relevant case in which genotypes are represented by sequences of more than two units, for example four nucleotides (DNA) or 20 amino acids (proteins), and the mutational graph is not the hypercube. Here we investigate accessibility of the best-adapted genotype in the general case of K > 2 units. Using computer generated and experimental fitness landscapes we show that accessibility of the global fitness maximum increases with K and can be much higher than for binary sequences. The increase in accessibility comes from the increase in the number of indirect trajectories exploited by evolution for higher K. As one of the consequences, the fraction of genotypes that are accessible increases by three orders of magnitude when the number of units K increases from 2 to 16 for landscapes of size N ∼ 10⁶ genotypes. This suggests that evolution can follow many different trajectories on such landscapes and the reconstruction of evolutionary pathways from experimental data might be an extremely difficult task.

Biological evolution is driven by heritable, genetic alterations that affect the fitness of organisms. However, the pool of “fitter” variants (genotypes) is often restricted and it is not at all obvious how evolution finds its way from low-fitness to high-fitness genotypes in a complex, multidimensional “fitness landscapes” with many peaks (fit organisms) and valleys (unfit ones). To address this question we investigate how likely it is for biological evolution to find a way “uphill” from a lower-fitness organism to the best adapted organism. We discover that the accessibility of the fittest organism depends on the number of types of basic “units” used to encode genotypes. These units can be, for example, the four DNA nucleotides A,T,C,G, or the ∼20 amino acids used for synthesizing proteins, and the choice of the most appropriate unit is dictated by how the genotypes and the fitnesses are related—a relationship that researchers have begun to unveil only recently. We find that increasing the number of units strongly increases the probability that there will be at least one uphill path to the best-adapted genotype, and the number of evolutionary pathways leading to it. Our findings suggest that biological evolution can follow many more pathways than previously thought.

Experimental Estimation of the Effects of All Amino-Acid Mutations to HIV's Envelope Protein on Viral Replication in Cell Culture

HIV is notorious for its capacity to evade immunity and anti-viral drugs through rapid sequence evolution. Knowledge of the functional effects of mutations to HIV is critical for understanding this evolution. HIV's most rapidly evolving protein is its envelope (Env). Here we use deep mutational scanning to experimentally estimate the effects of all amino-acid mutations to Env on viral replication in cell culture. Most mutations are under purifying selection in our experiments, although a few sites experience strong selection for mutations that enhance HIV's replication in cell culture. We compare our experimental measurements of each site's preference for each amino acid to the actual frequencies of these amino acids in naturally occurring HIV sequences. Our measured amino-acid preferences correlate with amino-acid frequencies in natural sequences for most sites. However, our measured preferences are less concordant with natural amino-acid frequencies at surface-exposed sites that are subject to pressures absent from our experiments such as antibody selection. Our data enable us to quantify the inherent mutational tolerance of each site in Env. We show that the epitopes of broadly neutralizing antibodies have a significantly reduced inherent capacity to tolerate mutations, rigorously validating a pervasive idea in the field. Overall, our results help disentangle the role of inherent functional constraints and external selection pressures in shaping Env's evolution.

Effect of Host Species on Topography of the Fitness Landscape for a Plant RNA Virus

Adaptive fitness landscapes are a fundamental concept in evolutionary biology that relate the genotypes of individuals to their fitness. In the end, the evolutionary fate of evolving populations depends on the topography of the landscape, that is, the numbers of accessible mutational pathways and possible fitness peaks (i.e., adaptive solutions). For a long time, fitness landscapes were only theoretical constructions due to a lack of precise information on the mapping between genotypes and phenotypes. In recent years, however, efforts have been devoted to characterizing the properties of empirical fitness landscapes for individual proteins or for microbes adapting to artificial environments. In a previous study, we characterized the properties of the empirical fitness landscape defined by the first five mutations fixed during adaptation of tobacco etch potyvirus (TEV) to a new experimental host, Arabidopsis thaliana Here we evaluate the topography of this landscape in the ancestral host Nicotiana tabacum By comparing the topographies of the landscapes for the two hosts, we found that some features remained similar, such as the existence of fitness holes and the prevalence of epistasis, including cases of sign and reciprocal sign epistasis that created rugged, uncorrelated, and highly random topographies. However, we also observed significant differences in the fine-grained details between the two landscapes due to changes in the fitness and epistatic interactions of some genotypes. Our results support the idea that not only fitness tradeoffs between hosts but also topographical incongruences among fitness landscapes in alternative hosts may contribute to virus specialization. IMPORTANCE Despite its importance for understanding virus evolutionary dynamics, very little is known about the topography of virus adaptive fitness landscapes, and even less is known about the effects that different host species and environmental conditions may have on this topography. To bridge this gap, we evaluated the topography of a small fitness landscape formed by all genotypes that result from every possible combination of the first five mutations fixed during adaptation of TEV to the novel host A. thaliana To assess the effect that host species may have on this topography, we evaluated the fitness of every genotype in both the ancestral and novel hosts. We found that both landscapes share some macroscopic properties, such as the existence of holes and being highly rugged and uncorrelated, yet they differ in microscopic details due to changes in the magnitude and sign of fitness and epistatic effects.

Adaptation in protein fitness landscapes is facilitated by indirect paths

The structure of fitness landscapes is critical for understanding adaptive protein evolution. Previous empirical studies on fitness landscapes were confined to either the neighborhood around the wild type sequence, involving mostly single and double mutants, or a combinatorially complete subgraph involving only two amino acids at each site. In reality, the dimensionality of protein sequence space is higher (20^L) and there may be higher-order interactions among more than two sites. Here we experimentally characterized the fitness landscape of four sites in protein GB1, containing 20⁴ = 160,000 variants. We found that while reciprocal sign epistasis blocked many direct paths of adaptation, such evolutionary traps could be circumvented by indirect paths through genotype space involving gain and subsequent loss of mutations. These indirect paths alleviate the constraint on adaptive protein evolution, suggesting that the heretofore neglected dimensions of sequence space may change our views on how proteins evolve.

DOI:http://dx.doi.org/10.7554/eLife.16965.001

Proteins can evolve over time by changing their component parts, which are called amino acids. These changes usually happen one at a time and natural selection tends to preserve those changes that make the protein more efficient at its specific tasks, while discarding those that impair the protein’s activity. However the effect of each change depends on the protein as a whole, and so two changes that separately make the protein worse can make it much better if they occur together. This phenomenon is called epistasis and in some cases it can trap proteins in a sub-optimal form and prevent them from improving further.

Proteins are made from twenty different kinds of amino acid, and there are millions of different combinations of amino acids that could, in theory, make a protein of a given length. Studying protein evolution involves making variants of the same protein, each with just a few changes, and comparing how efficient, or “fit”, they are. Previous studies only measured the fitness of a few variants and showed that epistasis could block protein evolution by requiring the protein to lose some fitness before it could improve further. However, new techniques have now made it easier to study protein evolution by testing many more protein variants.

Wu, Dai et al. focused on four amino acids in part of a protein called GB1 and tested the efficiency of every possible combination of these four amino acids, a total of 160,000 (20⁴) variants. Contrary to expectations, the results suggested that the protein could evolve quickly to maximise fitness despite there being epistasis between the four amino acids. Overcoming epistasis typically involved making a change to one amino acid that paved the way for further changes while avoiding the need to lose fitness. The original change could then be reversed once the epistasis was overcome. The complexity of this solution means it can only be seen by studying a large number of protein variants that represent many alternative sequences of protein changes.

Wu, Dai et al. conclude that proteins are able to achieve a higher level of fitness through evolution by exploring a large number of changes. There are many possible changes for each protein and it is this variety that, despite epistasis, allows proteins to become naturally optimised for the tasks that they perform. While the full complexity of protein evolution cannot be explored at the moment, as technology advances it will become possible to study more protein variants. Such advances would therefore hopefully allow researchers to discover even more about the natural mechanisms of protein evolution.

DOI:http://dx.doi.org/10.7554/eLife.16965.002

How Good Are Statistical Models at Approximating Complex Fitness Landscapes?

Fitness landscapes determine the course of adaptation by constraining and shaping evolutionary trajectories. Knowledge of the structure of a fitness landscape can thus predict evolutionary outcomes. Empirical fitness landscapes, however, have so far only offered limited insight into real-world questions, as the high dimensionality of sequence spaces makes it impossible to exhaustively measure the fitness of all variants of biologically meaningful sequences. We must therefore revert to statistical descriptions of fitness landscapes that are based on a sparse sample of fitness measurements. It remains unclear, however, how much data are required for such statistical descriptions to be useful. Here, we assess the ability of regression models accounting for single and pairwise mutations to correctly approximate a complex quasi-empirical fitness landscape. We compare approximations based on various sampling regimes of an RNA landscape and find that the sampling regime strongly influences the quality of the regression. On the one hand it is generally impossible to generate sufficient samples to achieve a good approximation of the complete fitness landscape, and on the other hand systematic sampling schemes can only provide a good description of the immediate neighborhood of a sequence of interest. Nevertheless, we obtain a remarkably good and unbiased fit to the local landscape when using sequences from a population that has evolved under strong selection. Thus, current statistical methods can provide a good approximation to the landscape of naturally evolving populations.

Strong Selection Significantly Increases Epistatic Interactions in the Long-Term Evolution of a Protein

Epistatic interactions between residues determine a protein’s adaptability and shape its evolutionary trajectory. When a protein experiences a changed environment, it is under strong selection to find a peak in the new fitness landscape. It has been shown that strong selection increases epistatic interactions as well as the ruggedness of the fitness landscape, but little is known about how the epistatic interactions change under selection in the long-term evolution of a protein. Here we analyze the evolution of epistasis in the protease of the human immunodeficiency virus type 1 (HIV-1) using protease sequences collected for almost a decade from both treated and untreated patients, to understand how epistasis changes and how those changes impact the long-term evolvability of a protein. We use an information-theoretic proxy for epistasis that quantifies the co-variation between sites, and show that positive information is a necessary (but not sufficient) condition that detects epistasis in most cases. We analyze the “fossils” of the evolutionary trajectories of the protein contained in the sequence data, and show that epistasis continues to enrich under strong selection, but not for proteins whose environment is unchanged. The increase in epistasis compensates for the information loss due to sequence variability brought about by treatment, and facilitates adaptation in the increasingly rugged fitness landscape of treatment. While epistasis is thought to enhance evolvability via valley-crossing early-on in adaptation, it can hinder adaptation later when the landscape has turned rugged. However, we find no evidence that the HIV-1 protease has reached its potential for evolution after 9 years of adapting to a drug environment that itself is constantly changing. We suggest that the mechanism of encoding new information into pairwise interactions is central to protein evolution not just in HIV-1 protease, but for any protein adapting to a changing environment.

Evolution is often viewed as a process that occurs “mutation by mutation”, suggesting that the effect of each mutation is independent of that of others. However, in reality the effect of a mutation often depends on the context of other mutations, a dependence known as “epistasis”. Even though epistasis can constrain protein evolution, it is actually very common. Such interactions are particularly pervasive in proteins that evolve resistance to a drug via mutations that create defects, and that must be repaired with compensatory mutations. We study how epistasis between protein residues evolves over time in a new and changing environment, and compare these findings to protein evolution in a constant environment. We analyze the sequences of the human immunodeficiency virus type 1 (HIV-1) protease enzyme collected over a period of 9 years from patients treated with anti-viral drugs (as well as from patients that went untreated), and find that epistasis between residues continues to increase as more potent anti-viral drugs enter the market, while epistasis is unchanging in the proteins exposed to a constant environment. Yet, the proteins adapting to the changing landscape do not appear to be constrained by the epistatic interactions and continue to manage to evade new drugs.

Adaptive Landscape by Environment Interactions Dictate Evolutionary Dynamics in Models of Drug Resistance

The adaptive landscape analogy has found practical use in recent years, as many have explored how their understanding can inform therapeutic strategies that subvert the evolution of drug resistance. A major barrier to applications of these concepts is a lack of detail concerning how the environment affects adaptive landscape topography, and consequently, the outcome of drug treatment. Here we combine empirical data, evolutionary theory, and computer simulations towards dissecting adaptive landscape by environment interactions for the evolution of drug resistance in two dimensions-drug concentration and drug type. We do so by studying the resistance mediated by Plasmodium falciparum dihydrofolate reductase (DHFR) to two related inhibitors-pyrimethamine and cycloguanil-across a breadth of drug concentrations. We first examine whether the adaptive landscapes for the two drugs are consistent with common definitions of cross-resistance. We then reconstruct all accessible pathways across the landscape, observing how their structure changes with drug environment. We offer a mechanism for non-linearity in the topography of accessible pathways by calculating of the interaction between mutation effects and drug environment, which reveals rampant patterns of epistasis. We then simulate evolution in several different drug environments to observe how these individual mutation effects (and patterns of epistasis) influence paths taken at evolutionary "forks in the road" that dictate adaptive dynamics in silico. In doing so, we reveal how classic metrics like the IC50 and minimal inhibitory concentration (MIC) are dubious proxies for understanding how evolution will occur across drug environments. We also consider how the findings reveal ambiguities in the cross-resistance concept, as subtle differences in adaptive landscape topography between otherwise equivalent drugs can drive drastically different evolutionary outcomes. Summarizing, we discuss the results with regards to their basic contribution to the study of empirical adaptive landscapes, and in terms of how they inform new models for the evolution of drug resistance.

Empirical fitness models for hepatitis C virus immunogen design

Hepatitis C virus (HCV) afflicts 170 million people worldwide, 2%-3% of the global population, and kills 350 000 each year. Prophylactic vaccination offers the most realistic and cost effective hope of controlling this epidemic in the developing world where expensive drug therapies are not available. Despite 20 years of research, the high mutability of the virus and lack of knowledge of what constitutes effective immune responses have impeded development of an effective vaccine. Coupling data mining of sequence databases with spin glass models from statistical physics, we have developed a computational approach to translate clinical sequence databases into empirical fitness landscapes quantifying the replicative capacity of the virus as a function of its amino acid sequence. These landscapes explicitly connect viral genotype to phenotypic fitness, and reveal vulnerable immunological targets within the viral proteome that can be exploited to rationally design vaccine immunogens. We have recovered the empirical fitness landscape for the HCV RNA-dependent RNA polymerase (protein NS5B) responsible for viral genome replication, and validated the predictions of our model by demonstrating excellent accord with experimental measurements and clinical observations. We have used our landscapes to perform exhaustive in silico screening of 16.8 million T-cell immunogen candidates to identify 86 optimal formulations. By reducing the search space of immunogen candidates by over five orders of magnitude, our approach can offer valuable savings in time, expense, and labor for experimental vaccine development and accelerate the search for a HCV vaccine.

ABBREVIATIONS

HCV-hepatitis C virus, HLA-human leukocyte antigen, CTL-cytotoxic T lymphocyte, NS5B-nonstructural protein 5B, MSA-multiple sequence alignment, PEG-IFN-pegylated interferon.

From System-Wide Differential Gene Expression to Perturbed Regulatory Factors: A Combinatorial Approach

High-throughput experiments such as microarrays and deep sequencing provide large scale information on the pattern of gene expression, which undergoes extensive remodeling as the cell dynamically responds to varying environmental cues or has its function disrupted under pathological conditions. An important initial step in the systematic analysis and interpretation of genome-scale expression alteration involves identification of a set of perturbed transcriptional regulators whose differential activity can provide a proximate hypothesis to account for these transcriptomic changes. In the present work, we propose an unbiased and logically natural approach to transcription factor enrichment. It involves overlaying a list of experimentally determined differentially expressed genes on a background regulatory network coming from e.g. literature curation or computational motif scanning, and identifying that subset of regulators whose aggregated target set best discriminates between the altered and the unaffected genes. In other words, our methodology entails testing of all possible regulatory subnetworks, rather than just the target sets of individual regulators as is followed in most standard approaches. We have proposed an iterative search method to efficiently find such a combination, and benchmarked it on E. coli microarray and regulatory network data available in the public domain. Comparative analysis carried out on artificially generated differential expression profiles, as well as empirical factor overexpression data for M. tuberculosis, shows that our methodology provides marked improvement in accuracy of regulatory inference relative to the standard method that involves evaluating factor enrichment in an individual manner.

The impact of high-order epistasis in the within-host fitness of a positive-sense plant RNA virus

RNA viruses are the main source of emerging infectious diseases because of the evolutionary potential bestowed by their fast replication, large population sizes and high mutation and recombination rates. However, an equally important property, which is usually neglected, is the topography of the fitness landscape. How many fitness maxima exist and how well they are connected is especially interesting, as this determines the number of accessible evolutionary pathways. To address this question, we have reconstructed a region of the fitness landscape of tobacco etch potyvirus constituted by mutations observed during the experimental adaptation of the virus to the novel host Arabidopsis thaliana. Fitness was measured for many genotypes and showed the existence of multiple peaks and holes in the landscape. We found prevailing epistatic effects between mutations, with cases of reciprocal sign epistasis being common among pairs of mutations. We also found that high-order epistasis was as important as pairwise epistasis in their contribution to fitness. Therefore, results suggest that the landscape was rugged due to the existence of holes caused by lethal genotypes, that a very limited number of potential neutral paths exist and that it contained a single adaptive peak.

Steering Evolution with Sequential Therapy to Prevent the Emergence of Bacterial Antibiotic Resistance

The increasing rate of antibiotic resistance and slowing discovery of novel antibiotic treatments presents a growing threat to public health. Here, we consider a simple model of evolution in asexually reproducing populations which considers adaptation as a biased random walk on a fitness landscape. This model associates the global properties of the fitness landscape with the algebraic properties of a Markov chain transition matrix and allows us to derive general results on the non-commutativity and irreversibility of natural selection as well as antibiotic cycling strategies. Using this formalism, we analyze 15 empirical fitness landscapes of E. coli under selection by different β-lactam antibiotics and demonstrate that the emergence of resistance to a given antibiotic can be either hindered or promoted by different sequences of drug application. Specifically, we demonstrate that the majority, approximately 70%, of sequential drug treatments with 2-4 drugs promote resistance to the final antibiotic. Further, we derive optimal drug application sequences with which we can probabilistically 'steer' the population through genotype space to avoid the emergence of resistance. This suggests a new strategy in the war against antibiotic-resistant organisms: drug sequencing to shepherd evolution through genotype space to states from which resistance cannot emerge and by which to maximize the chance of successful therapy.

A tortoise-hare pattern seen in adapting structured and unstructured populations suggests a rugged fitness landscape in bacteria

In the context of Wright's adaptive landscape, genetic epistasis can yield a multipeaked or "rugged" topography. In an unstructured population, a lineage with selective access to multiple peaks is expected to fix rapidly on one, which may not be the highest peak. In a spatially structured population, on the other hand, beneficial mutations take longer to spread. This slowdown allows distant parts of the population to explore the landscape semiindependently. Such a population can simultaneously discover multiple peaks, and the genotype at the highest discovered peak is expected to dominate eventually. Thus, structured populations sacrifice initial speed of adaptation for breadth of search. As in the fable of the tortoise and the hare, the structured population (tortoise) starts relatively slow but eventually surpasses the unstructured population (hare) in average fitness. In contrast, on single-peak landscapes that lack epistasis, all uphill paths converge. Given such "smooth" topography, breadth of search is devalued and a structured population only lags behind an unstructured population in average fitness (ultimately converging). Thus, the tortoise-hare pattern is an indicator of ruggedness. After verifying these predictions in simulated populations where ruggedness is manipulable, we explore average fitness in metapopulations of Escherichia coli. Consistent with a rugged landscape topography, we find a tortoise-hare pattern. Further, we find that structured populations accumulate more mutations, suggesting that distant peaks are higher. This approach can be used to unveil landscape topography in other systems, and we discuss its application for antibiotic resistance, engineering problems, and elements of Wright's shifting balance process.

Hsp90: a chaperone for HIV-1

HIV-1 replication has been intensively investigated over the past 30 years. Hsp90 is one of the most abundant proteins in human cells, important in the formation and function of several protein complexes that maintain cell homeostasis. Remarkably, the impact of Hsp90 on HIV-1 infection has started to be appreciated only recently. Hsp90 has been shown to (a) promote HIV-1 gene expression in acutely infected cells, (b) localize at the viral promoter DNA, (c) mediate enhanced replication in conditions of hyperthermia and (d) activate the P-TEFb complex, which is essential for efficient HIV-1 transcription. Hsp90 has been implicated in buffering deleterious mutations of the viral core and in the regulation of innate and acquired immune responses to HIV-1 infection. Therefore, Hsp90 is an important host factor promoting several steps of the HIV-1 life cycle. Several small Hsp90 inhibitors are in Phase II clinical trials for human cancers and might potentially be used to inhibit HIV-1 infection at multiple levels.

Eight challenges in phylodynamic inference

The field of phylodynamics, which attempts to enhance our understanding of infectious disease dynamics using pathogen phylogenies, has made great strides in the past decade. Basic epidemiological and evolutionary models are now well characterized with inferential frameworks in place. However, significant challenges remain in extending phylodynamic inference to more complex systems. These challenges include accounting for evolutionary complexities such as changing mutation rates, selection, reassortment, and recombination, as well as epidemiological complexities such as stochastic population dynamics, host population structure, and different patterns at the within-host and between-host scales. An additional challenge exists in making efficient inferences from an ever increasing corpus of sequence data.

Evolution of RNA-Based Networks

RNA molecules have served for decades as a paradigmatic example of molecular evolution that is tractable both in in vitro experiments and in detailed computer simulation. The adaptation of RNA sequences to external selection pressures is well studied and well understood. The de novo innovation or optimization of RNA aptamers and riboswitches in SELEX experiments serves as a case in point. Likewise, fitness landscapes building upon the efficiently computable RNA secondary structures have been a key toward understanding realistic fitness landscapes. Much less is known, however, on models in which multiple RNAs interact with each other, thus actively influencing the selection pressures acting on them. From a computational perspective, RNA-RNA interactions can be dealt with by same basic methods as the folding of a single RNA molecule, although many details become more complicated. RNA-RNA interactions are frequently employed in cellular regulation networks, e.g., as miRNA bases mRNA silencing or in the modulation of bacterial mRNAs by small, often highly structured sRNAs. In this chapter, we summarize the key features of networks of replicators. We highlight the differences between quasispecies-like models describing templates copied by an external replicase and hypercycle similar to autocatalytic replicators. Two aspects are of importance: the dynamics of selection within a population, usually described by conventional dynamical systems, and the evolution of replicating species in the space of chemical types. Product inhibition plays a key role in modulating selection dynamics from survival of the fittest to extinction of unfittest. The sequence evolution of replicators is rather well understood as approximate optimization in a fitness landscape for templates that is shaped by the sequence-structure map of RNA. Some of the properties of this map, in particular shape space covering and extensive neutral networks, give rise to evolutionary patterns such as drift-like motion in sequence space, akin to the behavior of RNA quasispecies. In contrast, very little is known about the influence of sequence-structure maps on autocatalytic replication systems.

What Is a Quasispecies? Historical Origins and Current Scope

The quasispecies concept is introduced by means of a simple theoretical model that uses as little chemical kinetics and mathematics as possible but fully in the spirit of Albert Einstein who said: "Things should be made as simple as possible but not simpler." More elaborate treatments follow in the forthcoming chapters. It is shown that the most important results of the theory, in particular the existence of error thresholds, are not dependent on simplifying assumptions concerning the distribution of fitness values. Error thresholds are regularly found on landscapes with large and irregular scatter of fitness. After the introduction to theory, it will be shown how experimental data on the evolution of molecules or viruses may be fit to the theoretical model.

Quasispecies on Fitness Landscapes

Selection-mutation dynamics is studied as adaptation and neutral drift on abstract fitness landscapes. Various models of fitness landscapes are introduced and analyzed with respect to the stationary mutant distributions adopted by populations upon them. The concept of quasispecies is introduced, and the error threshold phenomenon is analyzed. Complex fitness landscapes with large scatter of fitness values are shown to sustain error thresholds. The phenomenological theory of the quasispecies introduced in 1971 by Eigen is compared to approximation-free numerical computations. The concept of strong quasispecies understood as mutant distributions, which are especially stable against changes in mutations rates, is presented. The role of fitness neutral genotypes in quasispecies is discussed.

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.