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

Mutual information networks reveal evolutionary relationships within the influenza A virus polymerase

The influenza A virus (IAV) RNA polymerase is an essential driver of IAV evolution. Mutations that the polymerase introduces into viral genome segments during replication are the ultimate source of genetic variation, including within the three subunits of the IAV polymerase (polymerase basic protein 2, polymerase basic protein 1, and polymerase acidic protein). Evolutionary analysis of the IAV polymerase is complicated, because changes in mutation rate, replication speed, and drug resistance involve epistatic interactions among its subunits. In order to study the evolution of the human seasonal H3N2 polymerase since the 1968 pandemic, we identified pairwise evolutionary relationships among ∼7000 H3N2 polymerase sequences using mutual information (MI), which measures the information gained about the identity of one residue when a second residue is known. To account for uneven sampling of viral sequences over time, we developed a weighted MI (wMI) metric and demonstrate that wMI outperforms raw MI through simulations using a well-sampled severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) dataset. We then constructed wMI networks of the H3N2 polymerase to extend the inherently pairwise wMI statistic to encompass relationships among larger groups of residues. We included hemagglutinin (HA) in the wMI network to distinguish between functional wMI relationships within the polymerase and those potentially due to hitch-hiking on antigenic changes in HA. The wMI networks reveal coevolutionary relationships among residues with roles in replication and encapsidation. Inclusion of HA highlighted polymerase-only subgraphs containing residues with roles in the enzymatic functions of the polymerase and host adaptability. This work provides insight into the factors that drive and constrain the rapid evolution of influenza viruses.

Contingency and Entrenchment of Drug-Resistance Mutations in HIV Viral Proteins

The ability of HIV-1 to rapidly mutate leads to antiretroviral therapy (ART) failure among infected patients. Drug-resistance mutations (DRMs), which cause a fitness penalty to intrinsic viral fitness, are compensated by accessory mutations with favorable epistatic interactions which cause an evolutionary trapping effect, but the kinetics of this overall process has not been well characterized. Here, using a Potts Hamiltonian model describing epistasis combined with kinetic Monte Carlo simulations of evolutionary trajectories, we explore how epistasis modulates the evolutionary dynamics of HIV DRMs. We show how the occurrence of a drug-resistance mutation is contingent on favorable epistatic interactions with many other residues of the sequence background and that subsequent mutations entrench DRMs. We measure the time-autocorrelation of fluctuations in the likelihood of DRMs due to epistatic coupling with the sequence background, which reveals the presence of two evolutionary processes controlling DRM kinetics with two distinct time scales. Further analysis of waiting times for the evolutionary trapping effect to reverse reveals that the sequences which entrench (trap) a DRM are responsible for the slower time scale. We also quantify the overall strength of epistatic effects on the evolutionary kinetics for different mutations and show these are much larger for DRM positions than polymorphic positions, and we also show that trapping of a DRM is often caused by the collective effect of many accessory mutations, rather than a few strongly coupled ones, suggesting the importance of multiresidue sequence variations in HIV evolution. The analysis presented here provides a framework to explore the kinetic pathways through which viral proteins like HIV evolve under drug-selection pressure.

Emergence of functional information from multivariate correlations

The information content of symbolic sequences (such as nucleic or amino acid sequences, but also neuronal firings or strings of letters) can be calculated from an ensemble of such sequences, but because information cannot be assigned to single sequences, we cannot correlate information to other observables attached to the sequence. Here we show that an information score obtained from multivariate (multiple-variable) correlations within sequences of a 'training' ensemble can be used to predict observables of out-of-sample sequences with an accuracy that scales with the complexity of correlations, showing that functional information emerges from a hierarchy of multi-variable correlations. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.

Evolutionary velocity with protein language models predicts evolutionary dynamics of diverse proteins

The degree to which evolution is predictable is a fundamental question in biology. Previous attempts to predict the evolution of protein sequences have been limited to specific proteins and to small changes, such as single-residue mutations. Here, we demonstrate that by using a protein language model to predict the local evolution within protein families, we recover a dynamic "vector field" of protein evolution that we call evolutionary velocity (evo-velocity). Evo-velocity generalizes to evolution over vastly different timescales, from viral proteins evolving over years to eukaryotic proteins evolving over geologic eons, and can predict the evolutionary dynamics of proteins that were not used to develop the original model. Evo-velocity also yields new evolutionary insights by predicting strategies of viral-host immune escape, resolving conflicting theories on the evolution of serpins, and revealing a key role of horizontal gene transfer in the evolution of eukaryotic glycolysis.

Limits to detecting epistasis in the fitness landscape of HIV

The rapid evolution of HIV is constrained by interactions between mutations which affect viral fitness. In this work, we explore the role of epistasis in determining the mutational fitness landscape of HIV for multiple drug target proteins, including Protease, Reverse Transcriptase, and Integrase. Epistatic interactions between residues modulate the mutation patterns involved in drug resistance, with unambiguous signatures of epistasis best seen in the comparison of the Potts model predicted and experimental HIV sequence "prevalences" expressed as higher-order marginals (beyond triplets) of the sequence probability distribution. In contrast, experimental measures of fitness such as viral replicative capacities generally probe fitness effects of point mutations in a single background, providing weak evidence for epistasis in viral systems. The detectable effects of epistasis are obscured by higher evolutionary conservation at sites. While double mutant cycles in principle, provide one of the best ways to probe epistatic interactions experimentally without reference to a particular background, we show that the analysis is complicated by the small dynamic range of measurements. Overall, we show that global pairwise interaction Potts models are necessary for predicting the mutational landscape of viral proteins.

Information-theoretic characterization of the complete genotype-phenotype map of a complex pre-biotic world: Comment on "From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics" by Susanna Manrubia et al

How information is encoded in bio-molecular sequences is difficult to quantify since such an analysis usually requires sampling an exponentially large genetic space. Here we show how information theory reveals both robust and compressed encodings in the largest complete genotype-phenotype map (over 5 trillion sequences) obtained to date.

Enzyme Evolution: An Epistatic Ratchet versus a Smooth Reversible Transition

Evolutionary trajectories are deemed largely irreversible. In a newly diverged protein, reversion of mutations that led to the functional switch typically results in loss of both the new and the ancestral functions. Nonetheless, evolutionary transitions where reversions are viable have also been described. The structural and mechanistic causes of reversion compatibility versus incompatibility therefore remain unclear. We examined two laboratory evolution trajectories of mammalian paraoxonase-1, a lactonase with promiscuous organophosphate hydrolase (OPH) activity. Both trajectories began with the same active-site mutant, His115Trp, which lost the native lactonase activity and acquired higher OPH activity. A neo-functionalization trajectory amplified the promiscuous OPH activity, whereas the re-functionalization trajectory restored the native activity, thus generating a new lactonase that lacks His115. The His115 revertants of these trajectories indicated opposite trends. Revertants of the neo-functionalization trajectory lost both the evolved OPH and the original lactonase activity. Revertants of the trajectory that restored the original lactonase function were, however, fully active. Crystal structures and molecular simulations show that in the newly diverged OPH, the reverted His115 and other catalytic residues are displaced, thus causing loss of both the original and the new activity. In contrast, in the re-functionalization trajectory, reversion compatibility of the original lactonase activity derives from mechanistic versatility whereby multiple residues can fulfill the same task. This versatility enables unique sequence-reversible compositions that are inaccessible when the active site was repurposed toward a new function.

Epistasis and entrenchment of drug resistance in HIV-1 subtype B

The development of drug resistance in HIV is the result of primary mutations whose effects on viral fitness depend on the entire genetic background, a phenomenon called 'epistasis'. Based on protein sequences derived from drug-experienced patients in the Stanford HIV database, we use a co-evolutionary (Potts) Hamiltonian model to provide direct confirmation of epistasis involving many simultaneous mutations. Building on earlier work, we show that primary mutations leading to drug resistance can become highly favored (or entrenched) by the complex mutation patterns arising in response to drug therapy despite being disfavored in the wild-type background, and provide the first confirmation of entrenchment for all three drug-target proteins: protease, reverse transcriptase, and integrase; a comparative analysis reveals that NNRTI-induced mutations behave differently from the others. We further show that the likelihood of resistance mutations can vary widely in patient populations, and from the population average compared to specific molecular clones.

Impact of antiretroviral resistance and virological failure on HIV-1 informational entropy

Objectives

The present study investigated the relationship between genomic variability and resistance of HIV-1 sequences in protease (PR) and reverse transcriptase (RT) regions of the pol gene. In addition, we analysed the resistance among 651 individuals presenting antiretroviral virological failure, from 2009 to 2011, in the state of São Paulo, Brazil.

Methods

The genomic variability was quantified by using informational entropy methods and the relationship between resistance and replicative fitness, as inferred by the residual viral load and CD4+ T cell count.

Results

The number of antiretroviral schemes is related to the number of resistance mutations in the HIV-1 PR (α = 0.2511, P = 0.0003, R2 = 0.8672) and the RT (α = 0.7892, P = 0.0001, R2 = 0.9141). Increased informational entropy rate is related to lower levels of HIV-1 viral loads (α = -0.0121, P = 0.0471, R2 = 0.7923), lower levels of CD4+ T cell counts (α = -0.0120, P = 0.0335, R2 = 0.8221) and a higher number of antiretroviral resistance-related mutations.

Conclusions

Less organized HIV genomes as inferred by higher levels of informational entropy relate to less competent host immune systems, lower levels of HIV replication and HIV genetic evolution as a consequence of antiretroviral resistance.

Full-Length Envelope Analyzer (FLEA): A tool for longitudinal analysis of viral amplicons

Next generation sequencing of viral populations has advanced our understanding of viral population dynamics, the development of drug resistance, and escape from host immune responses. Many applications require complete gene sequences, which can be impossible to reconstruct from short reads. HIV env, the protein of interest for HIV vaccine studies, is exceptionally challenging for long-read sequencing and analysis due to its length, high substitution rate, and extensive indel variation. While long-read sequencing is attractive in this setting, the analysis of such data is not well handled by existing methods. To address this, we introduce FLEA (Full-Length Envelope Analyzer), which performs end-to-end analysis and visualization of long-read sequencing data. FLEA consists of both a pipeline (optionally run on a high-performance cluster), and a client-side web application that provides interactive results. The pipeline transforms FASTQ reads into high-quality consensus sequences (HQCSs) and uses them to build a codon-aware multiple sequence alignment. The resulting alignment is then used to infer phylogenies, selection pressure, and evolutionary dynamics. The web application provides publication-quality plots and interactive visualizations, including an annotated viral alignment browser, time series plots of evolutionary dynamics, visualizations of gene-wide selective pressures (such as dN/dS) across time and across protein structure, and a phylogenetic tree browser. We demonstrate how FLEA may be used to process Pacific Biosciences HIV env data and describe recent examples of its use. Simulations show how FLEA dramatically reduces the error rate of this sequencing platform, providing an accurate portrait of complex and variable HIV env populations. A public instance of FLEA is hosted at http://flea.datamonkey.org. The Python source code for the FLEA pipeline can be found at https://github.com/veg/flea-pipeline. The client-side application is available at https://github.com/veg/flea-web-app. A live demo of the P018 results can be found at http://flea.murrell.group/view/P018.

Viral populations constantly evolve and diversify. In this article we introduce a method, FLEA, for reconstructing and visualizing the details of evolutionary changes. FLEA specifically processes data from sequencing platforms that generate reads that are long, but error-prone. To study the evolutionary dynamics of entire genes during viral infection, data is collected via long-read sequencing at discrete time points, allowing us to understand how the virus changes over time. However, the experimental and sequencing process is imperfect, so the resulting data contain not only real evolutionary changes, but also mutations and other genetic artifacts caused by sequencing errors. Our method corrects most of these errors by combining thousands of erroneous sequences into a much smaller number of unique consensus sequences that represent biologically meaningful variation. The resulting high-quality sequences are used for further analysis, such as building an evolutionary tree that tracks and interprets the genetic changes in the viral population over time. FLEA is open source, and is freely available online.

Inference of epistatic effects in a key mitochondrial protein

We use Potts model inference to predict pair epistatic effects in a key mitochondrial protein-cytochrome c oxidase subunit 2-for ray-finned fishes. We examine the effect of phylogenetic correlations on our predictions using a simple exact fitness model, and we find that, although epistatic effects are underpredicted, they maintain a roughly linear relationship to their true (model) values. After accounting for this correction, epistatic effects in the protein are still relatively weak, leading to fitness valleys of depth 2Ns≃-5 in compensatory double mutants. Interestingly, positive epistasis is more pronounced than negative epistasis, and the strongest positive effects capture nearly all sites subject to positive selection in fishes, similar to virus proteins evolving under selection pressure in the context of drug therapy.

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.

Inferring genetic interactions from comparative fitness data

Darwinian fitness is a central concept in evolutionary biology. In practice, however, it is hardly possible to measure fitness for all genotypes in a natural population. Here, we present quantitative tools to make inferences about epistatic gene interactions when the fitness landscape is only incompletely determined due to imprecise measurements or missing observations. We demonstrate that genetic interactions can often be inferred from fitness rank orders, where all genotypes are ordered according to fitness, and even from partial fitness orders. We provide a complete characterization of rank orders that imply higher order epistasis. Our theory applies to all common types of gene interactions and facilitates comprehensive investigations of diverse genetic interactions. We analyzed various genetic systems comprising HIV-1, the malaria-causing parasite Plasmodium vivax, the fungus Aspergillus niger, and the TEM-family of β-lactamase associated with antibiotic resistance. For all systems, our approach revealed higher order interactions among mutations.

Highly expressed genes evolve under strong epistasis from a proteome-wide scan in E. coli

Epistasis or the non-additivity of mutational effects is a major force in protein evolution, but it has not been systematically quantified at the level of a proteome. Here, we estimated the extent of epistasis for 2,382 genes in E. coli using several hundreds of orthologs for each gene within the class Gammaproteobacteria. We found that the average epistasis is ~41% across genes in the proteome and that epistasis is stronger among highly expressed genes. This trend is quantitatively explained by the prevailing model of sequence evolution based on minimizing the fitness cost of protein unfolding and aggregation. The genes with the highest epistasis are also functionally involved in the maintenance of proteostasis, translation and central metabolism. In contrast, genes evolving with low epistasis mainly encode for membrane proteins and are involved in transport activity. Our results highlight the coupling between selection and epistasis in the long-term evolution of a proteome.

Inference of Epistatic Effects Leading to Entrenchment and Drug Resistance in HIV-1 Protease

Understanding the complex mutation patterns that give rise to drug resistant viral strains provides a foundation for developing more effective treatment strategies for HIV/AIDS. Multiple sequence alignments of drug-experienced HIV-1 protease sequences contain networks of many pair correlations which can be used to build a (Potts) Hamiltonian model of these mutation patterns. Using this Hamiltonian model, we translate HIV-1 protease sequence covariation data into quantitative predictions for the probability of observing specific mutation patterns which are in agreement with the observed sequence statistics. We find that the statistical energies of the Potts model are correlated with the fitness of individual proteins containing therapy-associated mutations as estimated by in vitro measurements of protein stability and viral infectivity. We show that the penalty for acquiring primary resistance mutations depends on the epistatic interactions with the sequence background. Primary mutations which lead to drug resistance can become highly advantageous (or entrenched) by the complex mutation patterns which arise in response to drug therapy despite being destabilizing in the wildtype background. Anticipating epistatic effects is important for the design of future protease inhibitor therapies.

Epistasis and Entropy

Epistasis is a key concept in the theory of adaptation. Indicators of epistasis are of interest for large systems where systematic fitness measurements may not be possible. Some recent approaches depend on information theory. We show that considering shared entropy for pairs of loci can be misleading. The reason is that shared entropy does not imply epistasis for the pair. This observation holds true also in the absence of higher order epistasis. We discuss a method for reducing the number of false positives. However, our main conclusion is that entropy-based approaches have serious limitations in this context.

Some recent approaches for identifying epistasis from sequence data depend on information theory. We show that considering shared entropy for pairs of loci can be misleading. The reason is that shared entropy does not imply epistasis for the pair. This observation holds true also in the absence of higher order epistasis. We discuss a method for reducing the number of false positives in the proposed method. However, our main conclusion is that shared entropy for pairs of loci is difficult to interpret. Gene frequencies reflect interactions in the entire system, and there is no natural way to decompose frequency data.

Potts Hamiltonian models of protein co-variation, free energy landscapes, and evolutionary fitness

Potts Hamiltonian models of protein sequence co-variation are statistical models constructed from the pair correlations observed in a multiple sequence alignment (MSA) of a protein family. These models are powerful because they capture higher order correlations induced by mutations evolving under constraints and help quantify the connections between protein sequence, structure, and function maintained through evolution. We review recent work with Potts models to predict protein structure and sequence-dependent conformational free energy landscapes, to survey protein fitness landscapes and to explore the effects of epistasis on fitness. We also comment on the numerical methods used to infer these models for each application.

What is information?†

Information is a precise concept that can be defined mathematically, but its relationship to what we call 'knowledge' is not always made clear. Furthermore, the concepts 'entropy' and 'information', while deeply related, are distinct and must be used with care, something that is not always achieved in the literature. In this elementary introduction, the concepts of entropy and information are laid out one by one, explained intuitively, but defined rigorously. I argue that a proper understanding of information in terms of prediction is key to a number of disciplines beyond engineering, such as physics and biology.

Information-Theoretic Considerations Concerning the Origin of Life

Research investigating the origins of life usually either focuses on exploring possible life-bearing chemistries in the pre-biotic Earth, or else on synthetic approaches. Comparatively little work has explored fundamental issues concerning the spontaneous emergence of life using only concepts (such as information and evolution) that are divorced from any particular chemistry. Here, I advocate studying the probability of spontaneous molecular self-replication as a function of the information contained in the replicator, and the environmental conditions that might enable this emergence. I show (under certain simplifying assumptions) that the probability to discover a self-replicator by chance depends exponentially on the relative rate of formation of the monomers. If the rate at which monomers are formed is somewhat similar to the rate at which they would occur in a self-replicating polymer, the likelihood to discover such a replicator by chance is increased by many orders of magnitude. I document such an increase in searches for a self-replicator within the digital life system avida.