Long-range linkage effects in adapting sexual populations.

In sexual populations, closely-situated genes have linked evolutionary fates, while genes spaced far in genome are commonly thought to evolve independently due to recombination. In the case where evolution depends essentially on supply of new mutations, this assumption has been confirmed by mathematical modeling. Here I examine it in the case of pre-existing genetic variation, where mutation is not important. A haploid population with [Formula: see text] genomes, [Formula: see text] loci, a fixed selection coefficient, and a small initial frequency of beneficial alleles [Formula: see text] is simulated by a Monte-Carlo algorithm. When the number of loci, L, is larger than a critical value of [Formula: see text] simulation demonstrates a host of linkage effects that decrease neither with the distance between loci nor the number of recombination crossovers. Due to clonal interference, the beneficial alleles become extinct at a fraction of loci [Formula: see text]. Due to a genetic background effect, the substitution rate varies broadly between loci, with the fastest value exceeding the one-locus limit by the factor of [Formula: see text] Thus, the far-situated parts of a long genome in a sexual population do not evolve as independent blocks. A potential link between these findings and the emergence of new Variants of Concern of SARS-CoV-2 is discussed.

Evolutionary implications of SARS-CoV-2 vaccination for the future design of vaccination strategies.

Once the first SARS-CoV-2 vaccine became available, mass vaccination was the main pillar of the public health response to the COVID-19 pandemic. It was very effective in reducing hospitalizations and deaths. Here, we discuss the possibility that mass vaccination might accelerate SARS-CoV-2 evolution in antibody-binding regions compared to natural infection at the population level. Using the evidence of strong genetic variation in antibody-binding regions and taking advantage of the similarity between the envelope proteins of SARS-CoV-2 and influenza, we assume that immune selection pressure acting on these regions of the two viruses is similar. We discuss the consequences of this assumption for SARS-CoV-2 evolution in light of mathematical models developed previously for influenza. We further outline the implications of this phenomenon, if our assumptions are confirmed, for the future design of SARS-CoV-2 vaccination strategies.

Measurement of selection coefficients from genomic samples of adapting populations by computer modeling.

The existing protocols of measuring the selection coefficients of loci neglect linkage effects existing between loci. This protocol is free from this limitation. The protocol inputs a set of DNA sequences at three time points, removes conserved sites, and estimates selection coefficients. If the user wishes to test the accuracy, it can ask the protocol to generate mock data by computer simulation of evolution. The main limitation is the need for sequence samples isolated from 30-100 populations adapting in parallel. For complete details on the use and execution of this protocol, please refer to Barlukova and Rouzine (2021).

A role for CD4 + helper cells in HIV control and progression.

OBJECTIVE: It remains unclear why HIV persists in most untreated individuals, and why a small minority of individuals can control the virus, either spontaneously or after an early treatment. Striking differences have been discovered between patient cohorts in CD4 + T-cell avidity but not in CD8 + T-cell avidity. The present work has the aim to explain the diverse outcome of infection and identify the key virological and immunological parameters predicting the outcome. DESIGN AND METHOD: A mathematical model informed by these experiments and taking into account the details of HIV virology is developed. RESULTS: The model predicts an arms race between viral dissemination and the proliferation of HIV-specific CD4 + helper cells leading to one of two states: a low-viremia state (controller) or a high-viremia state (progressor). Helper CD4 + cells with a higher avidity favor virus control. The parameter segregating spontaneous and posttreatment controllers is the infectivity difference between activated and resting CD4 + T cells. The model is shown to have a better connection to experiment than a previous model based on T-cell 'exhaustion'. CONCLUSION: Using the model informed by patient data, the timing of antiretroviral therapy can be optimized.

Experimental and mathematical insights on the interactions between poliovirus and a defective interfering genome.

During replication, RNA viruses accumulate genome alterations, such as mutations and deletions. The interactions between individual variants can determine the fitness of the virus population and, thus, the outcome of infection. To investigate the effects of defective interfering genomes (DI) on wild-type (WT) poliovirus replication, we developed an ordinary differential equation model, which enables exploring the parameter space of the WT and DI competition. We also experimentally examined virus and DI replication kinetics during co-infection, and used these data to infer model parameters. Our model identifies, and our experimental measurements confirm, that the efficiencies of DI genome replication and encapsidation are two most critical parameters determining the outcome of WT replication. However, an equilibrium can be established which enables WT to replicate, albeit to reduced levels.

An evolution-based high-fidelity method of epistasis measurement: Theory and application to influenza.

Linkage effects in a multi-locus population strongly influence its evolution. The models based on the traveling wave approach enable us to predict the average speed of evolution and the statistics of phylogeny. However, predicting statistically the evolution of specific sites and pairs of sites in the multi-locus context remains a mathematical challenge. In particular, the effects of epistasis, the interaction of gene regions contributing to phenotype, is difficult to predict theoretically and detect experimentally in sequence data. A large number of false-positive interactions arises from stochastic linkage effects and indirect interactions, which mask true epistatic interactions. Here we develop a proof-of-principle method to filter out false-positive interactions. We start by demonstrating that the averaging of haplotype frequencies over multiple independent populations is necessary but not sufficient for epistatic detection, because it still leaves high numbers of false-positive interactions. To compensate for the residual stochastic noise, we develop a three-way haplotype method isolating true interactions. The fidelity of the method is confirmed analytically and on simulated genetic sequences evolved with a known epistatic network. The method is then applied to a large sequence database of neurominidase protein of influenza A H1N1 obtained from various geographic locations to infer the epistatic network responsible for the difference between the pre-pandemic virus and the pandemic strain of 2009. These results present a simple and reliable technique to measure epistatic interactions of any sign from sequence data.

The evolutionary origin of the universal distribution of mutation fitness effect.

An intriguing fact long defying explanation is the observation of a universal exponential distribution of beneficial mutations in fitness effect for different microorganisms. To explain this effect, we use a population model including mutation, directional selection, linkage, and genetic drift. The multiple-mutation regime of adaptation at large population sizes (traveling wave regime) is considered. We demonstrate analytically and by simulation that, regardless of the inherent distribution of mutation fitness effect across genomic sites, an exponential distribution of fitness effects emerges in the long term. This result follows from the exponential statistics of the frequency of the less-fit alleles, f, that we predict to evolve, in the long term, for both polymorphic and monomorphic sites. We map the logarithmic slope of the distribution onto the previously derived fixation probability and demonstrate that it increases linearly in time. Our results demonstrate a striking difference between the distribution of fitness effects observed experimentally for naturally occurring mutations, and the "inherent" distribution obtained in a directed-mutagenesis experiment, which can have any shape depending on the organism. Based on these results, we develop a new method to measure the fitness effect of mutations for each variable residue using DNA sequences sampled from adapting populations. This new method is not sensitive to linkage effects and does not require the one-site model assumptions.

An Evolutionary Model of Progression to AIDS.

The time to the onset of AIDS symptoms in an HIV infected individual is known to correlate inversely with viremia and the level of immune activation. The correlation exists against the background of strong individual fluctuations demonstrating the existence of hidden variables depending on patient and virus parameters. At the moment, prognosis of the time to AIDS based on patient parameters is not possible. In addition, it is of paramount importance to understand the reason of progression to AIDS in untreated patients to be able to learn to control it by means other than anti-retroviral therapy. Here we develop a mechanistic mathematical model to predict the speed of progression to AIDS in individual untreated patients and patients treated with suboptimal therapy, based on a single-time measurement of several virological and immunological parameters. We show that the gradual increase in virus fitness during a chronic infection causes slow gradual depletion of CD4 T cells. Using the existing evolution models of HIV, we obtain general expressions predicting the time to the onset of AIDS symptoms in terms of the patient parameters, for low-viremia and high-viremia patients separately. We show that the evolution model of AIDS fits the existing data on virus-time correlations better than the alternative model of the deregulation of homeostatic response.

Correction: Antigenic evolution of viruses in host populations.

[This corrects the article DOI: 10.1371/journal.ppat.1007291.].

Epistasis detectably alters correlations between genomic sites in a narrow parameter window.

Different genomic sites evolve inter-dependently due to the combined action of epistasis, defined as a non-multiplicative contribution of alleles at different loci to genome fitness, and the physical linkage of different loci in genome. Both epistasis and linkage, partially compensated by recombination, cause correlations between allele frequencies at the loci (linkage disequilibrium, LD). The interaction and competition between epistasis and linkage are not fully understood, nor is their relative sensitivity to recombination. Modeling an adapting population in the presence of random mutation, natural selection, pairwise epistasis, and random genetic drift, we compare the contributions of epistasis and linkage. For this end, we use a panel of haplotype-based measures of LD and their various combinations calculated for epistatic and non-epistatic pairs separately. We compute the optimal percentages of detected and false positive pairs in a one-time sample of a population of moderate size. We demonstrate that true interacting pairs can be told apart in a sufficiently short genome within a narrow window of time and parameters. Outside of this parameter region, unless the population is extremely large, shared ancestry of individual sequences generates pervasive stochastic LD for non-interacting pairs masking true epistatic associations. In the presence of sufficiently strong recombination, linkage effects decrease faster than those of epistasis, and the detection of epistasis improves. We demonstrate that the epistasis component of locus association can be isolated, at a single time point, by averaging haplotype frequencies over multiple independent populations. These results demonstrate the existence of fundamental restrictions on the protocols for detecting true interactions in DNA sequence sets.

Antigenic evolution of viruses in host populations.

To escape immune recognition in previously infected hosts, viruses evolve genetically in immunologically important regions. The host's immune system responds by generating new memory cells recognizing the mutated viral strains. Despite recent advances in data collection and analysis, it remains conceptually unclear how epidemiology, immune response, and evolutionary factors interact to produce the observed speed of evolution and the incidence of infection. Here we establish a general and simple relationship between long-term cross-immunity, genetic diversity, speed of evolution, and incidence. We develop an analytic method fusing the standard epidemiological susceptible-infected-recovered approach and the modern virus evolution theory. The model includes the factors of strain selection due to immune memory cells, random genetic drift, and clonal interference effects. We predict that the distribution of recovered individuals in memory serotypes creates a moving fitness landscape for the circulating strains which drives antigenic escape. The fitness slope (effective selection coefficient) is proportional to the reproductive number in the absence of immunity R0 and inversely proportional to the cross-immunity distance a, defined as the genetic distance of a virus strain from a previously infecting strain conferring 50% decrease in infection probability. Analysis predicts that the evolution rate increases linearly with the fitness slope and logarithmically with the genomic mutation rate and the host population size. Fitting our analytic model to data obtained for influenza A H3N2 and H1N1, we predict the annual infection incidence within a previously estimated range, (4-7)%, and the antigenic mutation rate of Ub = (5 - 8) ⋅ 10(-4) per transmission event per genome. Our prediction of the cross-immunity distance of a = (14 - 15) aminoacid substitutions agrees with independent data for equine influenza.

Evolutionary footprint of epistasis.

Variation of an inherited trait across a population cannot be explained by additive contributions of relevant genes, due to epigenetic effects and biochemical interactions (epistasis). Detecting epistasis in genomic data still represents a significant challenge that requires a better understanding of epistasis from the mechanistic point of view. Using a standard Wright-Fisher model of bi-allelic asexual population, we study how compensatory epistasis affects the process of adaptation. The main result is a universal relationship between four haplotype frequencies of a single site pair in a genome, which depends only on the epistasis strength of the pair defined regarding Darwinian fitness. We demonstrate the existence, at any time point, of a quasi-equilibrium between epistasis and disorder (entropy) caused by random genetic drift and mutation. We verify the accuracy of these analytic results by Monte-Carlo simulation over a broad range of parameters, including the topology of the interacting network. Thus, epistasis assists the evolutionary transit through evolutionary hurdles leaving marks at the level of haplotype disequilibrium. The method allows determining selection coefficient for each site and the epistasis strength of each pair from a sequence set. The resulting ability to detect clusters of deleterious mutation close to full compensation is essential for biomedical applications. These findings help to understand the role of epistasis in multiple compensatory mutations in viral resistance to antivirals and immune response.

Variability in viral pathogenesis: modeling the dynamic of acute and persistent infections.

Virus infection often results in diverse outcomes. This variability of virus pathogenesis is not well understood. Here we revise theoretical arguments to further our understanding of factors controlling infection and its severity. We propose that variability in these factors results in different clinical outcomes, which ultimately ensure virus reproduction.

Conflicting Selection Pressures Will Constrain Viral Escape from Interfering Particles: Principles for Designing Resistance-Proof Antivirals.

The rapid evolution of RNA-encoded viruses such as HIV presents a major barrier to infectious disease control using conventional pharmaceuticals and vaccines. Previously, it was proposed that defective interfering particles could be developed to indefinitely control the HIV/AIDS pandemic; in individual patients, these engineered molecular parasites were further predicted to be refractory to HIV's mutational escape (i.e., be 'resistance-proof'). However, an outstanding question has been whether these engineered interfering particles-termed Therapeutic Interfering Particles (TIPs)-would remain resistance-proof at the population-scale, where TIP-resistant HIV mutants may transmit more efficiently by reaching higher viral loads in the TIP-treated subpopulation. Here, we develop a multi-scale model to test whether TIPs will maintain indefinite control of HIV at the population-scale, as HIV ('unilaterally') evolves toward TIP resistance by limiting the production of viral proteins available for TIPs to parasitize. Model results capture the existence of two intrinsic evolutionary tradeoffs that collectively prevent the spread of TIP-resistant HIV mutants in a population. First, despite their increased transmission rates in TIP-treated sub-populations, unilateral TIP-resistant mutants are shown to have reduced transmission rates in TIP-untreated sub-populations. Second, these TIP-resistant mutants are shown to have reduced growth rates (i.e., replicative fitness) in both TIP-treated and TIP-untreated individuals. As a result of these tradeoffs, the model finds that TIP-susceptible HIV strains continually outcompete TIP-resistant HIV mutants at both patient and population scales when TIPs are engineered to express >3-fold more genomic RNA than HIV expresses. Thus, the results provide design constraints for engineering population-scale therapies that may be refractory to the acquisition of antiviral resistance.

RNA Recombination Enhances Adaptability and Is Required for Virus Spread and Virulence.

Mutation and recombination are central processes driving microbial evolution. A high mutation rate fuels adaptation but also generates deleterious mutations. Recombination between two different genomes may resolve this paradox, alleviating effects of clonal interference and purging deleterious mutations. Here we demonstrate that recombination significantly accelerates adaptation and evolution during acute virus infection. We identified a poliovirus recombination determinant within the virus polymerase, mutation of which reduces recombination rates without altering replication fidelity. By generating a panel of variants with distinct mutation rates and recombination ability, we demonstrate that recombination is essential to enrich the population in beneficial mutations and purge it from deleterious mutations. The concerted activities of mutation and recombination are key to virus spread and virulence in infected animals. These findings inform a mathematical model to demonstrate that poliovirus adapts most rapidly at an optimal mutation rate determined by the trade-off between selection and accumulation of detrimental mutations.

A hardwired HIV latency program.

Biological circuits can be controlled by two general schemes: environmental sensing or autonomous programs. For viruses such as HIV, the prevailing hypothesis is that latent infection is controlled by cellular state (i.e., environment), with latency simply an epiphenomenon of infected cells transitioning from an activated to resting state. However, we find that HIV expression persists despite the activated-to-resting cellular transition. Mathematical modeling indicates that HIV's Tat positive-feedback circuitry enables this persistence and strongly controls latency. To overcome the inherent crosstalk between viral circuitry and cellular activation and to directly test this hypothesis, we synthetically decouple viral dependence on cellular environment from viral transcription. These circuits enable control of viral transcription without cellular activation and show that Tat feedback is sufficient to regulate latency independent of cellular activation. Overall, synthetic reconstruction demonstrates that a largely autonomous, viral-encoded program underlies HIV latency­potentially explaining why cell-targeted latency-reversing agents exhibit incomplete penetrance.

An evolutionary role for HIV latency in enhancing viral transmission.

HIV latency is the chief obstacle to eradicating HIV but is widely believed to be an evolutionary accident providing no lentiviral fitness advantage. However, findings of latency being "hardwired" into HIV's gene-regulatory circuitry appear inconsistent with latency being an evolutionary accident, given HIV's rapid mutation rate. Here, we propose that latency is an evolutionary "bet-hedging" strategy whose frequency has been optimized to maximize lentiviral transmission by reducing viral extinction during mucosal infections. The model quantitatively fits the available patient data, matches observations of high-frequency latency establishment in cell culture and primates, and generates two counterintuitive but testable predictions. The first prediction is that conventional CD8-depletion experiments in SIV-infected macaques increase latent cells more than viremia. The second prediction is that strains engineered to have higher replicative fitness­via reduced latency­will exhibit lower infectivity in animal-model mucosal inoculations. Therapeutically, the theory predicts treatment approaches that may substantially enhance "activate-and-kill" HIV-cure strategies.

The route of HIV escape from immune response targeting multiple sites is determined by the cost-benefit tradeoff of escape mutations.

Cytotoxic T lymphocytes (CTL) are a major factor in the control of HIV replication. CTL arise in acute infection, causing escape mutations to spread rapidly through the population of infected cells. As a result, the virus develops partial resistance to the immune response. The factors controlling the order of mutating epitope sites are currently unknown and would provide a valuable tool for predicting conserved epitopes. In this work, we adapt a well-established mathematical model of HIV evolution under dynamical selection pressure from multiple CTL clones to include partial impairment of CTL recognition, [Formula: see text], as well as cost to viral replication, [Formula: see text]. The process of escape is described in terms of the cost-benefit tradeoff of escape mutations and predicts a trajectory in the cost-benefit plane connecting sequentially escaped sites, which moves from high recognition loss/low fitness cost to low recognition loss/high fitness cost and has a larger slope for early escapes than for late escapes. The slope of the trajectory offers an interpretation of positive correlation between fitness costs and HLA binding impairment to HLA-A molecules and a protective subset of HLA-B molecules that was observed for clinically relevant escape mutations in the Pol gene. We estimate the value of [Formula: see text] from published experimental studies to be in the range (0.01-0.86) and show that the assumption of complete recognition loss ([Formula: see text]) leads to an overestimate of mutation cost. Our analysis offers a consistent interpretation of the commonly observed pattern of escape, in which several escape mutations are observed transiently in an epitope. This non-nested pattern is a combined effect of temporal changes in selection pressure and partial recognition loss. We conclude that partial recognition loss is as important as fitness loss for predicting the order of escapes and, ultimately, for predicting conserved epitopes that can be targeted by vaccines.