Linking dynamical and population genetic models of persistent viral infection

Evolution of HIV-1 within untreated individuals and at the population scale in Uganda

HIV-1 undergoes multiple rounds of error-prone replication between transmission events, resulting in diverse viral populations within and among individuals. In addition, the virus experiences different selective pressures at multiple levels: during the course of infection, at transmission, and among individuals. Disentangling how these evolutionary forces shape the evolution of the virus at the population scale is important for understanding pathogenesis, how drug- and immune-escape variants are likely to spread in populations, and the development of preventive vaccines. To address this, we deep-sequenced two regions of the HIV-1 genome (p24 and gp41) from 34 longitudinally-sampled untreated individuals from Rakai District in Uganda, infected with subtypes A, D, and inter-subtype recombinants. This dataset substantially increases the availability of HIV-1 sequence data that spans multiple years of untreated infection, in particular for different geographical regions and viral subtypes. In line with previous studies, we estimated an approximately five-fold faster rate of evolution at the within-host compared to the population scale for both synonymous and nonsynonymous substitutions, and for all subtypes. We determined the extent to which this mismatch in evolutionary rates can be explained by the evolution of the virus towards population-level consensus, or the transmission of viruses similar to those that establish infection within individuals. Our findings indicate that both processes are likely to be important.

Effect of the Latent Reservoir on the Evolution of HIV at the Within- and Between-Host Levels

The existence of long-lived reservoirs of latently infected CD4+ T cells is the major barrier to curing HIV, and has been extensively studied in this light. However, the effect of these reservoirs on the evolutionary dynamics of the virus has received little attention. Here, we present a within-host quasispecies model that incorporates a long-lived reservoir, which we then nest into an epidemiological model of HIV dynamics. For biologically plausible parameter values, we find that the presence of a latent reservoir can severely delay evolutionary dynamics within a single host, with longer delays associated with larger relative reservoir sizes and/or homeostatic proliferation of cells within the reservoir. These delays can fundamentally change the dynamics of the virus at the epidemiological scale. In particular, the delay in within-host evolutionary dynamics can be sufficient for the virus to evolve intermediate viral loads consistent with maximising transmission, as is observed, and not the very high viral loads that previous models have predicted, an effect that can be further enhanced if viruses similar to those that initiate infection are preferentially transmitted. These results depend strongly on within-host characteristics such as the relative reservoir size, with the evolution of intermediate viral loads observed only when the within-host dynamics are sufficiently delayed. In conclusion, we argue that the latent reservoir has important, and hitherto under-appreciated, roles in both within- and between-host viral evolution.

The role of pathogen shedding in linking within- and between-host pathogen dynamics

A model linking within- and between-host pathogen dynamics via pathogen shedding (emission of pathogens throughout the course of infection) is developed, and several aspects of host availability and co-infection are considered. In this model, the rate of pathogen shedding affects both the pathogen population size within a host (also affecting host mortality) and the rate of infection of new hosts. Our goal is to ascertain how the rate of shedding is likely to evolve, and what factors permit coexistence of alternative shedding rates in a pathogen population. For a constant host population size (where an increase in infected hosts necessarily decreases susceptible hosts), important differences arise depending on whether pathogens compete only for susceptible (uninfected) hosts, or whether co-infection allows for competition for infected hosts. With no co-infection, the pathogen type that can persist with the lowest number of susceptible hosts will outcompete any other, which under the assumptions of the model is the pathogen with the highest basic reproduction number. This is often a pathogen with a relatively high shedding rate (s). If within-host competition is allowed, a trade-off develops due to the conflicting effects of shedding on within- and between-host pathogen dynamics, with within-host competition favoring clones with low shedding rates while between-host competition benefits clones with higher shedding rates. With within-host competition for the same host cells, low shedding rate clones should eliminate high-s clones in a co-infected host, if equilibrium is reached. With co-infection, but no within-host competition, pathogen clones still interact by affecting the mortality of co-infected hosts; here, coexistence is more likely. With co-infection, two clones can coexist if one is the superior competitor for uninfected hosts and the other for co-infected hosts.

Evolutionary reversion of live viral vaccines: Can genetic engineering subdue it?

Attenuated, live viral vaccines have been extraordinarily successful in protecting against many diseases. The main drawbacks in their development and use have been reliance on an unpredictable method of attenuation and the potential for evolutionary reversion to high virulence. Methods of genetic engineering now provide many safer alternatives to live vaccines, so if live vaccines are to compete with these alternatives in the future, they must either have superior immunogenicity or they must be able to overcome these former disadvantages. Several live vaccine designs that were historically inaccessible are now feasible because of advances in genome synthesis. Some of those methods are addressed here, with an emphasis on whether they enable predictable levels of attenuation and whether they are stable against evolutionary reversion. These new designs overcome many of the former drawbacks and position live vaccines to be competitive with alternatives. Not only do new methods appear to retard evolutionary reversion enough to prevent vaccine-derived epidemics, but it may even be possible to permanently attenuate live vaccines that are transmissible but cannot evolve to higher virulence under prolonged adaptation.

Baseline CD4+ T cell counts correlates with HIV-1 synonymous rate in HLA-B*5701 subjects with different risk of disease progression

HLA-B*5701 is the host factor most strongly associated with slow HIV-1 disease progression, although risk of progression may vary among patients carrying this allele. The interplay between HIV-1 evolutionary rate variation and risk of progression to AIDS in HLA-B*5701 subjects was studied using longitudinal viral sequences from high-risk progressors (HRPs) and low-risk progressors (LRPs). Posterior distributions of HIV-1 genealogies assuming a Bayesian relaxed molecular clock were used to estimate the absolute rates of nonsynonymous and synonymous substitutions for different set of branches. Rates of viral evolution, as well as in vitro viral replication capacity assessed using a novel phenotypic assay, were correlated with various clinical parameters. HIV-1 synonymous substitution rates were significantly lower in LRPs than HRPs, especially for sets of internal branches. The viral population infecting LRPs was also characterized by a slower increase in synonymous divergence over time. This pattern did not correlate to differences in viral fitness, as measured by in vitro replication capacity, nor could be explained by differences among subjects in T cell activation or selection pressure. Interestingly, a significant inverse correlation was found between baseline CD4⁺ T cell counts and mean HIV-1 synonymous rate (which is proportional to the viral replication rate) along branches representing viral lineages successfully propagating through time up to the last sampled time point. The observed lower replication rate in HLA-B*5701 subjects with higher baseline CD4⁺ T cell counts provides a potential model to explain differences in risk of disease progression among individuals carrying this allele.

The clinical course of HIV-1 infection is characterized by considerable variability in the rate of progression to acquired immunodeficiency syndrome (AIDS) among patients with different genetic background. The human leukocyte antigen (HLA) B*5701 is the host factor most strongly associated with slow HIV-1 disease progression. However, the risk of progression to AIDS also varies among patients carrying this specific allele. To gain a better understanding of the interplay between HIV-1 evolutionary rate variation and risk of disease progression, we followed untreated HLA-B*5701 subjects from early infection up to the onset of AIDS. The analysis of longitudinal viral sequences with advanced computational biology techniques based on coalescent Bayesian methods showed a highly significant association between lower synonymous substitution rates and higher baseline CD4⁺ T cell counts in HLA-B*5701 subjects. The finding provides a potential model to explain differences in risk of disease progression among individuals carrying this allele and might have translational impact on clinical practice, since synonymous rates, which are proportional to in vivo viral replication rates, could be used as a novel evolutionary marker of disease progression.

Viral substitution rate variation can arise from the interplay between within-host and epidemiological dynamics

The evolutionary rates of RNA viruses can differ from one another by several orders of magnitude. Much of this variation has been explained by differences in viral mutation rates and selective environments. However, substitution rates also vary considerably across viral populations belonging to the same species. In particular, viral lineages from epidemic regions tend to have higher substitution rates than those from endemic regions, and lineages from populations with higher contact rates tend to have higher substitution rates than those from populations with lower contact rates. We address the mechanism behind these patterns by using a nested modeling approach, whereby we integrate within-host viral replication dynamics with a population-level epidemiological model. Through numerical simulations and analytical approximations, we show that variation in viral substitution rates over the course of an infection, coupled with differences in age of infection of transmitting hosts under different epidemiological scenarios, can explain these evolutionary patterns. We further derive analytical estimates of expected substitution rate differences under epidemic versus endemic epidemiological conditions. By comparing these estimates to empirical data for four viral species, we show that these factors are sufficient to explain observed variation in substitution rates in three of four cases. This work shows that even in neutrally evolving viral populations, epidemiological dynamics can alter substitution rates via the interplay between within-host replication dynamics and population-level disease dynamics.

New insights into the evolutionary rate of HIV-1 at the within-host and epidemiological levels

Over calendar time, HIV-1 evolves considerably faster within individuals than it does at the epidemic level. This is a surprising observation since, from basic population genetic theory, we would expect the genetic substitution rate to be similar across different levels of biological organization. Three different mechanisms could potentially cause the observed mismatch in phylogenetic rates of divergence: temporal changes in selection pressure during the course of infection; frequent reversion of adaptive mutations after transmission; and the storage of the virus in the body followed by the preferential transmission of stored ancestral virus. We evaluate each of these mechanisms to determine whether they are likely to make a major contribution to the mismatch in phylogenetic rates. We conclude that the cycling of the virus through very long-lived memory CD4(+) T cells, a process that we call 'store and retrieve', is probably the major contributing factor to the rate mismatch. The preferential transmission of ancestral virus needs to be integrated into evolutionary models if we are to accurately predict the evolution of immune escape, drug resistance and virulence in HIV-1 at the population level. Moreover, early infection viruses should be the major target for vaccine design, because these are the viral strains primarily involved in transmission.

Phylogenetic and epidemic modeling of rapidly evolving infectious diseases

Epidemic modeling of infectious diseases has a long history in both theoretical and empirical research. However the recent explosion of genetic data has revealed the rapid rate of evolution that many populations of infectious agents undergo and has underscored the need to consider both evolutionary and ecological processes on the same time scale. Mathematical epidemiology has applied dynamical models to study infectious epidemics, but these models have tended not to exploit--or take into account--evolutionary changes and their effect on the ecological processes and population dynamics of the infectious agent. On the other hand, statistical phylogenetics has increasingly been applied to the study of infectious agents. This approach is based on phylogenetics, molecular clocks, genealogy-based population genetics and phylogeography. Bayesian Markov chain Monte Carlo and related computational tools have been the primary source of advances in these statistical phylogenetic approaches. Recently the first tentative steps have been taken to reconcile these two theoretical approaches. We survey the Bayesian phylogenetic approach to epidemic modeling of infection diseases and describe the contrasts it provides to mathematical epidemiology as well as emphasize the significance of the future unification of these two fields.

Optimal foraging by bacteriophages through host avoidance

Optimal foraging theory explains diet restriction as an adaptation to best utilize an array of foods differing in quality, the poorest items not worth the lost opportunity of finding better ones. Although optimal foraging has traditionally been applied to animal behavior, the model is easily applied to viral host range, which is genetically determined. The usual perspective for bacteriophages (bacterial viruses) is that expanding host range is always advantageous if fitness on former hosts is not compromised. However, foraging theory identifies conditions favoring avoidance of poor hosts even if larger host ranges have no intrinsic costs. Bacteriophage T7 rapidly evolved to discriminate among different Escherichia coli strains when one host strain was engineered to kill infecting phages but the other remained productive. After modifying bacteria to yield more subtle fitness effects on T7, we tested qualitative predictions of optimal foraging theory by competing broad and narrow host range phages against each other. Consistent with the foraging model, diet restriction was favored when good hosts were common or there was a large difference in host quality. Contrary to the model, the direction of selection was affected by the density of poor hosts because being able to discriminate was costly.

Evolutionary analysis of the dynamics of viral infectious disease

Many organisms that cause infectious diseases, particularly RNA viruses, mutate so rapidly that their evolutionary and ecological behaviours are inextricably linked. Consequently, aspects of the transmission and epidemiology of these pathogens are imprinted on the genetic diversity of their genomes. Large-scale empirical analyses of the evolutionary dynamics of important pathogens are now feasible owing to the increasing availability of pathogen sequence data and the development of new computational and statistical methods of analysis. In this Review, we outline the questions that can be answered using viral evolutionary analysis across a wide range of biological scales.

Adaptation to human populations is revealed by within-host polymorphisms in HIV-1 and hepatitis C virus

CD8(+) cytotoxic T-lymphocytes (CTLs) perform a critical role in the immune control of viral infections, including those caused by human immunodeficiency virus type 1 (HIV-1) and hepatitis C virus (HCV). As a result, genetic variation at CTL epitopes is strongly influenced by host-specific selection for either escape from the immune response, or reversion due to the replicative costs of escape mutations in the absence of CTL recognition. Under strong CTL-mediated selection, codon positions within epitopes may immediately "toggle" in response to each host, such that genetic variation in the circulating virus population is shaped by rapid adaptation to immune variation in the host population. However, this hypothesis neglects the substantial genetic variation that accumulates in virus populations within hosts. Here, we evaluate this quantity for a large number of HIV-1- (n > or = 3,000) and HCV-infected patients (n > or = 2,600) by screening bulk RT-PCR sequences for sequencing "mixtures" (i.e., ambiguous nucleotides), which act as site-specific markers of genetic variation within each host. We find that nonsynonymous mixtures are abundant and significantly associated with codon positions under host-specific CTL selection, which should deplete within-host variation by driving the fixation of the favored variant. Using a simple model, we demonstrate that this apparently contradictory outcome can be explained by the transmission of unfavorable variants to new hosts before they are removed by selection, which occurs more frequently when selection and transmission occur on similar time scales. Consequently, the circulating virus population is shaped by the transmission rate and the disparity in selection intensities for escape or reversion as much as it is shaped by the immune diversity of the host population, with potentially serious implications for vaccine design.

Modeling Within-Host Evolution of HIV: Mutation, Competition and Strain Replacement

Virus evolution during infection of a single individual is a well-known feature of disease progression in chronic viral diseases. However, the simplest models of virus competition for host resources show the existence of a single dominant strain that grows most rapidly during the initial period of infection and competitively excludes all other virus strains. Here, we examine the dynamics of strain replacement in a simple model that includes a convex trade-off between rapid virus reproduction and long-term host cell survival. Strains are structured according to their within-cell replication rate. Over the course of infection, we find a progression in the dominant strain from fast- to moderately-replicating virus strains featuring distinct jumps in the replication rate of the dominant strain over time. We completely analyze the model and provide estimates for the replication rate of the initial dominant strain and its successors. Our model lays the groundwork for more detailed models of HIV selection and mutation. We outline future directions and application of related models to other biological situations.

Synonymous substitution rates predict HIV disease progression as a result of underlying replication dynamics

Upon HIV transmission, some patients develop AIDS in only a few months, while others remain disease free for 20 or more years. This variation in the rate of disease progression is poorly understood and has been attributed to host genetics, host immune responses, co-infection, viral genetics, and adaptation. Here, we develop a new “relaxed-clock” phylogenetic method to estimate absolute rates of synonymous and nonsynonymous substitution through time. We identify an unexpected association between the synonymous substitution rate of HIV and disease progression parameters. Since immune activation is the major determinant of HIV disease progression, we propose that this process can also determine viral generation times, by creating favourable conditions for HIV replication. These conclusions may apply more generally to HIV evolution, since we also observed an overall low synonymous substitution rate for HIV-2, which is known to be less pathogenic than HIV-1 and capable of tempering the detrimental effects of immune activation. Humoral immune responses, on the other hand, are the major determinant of nonsynonymous rate changes through time in the envelope gene, and our relaxed-clock estimates support a decrease in selective pressure as a consequence of immune system collapse.

During the clinical course of HIV infection, an asymptomatic phase always precedes the acquired immunodeficiency syndrome (AIDS). The duration of this asymptomatic phase is highly variable among patients and reflects the rate at which the immune system gradually deteriorates. Although humoral and cell-mediated immune responses are mounted against HIV, continuous replication and adaptation allows the virus to escape host immune responses. To gain a better understanding of the role of viral evolution in disease progression, we developed a new computational technique that can estimate changes in the absolute rates of synonymous and nonsynonymous divergence through time from molecular sequences. Using this type of evolutionary inference, we have identified a previously unknown association between the “silent” evolutionary rate of HIV and the rate of disease progression in infected individuals. This finding demonstrates that cellular immune processes, which are already known to determine HIV pathogenesis, also determine viral replication rates and therefore impose important constraints on HIV evolution.

Optimality models of phage life history and parallels in disease evolution

Optimality models constitute one of the simplest approaches to understanding phenotypic evolution. Yet they have shortcomings that are not easily evaluated in most organisms. Most importantly, the genetic basis of phenotype evolution is almost never understood, and phenotypic selection experiments are rarely possible. Both limitations can be overcome with bacteriophages. However, phages have such elementary life histories that few phenotypes seem appropriate for optimality approaches. Here we develop optimality models of two phage life history traits, lysis time and host range. The lysis time models show that the optimum is less sensitive to differences in host density than suggested by earlier analytical work. Host range evolution is approached from the perspective of whether the virus should avoid particular hosts, and the results match optimal foraging theory: there is an optimal "diet" in which host types are either strictly included or excluded, depending on their infection qualities. Experimental tests of both models are feasible, and phages provide concrete illustrations of many ways that optimality models can guide understanding and explanation. Phage genetic systems already support the perspective that lysis time and host range can evolve readily and evolve without greatly affecting other traits, one of the main tenets of optimality theory. The models can be extended to more general properties of infection, such as the evolution of virulence and tissue tropism.

Evolutionary Feedback Mediated through Population Density, Illustrated with Viruses in Chemostats

A cornerstone of evolutionary ecology is that population density affects adaptation: r and K selection is the obvious example. The reverse is also appreciated: adaptation impacts population density. Yet, empirically demonstrating a direct connection between population density and adaptation is challenging. Here, we address both evolution and ecology of population density in models of viral (bacteriophage) chemostats. Chemostats supply nutrients for host cell growth, and the hosts are prey for viral reproduction. Two different chemostat designs have profoundly different consequences for viral evolution. If host and virus are confined to the same chamber, as in a predator-prey system, viral regulation of hosts feeds back to maintain low viral density (measured as infections per cell). Viral adaptation impacts host density but has a small effect on equilibrium viral density. More interesting are chemostats that supply the viral population with hosts from a virus-free refuge. Here, a type of evolutionary succession operates: adaptation at low viral density leads to higher density, but high density then favors competitive ability. Experiments support these models with both phenotypic and molecular data. Parallels to these designs exist in many natural systems, so these experimental systems may yield insights to the evolution and regulation of natural populations.

Viral infection in internally structured hosts. I. Conditions for persistent infection

For a virus population within its host, two important levels of structure can be considered: multiple cell types which can be infected, and tissue types or body compartments which may be coupled via movement. We develop a model with both types of structure. Migration between compartments can create "sources" and "sinks" within the virus population, where realized viral growth rate and abundance is lowered in some compartments compared to what would be observed in isolation. Using both analytical and numerical methods, we investigate how this within-host spatial structure affects the conditions for persistent viral infection. We find that migration between compartments makes the establishment of infection more difficult than it would be in the absence of migration, implying that within-host spatial structure combined with viral movement decreases the likelihood of viral establishment. If migration is symmetrical and compartments are heterogeneous, an increase in migration rates between compartments generally makes establishment less likely. This may help to explain the tissue specificity observed for many viruses. There are, however, important exceptions to this result. These include circumstances where the virus initially invades a compartment that is unfavorable to population growth and migration is necessary to infect other parts of the host body. Stochastic aspects of viral establishment may also favor increased migration as it tends to dampen the amplitude of fluctuations in population size during the initial transient phase of establishment.

A statistical characterization of consistent patterns of human immunodeficiency virus evolution within infected patients

Within-patient HIV populations evolve rapidly because of a high mutation rate, short generation time, and strong positive selection pressures. Previous studies have identified "consistent patterns" of viral sequence evolution. Just before HIV infection progresses to AIDS, evolution seems to slow markedly, and the genetic diversity of the viral population drops. This evolutionary slowdown could be caused either by a reduction in the average viral replication rate or because selection pressures weaken with the collapse of the immune system. The former hypothesis (which we denote "cellular exhaustion") predicts a simultaneous reduction in both synonymous and nonsynonymous evolution, whereas the latter hypothesis (denoted "immune relaxation") predicts that only nonsynonymous evolution will slow. In this paper, we present a set of statistical procedures for distinguishing between these alternative hypotheses using DNA sequences sampled over the course of infection. The first component is a new method for estimating evolutionary rates that takes advantage of the temporal information in longitudinal DNA sequence samples. Second, we develop a set of probability models for the analysis of evolutionary rates in HIV populations in vivo. Application of these models to both synonymous and nonsynonymous evolution affords a comparison of the cellular-exhaustion and immune-relaxation hypotheses. We apply the procedures to longitudinal data sets in which sequences of the env gene were sampled over the entire course of infection. Our analyses (1) statistically confirm that an evolutionary slowdown occurs late in infection, (2) strongly support the immune-relaxation hypothesis, and (3) indicate that the cessation of nonsynonymous evolution is associated with disease progression.

Modelling the past and future of whales and whaling

Historical reconstruction of the population dynamics of whales before, during and after exploitation is crucial to marine ecological restoration and for the consideration of future commercial whaling. Population dynamic models used by the International Whaling Commission require historical catch records, estimates of intrinsic rates of increase and current abundance, all of which are subject to considerable uncertainty. Population genetic parameters can be used for independent estimates of historical demography, but also have large uncertainty, particularly for rates of mutational substitution and gene flow. At present, demographic and genetic estimates of pre-exploitation abundance differ by an order of magnitude and, consequently, suggest vastly different baselines for judging recovery. Here, we review these two approaches and suggest the need for a synthetic analytical framework to evaluate uncertainty in key parameters. Such a framework could have broad application to modelling both historical and contemporary population dynamics in other exploited species.

Dynamic determination and analysis of serum virus load in patients with chronic HBV infection

AIM: To observe the variation of viral load and characteristics of within-host dynamics in patients with chronic hepatitis B virus infection without receiving antiviral therapy.

METHODS: Serum was collected consecutively from 3 patients with different clinical phenotype, ALT and total bilirubin were determined, and HBV DNA was measured by quantitative TaqMan fluorogenic PCR.

RESULTS: Spontaneous fluctuations of HBV DNA load were observed when measured daily, wkly and moly in our untreated patients with chronic HBV infection, but there was no determinate correlation between HBV DNA loads and ALT values.

CONCLUSION: The spontaneous fluctuation of viral load in untreated patients with different clinical phenotype displays some characteristic patterns. Here we propose a PID pattern for host feedback to virus using population quantity of HBV as variant, which may be used for the prediction of virus-host ecological evolution in persistent HBV infection.