Evolutionary Invasion and Escape in the Presence of Deleterious Mutations

Replicators such as parasites invading a new host species, species invading a new ecological niche, or cancer cells invading a new tissue often must mutate to adapt to a new environment. It is often argued that a higher mutation rate will favor evolutionary invasion and escape from extinction. However, most mutations are deleterious, and even lethal. We study the probability that the lineage will survive and invade successfully as a function of the mutation rate when both the initial strain and an adaptive mutant strain are threatened by lethal mutations. We show that mutations are beneficial, i.e. a non-zero mutation rate increases survival compared to the limit of no mutations, if in the no-mutation limit the survival probability of the initial strain is smaller than the average survival probability of the strains which are one mutation away. The mutation rate that maximizes survival depends on the characteristics of both the initial strain and the adaptive mutant, but if one strain is closer to the threshold governing survival then its properties will have greater influence. These conclusions are robust for more realistic or mechanistic depictions of the fitness landscapes such as a more detailed viral life history, or non-lethal deleterious mutations.     

INFLUENCE OF VIRAL REPLICATION MECHANISMS ON WITHIN‐HOST EVOLUTIONARY DYNAMICS

Viruses replicate their genomes using a variety of mechanisms, leading to different distributions of mutations among their progeny. Yet, models of viral evolution often only consider the mean mutation rate. To investigate when and how replication mechanisms impact viral evolution, we analyze the early dynamics of within‐host infection for two idealized cases: when all offspring virions from an infected cell carry the same genotype, mutated or not; and when mutations occur independently across offspring virions. Other replication life histories fall between these extremes. Using branching process models, we study the probability that viral infection becomes established when mutations are lethal, and in the more general case of two strains of different fitness. For a given mean mutation rate, we show that a lineage of viruses with correlated mutations is less likely to survive than with independent mutations, but when it survives, the viral population grows faster. While this holds true for all parameter regimes, replication life history has a quantitatively significant influence on viral dynamics when stochastic effects are important and when mutations are crucial for survival—conditions typical of evolutionary escape situations.     

Reversion of CTL escape-variant immunodeficiency viruses in vivo

Engendering cytotoxic T-lymphocyte (CTL) responses is likely to be an important goal of HIV vaccines. However, CTLs select for viral variants that escape immune detection. Maintenance of such escape variants in human populations could pose an obstacle to HIV vaccine development. We first observed that escape mutations in a heterogeneous simian immunodeficiency virus (SIV) isolate were lost upon passage to new animals. We therefore infected macaques with a cloned SIV bearing escape mutations in three immunodominant CTL epitopes, and followed viral evolution after infection. Here we show that each mutant epitope sequence continued to evolve in vivo, often re-establishing the original, CTL-susceptible sequence. We conclude that escape from CTL responses may exact a cost to viral fitness. In the absence of selective pressure upon transmission to new hosts, these original escape mutations can be lost. This suggests that some HIV CTL epitopes will be maintained in human populations.     

The balance between mutators and nonmutators in asexual populations

Mutator alleles, which elevate an individual's mutation rate from 10 to 10,000-fold, have been found at high frequencies in many natural and experimental populations. Mutators are continually produced from nonmutators, often due to mutations in mismatch-repair genes. These mutators gradually accumulate deleterious mutations, limiting their spread. However, they can occasionally hitchhike to high frequencies with beneficial mutations. We study the interplay between these effects. We first analyze the dynamics of the balance between the production of mutator alleles and their elimination due to deleterious mutations. We find that when deleterious mutation rates are high in mutators, there will often be many "young," recently produced mutators in the population, and the fact that deleterious mutations only gradually eliminate individuals from a population is important. We then consider how this mutator-nonmutator balance can be disrupted by beneficial mutations and analyze the circumstances in which fixation of mutator alleles is likely. We find that dynamics is crucial: even in situations where selection on average acts against mutators, so they cannot stably invade, the mutators can still occasionally generate beneficial mutations and hence be important to the evolution of the population.     

The exoneme helps malaria parasites to break out of blood cells

Malaria parasites must invade the erythrocytes of its host, to be able to grow and multiply. Having depleted the host cell of its nutrients, the parasites break out to invade new erythrocytes. In this issue of Cell, Yeoh et al. (2007) discover a new organelle, the exoneme, that contains a protease SUB1, which helps the parasite to escape from old erythrocytes and invade new ones.     

Niche opportunities and invasion dynamics in a desert annual community

Although many factors influence the ability of exotics to invade successfully, most studies focus on only a few variables to explain invasion; attempts at theoretical synthesis are largely untested. The niche opportunities framework proposes that the demographic success of an invader is largely affected by the availability of resources and the abundance of its enemies. Here, we use a 31‐year study from a desert ecosystem to examine the niche opportunities framework via the invasion of the annual plant Erodium cicutarium. While the invader remained rare for two decades, a decline in granivory combined with an ideal climate window created an opportunity for E. cicutarium to escape control and become the dominant annual plant in the community. We show that fluctuations in consumption and resources can create niche opportunities for invaders and highlight the need for additional long‐term studies to track the influence of changing climate and community dynamics on invasions.     

The role of recombination for the coevolutionary dynamics of HIV and the immune response

The evolutionary implications of recombination in HIV remain not fully understood. A plausible effect could be an enhancement of immune escape from cytotoxic T lymphocytes (CTLs). In order to test this hypothesis, we constructed a population dynamic model of immune escape in HIV and examined the viral-immune dynamics with and without recombination. Our model shows that recombination (i) increases the genetic diversity of the viral population, (ii) accelerates the emergence of escape mutations with and without compensatory mutations, and (iii) accelerates the acquisition of immune escape mutations in the early stage of viral infection. We see a particularly strong impact of recombination in systems with broad, non-immunodominant CTL responses. Overall, our study argues for the importance of recombination in HIV in allowing the virus to adapt to changing selective pressures as imposed by the immune system and shows that the effect of recombination depends on the immunodominance pattern of effector T cell responses.     

Fitness costs and diversity of the cytotoxic T lymphocyte (CTL) response determine the rate of CTL escape during acute and chronic phases of HIV infection

HIV-1 often evades cytotoxic T cell (CTL) responses by generating variants that are not recognized by CTLs. We used single-genome amplification and sequencing of complete HIV genomes to identify longitudinal changes in the transmitted/founder virus from the establishment of infection to the viral set point at 1 year after the infection. We found that the rate of viral escape from CTL responses in a given patient decreases dramatically from acute infection to the viral set point. Using a novel mathematical model that tracks the dynamics of viral escape at multiple epitopes, we show that a number of factors could potentially contribute to a slower escape in the chronic phase of infection, such as a decreased magnitude of epitope-specific CTL responses, an increased fitness cost of escape mutations, or an increased diversity of the CTL response. In the model, an increase in the number of epitope-specific CTL responses can reduce the rate of viral escape from a given epitope-specific CTL response, particularly if CD8+ T cells compete for killing of infected cells or control virus replication nonlytically. Our mathematical framework of viral escape from multiple CTL responses can be used to predict the breadth and magnitude of HIV-specific CTL responses that need to be induced by vaccination to reduce (or even prevent) viral escape following HIV infection.     

Analysis of a stochastic predator–prey model with applications to intrahost HIV genetic diversity

During an infection, HIV experiences strong selection by immune system T cells. Recent experimental work has shown that MHC escape mutations form an important pathway for HIV to avoid such selection. In this paper, we study a model of MHC escape mutation. The model is a predator–prey model with two prey, composed of two HIV variants, and one predator, the immune system CD8 cells. We assume that one HIV variant is visible to CD8 cells and one is not. The model takes the form of a system of stochastic differential equations. Motivated by well-known results concerning the short life-cycle of HIV intrahost, we assume that HIV population dynamics occur on a faster time scale then CD8 population dynamics. This separation of time scales allows us to analyze our model using an asymptotic approach. Using this model we study the impact of an MHC escape mutation on the population dynamics and genetic evolution of the intrahost HIV population. From the perspective of population dynamics, we show that the competition between the visible and invisible HIV variants can reach steady states in which either a single variant exists or in which coexistence occurs depending on the parameter regime. We show that in some parameter regimes the end state of the system is stochastic. From a genetics perspective, we study the impact of the population dynamics on the lineages of an HIV sample taken after an escape mutation occurs. We show that the lineages go through severe bottlenecks and that in certain parameter regimes the lineage distribution can be characterized by a Kingman coalescent. Our results depend on methods from diffusion theory and coalescent theory.     

Investigating the Consequences of Interference between Multiple CD8+ T Cell Escape Mutations in Early HIV Infection

During early human immunodeficiency virus (HIV) infection multiple CD8⁺ T cell responses are elicited almost simultaneously. These responses exert strong selective pressures on different parts of HIV’s genome, and select for mutations that escape recognition and are thus beneficial to the virus. Some studies reveal that the later these escape mutations emerge, the more slowly they go to fixation. This pattern of escape rate decrease(ERD) can arise by distinct mechanisms. In particular, in large populations with high beneficial mutation rates interference among different escape strains –an effect that can emerge in evolution with asexual reproduction and results in delayed fixation times of beneficial mutations compared to sexual reproduction– could significantly impact the escape rates of mutations. In this paper, we investigated how interference between these concurrent escape mutations affects their escape rates in systems with multiple epitopes, and whether it could be a source of the ERD pattern. To address these issues, we developed a multilocus Wright-Fisher model of HIV dynamics with selection, mutation and recombination, serving as a null-model for interference. We also derived an interference-free null model assuming initial neutral evolution before immune response elicitation. We found that interference between several equally selectively advantageous mutations can generate the observed ERD pattern. We also found that the number of loci, as well as recombination rates substantially affect ERD. These effects can be explained by the underexponential decline of escape rates over time. Lastly, we found that the observed ERD pattern in HIV infected individuals is consistent with both independent, interference-free mutations as well as interference effects. Our results confirm that interference effects should be considered when analyzing HIV escape mutations. The challenge in estimating escape rates and mutation-associated selective coefficients posed by interference effects cannot simply be overcome by improved sampling frequencies or sizes. This problem is a consequence of the fundamental shortcomings of current estimation techniques under interference regimes. Hence, accounting for the stochastic nature of competition between mutations demands novel estimation methodologies based on the analysis of HIV strains, rather than mutation frequencies.     

Stochastic dynamics of cancer initiation

Most human cancer types result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Once the first change (or changes) have arisen, tumorigenesis is initiated and the subsequent emergence of additional alterations drives progression to more aggressive and ultimately invasive phenotypes. Elucidation of the dynamics of cancer initiation is of importance for an understanding of tumor evolution and cancer incidence data. In this paper, we develop a novel mathematical framework to study the processes of cancer initiation. Cells at risk of accumulating oncogenic mutations are organized into small compartments of cells and proliferate according to a stochastic process. During each cell division, an (epi)genetic alteration may arise which leads to a random fitness change, drawn from a probability distribution. Cancer is initiated when a cell gains a fitness sufficiently high to escape from the homeostatic mechanisms of the cell compartment. To investigate cancer initiation during a human lifetime, a 'race' between this fitness process and the aging process of the patient is considered; the latter is modeled as a second stochastic Markov process in an aging dimension. This model allows us to investigate the dynamics of cancer initiation and its dependence on the mutational fitness distribution. Our framework also provides a methodology to assess the effects of different life expectancy distributions on lifetime cancer incidence. We apply this methodology to colorectal tumorigenesis while considering life expectancy data of the US population to inform the dynamics of the aging process. We study how the probability of cancer initiation prior to death, the time until cancer initiation, and the mutational profile of the cancer-initiating cell depends on the shape of the mutational fitness distribution and life expectancy of the population.     

Impaired immune evasion in HIV through intracellular delays and multiple infection of cells

With its high mutation rate, HIV is capable of escape from recognition, suppression and/or killing by CD8(+) cytotoxic T lymphocytes (CTLs). The rate at which escape variants replace each other can give insights into the selective pressure imposed by single CTL clones. We investigate the effects of specific characteristics of the HIV life cycle on the dynamics of immune escape. First, it has been found that cells in HIV-infected patients can carry multiple copies of proviruses. To investigate how this process affects the emergence of immune escape, we develop a mathematical model of HIV dynamics with multiple infections of cells. Increasing the frequency of multiple-infected cells delays the appearance of immune escape variants, slows down the rate at which they replace the wild-type variant and can even prevent escape variants from taking over the quasi-species. Second, we study the effect of the intracellular eclipse phase on the rate of escape and show that escape rates are expected to be slower than previously anticipated. In summary, slow escape rates do not necessarily imply inefficient CTL-mediated killing of HIV-infected cells, but are at least partly a result of the specific characteristics of the viral life cycle.     

Social evolution in micro-organisms and a Trojan horse approach to medical intervention strategies

Medical science is typically pitted against the evolutionary forces acting upon infective populations of bacteria. As an alternative strategy, we could exploit our growing understanding of population dynamics of social traits in bacteria to help treat bacterial disease. In particular, population dynamics of social traits could be exploited to introduce less virulent strains of bacteria, or medically beneficial alleles into infective populations. We discuss how bacterial strains adopting different social strategies can invade a population of cooperative wild-type, considering public good cheats, cheats carrying medically beneficial alleles (Trojan horses) and cheats carrying allelopathic traits (anti-competitor chemical bacteriocins or temperate bacteriophage viruses). We suggest that exploitation of the ability of cheats to invade cooperative, wild-type populations is a potential new strategy for treating bacterial disease.     

Stochastic roadmap simulation for the study of ligand-protein interactions

Understanding the dynamics of ligand-protein interactions is indispensable in the design of novel therapeutic agents. In this paper, we establish the use of Stochastic Roadmap Simulation (SRS) for the study of ligand-protein interactions through two studies. In our first study, we measure the effects of mutations on the catalytic site of a protein, a process called computational mutagenesis. In our second study, we focus on distinguishing the catalytic site from other putative binding sites. SRS compactly represents many Monte Carlo (MC) simulation paths in a compact graph structure, or roadmap. Furthermore, SRS allows us to analyze all the paths in this roadmap simultaneously. In our application of SRS to the domain of ligand-protein interactions, we consider a new parameter called escape time, the expected number of MC simulation steps required for the ligand to escape from the 'funnel of attraction' of the binding site, as a metric for analyzing such interactions. Although computing escape times would probably be infeasible with MC simulation, these computations can be performed very efficiently with SRS. Our results for six mutant complexes for the first study and seven ligand-protein complexes for the second study, are very promising: In particular, the first results agree well with the biological interpretation of the mutations, while the second results show that escape time is a good metric to distinguish the catalytic site for five out of seven complexes.     

Escape from a dominant HLA-B*15-restricted CD8+ T cell response against hepatitis C virus requires compensatory mutations outside the epitope

Antiviral CD8(+) T cells are a key component of the adaptive immune system against hepatitis C virus (HCV). For the development of immune therapies, it is essential to understand how CD8(+) T cells contribute to clearance of infection and why they fail so often. A mechanism for secondary failure is mutational escape of the virus. However, some substitutions in viral epitopes are associated with fitness costs and often require compensatory mutations. We hypothesized that compensatory mutations may point toward epitopes under particularly strong selection pressure that may be beneficial for vaccine design because of a higher genetic barrier to escape. We previously identified two HLA-B*15-restricted CD8(+) epitopes in NS5B (LLRHHNMVY(2450-2458) and SQRQKKVTF(2466-2474)), based on sequence analysis of a large HCV genotype 1b outbreak. Both epitopes are targeted in about 70% of HLA-B*15-positive individuals exposed to HCV. Reproducible selection of escape mutations was confirmed in an independent multicenter cohort in the present study. Interestingly, mutations were also selected in the epitope flanking region, suggesting that compensatory evolution may play a role. Covariation analysis of sequences from the database confirmed a significant association between escape mutations inside one of the epitopes (H2454R and M2456L) and substitutions in the epitope flanking region (S2439T and K2440Q). Functional analysis with the subgenomic replicon Con1 confirmed that the primary escape mutations impaired viral replication, while fitness was restored by the additional substitutions in the epitope flanking region. We concluded that selection of escape mutations inside an HLA-B*15 epitope requires secondary substitutions in the epitope flanking region that compensate for fitness costs.     

Influenza drift and epidemic size: the race between generating and escaping immunity

Influenza in humans is characterised by strongly annual dynamics and antigenic evolution leading to partial escape from prior host immunity. The variability of new epidemic strains depends on the amount of virus currently circulating. In this paper, the amount of antigenic variation produced each year is dependent on the epidemic size. Our model reduces to a one-dimensional map and a full mathematical analysis is presented. This simple system suggests some basic principles which may be more generally applicable. In particular, for diseases with antigenic drift, vaccination may be doubly beneficial. Not only does it protect the population through classical herd immunity, but the overall case reduction reduces the chance of new variants being produced; hence, subsequent epidemics may be milder as a result of this positive feedback. Also, a disease with a high innate rate of antigenic variation will always be able to invade a susceptible population, whereas a disease with less potential for variation may require several introduction events to become endemic.     

Cytotoxic T-lymphocyte escape mutations identified by HLA association favor those which escape and revert rapidly

Identifying human immunodeficiency virus (HIV) immune escape mutations has implications for understanding the impact of host immunity on pathogen evolution and guiding the choice of vaccine antigens. One means of identifying cytotoxic-T-lymphocyte (CTL) escape mutations is to search for statistical associations between mutations and host human leukocyte antigen (HLA) class I alleles at the population level. The impact of evolutionary rates on the strength of such associations is not well defined. Here, we address this topic using a mathematical model of within-host evolution and between-host transmission of CTL escape mutants that predicts the prevalence of escape mutants at the population level. We ask how the rates at which an escape mutation emerges in a host who bears the restricting HLA and reverts when transmitted to a host who does not bear the HLA affect the strength of an association. We consider the impact of these factors when using a standard statistical method to test for an association and when using an adaptation of that method that corrects for phylogenetic relationships. We show that with both methods, the average sample size required to identify an escape mutation is smaller if the mutation escapes and reverts quickly. Thus, escape mutations identified as HLA associated systematically favor those that escape and revert rapidly. We also present expressions that can be used to infer escape and reversion rates from cross-sectional escape prevalence data.     

New insights into the effect of mutations on affibody-Fc interaction,a molecular dynamics simulation approach

Staphylococcal protein A (SpA) domain B (the basis of affibody) has been widely used in affinity chromatography and found therapeutic applications against inflammatory diseases through targeting the Fc part of immunoglobulin G (IgG). We have performed extensive molecular dynamics simulation of 41 SpA mutants and compared their dynamics and conformations to wild type. The simulations revealed the molecular details of structural and dynamics changes that occurred due to introducing point mutations and helped to explain the SPR results. It was observed in some variants a point mutation caused extensive structural changes far from the mutation site, while an effect of some other mutations was limited to the site of the mutated residue. Also, the pattern of hydrogen bond networks and hydrophobic core arrangements were investigated. We figured out mutations that occurred at positions 128, 136, 150 and 153, affected two hydrophobic cores at the interface as well as mutations introduced at positions 129 and 154 interrupted two hydrogen bond networks of the interface, SPR data showed all of these mutations reduced binding affinity significantly. Overall, by scanning the SpA-Fc interface through the large numbers of introduced mutations, the new insights have been gained which would help to design high- affinity ligands of IgG.     

Oscillatory dynamics in rock-paper-scissors games with mutations

We study the oscillatory dynamics in the generic three-species rock-paper-scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with coexistence of all species; (b) for low mutation rates, there is a region of the parameter space characterized by a limit cycle resulting from a Hopf bifurcation; (c) in the absence of mutations, there is a region where heteroclinic cycles yield oscillations of large amplitude (not robust against noise). After a discussion on the main properties of the mean-field dynamics, we investigate the stochastic version of the model within an individual-based formulation. Demographic fluctuations are therefore naturally accounted and their effects are studied using a diffusion theory complemented by numerical simulations. It is thus shown that persistent erratic oscillations (quasi-cycles) of large amplitude emerge from a noise-induced resonance phenomenon. We also analytically and numerically compute the average escape time necessary to reach a (quasi-)cycle on which the system oscillates at a given amplitude.     

Haldane's sieve and adaptation from the standing genetic variation

We consider populations that adapt to a sudden environmental change by fixing alleles found at mutation-selection balance. In particular, we calculate probabilities of fixation for previously deleterious alleles, ignoring the input of new mutations. We find that "Haldane's sieve"--the bias against the establishment of recessive beneficial mutations--does not hold under these conditions. Instead probabilities of fixation are generally independent of dominance. We show that this result is robust to patterns of sex expression for both X-linked and autosomal loci. We further show that adaptive evolution is invariably slower at X-linked than autosomal loci when evolution begins from mutation-selection balance. This result differs from that obtained when adaptation uses new mutations, a finding that may have some bearing on recent attempts to distinguish between hitchhiking and background selection by contrasting the molecular population genetics of X-linked vs. autosomal loci. Last, we suggest a test to determine whether adaptation used new mutations or previously deleterious alleles from the standing genetic variation.