A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses

Mutation induced infection waves in diseases like COVID-19

After more than 6 million deaths worldwide, the ongoing vaccination to conquer the COVID-19 disease is now competing with the emergence of increasingly contagious mutations, repeatedly supplanting earlier strains. Following the near-absence of historical examples of the long-time evolution of infectious diseases under similar circumstances, models are crucial to exemplify possible scenarios. Accordingly, in the present work we systematically generalize the popular susceptible-infected-recovered model to account for mutations leading to repeatedly occurring new strains, which we coarse grain based on tools from statistical mechanics to derive a model predicting the most likely outcomes. The model predicts that mutations can induce a super-exponential growth of infection numbers at early times, which self-amplify to giant infection waves which are caused by a positive feedback loop between infection numbers and mutations and lead to a simultaneous infection of the majority of the population. At later stages-if vaccination progresses too slowly-mutations can interrupt an ongoing decrease of infection numbers and can cause infection revivals which occur as single waves or even as whole wave trains featuring alternative periods of decreasing and increasing infection numbers. This panorama of possible mutation-induced scenarios should be tested in more detailed models to explore their concrete significance for specific infectious diseases. Further, our results might be useful for discussions regarding the importance of a release of vaccine-patents to reduce the risk of mutation-induced infection revivals but also to coordinate the release of measures following a downwards trend of infection numbers.

Linear B-Cell Epitopes in Human Norovirus GII.4 Capsid Protein Elicit Blockade Antibodies

Human norovirus (HuNoV) is the leading cause of nonbacterial gastroenteritis worldwide with the GII.4 genotype accounting for over 80% of infections. The major capsid protein of GII.4 variants is evolving rapidly, resulting in new epidemic variants with altered antigenic potentials that must be considered for the development of an effective vaccine. In this study, we identify and characterize linear blockade B-cell epitopes in HuNoV GII.4. Five unique linear B-cell epitopes, namely P2A, P2B, P2C, P2D, and P2E, were predicted on the surface-exposed regions of the capsid protein. Evolving of the surface-exposed epitopes over time was found to correlate with the emergence of new GII.4 outbreak variants. Molecular dynamic simulation (MD) analysis and molecular docking revealed that amino acid substitutions in the putative epitopes P2B, P2C, and P2D could be associated with immune escape and the appearance of new GII.4 variants by affecting solvent accessibility and flexibility of the antigenic sites and histo-blood group antigens (HBAG) binding. Testing the synthetic peptides in wild-type mice, epitopes P2B (336-355), P2C (367-384), and P2D (390-400) were recognized as GII.4-specific linear blockade epitopes with the blocking rate of 68, 55 and 28%, respectively. Blocking rate was found to increase to 80% using the pooled serum of epitopes P2B and P2C. These data provide a strategy for expanding the broad blockade potential of vaccines for prevention of NoV infection.

Phylodynamic theory of persistence, extinction and speciation of rapidly adapting pathogens

Rapidly evolving pathogens like influenza viruses can persist by changing their antigenic properties fast enough to evade the adaptive immunity, yet they rarely split into diverging lineages. By mapping the multi-strain Susceptible-Infected-Recovered model onto the traveling wave model of adapting populations, we demonstrate that persistence of a rapidly evolving, Red-Queen-like state of the pathogen population requires long-ranged cross-immunity and sufficiently large population sizes. This state is unstable and the population goes extinct or 'speciates' into two pathogen strains with antigenic divergence beyond the range of cross-inhibition. However, in a certain range of evolutionary parameters, a single cross-inhibiting population can exist for times long compared to the time to the most recent common ancestor ([Formula: see text]) and gives rise to phylogenetic patterns typical of influenza virus. We demonstrate that the rate of speciation is related to fluctuations of [Formula: see text] and construct a 'phase diagram' identifying different phylodynamic regimes as a function of evolutionary parameters.

Modeling the Growth and Decline of Pathogen Effective Population Size Provides Insight into Epidemic Dynamics and Drivers of Antimicrobial Resistance

Nonparametric population genetic modeling provides a simple and flexible approach for studying demographic history and epidemic dynamics using pathogen sequence data. Existing Bayesian approaches are premised on stochastic processes with stationary increments which may provide an unrealistic prior for epidemic histories which feature extended period of exponential growth or decline. We show that nonparametric models defined in terms of the growth rate of the effective population size can provide a more realistic prior for epidemic history. We propose a nonparametric autoregressive model on the growth rate as a prior for effective population size, which corresponds to the dynamics expected under many epidemic situations. We demonstrate the use of this model within a Bayesian phylodynamic inference framework. Our method correctly reconstructs trends of epidemic growth and decline from pathogen genealogies even when genealogical data are sparse and conventional skyline estimators erroneously predict stable population size. We also propose a regression approach for relating growth rates of pathogen effective population size and time-varying variables that may impact the replicative fitness of a pathogen. The model is applied to real data from rabies virus and Staphylococcus aureus epidemics. We find a close correspondence between the estimated growth rates of a lineage of methicillin-resistant S. aureus and population-level prescription rates of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\beta$\end{document}-lactam antibiotics. The new models are implemented in an open source R package called skygrowth which is available at https://github.com/mrc-ide/skygrowth.

Computational Characterization of Transient Strain-Transcending Immunity against Influenza A

The enigmatic observation that the rapidly evolving influenza A (H3N2) virus exhibits, at any given time, a limited standing genetic diversity has been an impetus for much research. One of the first generative computational models to successfully recapitulate this pattern of consistently constrained diversity posits the existence of a strong and short-lived strain-transcending immunity. Building on that model, we explored a much broader set of scenarios (parameterizations) of a transient strain-transcending immunity, ran long-term simulations of each such scenario, and assessed its plausibility with respect to a set of known or estimated influenza empirical measures. We evaluated simulated outcomes using a variety of measures, both epidemiological (annual attack rate, epidemic duration, reproductive number, and peak weekly incidence), and evolutionary (pairwise antigenic diversity, fixation rate, most recent common ancestor, and kappa, which quantifies the potential for antigenic evolution). Taking cumulative support from all these measures, we show which parameterizations of strain-transcending immunity are plausible with respect to the set of empirically derived target values. We conclude that strain-transcending immunity which is milder and longer lasting than previously suggested is more congruent with the observed short- and long-term behavior of influenza.

Navigating the devious course of evolution: the importance of mechanistic models for identifying eco-evolutionary dynamics in nature

In proposing his genetic feedback mechanism, David Pimentel was one of the first biologists to argue that the reciprocal interplay of ecological and evolutionary dynamics is an important process regulating population dynamics and ultimately affecting community composition. Although the past decade has seen an increase in research activity on these so-called eco-evolutionary dynamics, there remains a conspicuous lack of compelling natural examples of such feedback. Here we argue that this lack may be due to an inherent difficulty in detecting eco-evolutionary dynamics in nature. By examining models of virulence evolution, host resistance evolution, and antigenic evolution, we show that the influence of evolution on ecological dynamics can often be obscured by other ecological processes that yield similar dynamics. We then show, however, that mechanistic models can be used to navigate this, in Pimentel's words, "devious" course of evolution when effectively combined with empirical data. We argue that these models, improving upon Pimentel's original mathematical models, will therefore play an increasingly important role in identifying more subtle, but possibly ubiquitous, eco-evolutionary dynamics in nature. To highlight the importance of identifying these potentially subtle dynamics in nature, we end by considering our ability to anticipate the effect of population control strategies in the presence of these eco-evolutionary feedbacks.

The impact of host immune status on the within-host and population dynamics of antigenic immune escape

Antigenically evolving pathogens such as influenza viruses are difficult to control owing to their ability to evade host immunity by producing immune escape variants. Experimental studies have repeatedly demonstrated that viral immune escape variants emerge more often from immunized hosts than from naive hosts. This empirical relationship between host immune status and within-host immune escape is not fully understood theoretically, nor has its impact on antigenic evolution at the population level been evaluated. Here, we show that this relationship can be understood as a trade-off between the probability that a new antigenic variant is produced and the level of viraemia it reaches within a host. Scaling up this intra-host level trade-off to a simple population level model, we obtain a distribution for variant persistence times that is consistent with influenza A/H3N2 antigenic variant data. At the within-host level, our results show that target cell limitation, or a functional equivalent, provides a parsimonious explanation for how host immune status drives the generation of immune escape mutants. At the population level, our analysis also offers an alternative explanation for the observed tempo of antigenic evolution, namely that the production rate of immune escape variants is driven by the accumulation of herd immunity. Overall, our results suggest that disease control strategies should be further assessed by considering the impact that increased immunity--through vaccination--has on the production of new antigenic variants.

Canalization of the evolutionary trajectory of the human influenza virus

BACKGROUND

Since its emergence in 1968, influenza A (H3N2) has evolved extensively in genotype and antigenic phenotype. However, despite strong pressure to evolve away from human immunity and to diversify in antigenic phenotype, H3N2 influenza shows paradoxically limited genetic and antigenic diversity present at any one time. Here, we propose a simple model of antigenic evolution in the influenza virus that accounts for this apparent discrepancy.

RESULTS

In this model, antigenic phenotype is represented by a N-dimensional vector, and virus mutations perturb phenotype within this continuous Euclidean space. We implement this model in a large-scale individual-based simulation, and in doing so, we find a remarkable correspondence between model behavior and observed influenza dynamics. This model displays rapid evolution but low standing diversity and simultaneously accounts for the epidemiological, genetic, antigenic, and geographical patterns displayed by the virus. We find that evolution away from existing human immunity results in rapid population turnover in the influenza virus and that this population turnover occurs primarily along a single antigenic axis.

CONCLUSIONS

Selective dynamics induce a canalized evolutionary trajectory, in which the evolutionary fate of the influenza population is surprisingly repeatable. In the model, the influenza population shows a 1- to 2-year timescale of repeatability, suggesting a window in which evolutionary dynamics could be, in theory, predictable.

Genetic mapping of a highly variable norovirus GII.4 blockade epitope: potential role in escape from human herd immunity

Noroviruses account for 96% of viral gastroenteritis cases worldwide, with GII.4 strains responsible >80% of norovirus outbreaks. Histo-blood group antigens (HBGAs) are norovirus binding ligands, and antigenic and preferential HBGA binding profiles vary over time as new GII.4 strains emerge. The capsid P2 subdomain facilitates HBGA binding, contains neutralizing antibody epitopes, and likely evolves in response to herd immunity. To identify amino acids regulating HBGA binding and antigenic differences over time, we created chimeric virus-like particles (VLPs) between the GII.4-1987 and GII.4-2006 strains by exchanging amino acids in putative epitopes and characterized their antigenic and HBGA binding profiles using anti-GII.4-1987 and -2006 mouse monoclonal antibodies (MAbs) and polyclonal sera, 1988 outbreak human sera, and synthetic HBGAs. The exchange of amino acids 393 to 395 between GII.4-1987 and GII.4-2006 resulted in altered synthetic HBGA binding compared to parental strains. Introduction of GII.4-1987 residues 294, 297 to 298, 368, and 372 (epitope A) into GII.4-2006 resulted in reactivity with three anti-GII.4-1987 MAbs and reduced reactivity with four anti-GII.4-2006 MAbs. The three anti-GII.4-1987 MAbs also blocked chimeric VLP-HBGA interaction, while an anti-GII.4-2006 blocking antibody did not, indicating that epitope A amino acids comprise a potential neutralizing epitope for GII.4-1987 and GII.4-2006. We also tested GII.4-1987-immunized mouse polyclonal sera and 1988 outbreak human sera for the ability to block chimeric VLP-HBGA interaction and found that epitope A amino acids contribute significantly to the GII.4-1987 blockade response. Our data provide insights that help explain the emergence of new GII.4 epidemic strains over time, may aid development of norovirus therapeutics, and may help predict the emergence of future epidemic strains.

Complex population dynamics and the coalescent under neutrality

Estimates of the coalescent effective population size N(e) can be poorly correlated with the true population size. The relationship between N(e) and the population size is sensitive to the way in which birth and death rates vary over time. The problem of inference is exacerbated when the mechanisms underlying population dynamics are complex and depend on many parameters. In instances where nonparametric estimators of N(e) such as the skyline struggle to reproduce the correct demographic history, model-based estimators that can draw on prior information about population size and growth rates may be more efficient. A coalescent model is developed for a large class of populations such that the demographic history is described by a deterministic nonlinear dynamical system of arbitrary dimension. This class of demographic model differs from those typically used in population genetics. Birth and death rates are not fixed, and no assumptions are made regarding the fraction of the population sampled. Furthermore, the population may be structured in such a way that gene copies reproduce both within and across demes. For this large class of models, it is shown how to derive the rate of coalescence, as well as the likelihood of a gene genealogy with heterochronous sampling and labeled taxa, and how to simulate a coalescent tree conditional on a complex demographic history. This theoretical framework encapsulates many of the models used by ecologists and epidemiologists and should facilitate the integration of population genetics with the study of mathematical population dynamics.