Date Published: September 12, 2018
Publisher: Public Library of Science
Author(s): Igor M. Rouzine, Ganna Rozhnova, Marco Vignuzzi.
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.
Spread of many RNA viruses occurs as a race between host immune responses and rapid viral evolution. The development of treatment and effective preventive measures such as vaccines and therapeutic interference particles [1–3] requires understanding of the mechanics of viral evolution at the scale of a population. To evade immune recognition by hosts previously exposed to infection, in a never-ending chase, viruses accumulate mutations in immunologically relevant regions of the genome . Despite advances in the collection and analysis of epidemiological and genomic data, it remains conceptually unclear how epidemiology, immune response, and evolutionary factors interact to produce the observed evolution speed and the incidence of infection.
The model described in the previous section establishes a general analytic relationship between immunological, epidemiological, and evolutionary properties of a virus causing non-chronic infection. Using the analytic approach described in the previous section, below we predict the evolution speed, the incidence of influenza in a population, and the time to the most recent common ancestor. Then, we test analytic results with stochastic simulation and compare them to available data on influenza strain A H3N2.
We investigated stochastic evolutionary dynamics of a virus driven by the pressure to escape immune recognition in previously infected individuals. We mapped this problem to an evolutionary model with fitness landscape expressed in terms of the cross-immunity function K(x) (Fig 2). Stochastic evolution occurs as a traveling wave with two population components structured in the antigenic variant space x, recovered individuals and the currently infected individuals, with different widths and total counts (Fig 1). The recovered distribution is broad and large. The infected distribution represents a narrow and small peak at the recovered distribution front. We expressed several observable parameters including the speed of viral evolution, the annual incidence of infection, and the average time to the most recent ancestor in terms of model parameters N, Ub, R0, K(x) (Table 1). The analytic predictions agree with simulation and are able to estimate correctly important parameters of viral evolution in host populations, as we illustrated using genomic data on influenza.
Merging the standard epidemiological approach and the modern traveling wave theory, we develop a general analytic approach that connects epidemiological and immunological parameters to the observed parameters of influenza evolution. We demonstrate that the distribution of recovered individuals in the genetic space effectively creates a fitness landscape for the infected individual distribution, and both distributions move together along quasi-one-dimensional path. Our predictions demonstrate a good experimental agreement with data on influenza A H3N2.