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. 2012 Aug 7;109(32):12980-5.
doi: 10.1073/pnas.1117201109. Epub 2012 Jul 23.

A Quantitative Quasispecies Theory-Based Model of Virus Escape Mutation Under Immune Selection

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Free PMC article

A Quantitative Quasispecies Theory-Based Model of Virus Escape Mutation Under Immune Selection

Hyung-June Woo et al. Proc Natl Acad Sci U S A. .
Free PMC article

Abstract

Viral infections involve a complex interplay of the immune response and escape mutation of the virus quasispecies inside a single host. Although fundamental aspects of such a balance of mutation and selection pressure have been established by the quasispecies theory decades ago, its implications have largely remained qualitative. Here, we present a quantitative approach to model the virus evolution under cytotoxic T-lymphocyte immune response. The virus quasispecies dynamics are explicitly represented by mutations in the combined sequence space of a set of epitopes within the viral genome. We stochastically simulated the growth of a viral population originating from a single wild-type founder virus and its recognition and clearance by the immune response, as well as the expansion of its genetic diversity. Applied to the immune escape of a simian immunodeficiency virus epitope, model predictions were quantitatively comparable to the experimental data. Within the model parameter space, we found two qualitatively different regimes of infectious disease pathogenesis, each representing alternative fates of the immune response: It can clear the infection in finite time or eventually be overwhelmed by viral growth and escape mutation. The latter regime exhibits the characteristic disease progression pattern of human immunodeficiency virus, while the former is bounded by maximum mutation rates that can be suppressed by the immune response. Our results demonstrate that, by explicitly representing epitope mutations and thus providing a genotype-phenotype map, the quasispecies theory can form the basis of a detailed sequence-specific model of real-world viral pathogens evolving under immune selection.

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Simulation of full immune escape dynamics of a single SIV epitope Tat28–35SL8. (A) Viral load. (B) Frequencies of WT and the dominant escape mutants (EM). Symbols represent experimental data from refs.  and , with each symbol corresponding to one of four different animals. Solid lines are from our stochastic quasispecies model with τ = 0.8 d, μ = 2.0 × 10-7 bp-1, b = 0.01 d-1, g = 0.2 d-1, and p = 2.0 × 10-4 d-1. The fitness function parameters were σ = 0.1 and ξ = 1 (Methods). The EM frequency is for a single trajectory while the rest are averages.
Fig. 2.
Fig. 2.
Typical disease progression patterns in the runaway regime from the multiepitope quasispecies model. (A) Viral load. (B) Total CTL levels. (C) Number of distinct phenotypes per epitope present in the population. The inset in A shows the viral load in linear scale for p = 1.0 × 10-3 d-1 and μ = 1.0 × 10-5 bp-1. Other parameter values were b = 0.02 d-1, g = 0.1 d-1, τ = 1 d, σ = 0.2, and ξ = 1. The units of p and μ in the legends are d-1 and bp-1, respectively. All data represent averages over trajectories.
Fig. 3.
Fig. 3.
Typical disease progression patterns in the extinction regime from the multi-epitope quasispecies model. (A) Viral load. (B) Total CTL levels. (C) Number of distinct phenotypes per epitope present in the population. The parameter values other than p and μ = 1.0 × 10-5 bp-1 were the same as in Fig. 2. The data shown are individual trajectories.
Fig. 4.
Fig. 4.
Crossover between the runaway and extinction regimes. (A) Variation of extinction time with mutation rate μ for different clearance rates p in the extinction regime. Error bars represent one standard deviation. Near the threshold, the extinction events occur increasingly in the edge of viral load fluctuations (Fig. 3A). (B) The estimated threshold between the runaway and extinction regimes in the p - μ parameter space (defined as the maximum μ for which the extinction time converges for a given p). The arrow illustrates the dynamic deterioration of immune response during HIV-1 infection. Other parameter values were the same as in Fig. 2.

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