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. 2014 Jan;88(2):1039-50.
doi: 10.1128/JVI.02958-13. Epub 2013 Nov 6.

Quantitative Modeling of Virus Evolutionary Dynamics and Adaptation in Serial Passages Using Empirically Inferred Fitness Landscapes

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Quantitative Modeling of Virus Evolutionary Dynamics and Adaptation in Serial Passages Using Empirically Inferred Fitness Landscapes

Hyung Jun Woo et al. J Virol. .
Free PMC article

Abstract

We describe a stochastic virus evolution model representing genomic diversification and within-host selection during experimental serial passages under cell culture or live-host conditions. The model incorporates realistic descriptions of the virus genotypes in nucleotide and amino acid sequence spaces, as well as their diversification from error-prone replications. It quantitatively considers factors such as target cell number, bottleneck size, passage period, infection and cell death rates, and the replication rate of different genotypes, allowing for systematic examinations of how their changes affect the evolutionary dynamics of viruses during passages. The relative probability for a viral population to achieve adaptation under a new host environment, quantified by the rate with which a target sequence frequency rises above 50%, was found to be most sensitive to factors related to sequence structure (distance from the wild type to the target) and selection strength (host cell number and bottleneck size). For parameter values representative of RNA viruses, the likelihood of observing adaptations during passages became negligible as the required number of mutations rose above two amino acid sites. We modeled the specific adaptation process of influenza A H5N1 viruses in mammalian hosts by simulating the evolutionary dynamics of H5 strains under the fitness landscape inferred from multiple sequence alignments of H3 proteins. In light of comparisons with experimental findings, we observed that the evolutionary dynamics of adaptation is strongly affected not only by the tendency toward increasing fitness values but also by the accessibility of pathways between genotypes constrained by the genetic code.

Figures

FIG 1
FIG 1
Viral growth, host cell infection, and within-host diversification dynamics predicted by the stochastic model for the following parameter values: La = 3 aa, V0 = 1 × 103, a = 1.0 × 10−3 day−1, b = 3.0 day−1, r0 = 6.0 day−1, μ = 1.0 × 10−5, and U0 = 1 × 106. (A) Viral titer and uninfected cell number U0. Symbols represent the experimental data from references and , plotted assuming a scaling factor of 1 viral count per 1 TCID50/ml. (B) Total numbers of genotypes (nucleotide and amino acid sequences) as a function of time.
FIG 2
FIG 2
Time dependence of viral population size and diversity over serial passage simulations without adaptation. The WT and MF coincide in the sequence space. The parameter values were the same as in Fig. 1 except that b = 1.0 day−1 and τ = 3 days.
FIG 3
FIG 3
Time dependence of population size and diversity (A) as well as mean distance to the MF sequence and the frequency of the MF (B). Parameter values were as follows: La = d = 2 aa, V0 = 1 × 104, U0 = 1 × 106, a = 1.0 × 10−3 day−1, b = 1.0 day−1, r0 = 20 day−1, μ = 1.0 × 10−5, and τ = 3 days.
FIG 4
FIG 4
Jumping rate (J) distributions from the sets of 103 realizations using parameter values as in Fig. 3 for two different distances: d = 1 aa (A) and d = 2 aa (B). The dashed lines show maximum-likelihood fits to linear combinations of normal distributions. The cluster of peaks in panel A centered at a J of ≈0.3 day−1, 0.16 day−1, 0.11 day−1, and 0.07 day−1 correspond to jumping events (MF frequency exceeding 50%) during the first, second, third, and fourth passage rounds, respectively. The peaks at a J of 0 arise from trajectories trapped at sequences without direct single substitution route to the MF sequence.
FIG 5
FIG 5
Dependence of jumping rate on the mutation rate for the WT-to-MF distance from 1 to 3 aa. Symbols represent averages and error bars represent 1 standard deviation over 100 realizations. Parameter values were as follows: V0 = 1 × 105, U0 = 1 × 106, a = 1.0 × 10−3 day−1, b = 0.1 day−1, r0 = 10 day−1, and τ = 3 days.
FIG 6
FIG 6
Dependence of jumping rate on other parameters. (A) Number of host cells U0. (B) Bottleneck size V0, or the number of virions selected at each passage round. (C) Passage period τ, or the time duration of each passage round. (D) Infection rate a. (E) Rate b of infected cell death and virus clearance. (F) Fitness landscape peak width parameter ξ of the MF sequence. Default values of parameters other than those varied in each case were the same as in Fig. 5, with d = 2 aa, μ = 1.0 × 10−5, and ξ = 1 aa.
FIG 7
FIG 7
Adaptation dynamics of the extended model given by equations 1, 2, and 4 and 6 to 8 explicitly including host immune response. Parameter values were the same as in Fig. 3 except for b = c = 0.1 day−1 and s = 0.01 day−1.
FIG 8
FIG 8
Fitness landscapes of an HA protein 4-aa segment inferred from MSA. (A) H5 landscape derived from H5N1 sequences. (B) H3 landscape from H3 sequences. The height of the bars represents the fitness values in units of rs = 1.0 day−1. The abscissa shows the list of genotypes sorted with decreasing order in fitness. In panel B, the rightmost bar shows the H5 WT, which is 251st in rank.
FIG 9
FIG 9
Time evolution of quasispecies composition during the H5-to-H3 adaptation of the model influenza virus segment, simulated under the empirically inferred fitness landscape of Fig. 8B. Panels A to I show the sequential snapshots at each time instance (immediately after a passage cycle), listing five genotypes with the highest frequencies (shown in logarithmic scale). The parameter values were as follows: V0 = 1 × 104, U0 = 1 × 106, a = 1.0 × 10−3 day−1, b = 1.0 day−1, μ = 1 × 10−5, and τ = 3 days.
FIG 10
FIG 10
Influenza virus genotype network corresponding to the fitness landscape in Fig. 8B. Nodes represent the genotypes (first two amino acids) and edges connect pairs for which there exists at least one single-nucleotide mutation separating the two nodes. The arrowheads on the edges reflect the direction of fitness increases (Fig. 8B). The shaded nodes are the dominant genotypes shown in Fig. 11. The length of a given path does not necessarily equal the number of nucleotide mutations: QA → LA → SA requires multiple mutations within the Leu-coding codons.
FIG 11
FIG 11
Mean frequencies of the top five dominant genotypes as functions of time from the influenza virus adaptation simulations. Up to 103 realizations under the condition of Fig. 9 were averaged. Other genotypes not shown have mean frequencies less than 1%.

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