Integrating influenza antigenic dynamics with molecular evolution
- University of Edinburgh, United Kingdom
- David Geffen School of Medicine, University of California, Los Angeles, United States
- UCLA Fielding School of Public Health, University of California, Los Angeles, United States
- Rega Institute, Katholieke Universiteit Leuven, Belgium
- MRC National Institute for Medical Research, United Kingdom
- University of Cambridge, United Kingdom
- Erasmus Medical Centre, Netherlands
- National Institutes of Health, United States
Figures
Figure 1
Pairwise correlations between genetic distance, measured as amino acid mutations or as phylogenetic distance, and antigenic distance for influenza A/H3N2, A/H1N1, B/Vic, and B/Yam.
The top row shows correlations between number of amino acid mutations in HA1 and average antigenic distance between 10,000 random pairs of viruses. The bottom row shows correlations between average phylogenetic distance, measured in terms of years, and average antigenic distance between 10,000 random pairs of viruses. Dashed lines show linear model fits, with R2 and slope noted, while solid lines show LOESS fits. Antigenic distances derive from model 2 of Table 1.
Figure 2
Antigenic locations of A/H3N2, A/H1N1, B/Vic, and B/Yam viruses showing evolutionary relationships between virus samples.
Circles represent a posterior sample of virus locations and have been shaded based on year of isolation. Antigenic units represent twofold dilutions of the HI assay. Absolute positioning of lineages, for example A/H3N2 and A/H1N1, is arbitrary. Lines represent mean posterior diffusion paths when virus locations are fixed. Prominent antigenic clusters are labeled after vaccine strains present within clusters, and are abbreviated from Hong Kong/68, England/72, Victoria/75, Bangkok/79, Sichuan/87, Beijing/89, Beijing/92, Wuhan/95, Sydney/97, Fujian/02, California/04, Wisconsin/05, Brisbane/07, Perth/09 (A/H3N2), USSR/77, Singapore/86, Beijing/95, New Caledonia/99, Solomon Islands/06 (H1N1), Victoria/87, Hong Kong/01, Malaysia/04, Brisbane/08 (Vic), Yamagata/88, Shanghai/02, Florida/06, Wisconsin/10 (Yam).
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Figure 2—source data 1
This tab-delimited text file lists every virus in Figures 2 and 3, including lineage, strain name, year of isolation, and coordinates in antigenic dimensions 1 and 2.
- https://doi.org/10.7554/eLife.01914.006
Figure 3
Antigenic drift of A/H3N2, A/H1N1, B/Vic and B/Yam viruses showing evolutionary relationships between virus samples.
Antigenic drift is shown in terms of change of location in the first antigenic dimension through time. Circles represent a posterior sample of virus locations and have been shaded based on year of isolation. Antigenic units represent twofold dilutions of the HI assay. Relative positioning of lineages, for example A/H3N2 and A/H1N1, in the vertical axis is arbitrary. Lines represent mean posterior diffusion paths when virus locations are fixed. Prominent antigenic clusters are labeled after vaccine strains present within clusters, and are abbreviated from Hong Kong/68, England/72, Victoria/75, Bangkok/79, Sichuan/87, Beijing/89, Beijing/92, Wuhan/95, Sydney/97, Fujian/02, California/04, Wisconsin/05, Brisbane/07, Perth/09 (A/H3N2), USSR/77, Singapore/86, Beijing/95, New Caledonia/99, Solomon Islands/06 (H1N1), Victoria/87, Hong Kong/01, Malaysia/04, Brisbane/08 (Vic), Yamagata/88, Shanghai/02, Florida/06, Wisconsin/10 (Yam).
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Figure 3—source data 1
This tab-delimited text file lists every virus in Figures 2 and 3, including lineage, strain name, year of isolation, and coordinates in antigenic dimensions 1 and 2.
- https://doi.org/10.7554/eLife.01914.008
Figure 4
Time-resolved phylogenetic trees of A/H3N2, A/H1N1, B/Vic and B/Yam viruses.
The maximium-clade credibility (MCC) tree is shown for each virus. These trees show genealogical relationships, so that branches are measured in terms of years rather than substitutions.
Figure 5
Year-to-year antigenic drift between 1992 and 2011 in A/H3N2, A/H1N1, B/Vic and B/Yam viruses.
(A) Timeseries of year-to-year antigenic drift between 1992 and 2011 in A/H3N2, A/H1N1, B/Vic and B/Yam viruses. Colored lines represent year-to-year antigenic drift, where drift for year i is measured as the mean of antigenic dimension 1 of phylogenetic lineages in year i compared to the mean of antigenic dimension 1 of phylogenetic lineages from the previous year i − 1. For example, 2000 represents difference in antigenic dimension 1 between viruses from 1999 to 2000. Error bars represent 50% Bayesian credible intervals of year-to-year drift. Gray dotted lines represent lineage-specific seasonal incidence in the USA taken as average influenza-like illness (ILI) multiplied by proportion of viruses attributable to a lineage for each season. Here, 2000 represents the 2000/2001 influenza season. (B) Distribution of year-to-year antigenic drift between 1992 and 2011 in A/H3N2, A/H1N1, B/Vic and B/Yam viruses.
Figure 6
Relationship between antigenic drift and seasonal incidence for years 1998 to 2009 in influenza A/H3N2, A/H1N1, B/Vic and B/Yam.
Antigenic drift from year i − 1 to year i is compared to incidence in the season i/i + 1. For example, year-to-year antigenic drift from 2000 to 2001 is measured against incidence in the 2001/2002 season.
Figure 7
Relationship between antigenic drift and sample counts for years 1998 to 2011 in influenza A/H3N2, A/H1N1, B/Vic and B/Yam.
Antigenic drift from year i − 1 to year i is compared to the ratio of sample counts in year i to counts in year i − 1. Only comparisons which had one or more samples in years i − 1 and i were retained, leaving 11 A/H3N2, 7 A/H1N1, 9 B/Vic and 10 B/Yam comparisons. Points are colored according to influenza lineage based on the color scheme in Figure 6.
Figure 8
Likelihood of HI titers in the BMDS model.
Here, we show the likelihoods of observing three different outcomes given , , and . The likelihood of observing a threshold titer of ‘<40’ is equal to the lower tail of the probability density function . The likelihood of observing a point measurement with an exact inhibiting titer of ‘90.5’ is equal to the density function . The likelihood of observing an interval measurement with an inhibiting titer somewhere between ‘160’ and ‘320’ is equal to
Figure 9
Schematic antigenic map with three viruses and two sera.
(A) Map with virus 1 and virus 3 antigenically similar. (B) Map with virus 1 and virus 3 antigenically divergent. Virus 1 is shown in blue, virus 2 is shown in red and virus 3 is shown in yellow. Virus isolates are represented by filled circles, sera raised against viruses are shown as open circles and map distances are shown as solid lines connecting viruses and sera. Sera from virus 1 is compared against viruses 1 and 2, while sera from virus 2 is compared against viruses 2 and 3. Configurations (A) and (B) represent cartographic models that would give equal likelihoods to a set of serological data .
Figure 10
Comparison of A/H3N2 antigenic locations estimated by Smith et al. (2004) using MDS and an equivalent BMDS model.
(A) MDS antigenic locations, reoriented so that the primary dimension lies on the x-axis rather than on the y-axis as in Figure 1 of Smith et al. (2004). (B) A posterior sample of antigenic locations from an equivalent BMDS model. In (A) and (B), viruses are shown as colored circles, with color denoting antigenic cluster inferred by (Smith et al., 2004), and sera are shown as gray points. (C) Antigenic distances between A/Bilthoven/16,190/1968 and all other viruses determined for both methods. (D) Antigenic distances between A/Fujian/411/2002 and all other viruses determined for both methods. (E) Antigenic distances between 750 random pairs of viruses determined for both methods. In (C), (D) and (E) red points show distances for the MDS model and gray bars show the 95% credible interval of distances for the BMDS model, while the red dashed line shows a LOESS regression to MDS distances, and the black dashed line shows a LOESS regression to the BMDS distances. The BMDS model has a Uniform (−100, 100) prior on antigenic locations and serum potencies fixed at maximum titer values.
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Figure 10—source data 1
This tab-delimited text file lists every virus and serum in Figure 10, including strain name, year of isolation, coordinates in antigenic dimensions 1 and 2, and potency for sera.
- https://doi.org/10.7554/eLife.01914.017
Figure 11
Comparison of A/H3N2 antigenic locations estimated by Smith et al. (2004) using MDS and an equivalent BMDS model under an alternative solution.
(A) MDS antigenic locations, reoriented so that the primary dimension lies on the x-axis rather than on the y-axis as in Figure 1 of Smith et al. (2004). (B) A posterior sample of antigenic locations from an equivalent BMDS model that has converged on the alternative solution. In (A) and (B), viruses are shown as colored circles, with color denoting antigenic cluster inferred by Smith et al. (2004), and sera are shown as gray points. (C) Antigenic distances between A/Bilthoven/16,190/1968 and all other viruses determined for both methods. (D) Antigenic distances between A/Fujian/411/2002 and all other viruses determined for both methods. (E) Antigenic distances between 750 random pairs of viruses determined for both methods. In (C), (D) and (E) red points show distances for the MDS model and gray bars show the 95% credible interval of distances for the BMDS model, while the red dashed line shows a LOESS regression to MDS distances, and the black dashed line shows a LOESS regression to the BMDS distances. The BMDS model has a Uniform (−100, 100) prior on antigenic locations and serum potencies fixed at maximum titer values.
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Figure 11—source data 1
This tab-delimited text file lists every virus and serum in Figure 11, including strain name, year of isolation, coordinates in antigenic dimensions 1 and 2, and potency for sera.
- https://doi.org/10.7554/eLife.01914.019
Figure 12
Comparison of A/H3N2 antigenic locations estimated by Smith et al. (2004) using MDS and an extended BMDS model that includes date-informed priors on antigenic locations.
(A) MDS antigenic locations, reoriented so that the primary dimension lies on the x-axis rather than on the y-axis as in Figure 1 of Smith et al. (2004). (B) A posterior sample of antigenic locations from a BMDS model that includes date-informed priors on antigenic locations. In (A) and (B), viruses are shown as colored circles, with color denoting antigenic cluster inferred by Smith et al. (2004), and sera are shown as gray points. (C) Antigenic distances between A/Bilthoven/16,190/1968 and all other viruses determined for both methods. (D) Antigenic distances between A/Fujian/411/2002 and all other viruses determined for both methods. (E) Antigenic distances between 750 random pairs of viruses determined for both methods. In (C), (D) and (E) red points show distances for the MDS model and gray bars show the 95% credible interval of distances for the BMDS model, while the red dashed line shows a LOESS regression to MDS distances, and the black dashed line shows a LOESS regression to the BMDS distances. The BMDS model has a date-informed prior on antigenic locations and serum potencies fixed at maximum titer values.
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Figure 12—source data 1
This tab-delimited text file lists every virus and serum in Figure 12, including strain name, year of isolation, coordinates in antigenic dimensions 1 and 2, and potency for sera.
- https://doi.org/10.7554/eLife.01914.021
Figure 13
Comparison of A/H3N2 antigenic locations estimated by Smith et al. (2004) using MDS and an extended BMDS model that estimates serum and virus avidities.
(A) MDS antigenic locations, reoriented so that the primary dimension lies on the x-axis rather than on the y-axis as in Figure 1 of Smith et al. (2004). (B) A posterior sample of antigenic locations from a BMDS model that estimates virus avidity and serum potency. In (A) and (B), viruses are shown as colored circles, with color denoting antigenic cluster inferred by Smith et al. (2004), and sera are shown as gray points. (C) Antigenic distances between A/Bilthoven/16,190/1968 and all other viruses determined for both methods. (D) Antigenic distances between A/Fujian/411/2002 and all other viruses determined for both methods. (E) Antigenic distances between 750 random pairs of viruses determined for both methods. In (C), (D), and (E) red points show distances for the MDS model and gray bars show the 95% credible interval of distances for the BMDS model, while the red dashed line shows a LOESS regression to MDS distances, and the black dashed line shows a LOESS regression to the BMDS distances. The BMDS model has a Uniform (−100, 100) prior on antigenic locations and virus avidities and serum potencies estimated in a hierarchical Bayesian fashion.
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Figure 13—source data 1
This tab-delimited text file lists every virus and serum in Figure 13, including strain name, year of isolation, coordinates in antigenic dimensions 1 and 2, potency for sera and avidity for viruses.
- https://doi.org/10.7554/eLife.01914.023
Tables
Table 1
Average absolute prediction error of log2 HI titer for test data across models and datasets
| Test error | |||||||||
|---|---|---|---|---|---|---|---|---|---|
| Model | Data | Dimen | Location prior | Serum potency | Virus avidity | A/H3N2 | A/H1N1 | B/Vic | B/Yam |
| 1 | HI | 1D | Uninformed | Fixed | None | 1.35 | 0.94 | 0.90 | 1.08 |
| 2 | HI | 2D | Uninformed | Fixed | None | 0.91 | 0.78 | 0.82 | 0.90 |
| 3 | HI | 3D | Uninformed | Fixed | None | 0.93 | 0.80 | 0.85 | 0.92 |
| 4 | HI | 4D | Uninformed | Fixed | None | 0.98 | 0.84 | 0.90 | 0.97 |
| 5 | HI | 5D | Uninformed | Fixed | None | 1.04 | 0.89 | 0.98 | 1.04 |
| 6 | HI/year | 2D | Drift | Fixed | None | 0.91 | 0.75 | 0.77 | 0.83 |
| 7 | HI/year/seq | 2D | Diffusion/Drift | Fixed | None | 0.89 | 0.74 | 0.74 | 0.83 |
| 8 | HI/year/seq | 2D | Diffusion/Drift | Estimated | None | 0.77 | 0.73 | 0.66 | 0.75 |
| 9 | HI/year/seq | 2D | Diffusion/Drift | Fixed | Estimated | 0.80 | 0.72 | 0.69 | 0.75 |
| 10 | HI/year/seq | 2D | Diffusion/Drift | Estimated | Estimated | 0.76 | 0.71 | 0.64 | 0.72 |
Table 2
Estimates of drift rate μ (in units per year), diffusion volatility (in units2 per year) and scaled effective population size (in years) for influenza A/H3N2, A/H1N1, B/Vic and B/Yam including posterior means and 95% highest posterior density intervals
| Lineage | Drift μ | Volatility | Effective pop size |
|---|---|---|---|
| A/H3N2 | 1.01 (0.98–1.04) | 1.25 (0.98–2.35) | 5.03 (4.42–5.73) |
| A/H1N1 | 0.62 (0.56–0.67) | 0.92 (0.65–1.56) | 6.38 (4.99–8.12) |
| B/Vic | 0.42 (0.32–0.51) | 1.22 (0.85–2.25) | 10.40 (8.42–12.80) |
| B/Yam | 0.32 (0.25–0.39) | 0.71 (0.46–1.36) | 9.48 (7.76–11.50) |
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Integrating influenza antigenic dynamics with molecular evolution
eLife 3:e01914.
https://doi.org/10.7554/eLife.01914
