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Prediction of Influenza B Vaccine Effectiveness from Sequence Data

Influenza is a contagious respiratory illness that causes significant human morbidity and mortality, affecting 5-15% of the population in a typical epidemic season. Human influenza epidemics are caused by types A and B, with roughly 25% of human cases due to influenza B. Influenza B is a single-stranded RNA virus with a high mutation rate, and both prior immune history and vaccination put significant pressure on the virus to evolve. Due to the high rate of viral evolution, the influenza B vaccine component of the annual influenza vaccine is updated, roughly every other year in recent years. To predict when an update to the vaccine is needed, an estimate of expected vaccine effectiveness against a range of viral strains is required. We here introduce a method to measure antigenic distance between the influenza B vaccine and circulating viral strains. The measure correlates well with effectiveness of the influenza B component of the annual vaccine in humans between 1979 and 2014. We discuss how this measure of antigenic distance may be used in the context of annual influenza vaccine design and prediction of vaccine effectiveness.


Introduction
Influenza is a highly contagious respiratory illness that infects all ages. It occurs seasonally worldwide, causing substantial morbidity and mortality [1]. In humans, influenza A/H3N1, A/H1N1, and B are the main causative agents. In each influenza season, influenza A generally spreads widely. Influenza B tends to be regionally dominant, causing seasonal epidemics every 2-4 years [2,3].
The major molecular factors of influenza accessible to the immune system are hemagglutinin and neuraminidase. Entry into host cells requires hemagglutinin, which is also the main target of neutralizing antibodies [4,5]. To protect against influenza infections, the World Health Organization (WHO) recommends the trivalent seasonal influenza vaccine, which includes the two main influenza type A strains, H1N1 and H3N2, and an influenza B strain from the Yamagata or Victoria lineages [6]. Hemagglutinin undergoes antigenic drift because of selective pressure, and this drift reduces vaccine effectiveness.
Influenza B virus is less prevalent than influenza A, and the morbidity and mortality associated with influenza B are often perceived to be lower than those caused by influenza A. Nonetheless, influenza B has attracted researchers' attention in recent years. An early modeling study with a two-tiered phylodynamic model for influenza B compared the evolution of A/H3N2, A/H3N8, and B [7].
In some recent studies, influenza A and B infections resulted in similar morbidity and mortality in hospitalized adults [8], and also caused similar clinical characteristics in outpatients [9]. These results indicate that influenza B virus can cause infections as severe as those caused by influenza A.
Influenza B is comprised of two distinct evolutionary lineages: B/Yamagata/16/88like and B/Victoria/2/87-like. These two lineages have co-circulated since the 1980s [10,11]. The lineage that predominates can change yearly. In the USA, there were 5 changes of the predominant lineage in the 10 seasons between 2001 and 2010 [12], often resulting in a mismatch between the vaccine strain and the dominant circulating strain. There is limited to no protection of a vaccine for one lineage against a viral strain from the other lineage. Moreover, the pro-tection of a vaccine for one lineage against viruses within that same lineage is not uniform, as it depends on the antigenic distance between the vaccine and virus. Compared to influenza A, there are relatively few studies of the relation between antigenic distance and vaccine effectiveness for influenza B.
We here introduce a method to estimate antigenic distance between the influenza B vaccine and circulating viral strains. Epitope regions were mapped from a standard influenza A/H3N2 virus. Additional amino acid sites that exhibited high entropy in influenza B sequences sampled from the human population were added to the epitope regions. Note that while the binding of a specific antibody in a specific individual against a specific antigen is typically dominated by 5-6 contacting amino acid residues in the antigen, here we consider typical regions of antibody binding among a distribution of 10 8 antibodies and a distribution of 7 × 10 9 people and against a mixture of antigens within a given influenza B strain. This is the reason for the rather large size of the generalized epitopes A-E in the hemagglutinin protein considered here. We here define an estimate of antigenic distance between the vaccine strain and the dominant circulating strain as p epitope , the fraction of amino acid site substitutions between the vaccine and circulating virus lineage in the dominant epitope region of HA1 [13]. We will show that this measure of antigenic distance correlates well with effectiveness of the influenza B component of the annual vaccine between 1979 and 2014.
To additionally detect the emergence of new influenza strains in the human population, we built a dimensionally reduced space using the multidimensional scaling method. This reduced space allowed for the visualization of the evolution of influenza B. In this representation, the emergence of new vaccine strain clusters is apparent. In particular, clades appear in this representation at antigenic distances sufficiently far from current dominating strains that immune recognition is ineffective.
This study provides a method to estimate influenza B antigenic distance and vaccine effectiveness. The measure of antigenic distance introduced here, which provides a novel tool for prediction of vaccine effectiveness in influenza B, may be used in the context of annual influenza vaccine design.

Sequence Data
Influenza B hemagglutinin protein sequences from human hosts in all regions were downloaded from the Influenza Virus Database of the National Center for Biotechnology Information (NCBI) [14]. Data were collected for the years 1979 to 2014. Only data containing the entire HA1 sequence were used.

Vaccine Strain and Circulating Strain
For each season, and for each epidemiological study, we determined the relevant vaccine strain and the relevant dominant circulating strain. For those studies that specified the vaccine strain used and the dominant circulating strain observed, we used those sequences. For the studies conducted in the USA that did not specify the strains, we used the vaccine strain and dominant circulating strain identified in the Center for Diseases Control and Prevention (CDC) "Morbidity and Mortality Weekly Report". For the remaining studies, we used the vaccine strain and dominant circulating strain identified in the annual WHO reports on "recommendations on the composition of influenza virus vaccines." We note that the vaccine and dominant circulating strains changed from year to year and from Northern to Southern Hemisphere studies.

Sequence Alignment
In each season, and in each epidemiological study, we determined whether the vaccine strain was a Yamagata or Victoria lineage strain. To do this, we first determined the lineage to which the vaccine strain belonged from the WHO report [6]. If the report was inconclusive, we used the lineage assigned by the Influenza Virus Database. If the database was inconclusive as well, typically only for the sequences from early years, we used the phylogenetic tree calculated by the maximum likelihood method of MEGA 6.06 [15] to determine the lineage to which a strain belonged. For each lineage, we used a standard crystal structure of HA1 to align the strains. For the Yamagata-like lineage, we used B/Yamanashi/166/1998 (PBD ID: 4M44). For the Victoria-like lineage, we used B/Brisbane/60/2008 (PBD ID: 4FQM). All protein sequences from a given Northern or Southern Hemisphere influenza season were aligned to the sequence determined by this procedure. The sequences were numbered with reference to these standards, with the first amino acid site of each model amino acid site 1. The Victoria sequence is one amino acid longer than the Yamagata model, and multi-sequence alignment using PRANK [16] showed a gap at amino acid site 163 in the Yamagata model.
The crystal structures of the two models are similar, with average root mean square deviation between them of 0.3671Å.There are six missing amino acid sites in the crystal structure of 4FQM and three missing amino acid sites in the structure of 4M44. These amino acid sites are in the tail region. They are far away from the epitope region and are not included in root mean square deviation calculations.

Epitope Mapping
We here mapped the epitopes of both Yamagata-like and Victoria-like influenza B virus from the 5 epitopes of the H3 subtype of influenza A virus [17,18,19,20,13,21,22] using PRANK, which allows for gaps in the alignment and takes evolutionary distances into account [16]. We note that various modifications of these epitopes have been proposed, which range from relatively minor additions of amino acid sites [23], to dramatic reassignments [24]. The latter is discussed in our previous study [25], and we note here that measures of antigenic distance based upon it correlate less well with A/H3N2 vaccine effectiveness in humans than do those based upon the original epitope definition.
We used the sequence and numbering of A/California/7/2004 for the reference, as in the H1N1 mapping studies [21,22]. If an epitope amino acid site  Table S1.

Antigenic Distance between the Vaccine Strain and the Dominant Circulating Strain
The antigenic distance between the vaccine strain and the dominant circulating strain was measured by p epitope , the fraction of amino acids in the dominant epitope region of HA1 that differ between the vaccine and circulating strain [13].
We additionally considered several alternative definitions of antigenic distance.
The first is p all epitopes , the fraction of amino acid substitutions in the entire set of all five epitope regions. The second is p sequence , the fraction of amino acid substitutions in the entire HA1 sequence. The third is p two epitopes , introduced in this study, which is the fraction of amino acid substitutions in the two epitopes with the highest individual amino acid substitution fractions. The model, Yamagata or Victoria, used in these calculations was that of the lineage to which the vaccine strain belongs for the influenza season under consideration. If there was a lineage mismatch when the vaccine strain was Victoria, the gap to which amino acid site 163 mapped was considered as a amino acid site substitution.
If there was a lineage mismatch when the vaccine strain was Yamagata, amino acid site 163 of the dominant strain, which mapped to a gap on the vaccine, was excluded from the substitution computation.

Estimation of Vaccine Effectiveness
Vaccine effectiveness data were collected from the epidemiological literature.
Data were collected from mostly healthy adults, typically aged 18-65. Epidemiological studies of influenza B are less common than those of influenza A, so studies with ideal experimental design are fewer in number. In roughly half of the studies used here, there was a minority of subjects in the range of 13% to 30% with conditions such as pregnancy, cardiovascular disease, diabetes, or body mass index of 40 kg/m 2 or greater. Interestingly, in all studies, the fraction of subjects testing positive for influenza B was higher in the subjects without comorbidity than in the subjects with comorbidity. All data on infections are from laboratory-confirmed samples, e.g. by RT-PCR or the HI test. Studies focusing on elderly people and children were excluded to avoid noise caused by the response of an immature immune system in children or the immunosenescence phenomenon in elder people. Only studies that used an inactivated vaccine, such as trivalent inactivated vaccine (TIV), were considered, to decrease bias caused by differences of vaccine type. The epidemiological data were grouped by season. For each study, the vaccine effectiveness was calculated from [13] where u is the rate at which unvaccinated people are infected with influenza, and v is the rate at which vaccinated people are infected with influenza, with u = n u /N u and v = n v /N v , where the total number of vaccinated subjects is N v , the total number of unvaccinated subjects is N u , the number of influenza B cases among the vaccinated subjects is n v , and the number of influenza B cases among the unvaccinated subjects is n u . Binomial statistics were assumed to calculate the error bars for the estimated effectiveness [13]: . For seasons that contained N studies, we used the average of the N effectiveness values, and the standard error was ε = i ε 2 i /N 2 where ε i is the standard error of the ith study.

Sequence Clustering Analysis
To gain a geometric understanding of historical influenza B evolution, we clustered the Influenza Virus Database HA1 sequences from the years 1960 to 2014. The multidimensional scaling method was used to reduce the sequences 7 from 348 amino acid dimensions to the 3 or 4 dimensions that best reproduce the Hamming distances between all sequences [26]. Details of this dimensional reduction are provided in the Supplemental Information.

Epitope Determination
The composition of the five epitope regions in the Victoria and Yamagata models were determined ( Table 1

Lineage Model Chosen
The main difference between the Victoria and Yamagata lineages is the gap of amino acid site 163 (Victoria numbering). This gap cannot be ignored because it is on epitope B, while the nearby amino acid sites 160 to 165 are also on epitope B. We used the methods described in Section 2.5 to estimate the vaccine effectiveness from several sequence-based measures of antigenic distance. When the vaccine lineage is Yamagata, amino acid site 163 (Victoria numbering) is eliminated from the antigenic distance calculation.

Vaccine Effectiveness Correlates with Antigenic Distance
The influenza B vaccine effectiveness values calculated by Eq. 1 from epidemiological studies are listed in Table 2. This table also presents the antigenic distances calculated from the epitopes defined above between the vaccine strain and the dominant circulating strain. Three additional measures of distance are also listed: p two epitopes , p all epitopes , and p sequence . Figure 1 represents how vaccine effectiveness declines with antigenic distance. A linear least squares fit shows that E = −0.864 p epitope + 0.6824.
From this equation, the antigenic distance at which vaccine effectiveness declines to zero is p epitope = 0.79. Using the size of each epitope and the frequency with which each epitope is dominant from Table 2, we calculated the average number of amino acid substitutions to which this value of p epitope corresponds (see Table S3), 19 for the p epitope metric. The number of substitutions at which the expected vaccine effectiveness declines to zero according to the linear least squares fits for the other three measures of antigenic distance are also displayed in this table.
A further sensitivity analysis was performed, limiting the data to laboratory genetically confirmed samples, such as by RT-PCR. There were 19 out of 25 data points meeting this requirement. The linear least squares fit using only those data is E = −0.8252 p epitope + 0.684, and R 2 = 0.58. This result is quite similar to that of Figure 1a, thus demonstrating limited sensitivity to such a data restriction. Since RT-PCR was lacking mostly in the early years, 1979-1988, and a relatively small fraction of the population was vaccinated in those years, the bias stemming from HI is expected to be relatively small.

Dynamics of Influenza B Evolution
Multidimensional scaling was used to reduce the dimensions to the three most informative dimensions. Figure   Because of the small difference in the eigenvalue associated with the third dimension and the fourth dimension, we also reduced the dimensions to a 4D space. Figure 2b shows the evolution, while the color coding represents the fourth dimension. This Figure shows that the Yamagata strain jumped out and back in the fourth dimension in the late 90s.
Two contour graphs were obtained from the Gaussian kernel density estimation. The results are shown in Figure 3. Figure 3a is the x-y axis projection, and Figure 3b is the x-z projection. Several representative influenza B sequences are indicated. From Figure 3, we can measure the distance between peaks, the evident clusters in density estimation. We measured the average distance between the major cluster transitions, shown as the dark lines in Figure 3. The average number of substitutions is approximately 12. We also measured the full width at half maximum for the major clusters. We find a width of approximately 6 substitutions. The corresponding peak-peak distance and cluster width for H3N2 are 6 and 3 amino acids, respectively. [27] Figure S2 shows the average seasonal entropy of each amino acid in sequence of the HA1 domain. Each amino acid site is color coded according to the five epitopes.

Dispersed Dominant Epitope in Each Season
The dominant epitope varies by season.

Evolution of Influenza B
In this study, we used dimensional reduction to characterize the evolution of influenza B. Phylogenetic trees are consistent with these results. We constructed a neighbor joining tree and a maximum likelihood tree based on the same sequence set for which we performed dimensional reduction. In these trees the Yamagata lineages and Victoria lineages are divided into two branches in the tree, originating from sequences obtained in the 1980s. These trees are very dense, however, and are hard to use to distinguish distances between clusters.
Thus, we provide a simplified phylogenetic tree in Figure S1. We can see the Yamagata and Victoria branches in Figure S1. The distances among each cluster and sub-cluster in the dimensionally reduced space are clearer than what the trees can provide. The dimensionally reduced space is an optimal representation of relative distances, unlike the phylogenetic trees that are constrained to a tree topology.
We further analyzed the distance among peaks in our Gaussian kernel density estimation. Based on Figure 3, the average distance between major peaks in the same lineage is approximately 12 amino acid sites. In this analysis, peaks in Victoria lineage and peaks in Yamagata lineage were measured separately.
Influenza B strains in the early years belonged to the Victoria lineage and then separated to two lineages in the 1980s. There is a small transitional peak in between these two lineage clusters The distance between these two lineages is approximately twice the average distance of 12 amino acid sites.

Antigenic Distance at which Vaccine Effectiveness is Zero
The number of substitutions at which vaccine effectiveness is predicted to decline to zero is shown in Table S3. For the p epitope estimate, vaccine effectiveness decays to zero at roughly 19 substitutions. This result of the p epitope estimate is the closest to the average distance observed between the evolving strain clusters in the dimensional reduction analysis, 12 amino acid sites. Thus, we chose p epitope as our metric for antigenic distance. In a previous study of H3 in influenza A [27], the average distance between consecutive H3 clusters was 6 amino acid sites, and the average substitution number when vaccine effectiveness decreases to zero was approximately 4. It appears influenza clusters emerge at just enough distance to evade prior immunity, whether induced by prior infection or vaccination in the human population.

Lower Selective Pressure Compared to Influenza A
Influenza A has high selection pressure, high mutant rate, and distinct dominant epitopes in each season [21,22,25]. Influenza A is generally more common For certain regions of the influenza B epitopes, the selective pressure may relatively be low, and antibody binding may be in a more random pattern. These results explain why in some seasons, the second most dominant epitope often has a similar fraction of amino acid substitutions as the dominant epitope.

Conclusion
In this paper we have considered how influenza B vaccine effectiveness depends on antigenic distance. We have defined a measure of antigenic distance for influenza B, p epitope . This measure is defined as the fraction of amino acid site substitutions between the vaccine and circulating virus lineage in the dominant epitope region of HA1 [13]. This measure correlates well with influenza B vaccine effectiveness in humans. We find that new, emergent strains of influenza B tend to occur at large values of p epitope , for which immune recognition will be minimal. In other words, influenza B evolves to escape immune recognition due to prior infection or vaccination in the human population.
This measure of antigenic distance provides a novel tool for prediction of vaccine effectiveness and may be used in the context of annual influenza vaccine design. The dimensional reduction technique illustrated here can be used to identify incipient dominant strains. In conjunction with other available data, such as ferret animal data, the p epitope measure can be used to estimate whether a new vaccine strain will be required, by measuring the antigenic distance between the existing vaccine strain and the incipient strain. The p epitope measure applies to both the Victoria and Yamagata lineages. The p epitope measure of antigenic distance may be used, again in conjunction with other available data, to select which vaccine strain in each lineage would be predicted to be most protective against the distribution of predicted or observed circulating viral strains.
It is also possible to perform this prediction on a geographically localized scale, predicting vaccines optimal for different parts of the world. The p epitope measure of antigenic distance may also be used to select among egg-viable, "like" strains 13 for those predicted to be most antigenically similar to the desired vaccine strain.
These capabilities complement existing analysis of sequence and animal model datasets.

Acknowledgments
Competing Financial Interests Authors declare no competing financial interests.
Correspondence Correspondence should be addressed to MWD (mwdeem@rice.edu).   8.50 [37,38] 109      of the 4M44 Yamagata model was 3.794Å, while the minimum distance between amino acid site 126 and a amino acid site in epitope A is 3.808Å. Comparing the ten closest epitopic amino acid sites to amino acid site 126 in 4M44, we found that it is closer to epitope A on average. Therefore, we determined that amino acid site 126 should be included in epitope A for the Yamagata model.

Sequence Clustering Analysis
The relative importance of each dimension in the multidimensional scaling is proportional to the eigenvalue associated with each reduced dimension: 0.05562, 0.02411, 0.00692, and 0.00640.
In the calculation each sequence was weighted by the inverse of the number of samples collected per year, to give each year roughly equal weight in the dimensional reduction procedure. Additionally Gaussian kernel density estimation was used to estimate the probability density of sequences in the reduced space identified by the weighted multidimensional scaling. The standard deviation of the Gaussian weight was σ x =0.03351265, σ y =0.01171378, and σ z =0.01177186.
The reconstructed probability density of the viruses in the reduced (x, y, z) ]. The peaks in this density estimate correspond to clusters of influenza B sequences. The fourth dimension in the 4D figure is indicated by the color bar.
The phylogenetic tree of these sequences was constructed using MEGA 6.06 [? ]. A neighbor joining tree was first constructed. A maximum likelihood tree was then constructed, whose structure confirmed that of the neighbor joining tree. The maximum likelihood tree was divided into three groups: Two Yamagata-like lineages and one Victoria-like lineage.

Dispersed High Entropy Amino Acid Sites
The distribution of high-entropy amino acid sites is dispersed, spread on the HA1 domain. Figure S2 represents the distribution of high entropy amino acid sites in the sequence, and Figure 3 shows part of the high entropy amino acid sites in the 3D structure. High entropy amino acid sites can be either inside or outside the epitope region, and they appear in every epitope. Some of these high entropy amino acid sites even have low RSA, indicating that they are not fully exposed on the surface.
If we set a critical value of high-entropy as 0.1 [? ], we find that some of these high-entropy amino acid sites do not cluster in any of the epitopes we  Figure S2.
Re-clustering all the high-entropy amino acid sites did not improve the correlation between vaccine effectiveness and antigenic distance. We analyzed se-quence data from the original dataset of dimensional reduction and clustered the behavior of high-entropy amino acid sites in each season into three novel agglomerative clusters using Cluster Analysis of MATLAB [? ]. There was no significant correlation among them and the original epitopes. Additionally, vaccine effectiveness became zero at p epitope or p all epitopes values larger than 1.
We also calculated the antigenic distances when all the low-entropy amino acid sites in epitopes were removed and correlated these antigenic distances determined from high-entropy amino acid sites only with vaccine effectiveness.
Epitope C was removed as it contained only one high-entropy amino acid site.
Therefore, in the Victoria lineage, 44 high-entropy amino acid sites were taken into account. The linear least squares fit of p epitope was E = −0.4408 p epitope + 0.6675, and p all epitopes was E = −0.5392 p all epitopes + 0.6735. The estimated substitution number of p epitope was 13.03, similar to that in Figure 1, further substantiating the p epitope is suitable as the measurement criteria. However, for p all epitopes , vaccine effectiveness would not decline to zero even if all these 44 high-entropy amino acid sites are substituted. A linear least squares fit of p two epitopes was E = −0.6662 p two epitopes + 0.6704. This result indicates that when all of the amino acid sites in the two dominant epitope region are mutated, vaccine effectiveness will decline to zero. Nonetheless, these highentropy amino acid sites contain only part of the surface amino acid sites. The region potentially recognized by the immune system should cover the surface of HA1. Thus, it is likely not enough to consider only high-entropy amino acid sites only in epitope determination. We look forward to both more epidemiological studies for influenza B and more sequence data to extend our dataset, in which case an updated calculation of the high-entropy amino acid sites may more fully cover the HA1 surface.

Role of High-Entropy Amino Acid Sites with low RSA
From Figure S2, our definition of the five epitopes includes most of the high entropy amino acid sites. Though we have already considered the high-entropy amino acid sites in epitope definition, we found that there are still some amino acid sites with average seasonal entropy greater than 0.1, such as amino acid site 262 and 267. The reason why they were not included is that they have a low RSA, and they are not likely to be recognized by antibodies because they are not on the surface of the protein.
We further tested if these amino acid sites can affect the correlation between antigenic distance and vaccine effectiveness. Though they are not fully exposed, substitutions in these amino acid sites could affect the epitope structure, and substitutions of these amino acid sites could change the shape of antibody recognition amino acid site, and affect vaccine effectiveness. We added these 7 high-entropy but low RSA amino acid sites to our 5 epitopes using the same method as described in Section 1.1. In the Victoria numbering, amino acid site 262, 266, and 267 were added to epitope B, amino acid site 29 was added to epitope C, amino acid sites 175 and 252 were added to epitope D, and amino acid site 76 was added to epitope E. These modifications did not quantitatively change the vaccine effectiveness and p epitope relation.    The first three dominant epitopes in each year in descending order and the antigenic distances associated with each epitope.