Chapter 2 Co-evolution Positions and Rules for Antigenic Variants of Influenza A (H3N2)
2.6. Summary
This study demonstrates our model is robust and feasible by considering both genetic and antigenic data. Based on decision tree, our method is able to identify critical amino acid positions of HA and the rules of antigenic variants for influenza H3N2 viruses. The accuracies of our method are 91.2% and 96.2% for the training set and independent data set, respectively, and our method is significantly better than the other two methods being compared on these two sets. The identified critical amino acid positions are similar to related works and the co-mutated positions are able to reflect the biological meanings. We believe that our method is useful for vaccine
Chapter 3
Changed Epitopes Drive the Antigenic Drift for Influenza A (H3N2) Viruses
3.1. Introduction
Influenza spreads around the world and causes significant morbidity and mortality [14]. The surface proteins HA and NA are the primary targets of the protective immune system. In circulating influenza viruses, gradually accumulated mutations on the HA, which interacts with infectivity-neutralizing antibodies, lead to the escape of immune system.
Most of methods measuring the antigenic variances on HA focused on amino acid position mutations, such as hamming distance [34] or phylogenic distance [31]. Recently, few studies discuss the relationships between the antigenic sites (epitopes) and vaccine efficiency [48].
3.2. Motivation and aim
We have identified critical positions and rules for antigenic variants in previous chapter.
However, the critical positions are widely distributed on HA structure and the antibody recognition is highly correlated to the conformation change on the epitopes, which locate on HA surface. Moreover, an antibody often utilizes complementarily-determining regions (CDRs) to bind two epitopes on the antigen (HA) [49]. To quantify a changed epitope for escaping from neutralizing antibodies is the basis for the antigenic drift and vaccine development.
Here, we have proposed a method to identify the antigenic drift of influenza A by quantifying the conformation change of an epitope. Our method is able to predict antigenic variants of a given pair of HA sequences which are often a vaccine strain and a circulating strain. Our model was evaluated to measure the antigenic drifts and vaccine updates on 2,789 circulating strains
(from year 1983 to 2008) and to predict the antigenic variants on two data sets (i.e. 343 and 31,878 HI assays). These observations demonstrate that our model is able to reflect the biological meanings and can explain the WHO vaccine strain selection.
3.3. Materials and Methods
Figure 3.1 presents the overview of our method for the antigenic drift of influenza A (H3N2) viruses by quantifying changed epitopes. We first identified the critical amino acid positions based on both the antigenic variant and genetic diversity. We then measured a changed epitope by calculating the accumulated conformation change based on critical amino acid mutations on an epitope. Finally, we evaluated our model for predicting antigenic variants and selecting the WHO vaccines.
and entropy of each amino
acid position
Identify changed epitopes for predicting “antigenic variants”
Evaluate the changed epitopes on the 2789 sequences and independent set
with 31,878 HI measurements
Figure 3.1 Overview of our method for the antigenic drift. (A) The overview of our method. (B) The structural locations of selected 64 critical amino acid positions on all the five epitopes (Epitope A in red; B in purple; C in orange; D in cyan; E in green). The sialic acid is in green. All
3.3.1. Changed epitopes
The changed epitope is the core of our method. Here, we defined a changed epitope as follows:
an antigenic site (epitope) on HA with accumulated amino acid mutations induces the conformation change to escape from the neutralizing antibody. The conformation change of a mutation depends on its position on HA structure and the mutation rate during 40 years. A changed epitope can be considered as a "key feature" for measuring antigenic variants of a pair of HA sequences. Here, a changed epitope can be used to predict antigenic variants and antigenic drifts for the selections of vaccine strains.
3.3.2. Data sets
To describe and evaluate the ability of the changed epitopes for predicting antigenic variants, we collected HI assays, describing the antigenic variants and similar viruses of the current global influenza surveillance system. The HI assay describes whether one (e.g. circulating) strain will be recognized by an antibody against the vaccine strain. We collected 343 H3N2 virus HI assays with 125 HA sequences from Weekly Epidemiological Record (WER) [50] (Table 3.1), World Health Organization (WHO) collaborating center [51] and related publications [52-54]. Each pair includes an HI assay value (i.e. antigenic distance) and a pair of HA sequences (329 amino acids).
In general, an influenza vaccine should be updated if an antigenic distance is more than 4.0 between the current vaccine strain and the circulating strain in next season [15] [55]. Among 343 pairs of HA sequences, 225 pairs with antigenic distance ≥ 4 are considered as "antigenic variants" and 118 pairs are considered as "similar viruses". For example, the antigenic distance of the pair of HA sequences, A/England/42/72 and A/PortChalmers/1/73, is 12 and this pair is considered as "antigenic variants". Conversely, the antigenic distance of the pair of HA sequences, A/Wuhan/359/95 and A/Nanchang/933/95, is 1 and this pair is considered as "similar viruses". In addition to the training set, we prepared another HI assay data set to independently evaluate our model for predicting antigenic variants proposed by Smith et al. [15]. We assume that a virus-pair in the same antigenic group is considered as a "similar viruses" pair and a virus-pair in different groups is considered as "antigenic variants" pair. Finally, we obtained 31,878 HI measurements from the supporting materials [15].
To study the antigenic drifts and WHO vaccine updates, we collected 2789 HA sequences with influenza season assignment from influenza virus resource [36] and influenza sequence
database [35].
Table 3.1 The number of HI assays, number of sequences in Smith's dataset and WER strains from 1968 to 2007
Year HI assay data set Number of strains WER strains2
1968 0 4 A/Hong Kong/1/68
1984 0 1 A/Phillipines/2/82
1985 3 [50] 4 A/Phillipines/2/82
1996 12 [50] 10 A/Johannesburg/33/94
1997 28 [56] 9 A/Wuhan/359/95
Total 343 pairs 253 sequences
1 the number of HI assays collected in the document.
2 we followed Plotkin's definition [34], WER strains were the dominant recommended virus based on HI assays in influenza season, as reported by the WHO in Weekly Epidemiological Record (WER).
3 for the purpose of detecting emerging variants, the later strain was selected to comparing with circulating strains.
4 the wildly used vaccine strain A/Panama/2007/99 was used instead in following years.
3.3.3. Identifying critical positions on HA
Recently, we proposed a method to identify critical positions [32] by utilizing both antigenic variants and genetic diversity. The Shannon entropy and information gain (IG) were used to measure genetic diversity and antigenic discriminating score for amino acid positions on HA, respectively. Here, we based on these rules to select 64 amino acid positions as critical positions.
Table 3.2 Summary of 4 models
Model Regarding HA positions Changed epitope Antigenic variants Model one 329 positions ≥1 mutation ≥2 changed epitopes Model two 329 positions ≥2 mutations ≥2 changed epitopes Model three 64 selected positions ≥2 mutations ≥2 changed epitopes
Model four 64 selected positions ≥3 mutations (epitope B) ≥2 mutations (others)
≥1 (epitopes A or B)
≥2 (others)
3.3.4. Models for antigenic variants based on changed epitopes
To address the issue of measuring accumulated mutations on an epitope to escape from neutralizing antibody, we proposed 4 models considering the number of amino acid mutations on 329 amino acids and 64 selected critical positions of HA (Table 3.2). Models one and two regarded an epitope as "changed" if there are more than 1 and 2 mutations within an epitope, respectively, based on 329 amino acids. A changed epitope of Model three is defined as two amino acid mutations on 64 critical positions. Models one, two, and three regarded a pair of HA sequences as "antigenic variants" if there are more than two changed epitopes. Conversely, one changed epitope is viewed as "similar viruses".
Model four treated one changed epitope (A or B) as "antigenic variants". Epitopes A and B, which are near the receptor-binding site, often play the key role for escaping from neutralizing antibody. Here, the epitopes A and B (denoted as "B+") were regarded as "changed" if there are more than 2 and 3 mutations, respectively. For the pair A/Mississippi/1/85 and A/Leningrad/360/86 (Table 3.3), the numbers of mutations were 1, 3, 0, 1, and 1 on epitopes A, B, C, D and E, respectively. The numbers of changed epitopes for Models one and two are 4 (epitopes A, B, D, and E) and 1 (epitope B), respectively. Models three and four regarded the epitope B as a changed epitope because these three mutations (i.e. positions 156, 159 and 188) were the selected critical positions.
Finally, we compared our models with two related methods [9, 25] for predicting antigenic variants. Wilson & Cox [9] suggested that a viral variant usually contains more than 4 residue mutations located on ≥ two of the five epitopes. Lee & Chen [25] proposed a model based on the hamming distance (HD) of 131 positions on all the five epitopes to predict antigenic variants.
Their models predicted a pair of HA sequences as "antigenic variants" if the number of mutation is more than 6.
Table 3.3 The changed epitopes and mutations of 11 virus-pairs under 4 models
Changed epitopes Mutation positions Virus A Virus B Type1 Model
A/Alaska/10/95 A/France/75/97 S ABCDE BC none none 12 135 128, 165 275, 312 226 262
A/Sydney/5/97 A/Ireland/10586/99 S ABDE ABD none none 7 137, 142192, 194 172,226 57
A/Mississippi/1/85 A/Leningrad/360/86 V ABDE B B B+ 6 138 156,
159, 188 226 88
A/Guizhou/54/89 A/Beijing/353/89 V ABC A A A 5 135,
144, 145159 44,
A/Wellington/1/2004 A/Victoria/505/2004 S ABDE AD none none 10 138, 145 189 219, 226, 227 94 A/Shangdong/9/93 A/Pennsylvania/9/93 S ABCD CD C C 12 135 164 53, 276
214, 219, 226, 229, 238
A/England/42/72 A/PortChalmers/1/73 V BDE B B B+ 6 160, 188,
193 208 63
A/NewYork/55/2004 A/Anhui/1239/2005 V ABD B B B+ 7 138, 156,
160, 193 219, 138,
A/Shanghai/16/89 A/Beijing/353/89 V AB A 'A' A 3 135, 145 159
1V represents antigenic variant and S represents similar virus.
2 denote hamming distance of a pair sequences
3 Bold is the antigenic critical position.
3.3.5. Variant ratio for measuring the antigenic drift
We used the variant ratio (VR) to measure the vaccine efficiency on year y. The VR is defined as
y y
N y V
VR( ) , where Ny is total number of circulating strains in the year y and Vy is the number of circulating strains which are "antigenic variants" against the vaccine strain in the year. Here, we considered an influenza vaccine should be updated and the circulating strains are emerging if the VR value is more or equal than 0.5.
3.4. Results
3.4.1. Antigenic critical positions
In this study, we continued our previous work to select the critical positions [32] having high IGs, statistically derived from 343 HI assays, and high entropies, which were calculated using 2789 HA sequences. 64 positions on HA were selected as critical positions (Table 3.4). Among these 64 critical positions, 54 positions locate on the epitopes (54/64) and 53 positions locate on the HA surface (Fig. 3.1B). Additionally, 13 and 42 of these 64 critical positions were the positive selections [31] and cluster substitutions [15], respectively.
Table 3.4 The list of 64 critical positions in the five different epitopes [9, 31]
List of critical positions Epitope A 122,124,126,131,133,135,137,140,143,144,145,146
Epitope B 128,155,156,157,158,159,160,164,186,188,189,193,196,197,198 Epitope C 50,53,54,275,276,278,307
Epitope D 121,172,174,201,207,213,216,217,230,242,244,248 Epitope E 62,63,75,78,82,83,260,262
Other area 2,3,9,25,31,199,202,222,225,326
3.4.2. Changed epitopes for antigenic variants
Currently, several methods measured a changed epitope to escape from neutralizing antibody [9].
Here, we utilized the degree of accumulated mutations within an epitope to evaluate a changed epitope according to 329 positions and 64 selected positions. Figures 3.2 and 3.3 show the relationships between changed epitopes and antigenic variants on 4 models.
0
Figure 3.2 The relationships between number of changed epitopes and antigenic variants based on four proposed models. (A) The first model considered an epitope as changed if there is at least one mutation within it. (B) The second model considered an epitope as changed if there are at least two mutations within it. (C) The third model considered an epitope as changed if there are at least two critical mutations within it. (D) The fourth model was derived from model three and further defined "1+" type if there are at least 2 and 3 critical mutations in epitope A and B.
respectively.
A
Figure 3.3 The changed-epitope composition and antigenic variants on 4 models. (A) Model one.
(B) Model two (C) Model three and (D) Model four.
Models one and two: Changed epitopes on 329 positions
Figures 3.2A (Model one) and 3.2B (Model two) show the relationships between number of changed epitopes and "antigenic variants" on 343 pair of HA sequences with HI assays. Among these 343 pairs for Model one, the changed epitopes of 225 "antigenic variants" pairs range from 1 to 5 and the changed epitopes of 118 "similar viruses" pairs range from 0 to 5. Among 34 similar viruses with more than 4 changed epitopes for Model one, we observed the following results: (1) the average number of changed epitopes was 4.2; (2) the average number of changed epitopes with only one mutation was 2.02 and 33 pairs have more than one changed epitope with only one mutation. For example, the virus pair, A/PortChalmers/1/73 and A/Singapore/4/75, has four changed epitopes with one mutation (i.e. Epitopes A, C, D, and E) (Table 3.3). In general, these 34 similar viruses should be regarded as "antigenic variants" because there are more than four changed epitopes. This result shows that the Model one is not reasonable.
For Model two, the average number of changed epitopes was 2.2 for these 34 similar viruses.
According to the distribution (Fig. 3.2B), Model two achieved the highest accuracy if more than two changed epitopes was considered as "antigenic variants". The accuracies were 74.9%
(257/343) and 92.2% (29410/31878) for predicting antigenic variants on the training set and independent set, respectively. This result was similar to the previous work [9].
Model three: Changed epitopes on 64 selected positions
Model three considered a changed epitope when the number of mutations on the 64 selected critical positions is more than 2. In Model two, the numbers of "antigenic variants" and "similar viruses" with ≥ 3 changed epitopes were 119 and 16, respectively (Fig. 3.2B). The averages of changed epitopes with ≥ 2 mutations on 329 positions for "antigenic variants" and "similar viruses" were 3.8 and 3.2, respectively. The averages of changed epitopes with ≥ 2 mutations on 64 selected critical positions for "antigenic variants" and "similar viruses" were 3.2 and 1.5, respectively (Fig. 3.2C). These observations show that Model three using mutations on 64 critical positions is better than Model two to discriminate "antigenic variants" from "similar viruses". For the "similar viruses", A/Alaska/10/95 and A/France/75/97, there are 12 mutations to drive zero changed epitope because no epitope with ≥ 2 mutations on selected 64 positions
Three HA/antibody complex structures [10] can be used to provide structural evidences for the changed epitopes (Fig. 3.4). Among these complexes, two antibodies bind to epitopes A and B (PDB code 1KEN [58] and 2VIR [59]), while the third binds to epitopes C and E (PDB code 1QFU [60]). The antibodies consistently bind to two epitopes and this result agrees to Models two and three. HA/antibody structures and Models two and three show that two position mutations often induce the conformational change of an epitope to escape from the antibody recognition. However, the numbers of changed epitopes of 48 "similar viruses" pairs are 2 (35 pairs) and ≥ 3 (16 pair) for Model two (Fig. 3.2B). Conversely, 14 "similar viruses" pairs have more than 2 changed epitopes for Model three (Fig. 3.2C).
A B C
Figure 3.4 The three HA-antibody complex structures. PDB codes are (A) 1KEN [58] (B) 2VIR [59] and (C) 1QFU [60]. All of the three structures of antibodies bind on two epitopes on HA by heavy chain (pink) and light chain (green). The five epitopes on HA are labelled (Epitope A in red; B in purple; C in orange; D in cyan; E in green).
Model four
Among 72 "antigenic variants" pairs with one changed epitope based on Model three, 70 pairs change on epitopes A or B. The single changed epitope on A or B, which can cause "antigenic variants", agreed to HA/antibody complex structures and the experiments. The receptor-binding site, surrounded by epitopes A and B, is a basis for HA for the neutralizing mechanism [58, 61]
(Fig. 3.1B).
Based on this observation, the epitopes A and B play a key role for neutralizing antibodies.
Model four based on Model three considered a pair of HA sequences as "antigenic variants"
when ≥ 2 changed epitopes or ≥ 1 changed epitope on A or B. In Model 4, a pair of HA sequences with ≥ 3 mutations on 64 critical positions for the epitope B is regarded as "antigenic variants". Thus, we annotated a virus-pair with single changed epitope on A or B as "1+" type (Fig. 3.3D). For example, the pair, A/Guizhou/54/89 and A/Beijing/353/89, occurs the changed epitope on A (i.e. mutation positions 135, 144 and 145) (Table 3.3). The accuracies of Model four were 81.6% and 94.0% on the training set and independent set, respectively. This model outperformed two compared methods, i.e. Wilson & Cox (89.7%) [9] and Lee & Chen (92.4%) [40], on the independent data set (Fig. 3.5).
73%
76% 74% 75% 77%
82%
90% 92%
90% 92% 92% 94%
50%
60%
70%
80%
90%
100%
Wilson &
Cox, 1990
Lee & Chen, 2004
Model One Model Two Model Three Model Four
A ccu racy
343 Pairs 31,878 Pairs
In the HA/antibody structure complex (PDB code 1KEN [58]), the antibody binds on epitopes A and B using two CDRs (i.e. CDR1 and CDR3) on the heavy chain and one CDR (i.e.
CDR2) on the light chain (Fig. 3.6). The interface of antibody and HA consists of 13 and 5 contacted residues locating on epitopes B and A, respectively. Among these 13 positions, 7 positions were selected as critical positions. Based on Model four, 46 "antigenic variants" pairs have one changed epitope B with 3 mutations on epitope B, denoted as "B+". This result suggested a single changed epitope B can cause antigenic variants. For example, the pair virus strains, A/NewYork/55/2004 and A/Anhui/1239/2005, have three critical mutations on epitope B (i.e. positions 156, 160 and 193) (Table 3.3). According to the HA/antibody structure (Fig. 3.6), the residue 156 interacts to CDR2 (position 55 on the antibody) and the residue 193 interacts with three residues on CDR2 (positions 50, 55 and 57) and one residue on CDR3 (position 105).
This structure suggested that mutations on residues 156, 160 and 193 can induce the conformation change on epitope B to escape from CDR2 and CDR3 of the neutralizing antibody.
CDR1 CDR3
CDR2
193 189 159 156
Antibody
HA
Figure 3.6 The HA/antibody structure and interface. (A) The antibody and HA trimer (PDB code 1KEN [58]). (B) The interface of the antibody and HA. The critical positions on epitope B and the CDRs of the antibody are labelled.
0 1 2 3 4
1982-1983 1983-1984 1984-1985 1985-1986 1986-1987 1987-1988 1988-1989 1989-1990 1990-1991 1991-1992 1992-1993 1993-1994 1994-1995 1995-1996 1996-1997 1997-1998 1998-1999 1999 1999-2000 2000 2000-2001 2001 2001-2002 2002 2002-2003 2003 2003-2004 2004 2004-2005 2005 2005-2006 2006 2006-2007 2007 2007-2008 2008
HD
0000 1982-1983 0000 1983-1984 0000 1984-1985 0000 1985-1986 0000 1986-1987 0000 1987-1988 0000 1988-1989 0000 1989-1990 0000 1990-1991 0000 1991-1992 0000 1992-1993 0000 1993-1994 0000 1994-1995 0000 1995-1996 0000 1996-1997 0000 1997-1998 0000 1998-1999 0000 1999 0000 1999-2000 0000 2000 0000 2000-2001 0000 2001 0000 2001-2002 0000 2002 0000 2002-2003 0000 2003 0000 2003-2004 0000 2004 0000 2004-2005 0000 2005 0000 2005-2006 0000 2006 0000 2006-2007 0000 2007 0000 2007-2008 0000 2008
Variant Ratio
Figure 3.7 The epitope evolution and the antigenic drift from 1982-1983 to 2008 influenza season. (A) The distributions of variant ratios of WER strains from 1982-1983 to 2008 season.
The match between Model four and WER are labelled (Match in red arrow; Not match in blue arrows). (B) The average hamming distances (HD) of 5 epitopes from 1982-1983 to 2008.
Antigenic drift and epitope evolution
We utilized the changed epitopes to study the antigenic drift on 2,789 circulating strains ranging from influenza season 1982-1983 to 2008 (36 influenza seasons). One of WHO surveillance network's purposes is to detect the emergence and spread of antigenic variants that may signal a need to update the composition of influenza vaccine [14-15]. Here, we considered an emerging antigenic variant according to WER strain, which was the dominant strain in each influenza season [34] (Table 3.1). For a selected season, we applied Model four, measuring changed epitopes for the pairs between the vaccine and circulating strains for "antigenic variants", and the
Among 36 influenza seasons, our model detected 12 seasons with emerging antigenic variants (VR ≥ 0.5) and 10 of them followed by the update of WER strain in the next season (Fig.
3.7A). For example, the 1885-1986 season, 80% of the circulating strains with changed epitope
"B+" (Fig. 3.7B), is the first emerging antigenic variants and the WER strain updated in the next season (i.e. from A/Mississippi/1/85 to A/Leningrad/360/86). Moreover, among seven "emerging antigenic variants" seasons (matching WHO vaccine updates), four seasons (i.e. 1989-1990, 1991-1992, 1995-1996 and 2002-2003) matched the antigenic cluster transitions proposed by Smith et al. [15]. The other three seasons, which were detected by one changed epitope on A or B, are consistent to the WER strain updates (i.e. 1985-1986, 1987-1988 and 1999). These observations suggested that "emerging antigenic variants" with ≥ 2 changed epitopes may cause the major antigenic drift while "emerging antigenic variants" with one changed epitope on A or B may cause the minor antigenic drift.
To observe the epitope evolution, Figure 3.7B illustrates the hamming distance (HD) on 64 critical positions of all the five epitopes. For example, the VR of the season 1985-1986 was 0.8 (Fig. 3.7A) and the epitope with the largest HD was epitope B (HD is 3.4). For 15 seasons with WER strain updates, the average HD of epitopes A, B, C, D and E were 1.2, 2.1, 0.5, 0.4 and 0.4 respectively. These observations showed that epitopes A and B change more frequently in vaccine update seasons and play a key role for the antigenic drift.
0.0 0.5 1.0
0000 1982-1983 0000 1983-1984 0000 1984-1985 0000 1985-1986 0000 1986-1987 0000 1987-1988 0000 1988-1989 0000 1989-1990 0000 1990-1991 0000 1991-1992 0000 1992-1993 0000 1993-1994 0000 1994-1995 0000 1995-1996 0000 1996-1997 0000 1997-1998 0000 1998-1999 0000 1999 0000 1999-2000 0000 2000 0000 2000-2001 0000 2001 0000 2001-2002 0000 2002 0000 2002-2003 0000 2003 0000 2003-2004 0000 2004 0000 2004-2005 0000 2005 0000 2005-2006 0000 2006 0000 2006-2007 0000 2007 0000 2007-2008 0000 2008
Variant Ratio
Model four Wilson & Cox Wilson & Cox & 64 A.A.s
MI8 5
LE86 BE92SD93 BR07
SH87
SI87 WU95
SY97
FU02 CA04 WI05
PH82 BE89 JO94 MW99
Influenza Season
WER strains
Figure 3.8 The comparison between our method and Wilson & Cox's model [9] in the antigenic drift from 1982-1983 to 2008 influenza season.
Table 3.5 Example of 13 antigenic variants without changed epitopes Fujian/140/2000 Chile/6416/2001 V S 12 144 186, 194 273 226, 246, 247
Hong_Kong/1/94 Guangdong/25/93 V S 8 124 47, 299 96, 216, 219, 226 92
Panama/2007/99 Chile/6416/2001 V S 7 144 186 246
Wellington/1/2004 Singapore/68/2004 V S 9 145 189 50 226, 227 94 Wellington/1/2004 Victoria/513/2004 V S 5 145 186, 190 167, 226 Wellington/1/2004 Wisconsin/19/2004 V S 5 138, 145 186 278 226
Fujian/140/2000 NewYork/55/2001 V V 12 144 186, 194 273 226, 229, 247
Victoria/3/75 Victoria/112/76 V V 2 229
1 the antigenic type of virus B relative to antisera against virus A.
2 the antigenic type of virus A relative to antisera against virus B.
3.5. Discussion
Based on the accumulated HI assays from 1968 to 2008, we identified 64 critical positions on HA. Among the 64 critical positions, we observed that 10 positions are not located on all the five epitopes. Furthermore, 4 of the 10 positions were almost conserved from 1968 to 2000 and underwent frequency switch [41] after year 2000 (positions 25, 202, 222 and 225). These new emerging positions suggested that the previously conserved positions may become new antibody binding sites and IG can identify new emerging positions from HI assay. Moreover, the emerging mutations also revealed a need to update the epitope definition that proposed before 1999 [9, 31].
According to the distribution of antigenic variants of Model four (Fig. 3.3D), it is interesting that the main samples (209/225 pairs) of the antigenic variants have the changed epitope on epitopes A or B. In addition to this, among the 85 pairs of antigenic variants which had one or no
According to the distribution of antigenic variants of Model four (Fig. 3.3D), it is interesting that the main samples (209/225 pairs) of the antigenic variants have the changed epitope on epitopes A or B. In addition to this, among the 85 pairs of antigenic variants which had one or no