J. Biomedical Science and Engineering, 2009, 2, 117-122
Published Online April 2009 in SciRes. http://www.scirp.org/journal/jbise JBiSE
Prediction of mutation position, mutated amino
acid and timing in hemagglutinins from North
America H1 influenza A virus
Shao-Min Yan1, Guang Wu2*
1Guangxi Academy of Sciences, 98 Daling Road, Nanning, Province Guangxi 530007, China. 2DreamSciTech Consulting, 301, Building 12, Nanyou A-zone,
Jiannan Road, Shenzhen, Province Guangdong 518054, China. Correspondence should be addressed to Guang Wu (hongguanglishibahao@yahoo.com)
Received Jan. 8th, 2009; revised Feb. 9th; 2009; accepted Feb. 10th, 2009
This study was trying to predict the mutations
in H1 hemagglutinins of influenza A virus from
North America including the predictions of mu-
tation position, the predictions of would-be-
mutated amino acids and the predictions of
time of occurrence of mutations. The results
paved a possible way for accurate, precise and
reliable prediction of mutation in proteins from
influenza A virus.
Keywords: Hemagglutinin, Influenza, Mutation,
Neural Network, Prediction
Mathematical modelling provides a promising hope to
predict the mutation in proteins from influenza A virus,
not only because the history shows that accurate, precise
and reliable predictions are mainly based on mathemati-
cal modelling, but also the prediction of mutations at
protein can be classified as prediction of mutation posi-
tion, prediction of mutated amino acid and timing of mu-
tation [1]. All these require the use of more sophisticated
mathematical tools.
Perhaps, the best way to predict the mutation is to find
its cause, thus a mutation could occur if the same cause
appears again. However, the causes, which led to his-
torical mutations, might not leave any sign to trace, and
the evolved proteins from influenza A virus may no
longer be sensitive to the causes, which led to mutations
in the past. All these mean that the mutation causes
would be poor predictors for prediction of mutations,
while the preparedness for possible pandemic/epidemic
of influenza would lag behind the appearance of influ-
enza without prediction. On the other hand, no matter
what mutation cause is, any cause would leave signs in a
protein, otherwise, no mutation would be recorded.
These signs can be arguably used for prediction. This is
the basic consideration for prediction of mutations using
Generally, the amino acids in a protein is represented
as alphabet, thus a number of models use amino-acid
symbols as operating units, for example, sequence align-
ment, phylogenetics, and multi-sequence comparison, by
which the history of proteins of interests can be traced
[2,3]. Unfortunately, these symbol-based approaches
cannot accurately and precisely answer the predictions
proposed, because they cannot operate in sophisticated
mathematical models, whose operating units are values.
In this view, the protein science actually is at the his-
torical phase of searching for the ways to represent a
protein sequence as a numeric sequence, and it is hoped
that the numeric sequence is sensitive to mutations, posi-
tions of amino acids in protein sequence, composition of
protein sequence, length of protein sequence, neighbour-
ing amino acids.
In fact, currently there are several ways to transfer a
protein sequence into a numeric sequence, and the most
profound one would be the use of the physicochemical
property to represent a protein sequence [4] as well as
related approaches [5-10].
On the other hand, other approaches are also devel-
oped, for example, the approaches based on random
mechanism to quantify each amino acid in a protein as
well as a protein in whole [1].
This study was designed to predict the mutation posi-
tions, the mutated amino acids and the time of occur-
rence of mutations in the hemagglutinins from North
America H1 influenza A viruses using neural network,
because the hemagglutinin is the major surface antigen
of influenza viruses, against which neutralizing antibod-
ies are elicited during virus infection and vaccination [11-
15]. Among various types, the H1 influenza virus is the
cause for several historical disasters, such as 1918 Spanish
flu, 1977 Russian flu, 1950 and 1988 epidemics [16-18].
The amino acid sequences and corresponding RNA se-
quences of 494 hemagglutinins from North America in-
fluenza A/H1 viruses isolated from 1918 to 2008 were
obtained from the influenza virus resources [19]. Forty-
SciRes Copyright © 2009
118 S. M. Yan et al. / J. Biomedical Science and Engineering 2 (2009) 117-122
SciRes Copyright © 2009 JBiSE
six identical hemagglutinins were excluded, thus the re-
maining 448 hemagglutinins were used in this study.
2.1 Amino-Acid Pair Predictability
According to the permutation [1, 20, 21], for example,
there are 47 asparagines “N” and 37 valines “V” in the
hemagglutinin, strain A/swine/Ontario/53518/03(H1N1),
accession number DQ280219, the frequency of amino-
acid pair NV is 3 (47/566×37/565×565=3.072), that is,
NV would appear three times in this hemagglutinin. Ac-
tually 3 NVs can be found in this hemagglutinin, so NV
is predictable and the difference between its predicted
and actual frequency is 0. Again, there are 48 leucines
“L” in DQ280219 hemagglutinin, and the frequency of
random presence of LL is 4 (48/566×47/565×
565=3.986), i.e. there would be four LLs in the hemag-
glutinin. But LL appears nine times in reality, so the dif-
ference between its predicted and actual frequency is -5.
After such calculations [22], each amino-acid pair had
its difference between predicted and actual frequency.
As a point mutation is relevant to a single amino acid,
which connects with two neighbouring amino acids
except for the terminal one and constructs two amino-
acid pairs, so each amino acid has the sum of differ-
ence between predicted and actual frequency in two
neighbouring amino-acid pairs, which is the first
quantification for each amino acid in a hemagglutinin.
Nevertheless, any hemagglutinin must have a certain
amount of predictable amino-acid pairs, by which the
percentage of how many amino-acid pairs predictable
can be found. This predictable portion is the quantifi-
cation for a whole hemagglutinin.
2.2 Amino-Acid Distribution Probability
According to the occupancy of subpopulations and parti-
tions, the positions of any type of amino acids in hemag-
glutinin can be viewed as a certain distribution [10, 23-
31], whose probability is r
××× !...!!
[32], where r is the number of amino acids, n is the num-
ber of partitions, rn is the number of amino acids in the n-
th partition, qn is the number of partitions with the same
number of amino acids, and ! is the factorial function.
For instance, there are 36 lysines “K” in DQ280219
hemagglutinin. Their predicted and actual distribution
probabilities are 0.0419 and 0.0020 [33], so the ratio of
predicted versus actual distribution probabilities is 20.95,
whose natural logarithm is 3.0421, which is the second
quantification for each amino acid in a hemagglutinin.
2.3 Future Composition of Amino Acids
The relationship between 64 RNA codons and translated
amino acids is governed by translation probability [1,
34-36], based on which the amino acid mutating prob-
ability can be determined. For example, alanine “A” has
the 12/36 chance of mutating to “A”, but cysteine “C”
has no chance of mutating to “A”, then both aspartic
acid “D” and glutamic acid “E” have the 2/18 chance of
mutating to “A”, and so on. In total, the future composi-
tion of amino acid “A” is 6.1271% in DQ280219 he-
magglutinin, whereas its current composition is only
5.1146% (29/567), and the ratio is 1.1980 (6.1271%
/5.1146%), thus the future composition of amino acids is
got [1], and assigned the ratio of predicted versus actual
compositions to each amino acid [37], which is the third
quantification for each amino acid in hemagglutinin [1].
Although there are countless mutation causes impact-
ing a parent protein, these causes should leave their
traces in the protein, which should be measured out us-
ing these three quantifications, which in fact represent
the countless mutation causes.
2.4 Prediction of Mutation Position
Any mutation cause can lead to occurrence or non-
occurrence of mutation, which can be classified as unity
and zero after comparing a parent protein with its daugh-
ter protein. In this way, the occurrence or non-
occurrence of mutation in a parent protein becomes a
binary sequence. Thus, two datasets can be got, the mu-
tation cause dataset, which are three quantifications, and
the mutation consequence dataset, which is a binary se-
quence. Moreover, these two datasets have the position-to-
position relationship (Table 1), which is the cause-
mutation relationship. Mathematically this relationship is
the problem of classification, which can be solved either
using the logistic regression in statistics or neural net-
work. The feed forward backpropagation neural network
Table 1. Inputs and target of DQ280219 hemagglutinin sequence.
Quantified hemagglutinin sequence
Position Amino acid I II III
Mutation se-
1 M -2 0.0000 1.2569 0
… … … … … …
276 R -2 1.2809 1.9392 0
277 G -1 2.3790 0.7887 0
278 H 0 0.0000 1.2396 1
279 G 0 2.3790 0.7887 1
280 S 1 4.0008 1.1081 0
… … … … … …
566 I -2 1.1285 0. 9590 0
S. M. YAN et al. / J. Biomedical Science and Engineering 2 (2009) 117-122 119
Published Online April 2009 in SciRes. http://www.scirp.org/journal/jbise JBiSE
would be applied to this relationship to predict the muta-
tion position.
2.5 Prediction of would-be-mutated Amino
The prediction was made using the amino-acid mutating
probability, which was based on the relationship be-
tween RNA codons and translated amino acids [1].
2.6 Timing of Mutation
As each hemagglutinin is different one from another due
to mutation, each hemagglutinin would be quantified
differently one from another. Along the time axis, all
hemagglutinins would construct their evolutionary proc-
ess, and the timing of the mutation would be possible by
detailed analysis of this evolutionary process.
2.7 Software and Statistics
The MatLab software [38] was used for prediction. The
prediction sensitivity, specificity and total correct rate
were calculated according to the published method [39].
The performance of modelling was measured using the pre-
diction sensitivity (42.9%±31.4%), specificity (99.5%
±0.4%) and total correct rate (99.0%±0.4%), because the
predicted mutation positions can be classified as the posi-
tives, false positives, negatives and false negatives when
comparing the predicted with the actual mutation positions.
As seen, the prediction sensitivity was still low although
the prediction specificity and total correct rate were quite
After the prediction of possible mutation positions us-
ing the neural network, the would-be-mutated amino ac-
ids at predicted positions can be predicted using the
amino-acid mutating probability [1]. Figure 1 illustrates
the prediction of possible mutation positions and mu-
tated amino acids at the predicted positions, where the
solid line in the lower panel is the predicted mutation
probability by the neural network with respect to each
amino acid in ABX58602 hemagglutinin and the dotted
line is the cut-off mutation probability of 0.5, that is, the
amino acid whose mutation probability is larger than 0.5
risks mutation. For this hemagglutinin, there were two
positions (98 and 507) whose mutation probability was
larger than 0.5, so the amino acid E at these positions
would have a larger chance of mutation. Meanwhile, the
would-be-mutated amino acid can be determined using
the amino-acid mutating probability (upper panel),
where the amino acid “D” has the largest chance to ap-
pear. So the lower panel indicates the possible mutation
positions with probability, and the upper panel displays
the would-be-mutated amino acids with probability.
Figure 2 displays the evolution of North America H1
hemagglutinins. This predictable portion fluctuated over
time, which represented the mutation process. With fast
Fourier transform, which is suitable to find the periodic-
ity in chaotic dataset, the mutation periodicity can be
found from Figure 2, where (i) the evolutionary process
of influenza A virus hemagglutinins from 1978 to 2008
contained many periodicities; (ii) each periodicity sug-
gested different number of mutations along the time
course; (iii) the periodicity with the biggest number of
mutations was about 5.6 years, thus the time when muta-
tions would occur in future can be estimated; and (iv)
the hemagglutinin periodicity provides the chance to
trace the possible mutation cause in nature, because each
periodicity may correspond to a natural phenomenon.
Figure 1. Prediction of mutation positions and would-be-mutated amino acids. On the lower panel: the x-axis represents the position of
ABX58602 hemagglutinin from 1 to 565, because ABX58602 hemagglutinin is composed of 565 amino acids; the y-axis represents the
mutation probability predicted using neural network model, where there are two probabilities larger than 0.5 at positions 98 and 507. On
the upper panel, the centre of pie is labelled as “E” glutamic acid, which is the amino acid at positions 98 and 507 of ABX58602 hemag-
glutinin. The other letters represent the would-be-mutated amino acids, and the area occupied by letter represents the probability to mu-
tate to this amino acid based on the amino-acid mutating probability, for example, “E” has the largest chance to mutate to “D”.
Position of ABX58602 hemagglutinin
050100150 200 250 300 350 400 450500 550
Mutation probability
Would-be-mutated amino acids with probability
Would-be-mutated amino acids with probability
Position of ABX58602 hemagglutinin
Mutation probability
120 S. M. Yan et al. / J. Biomedical Science and Engineering 2 (2009) 117-122
SciRes Copyright © 2009 JBiSE
1918 1927 1936 1945 1954 1963 1973 1982 1991 2000 2009
Predictable portion of amino-acid pairs (%)
Pandemic scares
Figure 2. Evolution of 448 hemagglutinins of North America H1 influenza viruses. The data
are presented as mean±SD. The dotted lines are regressed lines 95% confidence intervals.
Figure 3. Stratification of hemagglutinin evolution after finding the periodicity using fast Fourier transform.
Furthermore, an attempt was made to time the muta-
tion by stratifying the hemagglutinin evolution in Fig-
ure. 2 according to its periodicity, and Figure 3 shows
such an example, where the hemagglutinin evolution in
Figure 2 is stratified according to 6-year periodicity be-
cause it was the periodicity with biggest number of mu-
tations. Figure 3 shows that there would be a 2-year stable
period before possible more mutations would occur in 2010.
At this stage of development, it is yet to verify the
predictions made in this study. However, this is not un-
common phenomenon in science, because the first step
is to find a way to transfer the measurements into the
domain, where a mathematical model can be applied, the
second step is build a model, and the third step is to
make the predictions. These three steps are more related
to theoretical work. Thereafter the last step would be the
verification experimentally, which is certainly beyond
the scope of this paper. On the other hand, the science
advances so much, it is impossible to verity each hy-
pothesis and prediction, for example, the humans cannot
create another earth without global warming to compare
the effects on subjects of interests. With respect to the
predictions in this study, the verifications can be done by
using the same method in man-made mutations in indus-
trial enzymes, where each mutation can be recorded and
compared with prediction.
Predictable portion (%)
From 1976
From 1981
From 1987
From 1992
From 1999
From 2005
Predictable portion (%)
From 1976
From 1981
From 1987
From 1992
From 1999
From 2005
We are here in 2008.
0 1 2 3 4 5 6
S. M. Yav et al. / J. Biomedical Science and Engineering 2 (2009) 105-110 121
SciRes Copyright © 2009 JBiSE
The frequency of mutations is not identical along a
hemagglutinin sequence, namely, the different position
has different chance of mutations. In fact, the prediction
made in this study is consistent with this observation as
seen in Figure 1, where the predicted mutation probabil-
ity is not identical along the ABX58602 hemagglutinin.
To the best of knowledge, there are several models
conducted at different levels for the prediction of possi-
ble pandemic/epidemic of influenza. At epidemiological
level, the predictions were made using early indicators
[40], time series analysis [41,42], etc. At clinical level,
the prediction was made using medical visit [43], out-
break signatures [44], etc. At social level, the prediction
was made using sales of computer printers, elections,
and the Federal Reserve's decisions about interest rates
[45]. At seroarcheological level, the prediction was
made using accumulation of mutations or true recombi-
national events [46]. At protein level, the prediction was
made with epitope [47-49], conformation [50]. However,
no similar prediction was made with respect to the ap-
proached used in this study. The difference includes: (1)
the quantification of protein sequences in this study was
based on the random principle, (2) the occurrence and
non-occurrence of mutation was quantified as yes-no
event, (3) the cause-mutation relationship was defined
using neural network, (4) the would-be-mutated amino
acid was determined using the amino-acid mutating
probability, and (5) the time of mutation was determined
using the fast Fourier transform to stratify the time inter-
val between outbreak of influenza.
This study paved a possible way for accurate, precise
and reliable prediction of mutation in proteins from in-
fluenza A virus, because the model in prediction was the
cause-mutation model, which was helpful for under-
standing of underlined mutation mechanism.
This study was supported in part by National Natural Science Founda-
tion No. 20666002 (Guangxi Assignment No. 0728001).
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