Секция 1. Защита информации и компьютерный анализ данныхWe present two new highly efficient pyrosequencing error correction algorithms:
(i) k-mer – based error correction (KEC); and (ii) empirical frequency threshold
(ET). Both were compared to the recently published clustering algorithm
SHORAH to evaluate the relative performance using 24 experimental datasets obtained
by 454-sequencing of amplicons with known sequences. We found that all
three algorithms showed similar performance in terms of finding true haplotypes, but
KEC and ET methods significantly outperformed SHORAH both in terms of their
ability to remove false haplotypes and to estimate the frequency of true ones

Campo, D.

Dimitrova, Z.

Forbi, J.

Khudyakov, Y.

Rossi, L.

Skums, Р.

Vaughan, G.

Yokosawa, J.

Zelikovsky, A.

English

Электронная библиотека БГУ

 196
EFFICIENT  ERROR  CORRECTION  AND  HAPLOTYPES  
RECONSTRUCTION  FOR  DEEP  SEQUENCING 
OF  HEPATITIS  C AMPLICONS 
 
 
Pavel  Skums
1
 , Zoya  Dimitrova1, David  Campo1, Gilberto  Vaughan1,  
Livia  Rossi1, Joseph  Forbi1, Jonny  Yokosawa2, Alex  Zelikovsky3  
and  Yury  Khudyakov
1
 
1
Centers for Disease Control and Prevention 
Atlanta, USA 
2
Universidade Federal de Uberlândia 
Minas Gerais, Brazil 
3Georgia State University 
Atlanta, USA 
E-mail: skumsp@gmail.com 
 
We present two new highly efficient pyrosequencing error correction algo-
rithms: (i) k-mer – based error correction (KEC); and (ii) empirical frequency thresh-
old (ET). Both were compared to the recently published clustering algorithm 
SHORAH to evaluate the relative performance using 24 experimental datasets ob-
tained by 454-sequencing of amplicons with known sequences. We found that all 
three algorithms showed similar performance in terms of finding true haplotypes, but 
KEC and ET methods significantly outperformed SHORAH both in terms of their 
ability to remove false haplotypes and to estimate the frequency of true ones. 
 
Keywords: HCV, quasispecies, pyrosequencing, error correction. 
 
INTRODUCTION 
 
Hepatitis C virus (HCV) shows a very high level of sequence heterogeneity, which is 
responsible for its escape from neutralizing host immune responses and rapid development 
of drug resistance. Recent advances in high-throughput (HT) sequencing methods allow for 
analysis of the unprecedented number of HCV-genomic sequence variants from infected pa-
tients and present a novel opportunity for understanding HCV evolution, drug resistance and 
immune escape. However, owing to the massive scale of sequencing, sequence errors gener-
ated during HT sequencing require extensive computational processing with error correction 
algorithms in order to obtain high quality reads for genetic analysis. The key purpose of such 
algorithms is to discriminate between artifacts and actual sequences. This task becomes es-
pecially challenging for recognizing and preserving low-frequency natural variants in viral 
population.   
SHORAH [6][7] is currently one of the best error correction algorithms available. It 
uses probabilistic clustering approach based on the Dirichlet process mixture. Another ap-
proach to error correction is based on the use of k-mers, or substrings of reads of a fixed 
 197
length k [2][3][5]. These algorithms have good performance but high time- and memory-
consumption needs, together with the possibility of errors introduced during the correction 
phase [6]. To overcome these disadvantages, the authors of EDAR algorithm [1] developed 
an approach for the detection and deletion of sequence regions containing errors. This error 
deletion works well for shotgun experiments, but is unacceptable for the small amplicon 
reads commonly analyzed in viral samples. 
In this paper, we present two new efficient error correction algorithms: (i) k-mer-based 
error correction (KEC); and (ii) empirical frequency threshold (ET). KEC uses the EDAR 
algorithm optimized for amplicon sequencing for the detection of error regions and a novel 
algorithm for correction of errors associated with homopolymers. KEC does not require a 
reference sequence and is, therefore, suitable for de-novo sequencing. The ET algorithm 
uses estimation of a frequency threshold for indels and haplotypes calculated from experi-
mentally obtained clonal sequences, also correcting homopolymers. Both algorithms were 
compared to SHORAH to evaluate their relative performance using 25 experimental ampli-
con datasets with known sequences obtained using 454 sequencing.  
 
ALGORITHMS  DESCRIPTION 
 
KEC algorithm. The scheme of KEC includes 4 steps. 
 (1) Calculate k-mers and their frequencies (k-counts). We assume that k-mers with 
high k-counts (“solid” k-mers) are correct, while k-mers with low k-counts (“weak” k-mers) 
contain errors.  All data is stored using hash maps, which significantly speeds up the calcula-
tions. 
(2) Determine the threshold k-count (error threshold), which distinguishes solid k-mers 
from weak k-mers. The method uses the observation, that frequencies of k-counts of errone-
ous k-mers and correct k-mers follow different distributions (the exponential distribution 
and the mixture of distributions, respectively).   
(3) Find error regions. The error region is the segment [i,j] of read such that for every 
p∈[i,j] the k-mer starting at the position p is considered weak.  The algorithm uses the clus-
tering by the variable bandwidth mean-shift method [3] (as proposed in [1]). 
(4) Correct the errors in error regions. This stage consists of 2 substages: (4.1) error 
correction in error regions and (4.2) error correction and haplotypes reconstruction using 
local search algorithm based on the pairwise and multiple alignments. (4.1) is based on the 
following idea: correct the error in the read r by finding the minimum-size set of insertions, 
deletions and replacements, which transform the r  into read with all k-mers being solid. The 
dynamic programming algorithm for this problem was proposed in [3]. However, it has qua-
dratic complexity, and therefore is too slow for using for large data sets. We propose the ef-
ficient and fast heuristics for the problem, which is based on the observation, that the type 
and the correction of every error can be deduced by the length of the corresponding error 
region and the sequence of nucleotides following it. 
ET algorithm. The key idea of the procedure is to calculate the frequency of errone-
ous sequences in amplicon samples where only a single sequence was expected. Each single-
clone sample was processed in the following way:  First, each sequence is aligned against a 
set of external references of all known genotypes. For each sequence the best match of the 
external set is chosen. The aligned sequence is clipped to the size of the chosen external ref-
erence. The 20 most frequent sequences that do not create insertions or deletions are se-
 198
lected, constituting the internal reference set. Each sequence is aligned against each member 
of the internal references set and its best match is chosen.  
The frequency of erroneous indels and its standard deviation (s.d.) was calculated over 
all nucleotide positions for 15 single-clone samples. An indel threshold was defined as the 
average frequency of erroneous indels + 5 s.d. If a sequence contained an indel with a fre-
quency lower than the threshold, the sequence was removed. Then all homopolymers of at 
least 4 nucleotides were identified, followed by removal of the insertions and replacement of 
the deletions by the repeated nucleotide. The frequency of erroneous sequences and its s.d. 
were calculated over the 15 single-clone samples. A sequence threshold was defined as the 
average frequency of erroneous sequences + 5 s.d. All sequences with a frequency lower 
than the threshold were removed. This procedure was applied to each mixture sample. 
 
ALGORITHMS  COMPARISON 
 
Individual plasmid clones (n=10) containing different HCV hypervariable region 1 
sequences were purified and sequenced using dye-terminator sequencing. A set of plasmid 
samples was generated. 14 samples contained a single clone. 10 samples contained 8 clones 
mixed together in different proportions (from 1% to 93%). The E1/E2 region (309 nt) was 
amplified from each sample and sequenced using GS FLX Titanium Series Amplicon kits. 
Low quality reads were removed using the GS Run Processor (Roche, 2010). Each sequence 
file was then analyzed using ET, KEC or SHORAH error correction algorithms. SHORAH 
was applied several times under different parameters and the best attained results are 
reported here. All results are summarized in Table 1. 
 
 
Table 1. Test results of the single-clone (S) and mixture (M; n=8) samples. MT: 
Missing true sequences; FS: False sequences; MSE: root mean square error; HD: Average 
Hamming distance, averaged over all false sequences 
 
 ET KEC SHORAH 
 MT FS RMSE HD MT FS RMSE HD MT FS RMSE HD 
S1 0 0 0.00 0 0 2 1.63 2.5 0 351 29.02 4.84 
S2 0 0 0.00 0 0 0 0 0 0 269 30.12 4.44 
S3 0 1 1.09 1 0 0 0 0 0 292 23.44 5.31 
S4 0 1 0.98 2 0 0 0 0 0 271 44.68 5.39 
S5 0 0 0.00 0 0 0 0 0 0 319 9.63 4.47 
S6 0 1 5.26 2 0 0 0 0 0 194 18.70 3.94 
S7 0 0 0.00 0 0 0 0 0 0 496 21.52 6.70 
S8 0 0 0.00 0 0 0 0 0 0 262 14.37 4.58 
S9 0 0 0.00 0 0 0 0 0 0 183 6.23 6.97 
S10 0 0 0.00 0 0 0 0 0 0 288 7.77 5.11 
 199
 ET KEC SHORAH 
S11 0 1 0.53 2 0 0 0 0 0 717 24.71 5.03 
S12 0 0 0.00 0 0 0 0 0 0 611 25.94 5.52 
S13 0 0 0.00 0 0 0 0 0 0 156 5.53 4.93 
S14 0 0 0.00 0 0 0 0 0 0 161 6.83 6.60 
Mean 0.00 0.29 0.56 0.50 0 0.14 0.11 0.17 0.00 326.43 19.18 5.27 
M1 0 0 1.17 0 0 0 0.78 0 0 320 1.23 4.51 
M2 0 0 1.50 0 1 0 4.06 0 0 738 3.70 4.44 
M3 0 0 2.92 0 0 0 1.94 0 0 638 3.65 4.25 
M4 0 0 2.18 0 0 0 4.21 0 0 577 2.88 5.20 
M5 0 0 0.34 0 0 0 3.09 0 0 214 0.91 7.37 
M6 1 0 2.20 0 7 0 7 0 1 394 2.48 4.54 
M7 0 0 1.20 0 1 0 1.88 0 0 499 2.04 5.00 
M8 1 0 0.89 0 0 0 2.41 0 1 336 3.09 5.54 
M9 0 0 2.23 0 1 0 2.49 0 0 643 6.56 4.49 
M10 1 0 3.53 0 0 0 1.52 0 2 637 5.88 5.32 
Mean 0.30 0.00 1.82 0.00 1 0 2.94 0 0.40 499.60 3.24 5.07 
 
All methods found the correct sequence in each single-clone sample. However, ET and 
KEC retained the lower number of false sequences. Similarly, ET and KEC showed lower 
number of false sequences than SHORAH in each mixed samples. All three algorithms were 
successful in identifying most of true sequences, with ET being the most accurate. KEC did 
not detect true sequences representing ~1% in mixtures M5 and M9. The low root mean 
square error between observed and expected frequencies of true sequences indicates a high 
accuracy of ET and KEC, whereas SHORAH has much higher MSE, owing to the detection 
of a greater number of false sequences. Analysis of the Hamming distance between false 
sequences and their closest match shows that false sequences retained by KEC and ET are 
genetically closer to true sequences than sequences retained by SHORAH. 
 
CONCLUSIONS 
 
SHORAH, ET and KEC are equally efficient in finding true sequences. However, KEC 
and ET outperform SHORAH in removing false sequences and estimating the sequence fre-
quency. At the same time, in contrast to SHORAH and ET, KEC does not require a refer-
ence sequence. Both algorithms, KEC and ET, are highly suitable for rapid recovery of high 
quality sequences from reads obtained by deep sequencing of genomic regions from hetero-
geneous viruses such as HCV and HIV.  
 
 
200
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Efficient error correction and haplotypes reconstruction for deep sequencing of  hepatitis c amplicons

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Efficient error correction and haplotypes reconstruction for deep sequencing of hepatitis c amplicons

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