IPSJ SIG Technical Report Vol.2009-BIO-17 No /5/26 DNA 1 1 DNA DNA DNA DNA Correcting read errors on DNA sequences determined by Pyrosequencing

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DNA 1 1 DNA DNA DNA DNA Correcting read errors on DNA sequences determined by Pyrosequencing Youhei Namiki 1 and Yutaka Akiyama 1 Pyrosequencing, one of the DNA sequencing technologies, allows us to determine the order of nucleotides in a large amount of DNA at a time. However, this method has a tendency to contain some particular read errors in the result sequences when determining long DNA sequences. In this study, we developed a method correcting read errors on DNA sequences determined by Pyrosequencing. In our method, a simple pyrosequencing simulator is repeatedly used and a corrected sequence which gives a simulated pyrogram most similar to that of real experimental record is chosen. 1 Graduate School of Information Science and Engineering, Tokyo Institute of Technology 1. DNA DNA DNA DNA 454 Life Sciences GS20 DNA DNA DNA DNA DNA DNA DNA DNA DNA DNA 2. 2.1 (Pyrosequencing method) DNA (sequencing-by-synthesis) ( 1) 1990 Mostafa Ronagh 1)2). DNA ( 1 ) DNA DNA ( 2 ) A T G C 1 c 2009 Information Processing Society of Japan

DNA DNA 2005 454 Life Sciences DNA 100 ( ) 1 Fig. 1 Pyrosequencing method. 2 ( ) Fig. 2 Pyrogram. DNA ATP ( 3 ) ( 2) ( 4 ) (2) (3) DNA DNA 2.2 DNA 3) ( 1 ) ( 2 ) DNA DNA 2.2.1 (Incomplete-Hybridization) DNA DNA DNA (delay) DNA DNA DNA 2.2.2 (Miss-Washing) DNA DNA (gain) 3. (PyroSequencing Simulator) DNA 2007 4) DNA DNA 2 c 2009 Information Processing Society of Japan

4. DNA 4.1 DNA ( 1 ) DNA s 1 ( 2 ) s 1 p 0 DNA 1 1 DNA s 0 ŝ 0 sequencing s 0 (s 1, p 0 ) (1) error correction (s 1, p 0) ŝ 0 (2) 4.2 ( 3) ( 1 ) DNA s 1 DNA ŝ 0 ( 2 ) ( 3 ) ( 4 ) (1) (3) ŝ 0 4.3 3 ( 1 ) (AS: All-neighbor Search method) ( 2 ) (SS: Sequenial Search method) 3 4 Fig. 3 Error correction. Fig. 4 Candidate sequences numeration method. ( 3 ) (TSS: Threshold Sequential Search method) ŝ 0 ( 4) 4.4 1 (AS: All-neighbor Search method) ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) (2) (5) 4.4.1 S DNA DNA s 1 S S = {s 1 } (3) 4.4.2 C C = S s( S) (edit) DNA C ( 1 ) s 1 (insertion) ( 2 ) s 1 (mutation) 3 c 2009 Information Processing Society of Japan

( 3 ) s 1 (deletion) C = S + edit(s) (4) C s 1 DNA s L s insertion 4L mutation 3L deletion L 8L 4.4.3 c( C) DNA p c DNA 4.4.4 x i p 0 i x c,i p c i p 0 p c M 0 M c M = max{m 0, M c } p 0 = (x 1, x 2,..., x M0 ) (5) p c = (x c,1, x c,2,..., x c,mc ) (6) d c d c = M (x i x c,i ) 2 (7) i > M 0 x i = 0 i > M c x c,i = 0 i=1 d c p 0 DNA c DNA ( ) 4.4.5 4.4.4 (d c ) c N S 4.4.2 S 4.4.2 4.4.5 S DNA DNA 1 s 0 s 1 4.4.2 4.4.5 4.5 2 (SS: Sequential Search method) ( 1 ) ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) (2) (5) 4.5.1 S DNA DNA s 1 S i = 1 4.5.2 C C = S S = {s 1} (8) s( S) (edit) DNA C ( 1 ) s i 1 (insertion) ( 2 ) s i (mutation) ( 3 ) s i (deletion) C = S + edit(s, i) (9) s insertion 4 mutation 3 deletion 1 8 4.5.3 4.5.4 4.5.5 4.5.4 (d c 4 c 2009 Information Processing Society of Japan

) c N S S S i i 1 4.5.2 4.5.5 i s( S) S DNA 4.6 3 (TSS: Threshold Sequential Search method) ( 1 ) ( 2 ) ( 3 ) i ( 4 ) ( 5 ) ( 6 ) ( 7 ) ( 8 ) (2) (7) 4.6.1 S DNA DNA s 1 S S = {s 1 } (10) θ i = 1 4.6.2 i C s( S) p s = (x s,1, x s,2,..., x s,ms ) M = max{m 0, M s } s p 0 s p s i 5 Fig. 5 Calculation of the deference between two pyrograms. d s,i Fig. 6 6 The deference between two pyrograms. d s,i = (x i x s,i ) 2 (11) i > M 0 x i = 0 i > M s x s,i = 0 d s,i θ s C d s,i θ s ( C = ) i 1 4.6.2 4.6.3 i c ( C ) i 4.6.4 C C = S c ( C ) i i b i insertion, deletion C i b i b i C = S + edit(c, i, b i) (12) c insertion 1 deletion 1 2 4.6.5 4.6.6 5 c 2009 Information Processing Society of Japan

4.6.7 4.6.6 (d c ) c N S S S i i 1 4.6.2 5. 3 (AS, SS, TSS) Perl DNA 5.1 (GSIC) TSUB- AME 5.2 UCSC Genome Bioinformatics Web 1 DNA 50 (50b) 75 (75b) 500 DNA N(A, T, G, C ) 5.3 DNA s i DNA s i p i 2007 s i s i s i s i s i s i 50b 500 352 75b 500 490 50b 75b 200 s i p i D D = { } (s i, p i) s i s i (13) 1 1(AS) Table 1 The result of method1(as). 50b 169/200 (84.5%) 200/200 (100%) 75b 161/200 (80.5%) 199/200 (99.5%) 5.4 3 3(TSS) Table 3 The result of method3(tss). θ 2 2(SS) Table 2 The result of method2(ss). 50b 168/200 (84%) 196/200 (98%) 75b 161/200 (81.5%) 185/200 (92.5%) 50b 0.2 183/200 (91.5%) 183/200 (91.5%) 50b 0.1 186/200 (93%) 186/200 (93%) 50b 0.05 186/200 (93%) 186/200 (93%) 50b 0.01 183/200 (91.5%) 188/200 (94%) 50b 0.005 179/200 (89.5%) 192/200 (96%) 75b 0.2 141/200 (70.5%) 141/200 (70.5%) 75b 0.1 176/200 (88%) 176/200 (88%) 75b 0.05 179/200 (89.5%) 180/200 (90%) 75p 0.01 170/200 (85%) 180/200 (90%) 75p 0.005 171/200 (85.5%) 182/200 (91%) D s i p i s i p i TSUBAME 200 DNA 1CPU 5.5 1 3 1 1 5 (200) 7 8 M{ }_T{ 3 θ } ( M1 = 1 M3_T0.01 = 3, θ = 0.01) (match) (weak match) ( 1 6 c 2009 Information Processing Society of Japan

7 (match) (weak match) 50b Fig. 7 The numbers of matches and weak matches(50b). 8 (match) (weak match) 75b Fig. 8 The numbers of matches and weak matches(75b). ) 50b 75b 3 θ 0.05 90% 0.05 1 2 3 1 2 3 3 (DNA ) 3 0.1 (1 5 ) 1 2 3 2 50b 75b 3 θ = 0.05 5.6 4 6 ( ) 9 10 4 6 9 10 1 2 2 3 3 3 6. DNA 3 (Threshold 7 c 2009 Information Processing Society of Japan

4 1(AS) ( ) Table 4 The runtime(sec) of method1(as). Min. 1st Qu. Median Mean 3rd Qu. Max. 50b 309 1,852 2,832 3,523 4,411 12,830 75b 2,584 8,226 11,970 12,220 15,580 26,800 5 2(SS) ( ) Table 5 The runtime(sec) of method2(ss). Min. 1st Qu. Median Mean 3rd Qu. Max. 50b 176 309 439 502 626 1,469 75b 439 980 1,329 1,618 1,950 9,067 6 3(TSS) ( ) Table 6 The runtime(sec) of method3(tss). θ Min. 1st Qu. Median Mean 3rd Qu. Max. 50b 0.2 0.4 1.5 3.2 5.9 8.8 31 50b 0.1 0.4 1.5 3.1 5.5 7.2 25 50b 0.05 0.6 1.8 4.4 10 11 92 50b 0.01 0.6 3.6 8.7 19 22 209 50b 0.005 0.5 4.4 8.7 13 18 116 75b 0.2 1.9 11 21 24 36 64 75b 0.1 1.8 13 22 27 39 113 75b 0.05 1.7 16 31 43 48 253 75b 0.01 1.8 29 58 75 94 570 75b 0.005 4.0 30 51 61 84 233 Sequential Search method) θ = 0.05 50b DNA 93% 75b DNA 90% 454 Life Sciences DNA DNA 9 200 ( 50b) Fig. 9 The deviation of the runtime(50b). 10 200 ( 75b) Fig. 10 The deviation of the runtime(75b). 1) M. Ronaghi, M. Uhlen, P. Nyren: A Sequencing Method Based on Real-Time Pyrophosphate, Science 281:363-365 (1998). 2) Mostafa Ronaghi: Pyrosequencing Sheds Light on DNA Sequencing, Genome Research, 11:3-11 (2001). 3) Helmy Eltoukhy, Abbas El Gamal: Modeling and Base-Calling for DNA Sequencing- By-Synthesis, Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on, 2:II-II (2006). 4) Yutaka Akiyama: SimPyro: Pyrosequencing simulation software for analyzing random process with millions of reactions. Poster presentation, The 2nd International Workshop on Approaches to Single-Cell Analysis, Tokyo (2007). 8 c 2009 Information Processing Society of Japan

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