A sequence alignment algorithm using the transition quantity

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1 1 1 1 MTRAP A sequence alignment algorithm using the transition quantity Toshihide Hara, 1 Keiko Sato 1 and Masanori Ohya 1 We have been developed a sequence alignment algorithm using the transition quantity. The transition quantity is a new measure based on transition probability between two consecutive pairs of residues. In this paper, we compare the performance of our new algorithm called MTRAP and that of the other usual algorithm FASTA 18) BLAST 2) 1 Tokyo University of Science ClustalW 21), DIALIGN 14), T-Coffee 16), MAFFT 11), MUSCLE 7), Probcons 6) 40% 4) Anfinsen 3) α β Transition quantity MTRAP 8),9) HOMSTRAD (version November 1, 2008) 13),20) PREFAB4 7) 2. Transition Quantity Ω Ω Ω Ω Ω { } Ω Ω Ω Γ Ω Ω Γ Ω Ω n A = a 1a 2 a n B = b 1b 2 b n a i, b j Ω u 1 u 2 u n, u i = (a i, b i ) Γ u i 1 c 2010 Information Processing Society of Japan

2 p (A; B) R (A, B) = p (A) p (B) = p (a1, a2,, an; b1, b2,, bn) p (a 1, a 2,, a n ) p (b 1, b 2,, b n ). (1) p (a) a p (a; b) 1 p (A) = p (a), p (B) = p (b) and p (A, B) = p (a, b) 1, p (A; B) log p (A) p (B) = s (a i, b i ), (2) p (a; b) s (a, b) = log (3) p (a) p (b) a, b s (a, b) S = (s (a, b)) 2 3 1) 0 1 d sub (A, B) f s : [s min, s max ] R i f s (x) s max x, 0 f s (x) 1, (4) s max { s min } s max max max {S (u)}, gap cost, { u Γ } s min min {S (u)}, gap cost. min u Γ s (a, b) s (a, b) f s (s (a, b)), a, b Ω M = ( s (a, b)) A, B d sub (A, B) = s (a i, b i ). (5) d sub (A, B) A, B 0 9) R (A, B) i R our (A, B) = R (A, B) 1 ε R t (A, B) ε, (6) n 1 R t (A, B) p (u i+1 \ u i ) (7) i=1 ε Transition quantity t (u i, u i+1 ) t (u i, u i+1 ) f t (t (u i, u i+1 ) ; u i ), t (u i, u i+1) log p (u i+1 \ u i), (8) x f t (x; u) = max v Γ { t (u, v)}, if x > 0 (9) 1, otherwise Transition quantity n 1 d trans (A, B) = t (u i, u i+1). (10) d sub d trans i=1 d MTRAP (A, B) = (1 ε) d sub (A, B) + εd trans (A, B). (11) MTRAP 8) 17) 1 1 MTRAP 2 c 2010 Information Processing Society of Japan

3 Transition quantity PAM 5) BLOSUM 10) SABmark version ) superfamilies 9) 2.1 Structural Alignment HOM- STRAD PREFAB 4.0 ( 1 ) ( 2 ) ( 3 ) (2) ( 4 ) Q Score ( 5 ) (1) (4) ( 6 ) (1) (5) HOMSTRAD HOMSTRAD(HOMologous STRucture Alignment Database) 13) HOMSTRAD 0 %ID< %ID< %ID< %ID< %ID 100 ALL HOMSTRAD 630 %ID PREFAB4 PREFAB4 MUSCLE 7) 4 PREFAB PREFAB4 0 %ID< %ID< %ID< 45 ALL PREFAB %ID Q Score 7) Q Score Q Score L N {s 1,, s N } a ik Ω s i k s i a ik I ik a ik = 3 c 2010 Information Processing Society of Japan

4 I ik = 0 Q Score L N 1 N aik,a jk δ Iik,I jk k=1 i=1 j=i+1 Q Score =, L N 1 N aik,a jk { k=1 i=1 j=i+1 1, x and y x,y = 0, x = or y =. 2.2 HOMSTRAD PREFAB4 MTRAP Needle ClustalW2 MAFFT T-Coffee DIALIGN MUSCLE Probcons ( 1 ) Needle: Needle Needleman-Wunsch 15) EMBOSS 19) BLOSUM62 EMBOSS ver ( 2 ) ClustalW2: ClustalW2 12),21) ClustalW2 GONNET ClustalW2 ver ( 3 ) MAFFT: MAFFT 11) ver ( 4 ) T-Coffee: T-Coffee 16)?? Ver ( 5 ) DIALIGN: DIALIGN 14) segment-to-segment ver ( 6 ) MUSCLE: MUSCLE 7) Log-Expectation ver. 3.7 ( 7 ) Probcons: Probcons 6) Probabilistic Consistency ver ( 1 ) Q Score ( 2 ) Q Score Q Score MTRAP Needle ClustalW2 HOMSTRAD HOM- STRAD 630 Q score HOM- STRAD MTRAP MTRAP 80% e.g., PAM250 BLOSUM Needle ClustalW2 80% e.g. Needle PAM BLOSUM % MTRAP 3 HOMSTRAD MTRAP Matrix Sequence identity % Method 0-15% (25) 15-30% (207) 30-45% (173) ALL (630) PAM250 MTRAP Needle ClustalW BLOSUM62 MTRAP Needle ClustalW GONNET250 MTRAP ClustalW HOMSTRAD Q Score Needle GONNET 4 c 2010 Information Processing Society of Japan

5 PAM250 MTRAP 0-15% % PAM250 ClustalW2 0-15% % HOMSTRAD PREFAB4 PREFAB HOMSTRAD Q Score 2 Needle ClustalW2 Q Score MTRAP Q Score 60% 0-60% MTRAP 0-20% MTRAP Needle Q Score ClustalW2 PAM 1.4 BLOSUM 1.3 GONNET HOMSTRAD PREFAB4 MTRAP 11 2; Sum of pairs T-Coffee MAFFT DI- ALIGN MUSCLE ClustalW2 Probcons 4 5 MTRAP 30% 30% 4 10% 3. Transition quantity MTRAP 2 Q Score MTRAP Needle Q Score MTRAP ClustalW2 Q Score 5 c 2010 Information Processing Society of Japan

6 4 PREFAB4 MTRAP Method PREFAB %(423) 15-30%(917) 30-45%(148) All(1682) MTRAP a MAFFT DIALIGN b MUSCLE ClustalW Probcons T-Coffee PREFAB4 Q Score a MTRAP GONNET250 b DIALIGN Q Score 5 HOMSTRAD MTRAP Method HOMSTRAD 0-15%(25) 15-30%(207) 30-45%(173) All(630) MTRAP a MAFFT DIALIGN b MUSCLE ClustalW Probcons T-Coffee PREFAB4 Q Score 4 1) S.F. Altschul. Amino acid substitution matrices from an information theoretic perspective. J. Mol. Bd, 219: , ) S.F. Altschul, W. Gish, W. Miller, E.W. Myers, and D.J. Lipman. Basic local alignment search tool. Journal of molecular biology, 215(3): , ) C. B. Anfinsen. Principles that govern the folding of protein chains. Science, 181: , Jul ) G.Blackshields, I.M. Wallace, M.Larkin, and D.G. Higgins. Analysis and comparison of benchmarks for multiple sequence alignment. In Silico Biology, 6(4): , ) M.O. Dayhoff, R.M. Schwartz, and B.C. Orcutt. A model of evolutionary change in proteins. Atlas of Protein Sequence and Structure, 5(3): , ) C.B. Do, M.S.P. Mahabhashyam, M. Brudno, and S. Batzoglou. ProbCons: probabilistic consistency-based multiple sequence alignment. Genome Research, 15(2):330, ) R.C. Edgar. MUSCLE: multiple sequence alignment with high accuracy and high throughput. Nucleic Acids Res., 32: , ) Toshihide Hara, Keiko Sato, and Masanori Ohya. Mtrap: pairwise sequence alignment algorithm by a new measure based on transition probability between two consecutive pairs of residues. BMC Bioinformatics, 11:235, ) Toshihide Hara, Keiko Sato, and Masanori Ohya. Significant improvement of sequence alignment can be done by considering transition probability between two consecutive pairs of residues. QP-PQ: Quantum Probability and White Noise Analysis (Quantum Bio-Informatics III), 26: , ) S. Henikoff and J. G. Henikoff. Amino acid substitution matrices from protein blocks. Proc. Natl. Acad. Sci. U.S.A., 89: , Nov ) K.Katoh, K.Misawa, K.Kuma, and T.Miyata. MAFFT: a novel method for rapid multiple sequence alignment based on fast Fourier transform. Nucleic Acids Res., 30: , Jul ) M. A. Larkin, G. Blackshields, N. P. Brown, R. Chenna, P. A. McGettigan, H.McWilliam, F.Valentin, I.M. Wallace, A.Wilm, R.Lopez, J.D. Thompson, T.J. Gibson, and D.G. Higgins. Clustal W and Clustal X version 2.0. Bioinformatics, 6 c 2010 Information Processing Society of Japan

7 23: , Nov ) K.Mizuguchi, C.M. Deane, T.L. Blundell, and J.P. Overington. HOMSTRAD: a database of protein structure alignments for homologous families. Protein Sci., 7: , Nov ) B.Morgenstern. DIALIGN 2: improvement of the segment-to-segment approach to multiple sequence alignment. Bioinformatics, 15: , Mar ) S.B. Needleman and C.D. Wunsch. A general method applicable to the search for similarities in the amino acid sequence of two proteins. Journal of Molecular Biology, 48: , Mar ) C.Notredame, D.G. Higgins, and J.Heringa. T-Coffee: A novel method for fast and accurate multiple sequence alignment. J. Mol. Biol., 302: , Sep ) M.Ohya and Y.Uesaka. Amino acid sequences and DP matching:a new method of alignment, Information Sciences. Information Sciences, 63: , ) W.R. Pearson and D.J. Lipman. Improved tools for biological sequence comparison. Proceedings of the National Academy of Sciences, 85(8): , ) P.Rice, I.Longden, and A.Bleasby. EMBOSS: the European Molecular Biology Open Software Suite. Trends Genet., 16: , Jun ) L.A. Stebbings and K. Mizuguchi. HOMSTRAD: recent developments of the homologous protein structure alignment database. Nucleic acids research, 32(Database Issue):D203, ) J.D. Thompson, D.G. Higgins, and T.J. Gibson. CLUSTAL W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice. Nucleic Acids Res., 22: , Nov ) I.VanWalle, I.Lasters, and L.Wyns. SABmark a benchmark for sequence alignment that covers the entire known fold space. Bioinformatics, 21(7):1267, c 2010 Information Processing Society of Japan

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