Sequence Alignment Kun-Mao Chao (趙坤茂) Department of Computer Science and Information Engineering National Taiwan University, Taiwan E-mail: kmchao@csie.ntu.edu.tw WWW: http://www.csie.ntu.edu.tw/~kmchao

Bioinformatics

Bioinformatics and Computational Biology-Related Journals: Bioinformatics (previously called CABIOS) Bulletin of Mathematical Biology Computers and Biomedical Research Genome Research Genomics Journal of Bioinformatics and Computational Biology Journal of Computational Biology Journal of Molecular Biology Nature Nucleic Acid Research Science

Bioinformatics and Computational Biology-Related Conferences: Intelligent Systems for Molecular Biology (ISMB) Pacific Symposium on Biocomputing (PSB) The Annual International Conference on Research in Computational Molecular Biology (RECOMB) The IEEE Computer Society Bioinformatics Conference (CSB) ...

Bioinformatics and Computational Biology-Related Books: Calculating the Secrets of Life: Applications of the Mathematical Sciences in Molecular Biology, by Eric S. Lander and Michael S. Waterman (1995) Introduction to Computational Biology: Maps, Sequences, and Genomes, by Michael S. Waterman (1995) Introduction to Computational Molecular Biology, by Joao Carlos Setubal and Joao Meidanis (1996) Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology, by Dan Gusfield (1997) Computational Molecular Biology: An Algorithmic Approach, by Pavel Pevzner (2000) Introduction to Bioinformatics, by Arthur M. Lesk (2002)

Useful Websites MIT Biology Hypertextbook http://www.mit.edu:8001/afs/athena/course/other/esgbio/www/7001main.html The International Society for Computational Biology: http://www.iscb.org/ National Center for Biotechnology Information (NCBI, NIH): http://www.ncbi.nlm.nih.gov/ European Bioinformatics Institute (EBI): http://www.ebi.ac.uk/ DNA Data Bank of Japan (DDBJ): http://www.ddbj.nig.ac.jp/

Sequence Alignment

Dot Matrix Sequence A：CTTAACT Sequence B：CGGATCAT C G G A T C A T

Pairwise Alignment Sequence A: CTTAACT Sequence B: CGGATCAT An alignment of A and B: C---TTAACT CGGATCA--T Sequence A Sequence B

Pairwise Alignment Sequence A: CTTAACT Sequence B: CGGATCAT An alignment of A and B: Mismatch Match C---TTAACT CGGATCA--T Deletion gap Insertion gap

Alignment Graph C---TTAACT CGGATCA--T Sequence A: CTTAACT Sequence B: CGGATCAT C G G A T C A T C T T A A C T C---TTAACT CGGATCA--T

A simple scoring scheme Match: +8 (w(x, y) = 8, if x = y) Mismatch: -5 (w(x, y) = -5, if x ≠ y) Each gap symbol: -3 (w(-,x)=w(x,-)=-3) C - - - T T A A C T C G G A T C A - - T +8 -3 -3 -3 +8 -5 +8 -3 -3 +8 = +12 Alignment score

An optimal alignment -- the alignment of maximum score Let A=a1a2…am and B=b1b2…bn . Si,j: the score of an optimal alignment between a1a2…ai and b1b2…bj With proper initializations, Si,j can be computed as follows.

Computing Si,j j w(ai,bj) w(ai,-) i w(-,bj) Sm,n

Initializations C G G A T C A T -3 -6 -9 -12 -15 -18 -21 -24 -3 -6 -9 -12 -15 -18 -21 -24 C T T A A C T

S3,5 = ？ C G G A T C A T -3 -6 -9 -12 -15 -18 -21 -24 8 5 2 -1 -4 -7 -3 -6 -9 -12 -15 -18 -21 -24 8 5 2 -1 -4 -7 -10 -13 3 7 4 1 -2 -5 ? C T T A A C T

S3,5 = 5 C G G A T C A T -3 -6 -9 -12 -15 -18 -21 -24 8 5 2 -1 -4 -7 -3 -6 -9 -12 -15 -18 -21 -24 8 5 2 -1 -4 -7 -10 -13 3 7 4 1 -2 -5 9 6 -8 -11 -14 14 C T T A A C T optimal score

C T T A A C – T C G G A T C A T 8 – 5 –5 +8 -5 +8 -3 +8 = 14 8 – 5 –5 +8 -5 +8 -3 +8 = 14 C G G A T C A T -3 -6 -9 -12 -15 -18 -21 -24 8 5 2 -1 -4 -7 -10 -13 3 7 4 1 -2 -5 9 6 -8 -11 -14 14 C T T A A C T

Now try this example in class Sequence A: CAATTGA Sequence B: GAATCTGC Their optimal alignment？

Initializations G A A T C T G C -3 -6 -9 -12 -15 -18 -21 -24 -3 -6 -9 -12 -15 -18 -21 -24 C AA T T G A

S4,2 = ？ G A A T C T G C -3 -6 -9 -12 -15 -18 -21 -24 -5 -8 -11 -14 -4 -3 -6 -9 -12 -15 -18 -21 -24 -5 -8 -11 -14 -4 -7 -10 -13 3 11 8 5 2 -1 ? C AA T T G A

S5,5 = ？ G A A T C T G C -3 -6 -9 -12 -15 -18 -21 -24 -5 -8 -11 -14 -4 -3 -6 -9 -12 -15 -18 -21 -24 -5 -8 -11 -14 -4 -7 -10 -13 3 11 8 5 2 -1 19 16 13 10 7 ? C AA T T G A

S5,5 = 14 G A A T C T G C -3 -6 -9 -12 -15 -18 -21 -24 -5 -8 -11 -14 -3 -6 -9 -12 -15 -18 -21 -24 -5 -8 -11 -14 -4 -7 -10 -13 3 11 8 5 2 -1 19 16 13 10 7 14 24 21 18 32 29 1 27 C AA T T G A optimal score

C A A T - T G A G A A T C T G C -5 +8 +8 +8 -3 +8 +8 -5 = 27 -5 +8 +8 +8 -3 +8 +8 -5 = 27 G A A T C T G C -3 -6 -9 -12 -15 -18 -21 -24 -5 -8 -11 -14 -4 -7 -10 -13 3 11 8 5 2 -1 19 16 13 10 7 14 24 21 18 32 29 1 27 C AA T T G A

Global Alignment vs. Local Alignment

An optimal local alignment Si,j: the score of an optimal local alignment ending at ai and bj With proper initializations, Si,j can be computed as follows.

local alignment C G G A T C A T 8 5 2 3 13 11 ? C T T A A C T Match: 8 Mismatch: -5 Gap symbol: -3 C G G A T C A T 8 5 2 3 13 11 ? C T T A A C T

local alignment C G G A T C A T 8 5 2 3 13 11 10 7 18 C T T A A C T Match: 8 Mismatch: -5 Gap symbol: -3 C G G A T C A T 8 5 2 3 13 11 10 7 18 C T T A A C T The best score

A – C - T A T C A T 8-3+8-3+8 = 18 C G G A T C A T 8 5 2 3 13 11 10 7 8 5 2 3 13 11 10 7 18 C T T A A C T The best score

Now try this example in class Sequence A: CAATTGA Sequence B: GAATCTGC Their optimal local alignment？

Did you get it right? G A A T C T G C 8 5 2 3 16 13 10 7 4 1 24 21 18 8 5 2 3 16 13 10 7 4 1 24 21 18 15 12 19 29 26 23 37 34 32 C AA T T G A

A A T – T G A A T C T G 8+8+8-3+8+8 = 37 G A A T C T G C 8 5 2 3 16 13 10 7 4 1 24 21 18 15 12 19 29 26 23 37 34 32 C AA T T G A

Affine gap penalties C - - - T T A A C T C G G A T C A - - T Match: +8 (w(x, y) = 8, if x = y) Mismatch: -5 (w(x, y) = -5, if x ≠ y) Each gap symbol: -3 (w(-,x)=w(x,-)=-3) Each gap is charged an extra gap-open penalty: -4. -4 -4 C - - - T T A A C T C G G A T C A - - T +8 -3 -3 -3 +8 -5 +8 -3 -3 +8 = +12 Alignment score: 12 – 4 – 4 = 4

Affine gap panalties A gap of length k is penalized x + k·y. gap-open penalty Three cases for alignment endings: ...x ...x ...x ...- ...- ...x gap-symbol penalty an aligned pair a deletion an insertion

Affine gap penalties Let D(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj ending with a deletion. Let I(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj ending with an insertion. Let S(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj.

Affine gap penalties (A gap of length k is penalized x + k·y.)

Affine gap penalties S I D S I D -y w(ai,bj) -x-y S I D D -x-y I S -y

Constant gap penalties Match: +8 (w(x, y) = 8, if x = y) Mismatch: -5 (w(x, y) = -5, if x ≠ y) Each gap symbol: 0 (w(-,x)=w(x,-)=0) Each gap is charged a constant penalty: -4. -4 -4 C - - - T T A A C T C G G A T C A - - T +8 0 0 0 +8 -5 +8 0 0 +8 = +27 Alignment score: 27 – 4 – 4 = 19

Constant gap penalties Let D(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj ending with a deletion. Let I(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj ending with an insertion. Let S(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj.

Constant gap penalties

Restricted affine gap panalties A gap of length k is penalized x + f(k)·y. where f(k) = k for k <= c and f(k) = c for k > c Five cases for alignment endings: ...x ...x ...x ...- ...- ...x and 5. for long gaps an aligned pair a deletion an insertion

Restricted affine gap penalties

D(i, j) vs. D’(i, j) Case 1: the best alignment ending at (i, j) with a deletion at the end has the last deletion gap of length <= c D(i, j) >= D’(i, j) Case 2: the best alignment ending at (i, j) with a deletion at the end has the last deletion gap of length >= c D(i, j) <= D’(i, j)

k best local alignments Smith-Waterman (Smith and Waterman, 1981; Waterman and Eggert, 1987) FASTA (Wilbur and Lipman, 1983; Lipman and Pearson, 1985) BLAST (Altschul et al., 1990; Altschul et al., 1997)

FASTA Find runs of identities, and identify regions with the highest density of identities. Re-score using PAM matrix, and keep top scoring segments. Eliminate segments that are unlikely to be part of the alignment. Optimize the alignment in a band.

FASTA Step 1: Find runes of identities, and identify regions with the highest density of identities. Sequence B Sequence A

FASTA Step 2: Re-score using PAM matrix, and keep top scoring segments.

FASTA Step 3: Eliminate segments that are unlikely to be part of the alignment.

FASTA Step 4: Optimize the alignment in a band.

BLAST Basic Local Alignment Search Tool (by Altschul, Gish, Miller, Myers and Lipman) The central idea of the BLAST algorithm is that a statistically significant alignment is likely to contain a high-scoring pair of aligned words.

The maximal segment pair measure A maximal segment pair (MSP) is defined to be the highest scoring pair of identical length segments chosen from 2 sequences. (for DNA: Identities: +5; Mismatches: -4) The MSP score may be computed in time proportional to the product of their lengths. (How?) An exact procedure is too time consuming. BLAST heuristically attempts to calculate the MSP score. the highest scoring pair

BLAST Build the hash table for Sequence A. Scan Sequence B for hits. Extend hits.

BLAST Step 1: Build the hash table for Sequence A. (3-tuple example) For DNA sequences: Seq. A = AGATCGAT 12345678 AAA AAC .. AGA 1 .. ATC 3 .. CGA 5 .. GAT 2 6 .. TCG 4 .. TTT For protein sequences: Seq. A = ELVIS Add xyz to the hash table if Score(xyz, ELV) ≧ T; Add xyz to the hash table if Score(xyz, LVI) ≧ T; Add xyz to the hash table if Score(xyz, VIS) ≧ T;

BLAST Step2: Scan sequence B for hits.

BLAST Step2: Scan sequence B for hits. Step 3: Extend hits. BLAST 2.0 saves the time spent in extension, and considers gapped alignments. hit Terminate if the score of the sxtension fades away. (That is, when we reach a segment pair whose score falls a certain distance below the best score found for shorter extensions.)

Remarks Filtering is based on the observation that a good alignment usually includes short identical or very similar fragments. The idea of filtration was used in both FASTA and BLAST.