alignment

Sequence Alignment

Kun-Mao Chao (趙坤茂 )Department of Computer Science an

d Information EngineeringNational Taiwan University, Taiwan

E-mail: [email protected]

WWW: http://www.csie.ntu.edu.tw/~kmchao

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Bioinformatics

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Bioinformatics and Computational Biology-Related Journals:

• Bioinformatics (previously called CABIOS)• Bulletin of Mathematical Biology• Genome Research• Genomics• IEEE/ACM Transactions on Computational Biology and

Bioinformatics• Journal of Bioinformatics and Computational Biology• Journal of Computational Biology• Journal of Molecular Biology• Nature• Nucleic Acid Research• Science

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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)• Workshop on Algorithms in Bioinformatics

(WABI)• The IEEE Computer Society Bioinformatics Conf

erence (CSB)

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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)

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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/

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Sequence Alignment

8

Dot MatrixSequence A： CTTAACT

Sequence B： CGGATCATC G G A T C A T

C

T

T

A

A

C

T

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C---TTAACTCGGATCA--T

Pairwise AlignmentSequence A: CTTAACTSequence B: CGGATCAT

An alignment of A and B:

Sequence A

Sequence B

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Pairwise AlignmentSequence A: CTTAACTSequence B: CGGATCAT

An alignment of A and B:

Insertion gap

Match Mismatch

Deletion gap

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Alignment GraphSequence A: CTTAACT

Sequence B: CGGATCATC G G A T C A T

C

T

T

A

A

C

T


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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 TC G G A T C A - - T

+8 -3 -3 -3 +8 -5 +8 -3 -3 +8 = +12

Alignment score

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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 computedas follows.

),(

),(

),(

max

1,1

1,

,1

,

jiji

jji

iji

ji

baws

bws

aws

s

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Computing Si,j

i

j

w(ai,-)

w(-,bj)

w(ai,b

j)

Sm,n

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Initializations

0 -3 -6 -9 -12 -15 -18 -21 -24

-3

-6

-9

-12

-15

-18

-21

C G G A T C A T

C

T

T

A

A

C

T

16

S3,5 = ？

0 -3 -6 -9 -12 -15 -18 -21 -24

-3 8 5 2 -1 -4 -7 -10 -13

-6 5 3 0 -3 7 4 1 -2

-9 2 0 -2 -5 ?

-12

-15

-18

-21

C G G A T C A T

C

T

T

A

A

C

T

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S3,5 = 5

0 -3 -6 -9 -12 -15 -18 -21 -24

-3 8 5 2 -1 -4 -7 -10 -13

-6 5 3 0 -3 7 4 1 -2

-9 2 0 -2 -5 5 -1 -1 9

-12 -1 -3 -5 6 3 0 7 6

-15 -4 -6 -8 3 1 -2 8 5

-18 -7 -9 -11 0 -2 9 6 3

-21 -10 -12 -14 -3 8 6 4 14

C G G A T C A T

C

T

T

A

A

C

T

optimal score

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C T T A A C – TC G G A T C A T

0 -3 -6 -9 -12 -15 -18 -21 -24

-3 8 5 2 -1 -4 -7 -10 -13

-6 5 3 0 -3 7 4 1 -2

-9 2 0 -2 -5 5 -1 -1 9

-12 -1 -3 -5 6 3 0 7 6

-15 -4 -6 -8 3 1 -2 8 5

-18 -7 -9 -11 0 -2 9 6 3

-21 -10 -12 -14 -3 8 6 4 14

C G G A T C A T

C

T

T

A

A

C

T

8 – 5 –5 +8 -5 +8 -3 +8 = 14

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Now try this example in class

Sequence A: CAATTGASequence B: GAATCTGC

Their optimal alignment？

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Initializations

0 -3 -6 -9 -12 -15 -18 -21 -24

-3

-6

-9

-12

-15

-18

-21

G A A T C T G C

C

A

A

T

T

G

A

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S4,2 = ？

0 -3 -6 -9 -12 -15 -18 -21 -24

-3 -5 -8 -11 -14 -4 -7 -10 -13

-6 -8 3 0 -3 -6 -9 -12 -15

-9 -11 0 11 8 5 2 -1 -4

-12 -14 ?

-15

-18

-21

G A A T C T G C

C

A

A

T

T

G

A

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S5,5 = ？

0 -3 -6 -9 -12 -15 -18 -21 -24

-3 -5 -8 -11 -14 -4 -7 -10 -13

-6 -8 3 0 -3 -6 -9 -12 -15

-9 -11 0 11 8 5 2 -1 -4

-12 -14 -3 8 19 16 13 10 7

-15 -11 -6 5 16 ?

-18

-21

G A A T C T G C

C

A

A

T

T

G

A

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S5,5 = 14

0 -3 -6 -9 -12 -15 -18 -21 -24

-3 -5 -8 -11 -14 -4 -7 -10 -13

-6 -8 3 0 -3 -6 -9 -12 -15

-9 -11 0 11 8 5 2 -1 -4

-12 -14 -3 8 19 16 13 10 7

-15 -11 -6 5 16 14 24 21 18

-18 -7 -9 2 13 11 21 32 29

-21 -10 1 -1 10 8 18 29 27

G A A T C T G C

C

A

A

T

T

G

A

optimal score

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0 -3 -6 -9 -12 -15 -18 -21 -24

-3 -5 -8 -11 -14 -4 -7 -10 -13

-6 -8 3 0 -3 -6 -9 -12 -15

-9 -11 0 11 8 5 2 -1 -4

-12 -14 -3 8 19 16 13 10 7

-15 -11 -6 5 16 14 24 21 18

-18 -7 -9 2 13 11 21 32 29

-21 -10 1 -1 10 8 18 29 27

G A A T C T G C

C

A

A

T

T

G

A

-5 +8 +8 +8 -3 +8 +8 -5 = 27

C A A T - T G AG A A T C T G C

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Global Alignment vs. Local Alignment

• global alignment:

• local alignment:

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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 computedas follows.

),(

),(),(

0

max

1,1

1,

,1

,

jiji

jji

iji

ji

baws

bwsaws

s

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local alignment

0 0 0 0 0 0 0 0 0

0 8 5 2 0 0 8 5 2

0 5 3 0 0 8 5 3 13

0 2 0 0 0 8 5 2 11

0 0 0 0 8 5 3 ?

0

0

0

C G G A T C A T

C

T

T

A

A

C

T

Match: 8

Mismatch: -5

Gap symbol: -3

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local alignment

0 0 0 0 0 0 0 0 0

0 8 5 2 0 0 8 5 2

0 5 3 0 0 8 5 3 13

0 2 0 0 0 8 5 2 11

0 0 0 0 8 5 3 13 10

0 0 0 0 8 5 2 11 8

0 8 5 2 5 3 13 10 7

0 5 3 0 2 13 10 8 18

C G G A T C A T

C

T

T

A

A

C

T

Match: 8

Mismatch: -5

Gap symbol: -3

The best

score

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0 0 0 0 0 0 0 0 0

0 8 5 2 0 0 8 5 2

0 5 3 0 0 8 5 3 13

0 2 0 0 0 8 5 2 11

0 0 0 0 8 5 3 13 10

0 0 0 0 8 5 2 11 8

0 8 5 2 5 3 13 10 7

0 5 3 0 2 13 10 8 18

C G G A T C A T

C

T

T

A

A

C

T

The best

score

A – C - TA T C A T8-3+8-3+8 = 18

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Now try this example in class

Sequence A: CAATTGASequence B: GAATCTGC

Their optimal local alignment？

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Did you get it right?

0 0 0 0 0 0 0 0 0

0 0 0 0 0 8 5 2 8

0 0 8 8 5 5 3 0 5

0 0 8 16 13 10 7 4 2

0 0 5 13 24 21 18 15 12

0 0 2 10 21 19 29 26 23

0 8 5 7 18 16 26 37 34

0 5 16 13 15 13 23 34 32

G A A T C T G C

C

A

A

T

T

G

A

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0 0 0 0 0 0 0 0 0

0 0 0 0 0 8 5 2 8

0 0 8 8 5 5 3 0 5

0 0 8 16 13 10 7 4 1

0 0 5 13 24 21 18 15 12

0 0 2 10 21 19 29 26 23

0 8 5 7 18 16 26 37 34

0 5 16 13 15 13 23 34 32

G A A T C T G C

C

A

A

T

T

G

A

A A T – T GA A T C T G8+8+8-3+8+8 = 37

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Affine gap penalties• Match: +8 (w(x, y) = 8, if x = y)


• Each gap symbol: -3 (w(-,x)=w(x,-)=-3)

• Each gap is charged an extra gap-open penalty: -4.


+8 -3 -3 -3 +8 -5 +8 -3 -3 +8 = +12

-4 -4

Alignment score: 12 – 4 – 4 = 4

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Affine gap panalties• A gap of length k is penalized x + k·y.

gap-open penalty

gap-symbol penaltyThree cases for alignment endings:

1. ...x...x

2. ...x...-

3. ...-...x

an aligned pair

a deletion

an insertion

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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.

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),(

),(

),()1,1(

max),(

)1,(

)1,(max),(

),1(

),1(max),(

jiI

jiD

bawjiS

jiS

yxjiS

yjiIjiI

yxjiS

yjiDjiD

ji

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

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SI

D

SI

D

SI

D

SI

D

-y-x-y

-x-y

-y

w(ai,bj)

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Constant gap penalties• Match: +8 (w(x, y) = 8, if x = y)


• Each gap symbol: 0 (w(-,x)=w(x,-)=0)

• Each gap is charged a constant penalty: -4.


+8 0 0 0 +8 -5 +8 0 0 +8 = +27

-4 -4

Alignment score: 27 – 4 – 4 = 19

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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.

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Constant gap penalties

gap afor penalty gapconstant a is where

),(

),(

),()1,1(

max),(

)1,(

)1,(max),(

),1(

),1(max),(

x

jiI

jiD

bawjiS

jiS

xjiS

jiIjiI

xjiS

jiDjiD

ji

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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:

1. ...x...x

2. ...x...-

3. ...-...x

4. and 5. for long gaps

an aligned pair

a deletion

an insertion

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Restricted affine gap penalties

),(');,(

),(');,(

),()1,1(

max),(

)1,(

)1,('max),('

)1,(

)1,(max),(

),1(

),1('max),('

),1(

),1(max),(

jiIjiI

jiDjiD

bawjiS

jiS

cyxjiS

jiIjiI

yxjiS

yjiIjiI

cyxjiS

jiDjiD

yxjiS

yjiDjiD

ji

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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)

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Max{S(i,j)-x-ky, S(i,j)-x-cy}

kc

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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)

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FASTA

1) Find runs of identities, and identify regions with the highest density of identities.

2) Re-score using PAM matrix, and keep top scoring segments.

3) Eliminate segments that are unlikely to be part of the alignment.

4) Optimize the alignment in a band.

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FASTA

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

Sequence A

Sequence B

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FASTA

Step 2: Re-score using PAM matrix, andkeep top scoring segments.

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FASTA

Step 3: Eliminate segments that are unlikely to be part

of the alignment.

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FASTA

Step 4: Optimize the alignment in a band.

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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.

52

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 highest scoring pair

•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.

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BLAST

1) Build the hash table for Sequence A.

2) Scan Sequence B for hits.

3) Extend hits.

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BLASTStep 1: Build the hash table for Sequence A. (3-tuple example)

For DNA sequences:

Seq. A = AGATCGAT 12345678AAAAAC..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;≧

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BLASTStep2: Scan sequence B for hits.

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BLASTStep2: Scan sequence B for hits.

Step 3: Extend hits.

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.)

BLAST 2.0 saves the time spent in extension, and

considers gapped alignments.

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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.

alignment

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