Sequence Alignment Algorithms

8/3/2019 Sequence Alignment Algorithms

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Developing Pairwise Sequence Alignment Algorithms

Dr. Nancy Warter-Perez


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Developing Pairwise Sequence Alignment Algorithms 2

OutlineOverview of global and local alignment References for sequence alignment algorithms

Discussion of Needleman-Wunsch iterative approachto global alignment Discussion of Smith-Waterman recursive approach tolocal alignment Discussion of how LCS Algorithm can be extended for

Global alignment (Needleman-Wunsch)Local alignment (Smith-Waterman)

Affine gap penaltiesGroup assignments for project


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Overview of Pairwise

Sequence Alignment Dynamic Programming

Applied to optimization problemsUseful when

Problem can be recursively divided into sub-problemsSub-problems are not independent Needle man-Wunsch is a global alignment technique that usesan iterative algorithm and no gap penalty (could extend to fixedgap penalty).S mith-Wat e rman is a local alignment technique that uses a

recursive algorithm and can use alternative gap penalties (such asaffine ). Smith-Waterman s algorithm is an extension of Longest Common Substring (LCS) problem and can be generalized to solveboth local and global alignment.Note: Needleman-Wunsch is usually used to refer to globalalignment regardless of the algorithm used.


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Project Referenceshttp://www.sbc.su.se/~arne/kurser/swell/pairwise

_alignments.html

Computational Molecular Biology An Algorithmic Approach, Pavel PevznerIntroduction to Computational Biology Maps,sequences, and genomes, Michael Waterman

Algorithms on Strings, Trees, and Sequences Computer Science and Computational Biology, DanGusfield


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Classic PapersNeedleman, S.B. and Wunsch, C.D. A GeneralMethod Applicable to the Search for Similarities in

Amino Acid Sequence of Two Proteins. J. Mol. Biol. ,48, pp. 443-453, 1970.(http://www.cs.umd.edu/class/spring2003/cmsc838t/papers/needlemanandwunsch1970.pdf )Smith, T.F. and Waterman, M.S. Identification of Common Molecular Subsequences. J. Mol. Biol. ,147, pp. 195-197,1981.( http://www.cmb.usc.edu/papers/msw_papers/msw-042.pdf )


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Needleman-Wunsch (1 of 3)

Match = 1

Mismatch = 0

Gap = 0


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Needleman-Wunsch (2 of 3)


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Needleman-Wunsch (3 of 3)From page 446:

It is apparent that the above array operation can beginat any of a number of points along the borders of thearray, which is equivalent to a comparison of N-terminalresidues or C-terminal residues only. As long as the

appropriate rules for pathways are followed, themaximum match will be the same. The cells of thearray which contributed to the maximum match, may be determined by recording the origin of the number that was added to each cell when the array was

operated upon.


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Smith-Waterman (1 of 3) A lgorithm

The two molecular sequences will be A=a 1a 2 . . . a n, and B=b 1b2 . . . b m . Asimilarity s(a,b ) is given between sequence elements a and b . Deletions of

length k are given weight W k . To find pairs of segments with highdegrees of similarity, we set up a matrix H . First set

H k0 = H ol = 0 for 0


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Smith-Waterman (2 of 3)The formula for H ij follows by considering the possibilities for

ending the segments at any a i and b j .

(1 ) If a i and b j are associated, the similarity isH i-l,j-l + s (a i ,b j ).

(2 ) If a i is at the end of a deletion of length k, the similarity is

H i k, j - W k .

(3 ) If b j is at the end of a deletion of length 1, the similarity is

H i , j-l - W l . (typo in paper )

(4 ) Finally, a zero is included to prevent calculated negativesimilarity, indicating n o similarity up to a i and b j .


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Smith-Waterman (3 of 3)The pair of segments with maximum similarity isfound by first locating the maximum element of H. The other matrix elements leading to thismaximum value are than sequentially determinedwith a traceback procedure ending with an element of H equal to zero. This procedureidentifies the segments as well as produces the

corresponding alignment. The pair of segmentswith the next best similarity is found by applyingthe traceback procedure to the second largestelement of H not associated with the firsttraceback.


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LCS Problem (cont.)Similarity score

si-1,j

si,j = max { si,j-1si-1,j-1 + 1, if vi = wj


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Extend LCS to Global

Alignment si-1,j + H(vi, -)

si,j = max { si,j-1 + H(-, wj)si-1,j-1 + H(vi, wj)

H(vi, -) = H(-, wj) = - V = fixed gap penalty

H(vi, wj) = score for match or mismatch can befixed, from PAM or BLOSUMModify LCS and PRINT-LCS algorithms to support global alignment (On board discussion)


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Extend to Local Alignment 0 (no negative scores)si-1,j + H(vi, -)

si,j = max { si,j-1 + H(-, wj)si-1,j-1 + H(vi, wj)

H(vi, -) = H(-, wj) = - V = fixed gap penaltyH(vi, wj) = score for match or mismatch can

be fixed, from PAM or BLOSUM


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Discussion on adding

affine gap penalties Affine gap penalty

Score for a gap of length x-( V + Wx)

WhereV > 0 is the insert gap penaltyW> 0 is the extend gap penalty

On board example fromhttp://www.sbc.su.se/~arne/kurser/swell/pairwise_alignments.html


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Alignment with Gap PenaltiesCan apply to global or local (w/ zero) algorithms

o si,j = max { o si-1,j - Wsi-1,j - ( V + W)

n si,j = max { n si1,j-1 - Wsi,j-1 - ( V + W)

si-1,j-1 + H(vi, wj)si,j = max { o si,j

n si,j


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Project Teams and

Presentation AssignmentsBase Project (Global Alignment):

Shwe and LeightonExtension 1 (Ends-Free Global Alignment):

Ehsanul and Water TreeExtension 2 (Local Alignment):

Scott and BrianExtension 3 (Affine Gap Penalty):

Charlyn and DavidExtension 4 (Database):Daniel and Ashley

Extension 5 (Space Efficient Algorithm):Kendra and Qing


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WorkshopMeet with your group and develop forthe overall structure of your program

High-level algorithmIdentify the modules, functions (includingparameters), and global variablesDetermine who is responsible for eachmoduleDevise a development timeline and atesting strategy

Sequence Alignment Algorithms

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