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multiple_alignment

# multiple_alignment - University of North Texas Biocomputing...

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University of North Texas Biocomputing 1 Biocomputing University of North Texas Multiple Alignment Source: www.bioalgorithms.info University of North Texas Biocomputing Multiple Alignment versus Pairwise Alignment Up until now we have only tried to align two sequences. University of North Texas Biocomputing Multiple Alignment versus Pairwise Alignment Up until now we have only tried to align two sequences. What about more than two? And what for? A faint similarity between two sequences becomes significant if present in many Multiple alignments can reveal subtle similarities that pairwise alignments do not reveal University of North Texas Biocomputing Generalizing the Notion of Pairwise Alignment Alignment of 2 sequences is represented as a 2-row matrix In a similar way, we represent alignment of 3 sequences as a 3-row matrix A T _ G C G _ A _ C G T _ A A T C A C _ A Score: more conserved columns, better alignment University of North Texas Biocomputing Alignments = Paths in Align 3 sequences: ATGC, AATC,ATGC C -- T A A C G T -- A C G T A -- University of North Texas Biocomputing Alignment Paths 4 3 2 1 1 0 4 3 3 2 1 0 C -- T A A C G T -- A 4 3 2 1 0 0 C G T A -- Resulting path in (x,y,z) space: (0,0,0) (1,1,0) (1,2,1) (2,3,2) (3,3,3) (4,4,4) x coordinate y coordinate z coordinate

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University of North Texas Biocomputing 2 University of North Texas Biocomputing 2-D vs 3-D Alignment Grid V W 2-D edit graph 3-D edit graph University of North Texas Biocomputing Architecture of 3-D Alignment Cell (i-1,j-1,k-1) (i,j-1,k-1) (i,j-1,k) (i-1,j-1,k) (i-1,j,k) (i,j,k) (i-1,j,k-1) (i,j,k-1) University of North Texas Biocomputing Multiple Alignment: Dynamic Programming s i,j,k = max δ ( x, y, z ) is an entry in the 3 -D scoring matrix s i-1,j-1,k-1 + (v i , w j , u k ) s i-1,j-1,k + (v i , w j , _ ) s i-1,j,k-1 + (v i , _, u k ) s i,j-1,k-1 + (_, w j , u k ) s i-1,j,k + (v i , _ , _) s i,j-1,k + (_, w j , _) s i,j,k-1 + (_, _, u k ) cube diagonal: no indels face diagonal: one indel edge diagonal: two indels University of North Texas Biocomputing Multiple Alignment: Running Time For 3 sequences of length n , the run time is 7 n 3 ; O( n 3 ) For k sequences, build a k -dimensional Manhattan, with run time ( 2 k -1)( n k ); O( 2 k n k ) Conclusion: dynamic programming approach for alignment between two sequences is easily extended to k sequences but it is impractical due to exponential running time University of North Texas Biocomputing Multiple Alignment Induces Pairwise Alignments Every multiple alignment induces pairwise alignments x: AC-GCGG-C y: AC-GC-GAG z: GCCGC-GAG Induces: x: ACGCGG-C; x: AC-GCGG-C; y:
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multiple_alignment - University of North Texas Biocomputing...

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