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423f11-lec5-msa - Multiple Sequence Alignment CMSC 423 Carl...

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Multiple Sequence Alignment CMSC 423 Carl Kingsford
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Multiple Sequence Alignment (MSA) Multiple sequence alignment: find more subtle patterns & find common patterns between all sequence.
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Generalizing Alignment to > 2 Strings Input: Sequences S 1 , S 2 , ..., S p Let cost ( x 1 , x 2 ,... x p ) be a user-supplied function that computes the quality of a column: an alignment between characters x 1 , x 2 , ... x p . Goal : find alignment M to minimize cost of the columns: cost ( x 1 , x 2 ,... x p ) = cost( )
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Slow Dynamic Programming Suppose you had just 3 sequences. Apply the same DP idea as sequence alignment for 2 sequences, but now with a 3-dimensional matrix (i, j, k) (i, j-1, k) (i-1, j, k) (i-1, j-1, k) (i-1, j-1, k-1) (i, j-1, k-1) (i-1, j, k-1) (i, j, k-1)
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DP Recurrence for 3 sequences (i, j, k) (i, j-1, k) (i-1, j, k) (i-1, j-1, k) (i-1, j-1, k-1) (i, j-1, k-1) (i-1, j, k-1) (i, j, k-1) Every possible pattern for the gaps. A [ i, j, k ] = min 8 > > > > > > > > > > < > > > > > > > > > > : cost( x i , y j , z k ) + A [ i - 1 , j - 1 , k - 1] cost( x i , - , - ) + A [ i - 1 , j, k ] cost( x i , y j , - ) + A [ i - 1 , j - 1 , k ] cost( - , y j , z k ) + A [ i, j - 1 , k - 1] cost( - , y j , - ) + A [ i, j - 1 , k ] cost( x i , - , z k ) + A [ i - 1 , j, k - 1] cost( - , - , z k ) + A [ i, j, k - 1]
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Running time n 3 subproblems, each takes 2 3 time O( n 3 ) time. For p sequences: n p subproblems, each takes 2 p time for the max and p 2 to compute cost() O( p 2 n p 2 p ) Even O( n 3 ) is often too slow for the length of sequences encountered in practice. One solution: approximation algorithm.
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SP-Score SP-Score(M) = i<j d M (S i , S j ) S i S j d M (S i , S j ) = sum of all the scores of the pairwise alignments implied by M. A particular cost() function, the SP-Score, is commonly used and allows us to design an approximation algorithm for the MSA problem. d M (S i , S j ) = the cost of the alignment between S i and S j as implied by MSA M.
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MSA A multiple sequence alignment (MSA) implies a pairwise alignment between every pair of sequences.
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