Multiple Alignment. Slides revised and adapted to Bioinformática IST Ana Teresa Freitas

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1 n Introduction to Bioinformatics lgorithms Multiple lignment Slides revised and adapted to Bioinformática IS 2005 na eresa Freitas n Introduction to Bioinformatics lgorithms Outline Dynamic Programming in 3-D Progressive lignment Profile Progressive lignment (lustalw) Scoring Multiple lignments Entropy Sum of Pairs lignment

2 n Introduction to Bioinformatics lgorithms eneralizing the Notion of Pairwise lignment Up until now we have only tried to align two sequences to one another. What about more than two? lignment 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 _ Score: more conserved columns, better alignment n Introduction to Bioinformatics lgorithms lignments = Paths in lign 3 sequences:,,

3 n Introduction to Bioinformatics lgorithms lignment Paths x coordinate n Introduction to Bioinformatics lgorithms lignment Paths lign the following 3 sequences:,, x coordinate y coordinate -- 3

4 n Introduction to Bioinformatics lgorithms lignment Paths x coordinate y coordinate z coordinate Resulting path in (x,y,z) space: (0,0,0) (,,0) (,2,) (2,3,2) (3,3,3) (4,4,4) n Introduction to Bioinformatics lgorithms ligning hree Sequences Same strategy as aligning two sequences Use a 3-D Manhattan ube, with each axis representing a sequence to align For global alignments, go from source to sink source sink 4

5 n Introduction to Bioinformatics lgorithms 2-D vs 3-D lignment rid V W 2-D edit graph 3-D? n Introduction to Bioinformatics lgorithms rchitecture of 3-D lignment rid In 2-D, 3 edges in each unit square In 3-D, 7 edges in each unit cube 5

6 n Introduction to Bioinformatics lgorithms ell of 3-D lignment rid (i-,j-,k-) (i-,j,k-) (i-,j-,k) (i-,j,k) (i,j-,k-) (i,j,k-) (i,j-,k) (i,j,k) n Introduction to Bioinformatics lgorithms Multiple lignment: Dynamic Programming s i,j,k = max s i-,j-,k- + σ(v i, w j, u k ) s i-,j-,k + σ(v i, w j, _ ) s i-,j,k- + σ(v i, _, u k ) s i,j-,k- + σ(_, w j, u k ) s i-,j,k + σ(v i, _, _) s i,j-,k + σ(_, w j, _) s i,j,k- + σ(_, _, u k ) cube diagonal: no indels face diagonal: one indel edge diagonal: two indels σ(x, y, z) is an entry in the 3-D scoring matrix 6

7 n Introduction to Bioinformatics lgorithms Multiple lignment: Running ime For 3 sequences of length n, the run time is 7n 3 ; O(n 3 ) For k sequences, build a k-dimensional Manhattan, with run time (2 k -)(n k ); O(2 k n k ) onclusion: dynamic programming approach for alignment between two sequences is easily extended to k sequences but it is impractical due to exponential running time n Introduction to Bioinformatics lgorithms Inferring Multiple lignment from Pairwise lignments From an optimal multiple alignment, we can infer pairwise alignments between all sequences, but they are not necessarily optimal It is difficult to infer a ``good multiple alignment from optimal pairwise alignments between all sequences 7

8 n Introduction to Bioinformatics lgorithms ombining Optimal Pairwise lignments into Multiple lignment an combine pairwise alignments into multiple alignment an not combine pairwise alignments into multiple alignment n Introduction to Bioinformatics lgorithms Inferring Pairwise lignments 3 sequences, 3 comparisons 4 sequences, 6 comparisons 5 sequences, 0 comparisons 8

9 n Introduction to Bioinformatics lgorithms Multiple lignment: reedy pproach hoose most similar pair of strings and combine into a consensus, thereby reducing alignment of k sequences to an alignment of of k- sequences. Repeat his is a heuristic greedy method k u = u 2 = u 3 = u = --- u 2 = u k = k- u k = n Introduction to Bioinformatics lgorithms reedy pproach: Example onsider these 4 sequences s s2 s3 s4 9

10 n Introduction to Bioinformatics lgorithms reedy pproach: Example (cont d) here are 4 2 = 6 possible alignments s2 s4 (score = 2) s - s2 - (score = ) s - s3 - (score = ) s -- s4 - (score = 0) s2 - s3 - (score = -) s3 - s4 - (score = -) n Introduction to Bioinformatics lgorithms reedy pproach: Example (cont d) s2 and s4 are closest; combine: s2 s4 s s3 s2,4 s2,4 (consensus) here are many (4) alternative choices for the consensus, let s assume we randomly choose one new set becomes: 0

11 n Introduction to Bioinformatics lgorithms reedy pproach: Example (cont d) set is: s s3 s2,4 scores are: s - s3 - (score = ) s -- s2,4 -- (score = 0) s3 s2,4 - (score=-) ake best pair and form another consensus: s,3 = (arbitrarily break ties) n Introduction to Bioinformatics lgorithms reedy pproach: Example (cont d) new set is: s,3 s2,4 scores is: s,3 s2,4 - (score=-) Form consensus: s,3,2,4 = (arbitrarily break ties) s s2 s3 s4

12 n Introduction to Bioinformatics lgorithms Progressive lignment Progressive alignment is a variation of greedy algorithm with a somewhat more intelligent strategy for choosing a consensus Progressive alignment works well for close sequences, but deteriorates for distant sequences aps in consensus string are permanent Simplified representation of the alignments Better solution? Use a profile to represent consensus n Introduction to Bioinformatics lgorithms lustalw Popular multiple alignment tool today Several heuristics to improve accuracy: Sequences are weighted by relatedness Scoring matrix can be chosen on the fly Position-specific gap penalties 2

13 n Introduction to Bioinformatics lgorithms lustalw (cont d) hree-step process.) Pairwise alignment 2.) Build uide ree 3.) Progressive lignment n Introduction to Bioinformatics lgorithms Step : Pairwise lignment ligns each sequence again each other giving a distance matrix Distance = exact matches / sequence length (percent identity) S S 2 S 3 S 4 S S S S (.7 means 7 % identical) 3

14 n Introduction to Bioinformatics lgorithms Step 2: uide ree reate uide ree using the distance matrix lustalw uses the neighbor-joining method uide tree roughly reflects evolutionary relations n Introduction to Bioinformatics lgorithms Step 2: uide ree (cont d) S S 2 S 3 S 4 S S S S S S 3 S 4 S 2 alculate: s,3 = consensus(s, s3) s,3,4 = consensus((s,3),s4) s,3,4,2,2 = consensus((s,3,4),s2) 4

15 n Introduction to Bioinformatics lgorithms Step 3: Progressive lignment lign the two most similar sequences Following the guide tree, add in the next sequences, aligning to the existing alignment Insert gaps as necessary Sample output: FOS_R FOS_MOUSE FOS_HIK FOSB_MOUSE FOSB_HUMN PEEMSVS-LDLLPEPESEEFLPLLNDPEPK-PSLEPVKNISNMELKEPFD PEEMSVS-LDLLPESPESEEFLPLLNDPEPK-PSLEPVKSISNVELKEPFD SEELLDL----PSPEEFLPLMEPPVPPKEPS--SLELKEPFD PPPLEVRDLP-----SSKEDFWLLPPPPPPP LPFQ PPPLEVRDLP-----SPKEDFSWLLPPPPPPP LPFQ.. : **. :.. *:.* *. * **: Dots and stars show how well-conserved a column is. n Introduction to Bioinformatics lgorithms lustalw: Scoring lignments Distance between sequences determines which scoring matrix to use 80-00% Blosum % Blosum % Blosum % Blosum30 5

16 n Introduction to Bioinformatics lgorithms Multiple lignments: Scoring Number of matches (multiple longest common subsequence score) Entropy score Sum of pairs (SP-Score) n Introduction to Bioinformatics lgorithms Multiple LS Score column is a match if all the letters in the column are the same Only good for very similar sequences 6

17 n Introduction to Bioinformatics lgorithms Entropy Define frequencies for the occurrence of each letter in each column of multiple alignment p = or p = 0.75, p = 0.25 ompute entropy of each column X p X =,,, log p X n Introduction to Bioinformatics lgorithms Entropy: Example entropy = 0 Best case Worst case entropy = log 4 4 = 4( 2) = 2 4 7

18 n Introduction to Bioinformatics lgorithms Multiple lignment: Entropy Score Entropy for a multiple alignment is the sum of entropies of its columns: Σ over all columns Σ X=,,, p X logp X n Introduction to Bioinformatics lgorithms Entropy of an lignment: Example column entropy: ( p logp + p logp + p logp + p logp ) olumn = [*log() + 0*log0 + 0*log0 +0*log0] = 0 olumn 2 = [( / 4 )*log( / 4 ) + ( 3 / 4 )*log( 3 / 4 ) + 0*log0 + 0*log0] = [ ( / 4 )*(-2) + ( 3 / 4 )*(-.45) ] = -0.8 olumn 3 = [( / 4 )*log( / 4 )+( / 4 )*log( / 4 )+( / 4 )*log( / 4 ) +( / 4 )*log( / 4 )] = 4* -[( / 4 )*(-2)] = -2 lignment Entropy = =

19 n Introduction to Bioinformatics lgorithms Inferring Pairwise lignments from Multiple lignments From a multiple alignment, we can infer pairwise alignments between all sequences, but they are not necessarily optimal his is like projecting a 3-D multiple alignment path on to a 2-D face of the cube n Introduction to Bioinformatics lgorithms Multiple lignment Projections 3-D alignment can be projected onto the 2-D plane to represent an alignment between a pair of sequences. ll 3 Pairwise Projections of the Multiple lignment 9

20 n Introduction to Bioinformatics lgorithms Sum of Pairs Score(SP-Score) onsider pairwise alignment of sequences a i and a j imposed by a multiple alignment of k sequences Denote the score of this suboptimal (not necessarily optimal) pairwise alignment as s*(a i, a j ) Sum up the pairwise scores for a multiple alignment: s(a,,a k ) = Σ i,j s*(a i, a j ) n Introduction to Bioinformatics lgorithms omputing SP-Score ligning 4 sequences: 6 pairwise alignments iven a,a 2,a 3,a 4 : s(a a 4 ) = Σs*(a i,a j ) = s*(a,a 2 ) + s*(a,a 3 ) + s*(a,a 4 ) + s*(a 2,a 3 ) + s*(a 2,a 4 ) + s*(a 3,a 4 ) 20

21 n Introduction to Bioinformatics lgorithms SP-Score: Example s. s k = o calculate each column: ss ( a s * ( *... ak ) S ( ai, a j ) i, j n Pairs of Sequences 2 = 3 µ Score = 2µ µ olumn olumn 3 2

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