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Sequence Alignment

Sequence Alignment. Evolution. Evolution at the DNA level. Deletion. Mutation. …AC GGTG CAGT T ACCA…. SEQUENCE EDITS. …AC ---- CAGT C CACCA…. REARRANGEMENTS. Inversion. Translocation. Duplication. Sequence conservation implies function. Alignment is the key to

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Sequence Alignment

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  1. Sequence Alignment

  2. Evolution

  3. Evolution at the DNA level Deletion Mutation …ACGGTGCAGTTACCA… SEQUENCE EDITS …AC----CAGTCCACCA… REARRANGEMENTS Inversion Translocation Duplication

  4. Sequence conservation implies function • Alignment is the key to • Finding important regions • Determining function • Uncovering the evolutionary forces

  5. Sequence Alignment AGGCTATCACCTGACCTCCAGGCCGATGCCC TAGCTATCACGACCGCGGTCGATTTGCCCGAC -AGGCTATCACCTGACCTCCAGGCCGA--TGCCC--- TAG-CTATCAC--GACCGC--GGTCGATTTGCCCGAC Definition Given two strings x = x1x2...xM, y = y1y2…yN, an alignment is an assignment of gaps to positions 0,…, N in x, and 0,…, N in y, so as to line up each letter in one sequence with either a letter, or a gap in the other sequence

  6. What is a good alignment? AGGCTAGTT, AGCGAAGTTT AGGCTAGTT- 6 matches, 3 mismatches, 1 gap AGCGAAGTTT AGGCTA-GTT- 7 matches, 1 mismatch, 3 gaps AG-CGAAGTTT AGGC-TA-GTT- 7 matches, 0 mismatches, 5 gaps AG-CG-AAGTTT

  7. Scoring Function • Sequence edits: AGGCCTC • Mutations AGGACTC . • Insertions AGGGCCTC • Deletions AGG . CTC Scoring Function: Match: +m Mismatch: -s Gap: -d Score F = (# matches)  m - (# mismatches)  s – (#gaps)  d

  8. How do we compute the best alignment? AGTGCCCTGGAACCCTGACGGTGGGTCACAAAACTTCTGGA Too many possible alignments: >> 2N AGTGACCTGGGAAGACCCTGACCCTGGGTCACAAAACTC

  9. Alignment is additive Observation: The score of aligning x1……xM y1……yN is additive Say that x1…xi xi+1…xM aligns to y1…yj yj+1…yN The two scores add up: F(x[1:M], y[1:N]) = F(x[1:i], y[1:j]) + F(x[i+1:M], y[j+1:N])

  10. Dynamic Programming • There are only a polynomial number of subproblems • Align x1…xi to y1…yj • Original problem is one of the subproblems • Align x1…xM to y1…yN • Each subproblem is easily solved from smaller subproblems • ??? • Then, we can apply Dynamic Programming!!! Let F(i,j) = optimal score of aligning x1……xi y1……yj

  11. Dynamic Programming (cont’d) Notice three possible cases: • xi aligns to yj x1……xi-1 xi y1……yj-1 yj 2. xi aligns to a gap x1……xi-1 xi y1……yj - • yj aligns to a gap x1……xi - y1……yj-1 yj m, if xi = yj F(i,j) = F(i-1, j-1) + -s, if not F(i,j) = F(i-1, j) - d F(i,j) = F(i, j-1) - d

  12. Dynamic Programming (cont’d) How do we know which case is correct? Inductive assumption: F(i, j-1), F(i-1, j), F(i-1, j-1) are optimal Then, F(i-1, j-1) + s(xi, yj) F(i, j) = max F(i-1, j) – d F( i, j-1) – d Where s(xi, yj) = m, if xi = yj; -s, if not

  13. Pairwise Sequence Alignment • As we’ve seen, sequence similarity is an indicator of homology • There are other uses for sequence similarity • Database queries • Comparative genomics • …

  14. Pairwise Sequence Alignment • Example • Which one is better? HEAGAWGHEE PAWHEAE HEAGAWGHE-E HEAGAWGHE-E P-A--W-HEAE --P-AW-HEAE

  15. Scoring • To compare two sequence alignments, calculate a score • PAM or BLOSUM matrices • Matches and mismatches • Gap penalty • Initiating a gap • Gap extension penalty • Extending a gap

  16. C W W -8 17 PAM 250 A R N D C Q E G H I L K M F P S T W Y V B Z A 2 -2 0 0 -2 0 0 1 -1 -1 -2 -1 -1 -3 1 1 1 -6 -3 0 2 1 R -2 6 0 -1 -4 1 -1 -3 2 -2 -3 3 0 -4 0 0 -1 2 -4 -2 1 2 N 0 0 2 2 -4 1 1 0 2 -2 -3 1 -2 -3 0 1 0 -4 -2 -2 4 3 D 0 -1 2 4 -5 2 3 1 1 -2 -4 0 -3 -6 -1 0 0 -7 -4 -2 5 4 C -2 -4 -4 -5 12 -5 -5 -3 -3 -2 -6 -5 -5 -4 -3 0 -2 -8 0 -2 -3 -4 Q 0 1 1 2 -5 4 2 -1 3 -2 -2 1 -1 -5 0 -1 -1 -5 -4 -2 3 5 E 0 -1 1 3 -5 2 4 0 1 -2 -3 0 -2 -5 -1 0 0 -7 -4 -2 4 5 G 1 -3 0 1 -3 -1 0 5 -2 -3 -4 -2 -3 -5 0 1 0 -7 -5 -1 2 1 H -1 2 2 1 -3 3 1 -2 6 -2 -2 0 -2 -2 0 -1 -1 -3 0 -2 3 3 I -1 -2 -2 -2 -2 -2 -2 -3 -2 5 2 -2 2 1 -2 -1 0 -5 -1 4 -1 -1 L -2 -3 -3 -4 -6 -2 -3 -4 -2 2 6 -3 4 2 -3 -3 -2 -2 -1 2 -2 -1 K -1 3 1 0 -5 1 0 -2 0 -2 -3 5 0 -5 -1 0 0 -3 -4 -2 2 2 M -1 0 -2 -3 -5 -1 -2 -3 -2 2 4 0 6 0 -2 -2 -1 -4 -2 2 -1 0 F -3 -4 -3 -6 -4 -5 -5 -5 -2 1 2 -5 0 9 -5 -3 -3 0 7 -1 -3 -4 P 1 0 0 -1 -3 0 -1 0 0 -2 -3 -1 -2 -5 6 1 0 -6 -5 -1 1 1 S 1 0 1 0 0 -1 0 1 -1 -1 -3 0 -2 -3 1 2 1 -2 -3 -1 2 1 T 1 -1 0 0 -2 -1 0 0 -1 0 -2 0 -1 -3 0 1 3 -5 -3 0 2 1 W -6 2 -4 -7 -8 -5 -7 -7 -3 -5 -2 -3 -4 0 -6 -2 -5 17 0 -6 -4 -4 Y -3 -4 -2 -4 0 -4 -4 -5 0 -1 -1 -4 -2 7 -5 -3 -3 0 10 -2 -2 -3 V 0 -2 -2 -2 -2 -2 -2 -1 -2 4 2 -2 2 -1 -1 -1 0 -6 -2 4 0 0 B 2 1 4 5 -3 3 4 2 3 -1 -2 2 -1 -3 1 2 2 -4 -2 0 6 5 Z 1 2 3 4 -4 5 5 1 3 -1 -1 2 0 -4 1 1 1 -4 -3 0 5 6

  17. Example • Gap penalty: -8 • Gap extension: -8 HEAGAWGHE-E --P-AW-HEAE (-8) + (-8) + (-1) + 5 + 15 + (-8) + 10 + 6 + (-8) + 6 = 9 HEAGAWGHE-E Exercise: Calculate for P-A--W-HEAE

  18. Formal Description • Problem:PairSeqAlign • Input: Two sequences x,y Scoring matrix s Gap penalty d Gap extension penalty e • Output: The optimal sequence alignment

  19. How Difficult Is This? • Consider two sequences of length n • There are possible global alignments, and we need to find an optimal one from amongst those!

  20. So what? • So at n = 20, we have over 120 billion possible alignments • We want to be able to align much, much longer sequences • Some proteins have 1000 amino acids • Genes can have several thousand base pairs

  21. Dynamic Programming • General algorithmic development technique • Reuses the results of previous computations • Store intermediate results in a table for reuse • Look up in table for earlier result to build from

  22. Global Alignment • Needleman-Wunsch 1970 • Idea: Build up optimal alignment from optimal alignments of subsequences HEAG --P- -25 Add score from table HEAG- --P-A -33 HEAGA --P-A -20 HEAGA --P— -33 Gap with bottom Top and bottom Gap with top

  23. Global Alignment • Notation • xi – ith letter of string x • yj – jth letter of string y • x1..i – Prefix of x from letters 1 through I • F – matrix of optimal scores • F(i,j) represents optimal score lining up x1..i with y1..j • d – gap penalty • s – scoring matrix MSCS 230: Bioinformatics I - Pairwise Sequence Alignment

  24. Global Alignment • The work is to build up F • Initialize: F(0,0) = 0, F(i,0) = id, F(0,j)=jd • Fill from top left to bottom right using the recursive relation MSCS 230: Bioinformatics I - Pairwise Sequence Alignment

  25. Global Alignment yj aligned to gap Move ahead in both s(xi,yj) d d xi aligned to gap While building the table, keep track of where optimal score came from, reverse arrows MSCS 230: Bioinformatics I - Pairwise Sequence Alignment

  26. Example

  27. Completed Table

  28. The Needleman-Wunsch Matrix x1 ……………………………… xM Every nondecreasing path from (0,0) to (M, N) corresponds to an alignment of the two sequences y1 ……………………………… yN An optimal alignment is composed of optimal subalignments

  29. Performance • Time: O(NM) • Space: O(NM)

  30. Design a Perl Program • Is it doable by Perl? • How can we handle two-dimensional array?

  31. i-> j | V M S M[i, j] = S[j*len+i]

  32. Detail

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