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Alignments and Phylogenetic tree

Alignments and Phylogenetic tree. Reading: Introduction to Bioinformatics. Arthur M. Lesk . Fourth Edition Chapter 5. Sequence Alignment. Dot Matrix. Sequence A ： CTTAACT Sequence B ： CGGATCAT. C G G A T C A T. C T T A A C T. Pairwise Alignment.

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Alignments and Phylogenetic tree

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  1. Alignments and Phylogenetic tree Reading: Introduction to Bioinformatics. Arthur M. Lesk. Fourth Edition Chapter 5

  2. Sequence Alignment

  3. Dot Matrix Sequence A：CTTAACT Sequence B：CGGATCAT C G G A T C A T CTTAACT

  4. Pairwise Alignment Sequence A: CTTAACT Sequence B: CGGATCAT An alignment of A and B: C---TTAACTCGGATCA--T Sequence A Sequence B

  5. Pairwise Alignment Sequence A: CTTAACT Sequence B: CGGATCAT An alignment of A and B: Mismatch Match C---TTAACTCGGATCA--T Deletion gap Insertion gap

  6. Alignment Graph Sequence A: CTTAACT Sequence B: CGGATCAT C G G A T C A T CTTAACT C---TTAACTCGGATCA--T

  7. A simple scoring scheme • Match: +8 (w(x, y) = 8, if x = y) • Mismatch: -5 (w(x, y) = -5, if x ≠ y) • Each gap symbol: -3 (w(-,x)=w(x,-)=-3) C - - - T T A A C TC G G A T C A - - T +8 -3 -3 -3 +8 -5 +8 -3 -3 +8 = +12 Alignment score

  8. An optimal alignment-- the alignment of maximum score • Let A=a1a2…am and B=b1b2…bn . • Si,j: the score of an optimal alignment between a1a2…ai and b1b2…bj • With proper initializations, Si,j can be computedas follows.

  9. ComputingSi,j j w(ai,bj) w(ai,-) i w(-,bj) Sm,n

  10. Initializations C G G A T C A T CTTAACT

  11. S3,5 = ？ C G G A T C A T CTTAACT

  12. S3,5 = 5 C G G A T C A T CTTAACT optimal score

  13. C T T A A C – TC G G A T C A T 8 – 5 –5 +8 -5 +8 -3 +8 = 14 C G G A T C A T CTTAACT

  14. Now try this example in class Sequence A: CAATTGA Sequence B: GAATCTGC Their optimal alignment？

  15. Initializations G A A T C T G C CAATTGA

  16. S4,2 = ？ G A A T C T G C CAATTGA

  17. S5,5 = ？ G A A T C T G C CAATTGA

  18. S5,5 = 14 G A A T C T G C CAATTGA optimal score

  19. C A A T - T G AG A A T C T G C -5 +8 +8 +8 -3 +8 +8 -5 = 27 G A A T C T G C CAATTGA

  20. Global Alignment vs. Local Alignment • global alignment: • local alignment:

  21. An optimal local alignment • Si,j: the score of an optimal local alignment ending at ai and bj • With proper initializations, Si,j can be computedas follows.

  22. Match: 8 Mismatch: -5 Gap symbol: -3 local alignment C G G A T C A T CTTAACT

  23. Match: 8 Mismatch: -5 Gap symbol: -3 local alignment C G G A T C A T CTTAACT The best score

  24. A – C - TA T C A T 8-3+8-3+8 = 18 C G G A T C A T CTTAACT The best score

  25. Now try this example in class Sequence A: CAATTGA Sequence B: GAATCTGC Their optimal local alignment？

  26. Did you get it right? G A A T C T G C CAATTGA

  27. A A T – T GA A T C T G 8+8+8-3+8+8 = 37 G A A T C T G C CAATTGA

  28. Affine gap penalties • Match: +8 (w(x, y) = 8, if x = y) • Mismatch: -5 (w(x, y) = -5, if x ≠ y) • Each gap symbol: -3 (w(-,x)=w(x,-)=-3) • Each gap is charged an extra gap-open penalty: -4. -4 -4 C - - - T T A A C TC G G A T C A - - T +8 -3 -3 -3 +8 -5 +8 -3 -3 +8 = +12 Alignment score: 12 – 4 – 4 = 4

  29. Affine gap panalties • A gap of length k is penalized x + k·y. gap-open penalty • Three cases for alignment endings: • ...x...x • ...x...- • ...-...x gap-symbol penalty an aligned pair a deletion an insertion

  30. Affine gap penalties • Let D(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj endingwith a deletion. • Let I(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj endingwith an insertion. • Let S(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj.

  31. Affine gap penalties (A gap of length k is penalized x + k·y.)

  32. D D D I I I S S S Affine gap penalties -y w(ai,bj) -x-y D -x-y I S -y

  33. Constant gap penalties • Match: +8 (w(x, y) = 8, if x = y) • Mismatch: -5 (w(x, y) = -5, if x ≠ y) • Each gap symbol: 0 (w(-,x)=w(x,-)=0) • Each gap is charged a constant penalty: -4. -4 -4 C - - - T T A A C TC G G A T C A - - T +8 0 0 0 +8 -5 +8 0 0 +8 = +27 Alignment score: 27 – 4 – 4 = 19

  34. Constant gap penalties • Let D(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj endingwith a deletion. • Let I(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj endingwith an insertion. • Let S(i, j) denote the maximum score of any alignment between a1a2…ai and b1b2…bj.

  35. Constant gap penalties

  36. Restricted affine gap panalties • A gap of length k is penalized x + f(k)·y. where f(k) = k for k <= c and f(k) = c for k > c • Five cases for alignment endings: • ...x...x • ...x...- • ...-...x • and 5. for long gaps an aligned pair a deletion an insertion

  37. Restricted affine gap penalties

  38. D(i, j) vs. D’(i, j) • Case 1: the best alignment ending at (i, j) with a deletion at the end has the last deletion gap of length <= c D(i, j) >= D’(i, j) • Case 2: the best alignment ending at (i, j) with a deletion at the end has the last deletion gap of length >= c D(i, j) <= D’(i, j)

  39. Max{S(i,j)-x-ky, S(i,j)-x-cy} c k

  40. k best local alignments • Smith-Waterman(Smith and Waterman, 1981; Waterman and Eggert, 1987) • FASTA(Wilbur and Lipman, 1983; Lipman and Pearson, 1985) • BLAST(Altschul et al., 1990; Altschul et al., 1997)

  41. FASTA • Find runs of identities, and identify regions with the highest density of identities. • Re-score using PAM matrix, and keep top scoring segments. • Eliminate segments that are unlikely to be part of the alignment. • Optimize the alignment in a band.

  42. FASTA Step 1: Find runes of identities, and identify regions with the highest density of identities. Sequence B Sequence A

  43. FASTA Step 2: Re-score using PAM matrix, andkeep top scoring segments.

  44. FASTA Step 3: Eliminate segments that are unlikely to be part of the alignment.

  45. FASTA Step 4: Optimize the alignment in a band.

  46. BLAST • Basic Local Alignment Search Tool(by Altschul, Gish, Miller, Myers and Lipman) • The central idea of the BLAST algorithm is that a statistically significant alignment is likely to contain a high-scoring pair of aligned words.

  47. The maximal segment pair measure • A maximal segment pair (MSP) is defined to be the highest scoring pair of identical length segments chosen from 2 sequences.(for DNA: Identities: +5; Mismatches: -4) • The MSP score may be computed in time proportional to the product of their lengths. (How?) An exact procedure is too time consuming. • BLAST heuristically attempts to calculate the MSP score. the highest scoring pair

  48. BLAST • Build the hash table for Sequence A. • Scan Sequence B for hits. • Extend hits.

  49. BLAST Step 1: Build the hash table for Sequence A. (3-tuple example) For protein sequences: Seq. A = ELVISAdd xyz to the hash table if Score(xyz, ELV) ≧ T;Add xyz to the hash table if Score(xyz, LVI) ≧ T;Add xyz to the hash table if Score(xyz, VIS) ≧ T; For DNA sequences: Seq. A = AGATCGAT 12345678 AAAAAC..AGA 1..ATC 3..CGA 5..GAT 2 6..TCG 4..TTT

  50. BLAST Step2: Scan sequence B for hits.

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