1. Sequence Alignment Kun-Mao Chao (趙坤茂)
Department of Computer Science and Information Engineering
National Taiwan University, Taiwan
WWW:

2. Bioinformatics

3. Bioinformatics and Computational Biology-Related Journals:
Bioinformatics (previously called CABIOS)
Bulletin of Mathematical Biology
Computers and Biomedical Research
Genome Research
Genomics
Journal of Bioinformatics and Computational Biology
Journal of Computational Biology
Journal of Molecular Biology
Nature
Nucleic Acid Research
Science

4. Bioinformatics and Computational Biology-Related Conferences:
Intelligent Systems for Molecular Biology (ISMB)
Pacific Symposium on Biocomputing (PSB)
The Annual International Conference on Research in Computational Molecular Biology (RECOMB)
The IEEE Computer Society Bioinformatics Conference (CSB)
...

5. Bioinformatics and Computational Biology-Related Books:
Calculating the Secrets of Life: Applications of the Mathematical Sciences in Molecular Biology, by Eric S. Lander and Michael S. Waterman (1995)
Introduction to Computational Biology: Maps, Sequences, and Genomes, by Michael S. Waterman (1995)
Introduction to Computational Molecular Biology, by Joao Carlos Setubal and Joao Meidanis (1996)
Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology, by Dan Gusfield (1997)
Computational Molecular Biology: An Algorithmic Approach, by Pavel Pevzner (2000)
Introduction to Bioinformatics, by Arthur M. Lesk (2002)

6. Useful Websites MIT Biology Hypertextbook
The International Society for Computational Biology:
National Center for Biotechnology Information (NCBI, NIH):
European Bioinformatics Institute (EBI):
DNA Data Bank of Japan (DDBJ):

7. Sequence Alignment

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

9. Pairwise Alignment Sequence A: CTTAACT Sequence B: CGGATCAT
An alignment of A and B:
C---TTAACT CGGATCA--T
Sequence A
Sequence B

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

11. Alignment Graph C---TTAACT CGGATCA--T Sequence A: CTTAACT
Sequence B: CGGATCAT
C G G A T C A T
C T T A A C T
C---TTAACT CGGATCA--T

12. 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 T C G G A T C A - - T
= +12
Alignment score

13. 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 computed as follows.

14. Computing Si,j j
w(ai,bj)
w(ai,-) i
w(-,bj)
Sm,n

15. Initializations C G G A T C A T -3 -6 -9 -12 -15 -18 -21 -24-3 -6 -9
-12
-15
-18
-21
-24
C T T A A C T

16. S3,5 = ？ C G G A T C A T -3 -6 -9 -12 -15 -18 -21 -24 8 5 2 -1 -4 -7-3 -6 -9
-12
-15
-18
-21
-24 8 5 2 -1 -4 -7
-10
-13 3 7 4 1 -2 -5 ?
C T T A A C T

17. S3,5 = 5 C G G A T C A T -3 -6 -9 -12 -15 -18 -21 -24 8 5 2 -1 -4 -7-3 -6 -9
-12
-15
-18
-21
-24 8 5 2 -1 -4 -7
-10
-13 3 7 4 1 -2 -5 9 6 -8
-11
-14 14
C T T A A C T
optimal score

18. C T T A A C – T C G G A T C A T 8 – 5 –5 +8 -5 +8 -3 +8 = 14
8 – 5 – = 14
C G G A T C A T -3 -6 -9
-12
-15
-18
-21
-24 8 5 2 -1 -4 -7
-10
-13 3 7 4 1 -2 -5 9 6 -8
-11
-14 14
C T T A A C T

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

20. Initializations G A A T C T G C -3 -6 -9 -12 -15 -18 -21 -24-3 -6 -9
-12
-15
-18
-21
-24
C AA T T G A

21. S4,2 = ？ G A A T C T G C -3 -6 -9 -12 -15 -18 -21 -24 -5 -8 -11 -14 -4-3 -6 -9
-12
-15
-18
-21
-24 -5 -8
-11
-14 -4 -7
-10
-13 3 11 8 5 2 -1 ?
C AA T T G A

22. S5,5 = ？ G A A T C T G C -3 -6 -9 -12 -15 -18 -21 -24 -5 -8 -11 -14 -4-3 -6 -9
-12
-15
-18
-21
-24 -5 -8
-11
-14 -4 -7
-10
-13 3 11 8 5 2 -1 19 16 13 10 7 ?
C AA T T G A

23. S5,5 = 14 G A A T C T G C -3 -6 -9 -12 -15 -18 -21 -24 -5 -8 -11 -14-3 -6 -9
-12
-15
-18
-21
-24 -5 -8
-11
-14 -4 -7
-10
-13 3 11 8 5 2 -1 19 16 13 10 7 14 24 21 18 32 29 1 27
C AA T T G A
optimal score

24. C A A T - T G A G A A T C T G C -5 +8 +8 +8 -3 +8 +8 -5 = 27
= 27
G A A T C T G C -3 -6 -9
-12
-15
-18
-21
-24 -5 -8
-11
-14 -4 -7
-10
-13 3 11 8 5 2 -1 19 16 13 10 7 14 24 21 18 32 29 1 27
C AA T T G A

25. Global Alignment vs. Local Alignment

26. 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 computed as follows.

27. local alignment C G G A T C A T 8 5 2 3 13 11 ? C T T A A C T Match: 8
Mismatch: -5
Gap symbol: -3
C G G A T C A T 8 5 2 3 13 11 ?
C T T A A C T

28. local alignment C G G A T C A T 8 5 2 3 13 11 10 7 18 C T T A A C T
Match: 8
Mismatch: -5
Gap symbol: -3
C G G A T C A T 8 5 2 3 13 11 10 7 18
C T T A A C T
The best score

29. A – C - T A T C A T 8-3+8-3+8 = 18 C G G A T C A T 8 5 2 3 13 11 10 78 5 2 3 13 11 10 7 18
C T T A A C T
The best score

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

31. Did you get it right? G A A T C T G C 8 5 2 3 16 13 10 7 4 1 24 21 188 5 2 3 16 13 10 7 4 1 24 21 18 15 12 19 29 26 23 37 34 32
C AA T T G A

32. A A T – T G A A T C T G
= 37
G A A T C T G C 8 5 2 3 16 13 10 7 4 1 24 21 18 15 12 19 29 26 23 37 34 32
C AA T T G A

33. Affine gap penalties C - - - T T A A C T C G G A T C A - - T
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 T C G G A T C A - - T
= +12
Alignment score: 12 – 4 – 4 = 4

34. 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

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

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

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

38. 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 T C G G A T C A - - T
= +27
Alignment score: 27 – 4 – 4 = 19

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

40. Constant gap penalties

41. 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

42. Restricted affine gap penalties

43. 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)

44. 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)

45. 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.

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

47. FASTA
Step 2: Re-score using PAM matrix, and keep top scoring segments.

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

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

50. 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.

51. 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

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

53. BLAST Step 1: Build the hash table for Sequence A. (3-tuple example)
For DNA sequences:
Seq. A = AGATCGAT
AAA AAC .. AGA ATC CGA GAT TCG TTT
For protein sequences:
Seq. A = ELVIS Add 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;

54. BLAST
Step2: Scan sequence B for hits.

55. BLAST Step2: Scan sequence B for hits. Step 3: Extend hits.
BLAST 2.0 saves the time spent in extension, and considers gapped alignments.
hit
Terminate if the score of the sxtension fades away. (That is, when we reach a segment pair whose score falls a certain distance below the best score found for shorter extensions.)

56. Remarks
Filtering is based on the observation that a good alignment usually includes short identical or very similar fragments.
The idea of filtration was used in both FASTA and BLAST.