1. About optimal sequence alignment
A short glimpse into bioinformatics
April 24, 2010
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2. Pairwise sequence alignment
Assumptions:
sequences S1 and S2 are homologous, they share a common
ancestor;
differences between them are due to only two kinds of events,
substitutions and insertion-deletions.
Strategy:
choose a scoring matrix (reward for match, penalty for
mismatch and gap);
compute the editing distance (number of matches,
mismatches and gaps) to go from one sequence to the other;
keep the alignment with the highest score.
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3. Needleman-Wunsch algorithm
Aim: find the optimal global alignment of sequences S1 and S2
Recursion rule:

D(i − 1, j − 1) + score(S1 [i], S2 [j])

D(i, j) = max D(i − 1, j) + gap (1)

D(i, j − 1) + gap

Scoring scheme: identity=0 transition=-2 transversion=-5
gap=-10
Sequences: S1 =TTGT S2 =CTAGG
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4. Fill the matrix
C T A G G
T
T
G
T
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5. Fill the matrix
C T A G G
0
T
T
G
T
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6. Fill the matrix
C T A G G
0 → -10
T
T
G
T
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7. Fill the matrix
C T A G G
0 → -10 → -20
T
T
G
T
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8. Fill the matrix
C T A G G
0 → -10 → -20 → -30 → -40 → -50
T
T
G
T
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9. Fill the matrix
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓
T -10
↓
T -20
↓
G -30
↓
T -40
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10. Fill the matrix
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓
T -10 →
↓
T -20
↓
G -30
↓
T -40
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11. Fill the matrix
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓
T -10 → -2
↓
T -20
↓
G -30
↓
T -40
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12. Fill the matrix
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓ ↓ ↓ ↓ ↓
T -10 → -2 → -10 → -20 → -30 → -40
↓
T -20
↓
G -30
↓
T -40
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13. Fill the matrix
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓ ↓ ↓ ↓ ↓
T -10 → -2 → -10 → -20 → -30 → -40
↓ ↓ ↓ ↓ ↓ ↓
T -20 → → → → →
↓ ↓ ↓ ↓ ↓ ↓
G -30 → → → → →
↓ ↓ ↓ ↓ ↓ ↓
T -40 → → → → →
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14. Fill the matrix
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓ ↓ ↓ ↓ ↓
T -10 → -2 → -10 → -20 → -30 → -40
↓ ↓ ↓ ↓ ↓ ↓
T -20 → -12 → -2 → -12 → -22 → -32
↓ ↓ ↓ ↓ ↓ ↓
G -30 → -22 → -12 → -4 → -12 → -22
↓ ↓ ↓ ↓ ↓ ↓
T -40 → -32 → -22 → -14 → -9 → -17
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15. Traceback
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓ ↓ ↓ ↓ ↓
T -10 → -2 → -10 → -20 → -30 → -40
↓ ↓ ↓ ↓ ↓ ↓
T -20 → -12 → -2 → -12 → -22 → -32
↓ ↓ ↓ ↓ ↓ ↓
G -30 → -22 → -12 → -4 → -12 → -22
↓ ↓ ↓ ↓ ↓ ↓
T -40 → -32 → -22 → -14 → -9 → -17
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16. Traceback
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓ ↓ ↓ ↓ ↓
T -10 → -2 → -10 → -20 → -30 → -40
↓ ↓ ↓ ↓ ↓ ↓
T -20 → -12 → -2 → -12 → -22 → -32
↓ ↓ ↓ ↓ ↓ ↓
G -30 → -22 → -12 → -4 → -12 → -22
↓ ↓ ↓ ↓ ↓ ↓
T -40 → -32 → -22 → -14 → -9 → -17
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17. Traceback
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓ ↓ ↓ ↓ ↓
T -10 → -2 → -10 → -20 → -30 → -40
↓ ↓ ↓ ↓ ↓ ↓
T -20 → -12 → -2 → -12 → -22 → -32
↓ ↓ ↓ ↓ ↓ ↓
G -30 → -22 → -12 → -4 → -12 → -22
↓ ↓ ↓ ↓ ↓ ↓
T -40 → -32 → -22 → -14 → -9 → -17
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18. Traceback
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓ ↓ ↓ ↓ ↓
T -10 → -2 → -10 → -20 → -30 → -40
↓ ↓ ↓ ↓ ↓ ↓
T -20 → -12 → -2 → -12 → -22 → -32
↓ ↓ ↓ ↓ ↓ ↓
G -30 → -22 → -12 → -4 → -12 → -22
↓ ↓ ↓ ↓ ↓ ↓
T -40 → -32 → -22 → -14 → -9 → -17
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19. Traceback
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓ ↓ ↓ ↓ ↓
T -10 → -2 → -10 → -20 → -30 → -40
↓ ↓ ↓ ↓ ↓ ↓
T -20 → -12 → -2 → -12 → -22 → -32
↓ ↓ ↓ ↓ ↓ ↓
G -30 → -22 → -12 → -4 → -12 → -22
↓ ↓ ↓ ↓ ↓ ↓
T -40 → -32 → -22 → -14 → -9 → -17
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20. Traceback
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓ ↓ ↓ ↓ ↓
T -10 → -2 → -10 → -20 → -30 → -40
↓ ↓ ↓ ↓ ↓ ↓
T -20 → -12 → -2 → -12 → -22 → -32
↓ ↓ ↓ ↓ ↓ ↓
G -30 → -22 → -12 → -4 → -12 → -22
↓ ↓ ↓ ↓ ↓ ↓
T -40 → -32 → -22 → -14 → -9 → -17
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21. Traceback
C T A G G
0 → -10 → -20 → -30 → -40 → -50
↓ ↓ ↓ ↓ ↓ ↓
T -10 → -2 → -10 → -20 → -30 → -40
↓ ↓ ↓ ↓ ↓ ↓
T -20 → -12 → -2 → -12 → -22 → -32
↓ ↓ ↓ ↓ ↓ ↓
G -30 → -22 → -12 → -4 → -12 → -22
↓ ↓ ↓ ↓ ↓ ↓
T -40 → -32 → -22 → -14 → -9 → -17
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22. Output
Plot the optimal alignment:
CTAGG
*| |*
TT-GT
Score: -17
Complexity in time: O(nm)
Complexity in memory: O(nm)
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23. Acknowledgments
Bellman; Levenstein; Needleman and Wunsch; Sankoff and Sellers;
Hirschberg; Smith and Waterman; Gotoh; Ukkonen, Myers and
Fickett; and many others...
Want to know more? start reading!
http://lectures.molgen.mpg.de/online_lectures.html
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