Dynamic Programing
Dynamic Programing Dynamic Programing
Needleman-Wunsch Algorithm (Cont.) Traceback To recover the optimal alignment, arrows indicating forward calculation paths, are placed in each entry. 0 w1 ... wj ... wm : NW(i,j) = NW(i-1,j-1) + s(vi,wj) v1 : vi : vn Optimal alignment score : NW(i,j) = NW(i-1,j) + gap : NW(i,j) = NW(i,j-1) + gap Determine alignment from the end of the sequences A B C D E F - - A B C D E F - - Traceback path Beginning traceback
Needleman-Wunsch Algorithm (Cont.) Example Optimal global alignment of V = THISLINE and W= ISALIGNED with gap = -4ngap , score matrix = BLOSUM62 I S A L I G N E D 0 -4 -8 -12 -16 -20 -24 -28 -32 -36 T -4 -1 -3 -7 -11 -15 -19 -23 -27 -31 H -8 -5 -2 -5 -9 -13 -17 -18 -22 -26 I -12 -4 -6 -3 -3 -5 -9 -13 -17 -21 S -16 -8 0 -4 -5 -5 -5 -8 -12 -16 L -20 -12 -4 -1 0 -3 -7 -8 -11 -15 I -24 -16 -8 -5 1 4 0 -4 -8 -12 N -28 -20 -12 -9 -3 0 4 6 2 -2 E -32 -24 -16 -13 -7 -4 0 4 11 7 From: Understanding Bioinformatics by Zvelebil, Baum V: T H I S - L I - N E - W: - - I S A L I G N E D
- Page 1 and 2: Dynamic Programming and Pairwise Se
- Page 3 and 4: Importance of Sequence Alignment
- Page 5 and 6: Alignment Operation Transforming on
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- Page 9 and 10: Efficient way to find a best alignm
- Page 11 and 12: Problems Solvable by Dynamic Progra
- Page 13: Property of DP problems • Have ov
- Page 16 and 17: I. Global Alignment Classes of Pair
- Page 18 and 19: Classes of Pairwise Alignment: I. G
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- Page 22 and 23: Global Alignment spans all the resi
- Page 24 and 25: Scoring matrix represents a specifi
- Page 26 and 27: Needleman-Wunsch Algorithm (Cont.)
- Page 28 and 29: Needleman-Wunsch Algorithm (Cont.)
- Page 32 and 33: Needleman-Wunsch Algorithm Efficien
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- Page 36 and 37: Needleman-Wunsch Algorithm for any
- Page 38 and 39: Local Alignment finds the most simi
- Page 40 and 41: Smith-Waterman Algorithm (Cont.)
- Page 42 and 43: Smith-Waterman Algorithm (Cont.) v1
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- Page 54 and 55: Which alignment to use (Cont.) Exam
- Page 56 and 57: Versatility of DP Algorithm • Mem
- Page 58 and 59: References - Gusfield D. Algorithms
Needleman-Wunsch Algorithm (Cont.)<br />
Traceback<br />
To recover the optimal alignment, arrows indicating forward calculation paths, are placed in each entry.<br />
0<br />
w1 ... wj ... wm<br />
: NW(i,j) = NW(i-1,j-1) + s(vi,wj)<br />
v1<br />
:<br />
vi<br />
:<br />
vn<br />
Optimal<br />
alignment<br />
score<br />
: NW(i,j) = NW(i-1,j) + gap<br />
: NW(i,j) = NW(i,j-1) + gap<br />
Determine alignment from the end of the sequences<br />
A B C<br />
D<br />
E<br />
F<br />
- - A B C<br />
D E F - -<br />
Traceback path<br />
Beginning<br />
traceback
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