The document discusses algorithms for optimal sequence alignment using dynamic programming. It describes the Needleman-Wunsch algorithm for global alignment and the Smith-Waterman algorithm for local alignment. Both algorithms use dynamic programming to find the highest scoring alignment between two sequences by dividing the problem into independent subproblems. The Needleman-Wunsch algorithm allows gaps across the entire length of the sequences, while Smith-Waterman only considers local regions with high similarity.

1. S.Prasanth Kumar, Bioinformatician Genomics Sequence Alignment : Complete Coverage-I S.Prasanth Kumar Dept. of Bioinformatics Applied Botany Centre (ABC) Gujarat University, Ahmedabad, INDIA www.facebook.com/Prasanth Sivakumar FOLLOW ME ON ACCESS MY RESOURCES IN SLIDESHARE prasanthperceptron CONTACT ME [email_address]

2. Alignment scoring schemes Alignment of ATCGGATCT and ACGGACT match: +2 mismatch: -1 indel –2 6 * 2 + 1 * -1 + 2 * -2 = 7 6 matches, 1 mismatch, and 2 indels

3. Optimal alignment of two sequences Brute Force Method Suppose there are two sequences X and Z to be aligned, where |X| = m and |Z| = n If gaps are allowed in the sequences, then the potential length of both the first and second sequences is m+n. 2 m+n subsequences with spaces for the sequence X 2 m+n subsequences with spaces for the sequence Z Alignment = 2 m+n * 2 m+n = 2 (2(m+n)) = 4 m+n comparisons

4. Optimal alignment of two sequences Dynamic Programming DP align two sequences by beginning at the ends of the two sequences and attempting to align all possible pairs of characters (one from each sequence) using a scoring scheme for matches, mismatches, and gaps. The highest set of scores defines the optimal alignment between the two sequences DP algorithms solve optimization problems by dividing the problem into independent subproblems

5. Optimal alignment of two sequences Dynamic Programming Matrix s(a i b j ) = +5 if a i = b j (match score) s(a i b j ) = -3 if a i ≠ b j (mismatch score) w = -4 (gap penalty) • Initialization • Matrix Fill (scoring) • Traceback (alignment)

6. Global Alignment: Needleman-Wunsch Algorithm Initialization Step Each row S i,0 is set to w * i Each column S 0,j is set to w * j

7. Global Alignment: Needleman-Wunsch Algorithm Matrix Fill Step G-G  match score = +5 Si,j = MAX [0 + 5 , -4 + -4 , -4 + -4 ] = MAX [ 5 , -8 , -8 ] = 5 Confusing ? Diagonal + Match/Mismatch Score Left + Gap penalty Right + Gap penalty

8. Global Alignment: Needleman-Wunsch Algorithm G-A  mismatch score = -3 Si,j = MAX [-4 + -3 , 5 + -4 , -8 + -4 ] = MAX [ -7 , 1 , -12 ] = 1

9. Global Alignment: Needleman-Wunsch Algorithm Trace backing Easy ; Find the lowermost right corner and follow arrow

10. Global Alignment: Needleman-Wunsch Algorithm 5 – 3 + 5 – 4 + 5 + 5 – 4 + 5 – 4 – 4 + 5 = 11

11. Local Alignment: Smith-Waterman Algorithm Initialization Step Each row S i,0 is set to 0 Each column S 0,j is set to 0 Same Rule Initialization different Trace backing need attention

12. Local Alignment: Smith-Waterman Algorithm There are two cells having 14. There are multiple alignments producing the maximal alignment score What to consider ? Value in last row means aligned fully

13. Local Alignment: Smith-Waterman Algorithm Two trace back pathway pointers The two local alignments resulting in a score of 14

14. Local Alignment: Smith-Waterman Algorithm 5 matches, 1 mismatch, and 2 gaps score = 5 *5 – 1 *3 – 2 *4 = 25 – 3 – 8 = 14

15. What in Next Coverage ? Scoring Matrices: PAM & BLOSUM Assessing the significance of sequence alignments

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