Traceback and local alignment

1. Traceback and local alignment Prof. William Stafford Noble Department of Genome SciencesDepartment of Computer Science and Engineering University of Washington thabangh@gmail.com

2. Outline • Responses from last class • Sequence alignment • Motivation • Scoring alignments • Python

3. One-minute responses • Thank you for doing the one-minute responses and the revisions. • Liked that you let us solve the DP. • Liked going to lab in second half of lecture. • More slowly with Python programming. • Please explain more about string handling in Python, especially sys.argv. • sys.argv is now more clear. • Need more practical problems using sys. • I know how to compute the DP score but not how to get the alignment. • I still do not get how sequence alignment works. • Can we go over DP again? • Please don’t give us a test because our essay phase has begun already. • Please limit the number of questions in class. • Moving too slow with previous work and too fast with current work. • I understood about 95% of the lecture. • Can you give us some Python documentation or some interesting web site to improve and learn?

4. Revision • What two things are needed to score a pairwise alignment? • A substitution matrix and a gap penalty. • What does entry (i,j) in the DP matrix store? • The score of the best-scoring alignment up to those positions. • What are the three valid moves when filling in the DP matrix? • Horizontal and vertical, corresponding to gaps. Diagonal, corresponding to a substitution.

5. A small example Find the optimal alignment of AAG and AGC. Use a gap penalty of d=-5.

6. A simple example Find the optimal alignment of AAG and AGC. Use a gap penalty of d=-5.

7. A simple example Find the optimal alignment of AAG and AGC. Use a gap penalty of d=-5.

8. Traceback • Start from the lower right corner and trace back to the upper left. • Each arrow introduces one character at the end of each aligned sequence. • A horizontal move puts a gap in the left sequence. • A vertical move puts a gap in the top sequence. • A diagonal move uses one character from each sequence.

9. A simple example Find the optimal alignment of AAG and AGC. Use a gap penalty of d=-5. • Start from the lower right corner and trace back to the upper left. • Each arrow introduces one character at the end of each aligned sequence. • A horizontal move puts a gap in the left sequence. • A vertical move puts a gap in the top sequence. • A diagonal move uses one character from each sequence.

10. A simple example Find the optimal alignment of AAG and AGC. Use a gap penalty of d=-5. • Start from the lower right corner and trace back to the upper left. • Each arrow introduces one character at the end of each aligned sequence. • A horizontal move puts a gap in the left sequence. • A vertical move puts a gap in the top sequence. • A diagonal move uses one character from each sequence. AAG- AAG- -AGC A-GC

11. GA-ATC CATA-C DP matrix

12. GAAT-C CA-TAC DP matrix

13. GAAT-C C-ATAC DP matrix

14. GAAT-C -CATAC DP matrix

15. Multiple solutions • When a program returns a sequence alignment, it may not be the only best alignment. GA-ATC CATA-C GAAT-C CA-TAC GAAT-C C-ATAC GAAT-C -CATAC

16. Traceback problem #1 Write down the alignment corresponding to the circled score.

17. GA CA Solution #1 Write down the alignment corresponding to the circled score.

18. Traceback problem #2 Write down three alignments corresponding to the circled score.

19. Solution #2 GAATC CA--- Write down three alignments corresponding to the circled score.

20. Solution #2 GAATC C-A-- GAATC CA--- Write down three alignments corresponding to the circled score.

21. Solution #2 GAATC -CA-- GAATC C-A-- GAATC CA--- Write down three alignments corresponding to the circled score.

22. Local alignment • A protein may be homologous to a region within a second protein. • Usually, an alignment that spans the complete length of both sequences is not required.

23. BLAST allows local alignments Global alignment Local alignment

24. Global alignment DP • Align sequence x and y. • F is the DP matrix; s is the substitution matrix; d is the linear gap penalty.

25. Local alignment DP • Align sequence x and y. • F is the DP matrix; s is the substitution matrix; d is the linear gap penalty.

26. Local DP in equation form 0

27. A simple example Find the optimal local alignment of AAG and AGC. Use a gap penalty of d=-5. 0

28. A simple example Find the optimal local alignment of AAG and AGC. Use a gap penalty of d=-5. 0

29. A simple example Find the optimal local alignment of AAG and AGC. Use a gap penalty of d=-5. 0 2 -5 -5 0 0

30. A simple example Find the optimal local alignment of AAG and AGC. Use a gap penalty of d=-5. 0

31. A simple example Find the optimal local alignment of AAG and AGC. Use a gap penalty of d=-5. 0

32. A simple example Find the optimal local alignment of AAG and AGC. Use a gap penalty of d=-5. 0

33. Local alignment • Two differences with respect to global alignment: • No score is negative. • Traceback begins at the highest score in the matrix and continues until you reach 0. • Global alignment algorithm: Needleman-Wunsch. • Local alignment algorithm: Smith-Waterman.

34. A simple example Find the optimal local alignment of AAG and AGC. Use a gap penalty of d=-5. 0 AG AG

35. Local alignment Find the optimal local alignment of AAG and GAAGGC. Use a gap penalty of d=-5. 0

36. Local alignment Find the optimal local alignment of AAG and GAAGGC. Use a gap penalty of d=-5. 0

37. Local alignment Find the optimal local alignment of AAG and GAAGGC. Use a gap penalty of d=-5. AAG AAG 0

38. Summary • Local alignment finds the best match between subsequences. • Smith-Waterman local alignment algorithm: • No score is negative. • Trace back from the largest score in the matrix.

39. Sample problem #1 • Given: • Two letters • A substitution matrix written as three columns (letter, letter, value) A C 0 A D -2 • Return: • The value associated with the two letters • You must store the substitution matrix in memory. • You must account for the fact that the order of the letters doesn’t matter.

40. Solution outline • Read the substitution matrix into a dictionary. • Each line of the file has three values. A C 4 A D -2 • Each line is stored in a dictionary with the first two entries as a tuple key and the last entry as the value. substitionMatrix[(letter1, letter2)] = value

41. Sample problem #2 • Given: • A file containing two sequences of equal length (one per line) • A substitution matrix written as three columns (letter, letter, value) • Return: • The score of the ungapped alignment between the sequences • Test using input files from class web page. • Solutions: 1 = 69, 2 = 104, 3 = 153

42. Solution outline • Store the substitution matrix in memory, as before. • Check to be sure the sequences are the same length, and report an error if they are not. • Use a for loop to traverse both sequences at once.

43. One-minute response At the end of each class • Write for about one minute. • Provide feedback about the class. • Was part of the lecture unclear? • What did you like about the class? • Do you have unanswered questions? I will begin the next class by responding to the one-minute responses