1. Sequence comparison: More dynamic programming Genome 559: Introduction to Statistical and Computational Genomics Prof. William Stafford Noble

2. One-minute responses • WAY TOO FAST. Please walk around more during sample problems. I was completely lost. • Today I felt a bit lost. Most times I was still trying to figure out one slide or problem, while the class was on the next one. • It was fast today, but after the reading I was prepared to take things more quickly and I understood things much better today. • I enjoyed class today. I thought it moved at a great pace. • I thought the pace was good today. • I liked the pace of the lecture – even though you said we spent too much time on the dynamic programming, it gave me time to understand. • The pace is great and gives me time to explore. • I thought this lecture built nicely on the last lecture. I struggled last class but it clicked today.

3. One-minute responses • The matrix exercise was very helpful, even though I’m not fully clear on how it works yet. • I found today’s class time much more understandable. • I struggled a little bit to grasp the matrix, but by the end I had it. The pace and numerous examples helped. • The DP matrix was simple to grasp after computing one or two matrix values, so the portion of the lecture could go faster. • I like the sample problems. • Dynamic programming reminded me of sudoku, which was fun. • Going through the alignment table helped a lot. • It was nice to do examples with DNA sequences. • I’m feeling a lot better about it all. I really like going through examples. • Again, the small steps with programming problems helped, although the first problem was overly challenging (when explained in a different way it was fine). • I was a little confused when writing the program. I think more practice is required. The practice problems will help. • Today’s class was much better since we had appropriate reading first. The sample problems were interesting since they actually relate to biology.

4. One-minute responses • Is there a place to get more samples of simple code to use to help see patterns of how this works? Or is there plenty in the book? • There are lots of examples in the book. And of course, you can easily find lots of examples on the web. For a reference book with examples, try Python Cookbook, by Martelli, Ravenscroft and Ascher. • I’m a little fuzzy about how dynamic programming differs from other sorts of programming, but everything else was really clear. • The term “dynamic programming” predates computers. There is no relationship between this use of the word “programming” and what we are learning to do in Python.

5. DP matrix

6. Three legal moves • A diagonal move aligns a character from the left sequence with a character from the top sequence. • A vertical move introduces a gap in the sequence along the top edge. • A horizontal move introduces a gap in the sequence along the left edge.

7. GA-ATC CATA-C DP matrix

8. GAAT-C CA-TAC DP matrix

9. GAAT-C C-ATAC DP matrix

10. GAAT-C -CATAC DP matrix

11. 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

12. DP in equation form • Align sequence x and y. • F is the DP matrix; s is the substitution matrix; d is the linear gap penalty.

13. DP in equation form

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

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

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

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

18. 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.

19. 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.

20. 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

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

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

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

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

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

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