1. DNA Alignment

2. Dynamic Programming R. Bellman ~ 1950

3. Bellman’s Optimality Principle States of the system Sequence of decisions to be made Optimality index Optimal decision depends on the present state of the system – does not depend on previous decisions

4. Example 1 We can go up, right or up-right: Find minimal – cost path

5. Solution

6. Cumulative scores matrix Decisions matrix

7. Example 2 c1c1 c2c2 c3c3 c4c4 c5c5 c i – cost per unit length – find the cheapest way

8. Remarks Example 1 – cost assigned to states, no cost of decisions Example 2 – cost assigned to decisions no cost of states

9. Alignments for comparing two DNA sequences For measuring the degree of similarity between them For looking for mutations

10. Dot matrix plots Formulation DNA alignment as dynamic programming problem

11. Needleman and Wunsch algorithm 1.Draw dot – matrix plot 2.Alignment = find a path through dot – matrix plot which maximizes cumulative score, s ij score for math-mismatch beteween elements, W k = a+bk – penalty for gap

12. Smith and Waterman algorithm 1.If a cumulative similarity score becomes negative it is reset to zero. Remote dissimilarities are removed this way 2.The end of an alignment occurs at the largest score in the cumulative score matrix

13. Software for DNA alignment BLAST, FAST BioEdit http://www.mbio.ncsu.edu/BioEdit/bioedit.html BioEdit version 5.0.6 Copyright ©1997-2001 Tom Hall North Carolina State University, Department of Microbiology so nice