Text Comparison of Genetic Sequences

1. Text Comparison of Genetic Sequences Shiri Azenkot Pomona College DIMACS REU 2004

2. Comparing Two Strings Definition: A string is a set of consecutive characters. Examples: • “hello world” • “0123456” • DNA sequences • text file

3. Comparing Two Strings If X and Y are strings, how similar are they? Edit distance, d(X, Y) – smallest number of operations needed to make X look like Y. • Allowed operations: • Insert a character • Delete a character • Replace a character • Running time: O(mn) with a dynamic programming algorithm

4. Comparing Two Strings If X and Y are strings, how similar are they? Edit distance, d(X, Y) – smallest number of operations needed to make X look like Y. X = abcdef Y = defabc d(X, Y)= ? # operations =

5. Comparing Two Strings If X and Y are strings, how similar are they? Edit distance, d(X, Y) – smallest number of operations needed to make X look like Y. X = bcdef Y = defabc d(X, Y)= ? # operations = 1

6. Comparing Two Strings If X and Y are strings, how similar are they? Edit distance, d(X, Y) – smallest number of operations needed to make X look like Y. X = cdef Y = defabc d(X, Y)= ? # operations = 2

7. Comparing Two Strings If X and Y are strings, how similar are they? Edit distance, d(X, Y) – smallest number of operations needed to make X look like Y. X = def Y = defabc d(X, Y)= ? # operations = 3

8. Comparing Two Strings If X and Y are strings, how similar are they? Edit distance, d(X, Y) – smallest number of operations needed to make X look like Y. X = defa Y = defabc d(X, Y)= ? # operations = 4

9. Comparing Two Strings If X and Y are strings, how similar are they? Edit distance, d(X, Y) – smallest number of operations needed to make X look like Y. X = defab Y = defabc d(X, Y)= ? # operations = 5

10. Comparing Two Strings If X and Y are strings, how similar are they? Edit distance, d(X, Y) – smallest number of operations needed to make X look like Y. X = defabc Y = defabc d(X, Y)= 6 # operations = 6 Does this seem too high?

11. Edit Distance with Moves • d(X, Y): smallest number of operations to make X look like Y. • New operation: move a substring X = abcdef Y = defabc d(X, Y)= 1

12. Edit Distance with Moves • d(X, Y): smallest number of operations to make X look like Y. • New operation: move a substring • Some applications • Computational biology – DNA sequences • Text editing • Webpage updating

13. Edit Distance with Moves • Edit Sensitive Parsing (ESP) Algorithm: • Parse each string into a 2-3 tree • Compare nodes (substrings) of the trees to compute edit distance approximation: • The problem is NP-hard • Algorithm approximates d(X, Y) deterministically • Run time: O(n log n)

14. bagca b a g c a b a g e h e a d Edit Distance with MovesAlgorithm • Parse each string into a 2-3 tree Every node represents a substring X = bagcabagehead

15. c a a e h e a a b g d b g Edit Distance with MovesAlgorithm • Parse each string into a 2-3 tree Every node represents aa substring Y = cabageheadbag

16. bagca bagehead 1 1 bag ca ba geh ead 1 1 1 1 1 Edit Distance with MovesAlgorithm • Compare nodes (substrings) of the trees to compute edit distance approximation 2.1 Find frequencies of occurrence of each substring. X: b a g c a b a g e h e a d

17. Edit Distance with MovesAlgorithm • Compare nodes (substrings) of the trees to compute edit distance approximation 2.1 Find frequencies of occurrence of each substring. Y: caba gehea dbag 1 1 1 ca ba geh ea db ag 1 1 1 1 1 1 c a a e h e a a b g d b g

18. = 10 Edit Distance with MovesAlgorithm • Compare nodes (substrings) of the trees to compute edit distance approximation 2.1 Find frequencies of occurrence of each substring. 2.2 Subtract characteristic vectors to get approximation for d(X, Y) Bagca bagehead caba gehea dbag - 1 1 1 1 1 bag ca ba geh ead ca ba geh ea db ag 1 1 1 1 1 1 1 1 1 1 1

19. Edit Distance with MovesAlgorithm • Compare nodes (substrings) of the trees to compute edit distance approximation 2.1 Find frequencies of occurrence of each substring. 2.2 Subtract characteristic vectors to get approximation for d(X, Y) Actual edit distance with moves? 1 d(bagcabagehead, cabageheadbag) =

20. Edit Distance with Moves Goals for this project: • Implement this algorithm • Test algorithm on DNA sequences Questions to think about: • How accurate is the approximation? • How applicable is this technique for comparing large biological sequences? • This algorithm finds repeating structures within the sequences when comparing them. Do these structures have significance? • Do such structures exist for real sequences?

21. Acknowledgements • Mentor: Graham Cormode, DIMACS Postdoc • DIMACS REU 2004 • References: • Benedetto, D., Caglioti E., Loreto V., “Language Trees and Zipping”. Physical Review Letters, 2002 • Cormode, G., Muthukrishnan, S., “The String Edit Distance Matching Problem with Moves”.