1. Subtrees Comparison of Phylogenetic Trees with Applications to Two Component Systems Sequence Classifications in Bacterial Genome Yaw-Ling Lin 1 Ming-Tat Ko 2 1 Dept Computer Sci. & Info. Management, Providence University, Taichung, Taiwan. 2 Institute of Information Science Academia Sinica, Taipei, Taiwan

2. Yaw-Ling Lin, Providence, Taiwan2 Motivation – Where the problems come from?

3. Yaw-Ling Lin, Providence, Taiwan3 Two-Component System Two-component systems (2CS): –Sensor histidine kinase –response regulator The major controlling machinery in order for bacteria to encounter a diverse and often hostile environment

4. Yaw-Ling Lin, Providence, Taiwan4 2CS in Pseudomonas aeruginosa PAO1 http://www.pseudomonas.com/ “Complete genome sequence of Pseudomonas aeruginosa PAO1, an opportunistic pathogen.” Nature. 2000 Aug 31;406(6799):947-8. by Stover CK, Pham XQ, Erwin AL, et al. Genome: 6.3M bp predicted genes: 5570 123 genes were classified as 2CSs.

5. Yaw-Ling Lin, Providence, Taiwan5 2CS in PAO1

6. Yaw-Ling Lin, Providence, Taiwan6 2CS in PAO1

7. Yaw-Ling Lin, Providence, Taiwan7 2CS in PAO1

8. Yaw-Ling Lin, Providence, Taiwan8 2CS in PAO1 There are 123 annotated 2CS genes in PAO1. Use systemic analysis of the evolutionary relationships between the sensor kinase and response regulator of a 2CS. Construct phylogenic trees using Clustal-W for 54 sensor kinases and 59 response regulators.

9. Yaw-Ling Lin, Providence, Taiwan9 2CS in PAO1 -- Sensor Tree

10. Yaw-Ling Lin, Providence, Taiwan10 2CS: Regulator Tree

11. Yaw-Ling Lin, Providence, Taiwan11 Subtrees Analysis of 2CS

12. Yaw-Ling Lin, Providence, Taiwan12 Co-evolution subtree Analysis Sensor TreeRegulator Tree versus

13. Yaw-Ling Lin, Providence, Taiwan13 Problem Definition A phylogenetic tree with n leaves is a (rooted binary) tree such that all the leaf nodes are uniquely labelled from 1 to n. Given two n-leaf phylogenetic trees, we wish to explore the subtrees relationships between subtrees of the two trees.

14. Yaw-Ling Lin, Providence, Taiwan14 Normalized cluster distance between two sets Symmetric set difference: Normalized cluster distance:

15. Yaw-Ling Lin, Providence, Taiwan15 All Pairs Subtrees Comparison – A naïve O(n 3 ) algorithm

16. Yaw-Ling Lin, Providence, Taiwan16 All Pairs Subtrees Comparison – Property

17. Yaw-Ling Lin, Providence, Taiwan17 All Pairs Subtrees Comparison – an O(n 2 ) algorithm

18. Yaw-Ling Lin, Providence, Taiwan18 Lowest Common Ancestor

19. Yaw-Ling Lin, Providence, Taiwan19 Confluent subtree

20. Yaw-Ling Lin, Providence, Taiwan20 Confluent subtree – Illustration

21. Yaw-Ling Lin, Providence, Taiwan21 Consructing confluent subtree

22. Yaw-Ling Lin, Providence, Taiwan22 Nearest subtree

23. Yaw-Ling Lin, Providence, Taiwan23 Nearest subtree: reasoning

24. Yaw-Ling Lin, Providence, Taiwan24 Nearest subtree: Algorithm

25. Yaw-Ling Lin, Providence, Taiwan25 k-agreement Problem

26. Yaw-Ling Lin, Providence, Taiwan26 Correlation analysis Does gene duplication tend to occur within a relative short distance on a bacterial genome? Idea: a dot-matrix plot will be created, with the X- axis being the physical distance, and Y-axis being the evolutionary distance, between two comparing 2CS. Some subset of 2CS, presumably functionally related, could possess the correlation between their physical and evolutionary distances.

27. Yaw-Ling Lin, Providence, Taiwan27 k-correlation Problem

28. Yaw-Ling Lin, Providence, Taiwan28 k-correlation is NP-complete Let M 1 be an adjacent matrix of a graph G, and M 2 be an zero matrix. If we can solve the k-correlation problem in polynomial time, then the maximum independent set problem will be polynomial solvable.

29. Yaw-Ling Lin, Providence, Taiwan29 Conclusion Identifying novel 2CS in other bacteria genomes as well as in eucaryotic genomes Clustering analysis of 2CS for functional prediction of uncharacterized genes Co-evolutionary analysis of 2CS

30. Yaw-Ling Lin, Providence, Taiwan30 Future Research Identifying novel 2CS in other bacteria genomes as well as in eucaryotic genomes Clustering analysis of 2CS for functional prediction of uncharacterized genes Co-evolutionary analysis of 2CS