Inferring Phylogeny using Permutation Patterns on Genomic Data

1. Inferring Phylogeny using Permutation Patterns on Genomic Data 1Md Enamul Karim 2Laxmi Parida 1Arun Lakhotia 1University of Louisiana at Lafayette 2IBM T. J. Watson Research Center

2. Phylogeny Reconstruction of the evolutionary relationship of a collection of organisms, usually in the form of a tree.

3. Phylogenetic data • Behavioral, morphological, metabolic, etc. • Molecular data: sequence data, gene-order data etc. gene-order data

4. Why gene order data? • Low error rate. • Rare evolutionary events unlikely to cause “silent" changes; can help inferring millions of years.

5. 1 2 3 9 -8 –7 –6 –5 –4 10 1 2 3 9 4 5 6 7 8 10 1 2 3 –8 –7 –6 –5 -4 9 10 Genomes rearrangements 1 2 3 4 5 6 7 8 9 10 • Transposition • InvertedTransposition • Inversion

6. Breakpoint distance • Breakpoints are number of adjacencies present in one genome, but not in the other. • For some datasets, a close-to-linear relationship between the breakpoints and evolutionary eventsmay exist. • Can be used for building phylogeny (Blanchette et al.). 1 2 3 4 5 6 7 8 9 10 1 –3 –2 4 5 9 6 7 8 10

7. Limitations of breakpoint • The number of breakpoints created by a certain number of inversions may vary. • Also, transpositions generally create more breakpoints than inversions. • Computing the breakpoint phylogeny is NP-hard.

8. MPBE (Maximum Parsimony on Binary Encoding) • A heuristic for the breakpoint phylogeny (Cosner et al.). • All ordered pairs of signed genes appearing consecutively are coded as binary features. • Exponential time complexity, however, much faster than BPAnalysis.

9. Limitations • May fail to find feasible solutions to the breakpoint phylogeny problem.

10. Observation: The closer is the evolution history, the more permutations (of different granularity) are in common 1 2 3 4 5 6 7 8 9 10 1 2 3 –8 –7 –6 –5 –4 9 10 1 8 –3 –2 –7 –6 –5 –4 9 10

11. Maximal pi-pattern (Eres et al.) • Matches permutations at different granularity. • Polynomial time complexity.

12. pi-pattern • Example : For S = and k=2 Pattern with minimum k permutations abc acb acb cab cab All pi-patterns are: ac, bc, abc, abcc

13. Cover P1 covers P2=> • Every P1 has a P2 • Every P2 is within a P1 • Example • In S = acbcab abc covers ac

14. Maximal pi-pattern • pi-pattern which is not covered • Example • In S = acbcab pi-patterns: ac, bc, abc, abcc not covered by abcc Maximal pi-patterns: abc, abcc

15. Results

16. Phylogeny for simulated evolution on synthetic data

17. 12 genera of Campanulaceaeand the outgroup tobacco

18. Tree1: MPBE tree

19. Tree2: Neighbor joining tree (using few different distances)

20. Tree3: Neighbor joining tree using permutation patterns • 167 Maximal pi-patterns(from 10769pi-patterns) used as binary feature • XOR Distance measure • Distance/Similarity matrix is created to find neighbor joining tree

21. Tree3 vs Tree2

22. Conclusion • Permutation patterns may preserve more evolutionary information. • Evolutionary events could be counted within permuted segments to develop a hybrid scheme. • Current approaches remain unable to handle unequal gene content, which could be solved using maximal pi-patterns.