The document describes the Gemoda algorithm for discovering motifs (patterns) in biomolecular data sequences. Gemoda is designed to be exhaustive in finding all maximal motifs and have descriptive power by using a generic, context-dependent definition of similarity. It proceeds in three steps: comparison of all pairwise windows to create a similarity graph, clustering similar windows into elementary motifs, and convolving the motifs to find longer, maximal motifs. Gemoda can be applied to problems like discovering protein domains, solving motif discovery challenges, and finding conserved structures in protein structures.

1. A generic motif discovery algorithm for diverse biomolecular data Kyle Jensen Gregory Stephanopoulos Department of Chemical Engineering Massachusetts Institute of Technology

3. Stock prices, protein structures MLRQGIAAQKKSFATLAAEQLLPKKYGGRYTVTLIPGDGVGKEVTDSVVKIFENENIPIDWETIDISGLENTENVQRAVESLKRNKVGLKGIWHTPADQTGHGSLNVALRKQLDIFANVALFKSIPGVKTRLNNIDMVIIRENTEGEYSGLEHESVPGVVESLKIMTRAKSERIARFAFDFALKNNRKSVCAVHKANIMKLGDGLFRNTVNEIGANEYPELDVKNIIVDNASMQAVAKPHQFDVLVTPNLYGSILGNIGSALIGGPGLVPGANFGREYAVFEPGSRHVGLDIKGQNVANPTAMILSSTLMLRHLGLNAYADRISKATYDVISEGKSTTRDIGGSASMLRQGIAAQKKSFATLAAEQLLPKKYGGRYTVTLIPGDGVGKEVTDSVVKIFENENIPIDWETIDISGLENTENVQRAVESLKRNKVGLKGIWHTPADQTGHGSLNVALRKQLDIFANVALFKSIPGVKTRLNNIDMVIIRENTEGEYSGLEHESVPGVVESLKIMTRAKSERIARFAFDFA A motif is just a collection of mutually similar regions in the data stream

6. MEME

7. Consensus TGCTGTATATACTCACAGCA AACTGTATATACACCCAGGG TACTGTATGAGCATACAGTA ACCTGAATGAATATACAGTA TACTGTACATCCATACAGTA TACTGTATATTCATTCAGGT AACTGTTTTTTTATCCAGTA ATCTGTATATATACCCAGCT TACTGTATATAAAAACAGTA CT[AT].[GT]....A..CAG

9. Gemoda proceeds in three steps: comparison, clustering, and convolution Jensen, K., Styczynski,M., Rigoutsos,I. and Stephanopoulos,G. (2005) A generic motif discovery algorithm for sequential data. Bioinformatics, in press

11. Comparison function is context-specific F(w 1 , w 2 )

17. Ave. length ~700 amino acids

19. Minimum Blosum62 bit score = 50 bits

20. Minimum support = 100% (8/8 sequences)

21. Clustering method = clique finding Can Gemoda find this known motif? How sensitive is Gemoda to “noise?”

22. (ppGpp)ase example: the comparison phase shows many regions of local similarity Dots indicate 50aa windows that are pairwise similar Streaks indicate regions that will probably be convolved into a maximal motif

23. (ppGpp)ase example: the clustering phase shows elementary motifs conserved between all 8 enzyme sequences

24. (ppGpp)ase example: the final motifs match the known rela_spot domain and the HD domain from NCBI's conserved domain database Maximal motif (one of three, ~100 aa in length) This particular cluster represents the first set of 8 50aa windows in the above motif. Results are insensitive to “noise”

25. The LD-motif problem models the subtle binding site discovery problem GACTCGATAGCGACG Sequence #1: ATGAT GA G TC T ATTG C G C CG CGATCAGCTAGCTAGCTACTATCTTATTCGACTAGTACGACTACGTACTACGATCTATCTATCAG... Sequence #2: ATGAGCTAGCTAGCTACTATCTTATTCGACTAGTACGACTACGTACTACGAATCAGCT CT CTCGAT T GCGAC T TTCGACTAGCTA... Sequence #3: ATGTACTACGA G T CTC C ATAGCG TT G CTCTATCTATCAGTACTACGACTCGTCGACTAGCTAGCTGACTCTATCTATCAGGATTT... Sequence #4: ATGACTATAGCTACTATCTTATTCGACTAGTACGACTATAGCTACTACGACTATAGCTATCTTATTCGAC GACTCG TGG GCG G CG ... ... Sequence #m: ATGCTACTATCTTATTCGACTAGTACGACTATAGCTACT GA T TCG TA AG G GACG ATAGCTACTATCTTATTCGACTAGTACGACT... Pevzner & Sze, Proc. ISMB, 2000

26. Gemoda can solve both the LD-motif problem and a more generalized version of the same GG GACTCGATAGCGACG CCG Sequence #1: ATGAT GA G TC T ATTG C G C CG CGATCAGCTAGCTAGCTACTATCTTATTCGACTAGTACGACTACGTACTACGATCTATCTATCAG... Sequence #2: ATGAGCTAGCTAGCTACTATCTTATTCGACTAGTACGACTACGTACTACGAATCAGCTCGATCGCTAGCTTTTAAATCTCTTCGACTAGCTA... Sequence #3: ATGTACTACGA G T CTC C ATAGCG TT G CTCTATCTATCAGTACTACGACTCGTCGACTAGCTAGCTGACTCTATCTATCAGGATTT... Sequence #4: ATGACTATAGCTACTATCTTATTCGACTAGTACGACTATAGCTACTACGACTATAGCTATCTTATTCGAC GACTCG TGG GCG G CG ... ... Sequence #m: ATGCTACTATCTTATTCGACTAGTACGACTATAGCTACT GA T TCG T TAG G GACG ATAGCTACTATCTTATTCGACTAGTACGACT... Total motif length ? Styczynski,M., Jensen,K., Rigoutsos,I. and Stephanopoulos,G. (2004) An extension and novel solution to the Motif Challenge Problem. Genome Informatics, 15 (2).

27. Gemoda can solve both the LD-motif problem and a more generalized version of the same GACTCGATAGCGACG X All sequences ? Sequence #1: ATGAT GA G TC T ATTG C G C CG CGATCAGCTAGCTAGCTACTATCTTATTCGACTAGTACGACTACGTACTACGATCTATCTATCAG... Sequence #2: ATGAGCTAGCTAGCTACTATCTTATTCGACTAGTACGACTACGTACTACGAATCAGCTCGATCGCTAGCTTTTAAATCTCTTCGACTAGCTA... Sequence #3: ATGTACTACGA G T CTC C ATAGCG TT G CTCTATCTATCAGTACTACGACTCGTCGACTAGCTAGCTGACTCTATCTATCAGGATTT... Sequence #4: ATGACTATAGCTACTATCTTATTCGACTAGTACGACTATAGCTACTACGACTATAGCTATCTTATTCGAC GACTCG TGG GCG G CG ... ... Sequence #m: ATGCTACTATCTTATTCGACTAGTACGACTATAGCTACT GA T TCG T TAG G GACG ATAGCTACTATCTTATTCGACTAGTACGACT...

28. Gemoda can solve both the LD-motif problem and a more generalized version of the same GACTCGATAGCGACG Number of mutations ? Sequence #1: ATGAT GA G TC T ATTG C G C CG CGATCAGCTAGCTAGCTACTATCTTATTCGACTAGTACGACTACGTACTACGATCTATCTATCAG... Sequence #2: ATGAGCTAGCTAGCTACTATCTTATTCGACTAGTACGACTACGTACTACGAATCAGCTCGATCGCTAGCTTTTAAATCTCTTCGACTAGCTA... Sequence #3: ATGTACTACGA G T CTC C ATAGCG TT G CTCTATCTATCAGTACTACGACTCGTCGACTAGCTAGCTGACTCTATCTATCAGGATTT... Sequence #4: ATGACTATAGCTACTATCTTATTCGACTAGTACGACTATAGCTACTACGACTATAGCTATCTTATTCGAC GACTCG TGG GCG G CG ... ... Sequence #m: ATGCTACTATCTTATTCGACTAGTACGACTATAGCTACT GA T TCG T TAG G GACG ATAGCTACTATCTTATTCGACTAGTACGACT...

29. Gemoda can solve both the LD-motif problem and a more generalized version of the same GACTCGATAGCGACG Sequence #1: ATGAT GA G TC T ATTG C G C CG CGATCAGCTAGCTAGCTACTATCTTATTCGACTAGTACGACTACGTACTACGATCTATCTATCAG... Sequence #2: ATGAGCTAGCTAGCTACTATCTTATTCGACTAGTACGACTACGTACTACGAATCAGCTCGATCGCTAGCTTTTAAATCTCTTCGACTAGCTA... Sequence #3: ATGTACTACGA G T CTC C ATAGCG TT G CTCTATCTATCAGTACTACGACTCGTCGACTAGCTAGCTGACTCTATCTATCAGGATTT... Sequence #4: ATGACTATAGCTACTATCTTATTCGACTAGTA TATCTGGTTCGACTT AGCTATCTATTCGAC GACTCG TGG GCG G CG ... ... Sequence #m: ATGCTAC TATCTTATTCGACTG AGTACGACTATAGCTACT GA T TCG T TAG G GACG ATAGCTACTATGACTAGTGACT... Number of unique motifs ?

31. unit-RMSD x 1 y 1 z 1 x 2 y 2 z 2 x 3 y 3 z 3 ........................... x M y M z M

32. Protein structure example: human FIT vs. uridylyltransferase

33. Questions?

35. Motifs are as specific as possible

37. No non-maximal motifs are found = motif1 = motif2

42. Support >= 2 Windows 1: moti 2: otif 3: moto 4: otor 5: poti 6: otio 7: tion Cluster 1 1: moti 3: moto 5: poti Cluster 2 2: otif 4: otor 6: otio Cluster 1 1: moti 3: moto Cluster 2 1: moti 5: poti Cluster 3 2: otif 6: otio Solid lines (vowel/cons): Dotted lines (identity):

43. Likewise, the final, convolved motifs depend on the similarity function choice Motif 1 motif motor potio Seq 1: motif Seq 2: motor Seq 3: potion Windows 1: moti 2: otif 3: moto 4: otor 5: poti 6: otio 7: tion Vowel/cons: Motif 1 motif potio Motif 2 moti moto Identity: Cluster 1 1: moti 3: moto 5: poti Cluster 2 2: otif 4: otor 6: otio Cluster 1 1: moti 3: moto Cluster 2 1: moti 5: poti Cluster 3 2: otif 6: otio Vowel/cons: Identity: