Gemoda

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

Motif discovery is the automated search for similar regions in streams of data
Un-sequential data
No “ordering”
Sequential data
A natural ordering of the data
Nucleotide and amino acid sequences
Stock prices, protein structures
MLRQGIAAQKKSFATLAAEQLLPKKYGGRYTVTLIPGDGVGKEVTDSVVKIFENENIPIDWETIDISGLENTENVQRAVESLKRNKVGLKGIWHTPADQTGHGSLNVALRKQLDIFANVALFKSIPGVKTRLNNIDMVIIRENTEGEYSGLEHESVPGVVESLKIMTRAKSERIARFAFDFALKNNRKSVCAVHKANIMKLGDGLFRNTVNEIGANEYPELDVKNIIVDNASMQAVAKPHQFDVLVTPNLYGSILGNIGSALIGGPGLVPGANFGREYAVFEPGSRHVGLDIKGQNVANPTAMILSSTLMLRHLGLNAYADRISKATYDVISEGKSTTRDIGGSASMLRQGIAAQKKSFATLAAEQLLPKKYGGRYTVTLIPGDGVGKEVTDSVVKIFENENIPIDWETIDISGLENTENVQRAVESLKRNKVGLKGIWHTPADQTGHGSLNVALRKQLDIFANVALFKSIPGVKTRLNNIDMVIIRENTEGEYSGLEHESVPGVVESLKIMTRAKSERIARFAFDFA A motif is just a collection of mutually similar regions in the data stream

There are two classes of motif discovery tools commonly used for sequence analysis
“Exhaustive” regular-expression based tools
Teiresias
Pratt
“Descriptive” position weight matrix-based tools
Gibbs sampler
MEME
Consensus
TGCTGTATATACTCACAGCA AACTGTATATACACCCAGGG TACTGTATGAGCATACAGTA ACCTGAATGAATATACAGTA TACTGTACATCCATACAGTA TACTGTATATTCATTCAGGT AACTGTTTTTTTATCCAGTA ATCTGTATATATACCCAGCT TACTGTATATAAAAACAGTA CT[AT].[GT]....A..CAG

“Gemoda” was designed to be exhaustive and have descriptive power
Gemoda exhaustively returns maximal motifs
Uses convolution of Teiresias
Way of “stiching together” smaller patterns combinatorially
Gets descriptiveness from similarity metric
Generic, context dependent definition of similarity
MLRQGIAAQKKSFATLAAEQLLPKKYGGRYTVTLIPGDGVGKEVTDSVVKIFENENIPIDWETIDISGLENTENVQRAVESLKRNKVGLKGIWHTPADQTGHGSLNVALRKQLDIFANVALFKSIPGVKTRLNNIDMVIIRENTEGEYSGLEHESVPGVVESLKIMTRAKSERIARFAFDFALKNNRKSVCAVHKANIMKLGDGLFRNTVNEIGANEYPELDVKNIIVDNASMQAVAKPHQFDVLVTPNLYGSILGNIGSALIGGPGLVPGANFGREYAVFEPGSRHVGLDIKGQNVANPTAMILSSTLMLRHLGLNAYADRISKATYDVISEGKSTTRDIGGSASMLRQGIAAQKKSFATLAAEQLLPKKYGGRYTVTLIPGDGVGKEVTDSVVKIFENENIPIDWETIDISGLENTENVQRAVESLKRNKVGLKGIWHTPADQTGHGSLNVALRKQLDIFANVALFKSIPGVKTRLNNIDMVIIRENTEGEYSGLEHESVPGVVESLKIMTRAKSERIARFAFDFA F(w 1 , w 2 ) = square error F(w 1 , w 2 ) = aa scoring matrix

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

The comparison stage is used to map the pairwise similarities between all windows in the data streams
Creates an distance matrix
Does an all-by-all comparison of windows in the data
Comparison function is context-specific
F(w 1 , w 2 )

The clustering phase is used to find groups of mutually similar windows
Different clustering functions have different uses
Clique-finding is provably exhaustive
K-means and other methods are faster
Output clusters become “elementary motifs” which are convolved to make longer, maximal motifs

The convolution phase is used to “stitch” together the clusters into maximal motifs
The motifs should be as long as possible, without decreasing the support
elementary motifs (clusters) window ordering

Here we show a few representative ways in which Gemoda can be used Motif discovery in...
Protein sequences
(ppGpp)ase enzymes & finding known domains
DNA sequences
The LD-motif challenge problem
Protein structures
Conserved structures without conserved sequences

Gemoda can be applied to amino acid sequences as well
Example: (ppGpp)ase family from ENZYME database
Guanosine-3',5'-bis(diphosphate) 3'-pyrophosphohydrolase enzymes
EC 3.1.7.2
Ave. length ~700 amino acids
8 sequences from 8 species
Searched using Gemoda
Minimum length = 50 amino acids
Minimum Blosum62 bit score = 50 bits
Minimum support = 100% (8/8 sequences)
Clustering method = clique finding
Can Gemoda find this known motif? How sensitive is Gemoda to “noise?”

(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

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

(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”

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

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).

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...

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...

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 ?

Gemoda can also be applied to protein structures
Treat protein structure as alpha-carbon trace
Series of x,y,z coordinates
Use a clustering function that compares x,y,z windows
Root mean square deviation (RMSD)
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

Protein structure example: human FIT vs. uridylyltransferase

Questions?

The Gemoda algorithm has guarantees of maximality and exhaustiveness
Maximality
Motifs are as long as possible
Motifs are as specific as possible
Motifs are not missing an occurrences
Exhaustiveness
All maximal motifs are found
No non-maximal motifs are found
= motif1 = motif2

Gemoda may be used with nucleotide sequences to find regulatory motifs
The LD-motif problem: an example for the board
>AACTG >AATTA >AATTG Look for motifs of at least 3 nucletides with a Hamming distance between any window of 3 of 1 or less given: 1 = AAC 2 = ACT 3 = CTG 4 = AAT 5 = ATT 6 = TTA 7 = AAT 8 = ATT 9 = TTG We get the following windows:

A simple natural language example
Choosing a window length of L=4 gives 7 unique windows in the three sequences
Seq 1: motif Seq 2: motor Seq 3: potion

Here we show the comparison phase using two different similarity metrics
X's and dotted lines
Identify matrix: ¾
O's and solid lines
Consonant/vowel matrix: ¾
Windows 1: moti 2: otif 3: moto 4: otor 5: poti 6: otio 7: tion Input sequences Seq 1: motif Seq 2: motor Seq 3: potion Similarity graph

The clustered windows (elementary motifs) are different depending on the similarity function
Clustering phase
Clique-finding
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):

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:

Gemoda

by Kyle Jensen on Jan 10, 2010

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