1. Motif discovery
GENOME 559: Introduction to Statistical and Computational Genomics
Prof. William Stafford Noble

2. One-minute response: Stuff folks liked
The motif section is pretty interesting.
It helps to talk about what we can actually apply these methods to.
Going stepwise over the code is really helping.
Good explanation and review of what we learned last time.
Writing loops is fun (so far).
I like reviewing p-values in the beginning since it can get confusing when switching applications.
Looping practice is really helpful.
Enjoyed learning about the p-value construction of motifs. x2
I liked comparing different ways to get p-values.
Good step-by-step explanation of how to determine p-value from motif sequences.
Python problems are getting more challenging, which is nice. X2
I like the ”bonus problems” at the – I get to them at home.

3. One-minute response: Pacing
I thought the pace of both sections was good.
Pace is just right.
Lecture was good pace.
Loved the pace and subject matter today.
Good pacing, good content.
Everything was presented at an appropriate pace & level.
Best pacing so far, in my opinion.
Pacing was good today. I like having lots of time to work on the sample problems.
Pacing was good.
Need more time to do the Python exercises.

4. One-minute response: Suggestions
It would be great to have one or two more complex programming homework problems rather than several simple ones.
People might be a little embarrassed to answer in-class questions when the answer is in front of them.
I wish the class was two hours so we could spend a full hour on coding.
It would have been nice to go over representing a motif as a PSSM briefly before learning about the p-value stuff.
I got a little confused in the converting scores to p-values slides. x3
While loops are confusing me.
Dynamic programming sample exercise could be helpful.
I am still not sold on ever using a while loop instead of a for loop.
I like talking about the key steps in a solution. If you could annotate those on the slides, that would be great.
Homework solutions are very helpful.

5. Dynamic programming for motif p-values1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1 2 3 4 5 A 10 6 8 C 7 G T

6. Dynamic programming for motif p-values1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1 2 3 4 5 A 10 6 8 C 7 G T
All length-1 sequences

7. Dynamic programming for motif p-values1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1 2 3 4 5 A 10 6 8 C 7 G T
All length-2 sequences starting with A

8. Dynamic programming for motif p-values1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1 2 3 4 5 A 10 6 8 C 7 G T
All length-2 sequences starting with A or C

9. Dynamic programming for motif p-values1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1 2 3 4 5 A 10 6 8 C 7 G T
All length-2 sequences

10. Dynamic programming for motif p-values1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1 2 3 4 5 A 10 6 8 C 7 G T

11. Motif discovery problem
Given sequences
Find motif
seq. 1
seq. 2
seq. 3
IGRGGFGEVY at position 515
LGEGCFGQVV at position 430
VGSGGFGQVY at position 682
seq. 1
seq. 2
seq. 3

12. Motif discovery problem (hard version)
Given:
a sequence or family of sequences.
Find:
the number of motifs
the width of each motif
the locations of motif occurrences

13. Why is this hard?
Input sequences are long (thousands or millions of residues).
Motif may be subtle
Instances are short.
Instances are only slightly similar. ? ?

14. xxxxxxxxxxx.xxxxxxxxx.xxxxx..........xxxxxx.xxxxxxx.xxxxxxxxxx.xxxxxxxxx
HAHU V.LSPADKTN..VKAAWGKVG.AHAGE YGAEAL.ERMFLSF..PTTKTYFPH.FDLS.HGSA
HAOR M.LTDAEKKE..VTALWGKAA.GHGEE YGAEAL.ERLFQAF..PTTKTYFSH.FDLS.HGSA
HADK V.LSAADKTN..VKGVFSKIG.GHAEE YGAETL.ERMFIAY..PQTKTYFPH.FDLS.HGSA
HBHU VHLTPEEKSA..VTALWGKVN.VDEVG G.EAL.GRLLVVY..PWTQRFFES.FGDL.STPD
HBOR VHLSGGEKSA..VTNLWGKVN.INELG G.EAL.GRLLVVY..PWTQRFFEA.FGDL.SSAG
HBDK VHWTAEEKQL..ITGLWGKVNvAD.CG A.EAL.ARLLIVY..PWTQRFFAS.FGNL.SSPT
MYHU G.LSDGEWQL..VLNVWGKVE.ADIPG HGQEVL.IRLFKGH..PETLEKFDK.FKHL.KSED
MYOR G.LSDGEWQL..VLKVWGKVE.GDLPG HGQEVL.IRLFKTH..PETLEKFDK.FKGL.KTED
IGLOB M.KFFAVLALCiVGAIASPLT.ADEASlvqsswkavsHNEVEIlAAVFAAY.PDIQNKFSQFaGKDLASIKD
GPUGNI A.LTEKQEAL..LKQSWEVLK.QNIPA HS.LRL.FALIIEA.APESKYVFSF.LKDSNEIPE
GPYL GVLTDVQVAL..VKSSFEEFN.ANIPK N.THR.FFTLVLEiAPGAKDLFSF.LKGSSEVPQ
GGZLB M.L.DQQTIN..IIKATVPVLkEHGVT ITTTF.YKNLFAK.HPEVRPLFDM.GRQ..ESLE
xxxxx.xxxxxxxxxxxxx..xxxxxxxxxxxxxxx..xxxxxxx.xxxxxxx...xxxxxxxxxxxxxxxx
HAHU QVKGH.GKKVADA.LTN......AVA.HVDDMPNA...LSALS.D.LHAHKL....RVDPVNF.KLLSHCLL
HAOR QIKAH.GKKVADA.L.S......TAAGHFDDMDSA...LSALS.D.LHAHKL....RVDPVNF.KLLAHCIL
HADK QIKAH.GKKVAAA.LVE......AVN.HVDDIAGA...LSKLS.D.LHAQKL....RVDPVNF.KFLGHCFL
HBHU AVMGNpKVKAHGK.KVLGA..FSDGLAHLDNLKGT...FATLS.E.LHCDKL....HVDPENF.RL.LGNVL
HBOR AVMGNpKVKAHGA.KVLTS..FGDALKNLDDLKGT...FAKLS.E.LHCDKL....HVDPENFNRL..GNVL
HBDK AILGNpMVRAHGK.KVLTS..FGDAVKNLDNIKNT...FAQLS.E.LHCDKL....HVDPENF.RL.LGDIL
MYHU EMKASeDLKKHGA.TVL......TALGGILKKKGHH..EAEIKPL.AQSHATK...HKIPVKYLEFISECII
MYOR EMKASaDLKKHGG.TVL......TALGNILKKKGQH..EAELKPL.AQSHATK...HKISIKFLEYISEAII
IGLOB T.GA...FATHATRIVSFLseVIALSGNTSNAAAV...NSLVSKL.GDDHKA....R.GVSAA.QF..GEFR
GPUGNI NNPK...LKAHAAVIFKTI...CESATELRQKGHAVwdNNTLKRL.GSIHLK....N.KITDP.HF.EVMKG
GPYL NNPD...LQAHAG.KVFKL..TYEAAIQLEVNGAVAs.DATLKSL.GSVHVS....K.GVVDA.HF.PVVKE
GGZLB Q......PKALAM.TVL......AAAQNIENLPAIL..PAVKKIAvKHCQAGVaaaH.YPIVGQEL.LGAIK
xxxxxxxxx.xxxxxxxxx.xxxxxxxxxxxxxxxxxxxxxxx..x
HAHU VT.LAA.H..LPAEFTPA..VHASLDKFLASV.STVLTS..KY..R
HAOR VV.LAR.H..CPGEFTPS..AHAAMDKFLSKV.ATVLTS..KY..R
HADK VV.VAI.H..HPAALTPE..VHASLDKFMCAV.GAVLTA..KY..R
HBHU VCVLAH.H..FGKEFTPP..VQAAYQKVVAGV.ANALAH..KY..H
HBOR IVVLAR.H..FSKDFSPE..VQAAWQKLVSGV.AHALGH..KY..H
HBDK IIVLAA.H..FTKDFTPE..CQAAWQKLVRVV.AHALAR..KY..H
MYHU QV.LQSKHPgDFGADAQGA.MNKALELFRKDM.ASNYKELGFQ..G
MYOR HV.LQSKHSaDFGADAQAA.MGKALELFRNDM.AAKYKEFGFQ..G
IGLOB TA.LVA.Y..LQANVSWGDnVAAAWNKA.LDN.TFAIVV..PR..L
GPUGNI ALLGTIKEA.IKENWSDE..MGQAWTEAYNQLVATIKAE..MK..E
GPYL AILKTIKEV.VGDKWSEE..LNTAWTIAYDELAIIIKKE..MKdaA
GGZLB EVLGDAAT..DDILDAWGK.AYGVIADVFIQVEADLYAQ..AV..E
Globin motifs

15. Transcription Factor Binding Sites
A Concrete Example:
Transcription Factor Binding Sites
We are given a set of promoters from
co-regulated genes.
TCTCTCTCCACGGCTAATTAGGTGATCATGAAAAAATGAAAAATTCATGAGAAAAGAGTCAGACATCGAAACATACAT
ATGGCAGAATCACTTTAAAACGTGGCCCCACCCGCTGCACCCTGTGCATTTTGTACGTTACTGCGAAATGACTCAACG
CACATCCAACGAATCACCTCACCGTTATCGTGACTCACTTTCTTTCGCATCGCCGAAGTGCCATAAAAAATATTTTTT
TGCGAACAAAAGAGTCATTACAACGAGGAAATAGAAGAAAATGAAAAATTTTCGACAAAATGTATAGTCATTTCTATC
ACAAAGGTACCTTCCTGGCCAATCTCACAGATTTAATATAGTAAATTGTCATGCATATGACTCATCCCGAACATGAAA
ATTGATTGACTCATTTTCCTCTGACTACTACCAGTTCAAAATGTTAGAGAAAAATAGAAAAGCAGAAAAAATAAATAA
GGCGCCACAGTCCGCGTTTGGTTATCCGGCTGACTCATTCTGACTCTTTTTTGGAAAGTGTGGCATGTGCTTCACACA
…HIS7
…ARO4
…ILV6
…THR4
…ARO1
…HOM2
…PRO3

16. Transcription Factor Binding Sites
A Concrete Example:
Transcription Factor Binding Sites
An unknown transcription factor binds to positions unknown to us, on either DNA strand.
5’- TCTCTCTCCACGGCTAATTAGGTGATCATGAAAAAATGAAAAATTCATGAGAAAAGAGTCAGACATCGAAACATACAT
5’- ATGGCAGAATCACTTTAAAACGTGGCCCCACCCGCTGCACCCTGTGCATTTTGTACGTTACTGCGAAATGACTCAACG
5’- CACATCCAACGAATCACCTCACCGTTATCGTGACTCACTTTCTTTCGCATCGCCGAAGTGCCATAAAAAATATTTTTT
5’- TGCGAACAAAAGAGTCATTACAACGAGGAAATAGAAGAAAATGAAAAATTTTCGACAAAATGTATAGTCATTTCTATC
5’- ACAAAGGTACCTTCCTGGCCAATCTCACAGATTTAATATAGTAAATTGTCATGCATATGACTCATCCCGAACATGAAA
5’- ATTGATTGACTCATTTTCCTCTGACTACTACCAGTTCAAAATGTTAGAGAAAAATAGAAAAGCAGAAAAAATAAATAA
5’- GGCGCCACAGTCCGCGTTTGGTTATCCGGCTGACTCATTCTGACTCTTTTTTGGAAAGTGTGGCATGTGCTTCACACA
…HIS7
…ARO4
…ILV6
…THR4
…ARO1
…HOM2
…PRO3
5’- TCTCTCTCCACGGCTAATTAGGTGATCATGAAAAAATGAAAAATTCATGAGAAAAGAGTCAGACATCGAAACATACAT
5’- ATGGCAGAATCACTTTAAAACGTGGCCCCACCCGCTGCACCCTGTGCATTTTGTACGTTACTGCGAAATGACTCAACG
5’- CACATCCAACGAATCACCTCACCGTTATCGTGACTCACTTTCTTTCGCATCGCCGAAGTGCCATAAAAAATATTTTTT
5’- TGCGAACAAAAGAGTCATTACAACGAGGAAATAGAAGAAAATGAAAAATTTTCGACAAAATGTATAGTCATTTCTATC
5’- ACAAAGGTACCTTCCTGGCCAATCTCACAGATTTAATATAGTAAATTGTCATGCATATGACTCATCCCGAACATGAAA
5’- ATTGATTGACTCATTTTCCTCTGACTACTACCAGTTCAAAATGTTAGAGAAAAATAGAAAAGCAGAAAAAATAAATAA
5’- GGCGCCACAGTCCGCGTTTGGTTATCCGGCTGACTCATTCTGACTCTTTTTTGGAAAGTGTGGCATGTGCTTCACACA
…HIS7
…ARO4
…ILV6
…THR4
…ARO1
…HOM2
…PRO3

17. Transcription Factor Binding Sites
A Concrete Example:
Transcription Factor Binding Sites
The DNA binding motif of the transcription factor can be described by a position-specific scoring matrix (PSSM).
5’- TCTCTCTCCACGGCTAATTAGGTGATCATGAAAAAATGAAAAATTCATGAGAAAAGAGTCAGACATCGAAACATACAT
5’- ATGGCAGAATCACTTTAAAACGTGGCCCCACCCGCTGCACCCTGTGCATTTTGTACGTTACTGCGAAATGACTCAACG
5’- CACATCCAACGAATCACCTCACCGTTATCGTGACTCACTTTCTTTCGCATCGCCGAAGTGCCATAAAAAATATTTTTT
5’- TGCGAACAAAAGAGTCATTACAACGAGGAAATAGAAGAAAATGAAAAATTTTCGACAAAATGTATAGTCATTTCTATC
5’- ACAAAGGTACCTTCCTGGCCAATCTCACAGATTTAATATAGTAAATTGTCATGCATATGACTCATCCCGAACATGAAA
5’- ATTGATTGACTCATTTTCCTCTGACTACTACCAGTTCAAAATGTTAGAGAAAAATAGAAAAGCAGAAAAAATAAATAA
5’- GGCGCCACAGTCCGCGTTTGGTTATCCGGCTGACTCATTCTGACTCTTTTTTGGAAAGTGTGGCATGTGCTTCACACA
…HIS7
…ARO4
…ILV6
…THR4
…ARO1
…HOM2
…PRO3

18. Transcription Factor Binding Sites
A Concrete Example:
Transcription Factor Binding Sites
The sequence motif discovery problem is to discover the sites (or the motif) given just the sequences.
5’- TCTCTCTCCACGGCTAATTAGGTGATCATGAAAAAATGAAAAATTCATGAGAAAAGAGTCAGACATCGAAACATACAT
5’- ATGGCAGAATCACTTTAAAACGTGGCCCCACCCGCTGCACCCTGTGCATTTTGTACGTTACTGCGAAATGACTCAACG
5’- CACATCCAACGAATCACCTCACCGTTATCGTGACTCACTTTCTTTCGCATCGCCGAAGTGCCATAAAAAATATTTTTT
5’- TGCGAACAAAAGAGTCATTACAACGAGGAAATAGAAGAAAATGAAAAATTTTCGACAAAATGTATAGTCATTTCTATC
5’- ACAAAGGTACCTTCCTGGCCAATCTCACAGATTTAATATAGTAAATTGTCATGCATATGACTCATCCCGAACATGAAA
5’- ATTGATTGACTCATTTTCCTCTGACTACTACCAGTTCAAAATGTTAGAGAAAAATAGAAAAGCAGAAAAAATAAATAA
5’- GGCGCCACAGTCCGCGTTTGGTTATCCGGCTGACTCATTCTGACTCTTTTTTGGAAAGTGTGGCATGTGCTTCACACA
…HIS7
…ARO4
…ILV6
…THR4
…ARO1
…HOM2
…PRO3

19. Gibbs sampling

20. Alternating approach Guess an initial weight matrix
Use weight matrix to predict instances in the input sequences
Use instances to predict a weight matrix
Repeat 2 & 3 until satisfied.

21. Initialization
Randomly guess an instance si from each of t input sequences {S1, ..., St}.
sequence 1
ACAGTGT
TTAGACC
GTGACCA
ACCCAGG
CAGGTTT
sequence 2
sequence 3
sequence 4
sequence 5

22. Gibbs sampler
Initially: randomly guess an instance si from each of t input sequences {S1, ..., St}.
Steps 2 & 3 (search):
Throw away an instance si: remaining (t - 1) instances define weight matrix.
Weight matrix defines instance probability at each position of input string Si
Pick new si according to probability distribution
Return highest-scoring motif seen

23. Sampler step illustration:
ACAGTGT
TAGGCGT
ACACCGT
???????
CAGGTTT A C G T
.45
.05
.25
.65
.85
ACAGTGT
TAGGCGT
ACACCGT
ACGCCGT
CAGGTTT
sequence 4
11%
ACGCCGT:20%
ACGGCGT:52%

24. The MEME Algorithm
MEME uses expectation maximization (EM) to discover sequence motifs.
5’- TCTCTCTCCACGGCTAATTAGGTGATCATGAAAAAATGAAAAATTCATGAGAAAAGAGTCAGACATCGAAACATACAT
5’- ATGGCAGAATCACTTTAAAACGTGGCCCCACCCGCTGCACCCTGTGCATTTTGTACGTTACTGCGAAATGACTCAACG
5’- CACATCCAACGAATCACCTCACCGTTATCGTGACTCACTTTCTTTCGCATCGCCGAAGTGCCATAAAAAATATTTTTT
5’- TGCGAACAAAAGAGTCATTACAACGAGGAAATAGAAGAAAATGAAAAATTTTCGACAAAATGTATAGTCATTTCTATC
5’- ACAAAGGTACCTTCCTGGCCAATCTCACAGATTTAATATAGTAAATTGTCATGCATATGACTCATCCCGAACATGAAA
5’- ATTGATTGACTCATTTTCCTCTGACTACTACCAGTTCAAAATGTTAGAGAAAAATAGAAAAGCAGAAAAAATAAATAA
5’- GGCGCCACAGTCCGCGTTTGGTTATCCGGCTGACTCATTCTGACTCTTTTTTGGAAAGTGTGGCATGTGCTTCACACA
…HIS7
…ARO4
…ILV6
…THR4
…ARO1
…HOM2
…PRO3

25. The MEME Algorithm
Step 1: Randomly guess the positions (and strands) of the sites.
5’- TCTCTCTCCACGGCTAATTAGGTGATCATGAAAAAATGAAAAATTCATGAGAAAAGAGTCAGACATCGAAACATACAT
5’- ATGGCAGAATCACTTTAAAACGTGGCCCCACCCGCTGCACCCTGTGCATTTTGTACGTTACTGCGAAATGACTCAACG
5’- CACATCCAACGAATCACCTCACCGTTATCGTGACTCACTTTCTTTCGCATCGCCGAAGTGCCATAAAAAATATTTTTT
5’- TGCGAACAAAAGAGTCATTACAACGAGGAAATAGAAGAAAATGAAAAATTTTCGACAAAATGTATAGTCATTTCTATC
5’- ACAAAGGTACCTTCCTGGCCAATCTCACAGATTTAATATAGTAAATTGTCATGCATATGACTCATCCCGAACATGAAA
5’- ATTGATTGACTCATTTTCCTCTGACTACTACCAGTTCAAAATGTTAGAGAAAAATAGAAAAGCAGAAAAAATAAATAA
5’- GGCGCCACAGTCCGCGTTTGGTTATCCGGCTGACTCATTCTGACTCTTTTTTGGAAAGTGTGGCATGTGCTTCACACA
…HIS7
…ARO4
…ILV6
…THR4
…ARO1
…HOM2
…PRO3

26. The MEME Algorithm Step 2: Build a PSSM from the sites. Alignment PSSM
1 AAAAGAGTCA
2 AAATGACTCA
AAGTGAGTCA
AAAAGAGTCA
GGATGAGTCA
N AAATGAGTCA
12 … w i j
PSSM
Count Matrix A C G T
Step 2: Build a PSSM from the sites.
5’- TCTCTCTCCACGGCTAATTAGGTGATCATGAAAAAATGAAAAATTCATGAGAAAAGAGTCAGACATCGAAACATACAT
5’- ATGGCAGAATCACTTTAAAACGTGGCCCCACCCGCTGCACCCTGTGCATTTTGTACGTTACTGCGAAATGACTCAACG
5’- CACATCCAACGAATCACCTCACCGTTATCGTGACTCACTTTCTTTCGCATCGCCGAAGTGCCATAAAAAATATTTTTT
5’- TGCGAACAAAAGAGTCATTACAACGAGGAAATAGAAGAAAATGAAAAATTTTCGACAAAATGTATAGTCATTTCTATC
5’- ACAAAGGTACCTTCCTGGCCAATCTCACAGATTTAATATAGTAAATTGTCATGCATATGACTCATCCCGAACATGAAA
5’- ATTGATTGACTCATTTTCCTCTGACTACTACCAGTTCAAAATGTTAGAGAAAAATAGAAAAGCAGAAAAAATAAATAA
5’- GGCGCCACAGTCCGCGTTTGGTTATCCGGCTGACTCATTCTGACTCTTTTTTGGAAAGTGTGGCATGTGCTTCACACA
…HIS7
…ARO4
…ILV6
…THR4
…ARO1
…HOM2
…PRO3

27. The MEME Algorithm Step 3: Scan each sequence with the motif. A C G T
5’- TCTCTCTCCACGGCTAATTAGGTGATCATGAAAAAATGAAAAATTCATGAGAAAAGAGTCAGACATCGAAACATACAT
5’- ATGGCAGAATCACTTTAAAACGTGGCCCCACCCGCTGCACCCTGTGCATTTTGTACGTTACTGCGAAATGACTCAACG
5’- CACATCCAACGAATCACCTCACCGTTATCGTGACTCACTTTCTTTCGCATCGCCGAAGTGCCATAAAAAATATTTTTT
5’- TGCGAACAAAAGAGTCATTACAACGAGGAAATAGAAGAAAATGAAAAATTTTCGACAAAATGTATAGTCATTTCTATC
5’- ACAAAGGTACCTTCCTGGCCAATCTCACAGATTTAATATAGTAAATTGTCATGCATATGACTCATCCCGAACATGAAA
5’- ATTGATTGACTCATTTTCCTCTGACTACTACCAGTTCAAAATGTTAGAGAAAAATAGAAAAGCAGAAAAAATAAATAA
5’- GGCGCCACAGTCCGCGTTTGGTTATCCGGCTGACTCATTCTGACTCTTTTTTGGAAAGTGTGGCATGTGCTTCACACA
…HIS7
…ARO4
…ILV6
…THR4
…ARO1
…HOM2
…PRO3

28. Expectation-maximization
best_score = 0
best_pssm = 0
for index in range(0, len(sequence) - width):
pssm = make_pssm(sequence[index:index+width])
counts = []
while (not equal(pssm, counts)):
counts = scan(sequence, pssm)
pssm = make_pssm(counts)
if (score_pssm(pssm) > best_score):
best_score = score_pssm(pssm)
best_pssm = pssm

29. MEME algorithm do for (width = min; width *= 2; width < max)
Consider various widths do
for (width = min; width *= 2; width < max)
for each possible starting point
run 1 iteration of EM
select candidate starting points
for each candidate
run EM to convergence
select best motif
erase motif occurrences
until (motif score < threshold)
Heuristic to speed things up
Find multiple motifs in one data set

30. Comparison Both EM and Gibbs sampling involve iterating over two steps
Convergence:
EM converges when the PSSM stops changing.
Gibbs sampling runs until you ask it to stop.
Solution:
EM may not find the motif with the highest score.
Gibbs sampling will provably find the motif with the highest score, if you let it run long enough.