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

2. Stuff folks liked Good pace. x3 Powerpoint was easy to follow. x2
Really appreciate reading the program step by step. x2
Helpful to go over the sample problems at the beginning of class.
I liked the connection between lecture materials and coding.
Extra class time on Python was helpful.
Enjoying the problems in class. It’s great that we can continue working on them after to solidify what we learned.
It helps when we break the problem into multiple steps and review the early steps to get started.
It’s getting more complicated and it takes me longer to do the sample problems in class, but I do them again by myself.
Nervous for second half of class.
HW level for programming has been good.
First time I finished one of the problems in class. Yay!
Merging coding part and concept parts makes it easier to understand the concepts.
Pace for practice problems was better today.
Explanation of the DP matrix was helpful.

3. Other feedback
In case we miss more class, would it be possible to post all the slides we may miss to learn on our own?
You will get all the slides.
Could we discuss how to remove items from a matrix into a string?
Not sure what you mean. Maybe we can discuss?
More feedback on HW code would be helpful. Is our program written “well”?
For this, I suggest meeting Jonathan individually. He can give detailed feedback for anyone who is interested.

4. 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

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
All length-1 sequences

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-2 sequences starting with A

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 or C

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

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

10. 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

11. 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

12. 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. ? ?

13. 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

14. 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

15. 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

16. 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

17. 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

18. Gibbs sampling

19. 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.

20. 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

21. 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

22. 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%

23. 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

24. 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

25. 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

26. 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

27. 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.