1. Motifs, logos, and Profile HMM’s
Ivan G. Costa
Centro de Informática
Universidade Federal de Pernambuco
Basead em slides de Morten Nielsen e Neils Jones

2. Overview Visualization of binding motifs
Construction of sequence logos
Understand the concepts of weight matrix construction
One of the most important methods of bioinformatics
Hidden Markov Profiles as they are just weight matrices with gaps

3. Controle da Regulação Gênica Eucarióticos

4. Fatores de Transcrição
Motifs indicam a preferência de ligação
Não são idênticos

5. Binding Motif. MHC class I with peptide
Anchor positions

6. Sequence information
SLLPAIVEL YLLPAIVHI TLWVDPYEV GLVPFLVSV KLLEPVLLL LLDVPTAAV LLDVPTAAV LLDVPTAAV
LLDVPTAAV VLFRGGPRG MVDGTLLLL YMNGTMSQV MLLSVPLLL SLLGLLVEV ALLPPINIL TLIKIQHTL
HLIDYLVTS ILAPPVVKL ALFPQLVIL GILGFVFTL STNRQSGRQ GLDVLTAKV RILGAVAKV QVCERIPTI
ILFGHENRV ILMEHIHKL ILDQKINEV SLAGGIIGV LLIENVASL FLLWATAEA SLPDFGISY KKREEAPSL
LERPGGNEI ALSNLEVKL ALNELLQHV DLERKVESL FLGENISNF ALSDHHIYL GLSEFTEYL STAPPAHGV
PLDGEYFTL GVLVGVALI RTLDKVLEV HLSTAFARV RLDSYVRSL YMNGTMSQV GILGFVFTL ILKEPVHGV
ILGFVFTLT LLFGYPVYV GLSPTVWLS WLSLLVPFV FLPSDFFPS CLGGLLTMV FIAGNSAYE KLGEFYNQM
KLVALGINA DLMGYIPLV RLVTLKDIV MLLAVLYCL AAGIGILTV YLEPGPVTA LLDGTATLR ITDQVPFSV
KTWGQYWQV TITDQVPFS AFHHVAREL YLNKIQNSL MMRKLAILS AIMDKNIIL IMDKNIILK SMVGNWAKV
SLLAPGAKQ KIFGSLAFL ELVSEFSRM KLTPLCVTL VLYRYGSFS YIGEVLVSV CINGVCWTV VMNILLQYV
ILTVILGVL KVLEYVIKV FLWGPRALV GLSRYVARL FLLTRILTI HLGNVKYLV GIAGGLALL GLQDCTMLV
TGAPVTYST VIYQYMDDL VLPDVFIRC VLPDVFIRC AVGIGIAVV LVVLGLLAV ALGLGLLPV GIGIGVLAA
GAGIGVAVL IAGIGILAI LIVIGILIL LAGIGLIAA VDGIGILTI GAGIGVLTA AAGIGIIQI QAGIGILLA
KARDPHSGH KACDPHSGH ACDPHSGHF SLYNTVATL RGPGRAFVT NLVPMVATV GLHCYEQLV PLKQHFQIV
AVFDRKSDA LLDFVRFMG VLVKSPNHV GLAPPQHLI LLGRNSFEV PLTFGWCYK VLEWRFDSR TLNAWVKVV
GLCTLVAML FIDSYICQV IISAVVGIL VMAGVGSPY LLWTLVVLL SVRDRLARL LLMDCSGSI CLTSTVQLV
VLHDDLLEA LMWITQCFL SLLMWITQC QLSLLMWIT LLGATCMFV RLTRFLSRV YMDGTMSQV FLTPKKLQC
ISNDVCAQV VKTDGNPPE SVYDFFVWL FLYGALLLA VLFSSDFRI LMWAKIGPV SLLLELEEV SLSRFSWGA
YTAFTIPSI RLMKQDFSV RLPRIFCSC FLWGPRAYA RLLQETELV SLFEGIDFY SLDQSVVEL RLNMFTPYI
NMFTPYIGV LMIIPLINV TLFIGSHVV SLVIVTTFV VLQWASLAV ILAKFLHWL STAPPHVNV LLLLTVLTV
VVLGVVFGI ILHNGAYSL MIMVKCWMI MLGTHTMEV MLGTHTMEV SLADTNSLA LLWAARPRL GVALQTMKQ
GLYDGMEHL KMVELVHFL YLQLVFGIE MLMAQEALA LMAQEALAF VYDGREHTV YLSGANLNL RMFPNAPYL
EAAGIGILT TLDSQVMSL STPPPGTRV KVAELVHFL IMIGVLVGV ALCRWGLLL LLFAGVQCQ VLLCESTAV
YLSTAFARV YLLEMLWRL SLDDYNHLV RTLDKVLEV GLPVEYLQV KLIANNTRV FIYAGSLSA KLVANNTRL
FLDEFMEGV ALQPGTALL VLDGLDVLL SLYSFPEPE ALYVDSLFF SLLQHLIGL ELTLGEFLK MINAYLDKL
AAGIGILTV FLPSDFFPS SVRDRLARL SLREWLLRI LLSAWILTA AAGIGILTV AVPDEIPPL FAYDGKDYI
AAGIGILTV FLPSDFFPS AAGIGILTV FLPSDFFPS AAGIGILTV FLWGPRALV ETVSEQSNV ITLWQRPLV

7. Sequence Information
Say that a peptide must have L at P2 in order to bind, and that A,F,W,and Y are found at P1. Which position has most information?
How many questions do I need to ask to tell if a peptide binds looking at only P1 or P2?
P1: 4 questions (at most)
P2: 1 question (L or not)
P2 has the most information
Calculate pa at each position
Entropy
Information content
Conserved positions
PV=1, P!v=0 => S=0, I=log(20)
Mutable positions
Paa=1/20 => S=log(20), I=0

8. Information content
We look at the frequencies of aminoacids at each position
A R N D C Q E G H I L K M F P S T W Y V S I

9. Sequence logos Height of a column equal to I
Relative height of a letter is p
Highly useful tool to visualize sequence motifs
HLA-A0201
High information
positions

10. Simple motifs Yes/No rules
10 MHC restricted peptides
ALAKAAAAM
ALAKAAAAN
ALAKAAAAR
ALAKAAAAT
ALAKAAAAV
GMNERPILT
GILGFVFTM
TLNAWVKVV
KLNEPVLLL
AVVPFIVSV
Only 11 of 212 peptides identified!
Need more flexible rules
If not fit P1 but fit P2 then ok
Not all positions are equally important
We know that P2 and P9 determines binding more than other positions
Cannot discriminate between good and very good binders

11. Extended motifs
Fitness of the amino acid at each position given by P(amino acid)
Example P1
PA = 6/10
PG = 2/10
PT = PK = 1/10
PC = PD = …PV = 0
Problems
Few data
ALAKAAAAM
ALAKAAAAN
ALAKAAAAR
ALAKAAAAT
ALAKAAAAV
GMNERPILT
GILGFVFTM
TLNAWVKVV
KLNEPVLLL
AVVPFIVSV
RLLDDTPEV 84 nM
GLLGNVSTV 23 nM
ALAKAAAAL 309 nM

12. Pseudo counts ALAKAAAAM
ALAKAAAAN
ALAKAAAAR
ALAKAAAAT
ALAKAAAAV
GMNERPILT
GILGFVFTM
TLNAWVKVV
KLNEPVLLL
AVVPFIVSV
I is not found at position P9. Does this mean that I is forbidden (P(I)=0)?
No! Use Blosum substitution matrix to estimate pseudo frequency of I at P9

13. Weight on pseudo count
ALAKAAAAM
ALAKAAAAN
ALAKAAAAR
ALAKAAAAT
ALAKAAAAV
GMNERPILT
GILGFVFTM
TLNAWVKVV
KLNEPVLLL
AVVPFIVSV
Pseudo counts are important when only limited data is available
With large data sets only “true” observation should count
 is the effective number of sequences (N-1),  is the weight on prior

14. Weight matrices
Estimate amino acid frequencies from alignment including sequence weighting and pseudo count
What do the numbers mean?
P2(V)>P2(M). Does this mean that V enables binding more than M.
In nature not all amino acids are found equally often
In nature V is found more often than M, so we must somehow rescale with the background
qM = 0.025, qV = 0.073
Finding 7% V is hence not significant, but 7% M highly significant
A R N D C Q E G H I L K M F P S T W Y V

15. Weight matrices A weight matrix is given as Wij = log(pij/qj)
where i is a position in the motif, and j an amino acid. qj is the background frequency for amino acid j.
W is a L x 20 matrix, L is motif length
A R N D C Q E G H I L K M F P S T W Y V

16. Scoring a sequence to a weight matrix
Score sequences to weight matrix by looking up and adding L values from the matrix
A R N D C Q E G H I L K M F P S T W Y V
Which peptide is most likely to bind?
Which peptide second?
RLLDDTPEV
GLLGNVSTV
ALAKAAAAL
11.9
14.7
4.3
84nM
23nM
309nM

17. HMMs and weight Matrices
Score sequences to weight matrix by looking up and adding L values from the matrix
A R N D C Q E G H I L K M F P S T W Y V M1 M2 M3 M9 1 1 1 1 …

18. HMMs and weight Matrices
Score sequences to weight matrix by looking up and adding L values from the matrix
A R N D C Q E G H I L K M F P S T W Y V
Emission is a row in the weight matrix M1 M2 M3 M9 1 1 1 1 …

19. Example from real life 10 peptides from MHCpep database
Bind to the MHC complex
Relevant for immune system recognition
Estimate sequence motif and weight matrix
Evaluate motif “correctness” on 528 peptides
ALAKAAAAM
ALAKAAAAN
ALAKAAAAR
ALAKAAAAT
ALAKAAAAV
GMNERPILT
GILGFVFTM
TLNAWVKVV
KLNEPVLLL
AVVPFIVSV

20. Prediction accuracy Measured affinity Prediction score
Pearson correlation 0.45
Measured affinity
Prediction score

21. Predictive performance

22. Hidden Markov Models
Weight matrices do not deal with insertions and deletions
In alignments, this is done in an ad-hoc manner by optimization of the two gap penalties for first gap and gap extension
HMM is a natural frame work where insertions/deletions are dealt with explicitly

23. HMM (a simple example) ACA---ATG TCAACTATC ACAC--AGC AGA---ATC
Example from A. Krogh
Core region defines the number of states in the HMM (red)
Insertion and deletion statistics are derived from the non-core part of the alignment (black)
ACA---ATG
TCAACTATC
ACAC--AGC
AGA---ATC
ACCG--ATC
Core of alignment

24. HMM construction ACA---ATG TCAACTATC ACAC--AGC AGA---ATC ACCG--ATC Gap.4 A C G T .2 .4 .2 .2 .6 .6 A C G T .8 A C G T A C G T .8 A C G T 1 A C G T A C G T 1. 1. .4 1. 1. .8 .2 .8 .2 .2 .2 .2 .8
ACA---ATG 0.8x1x0.8x1x0.8x0.4x1x1x0.8x1x0.2 = 3.3x10-2

25. HMM’s and weight matrices
In the case of un-gapped alignments HMM’s become simple weight matrices
To achieve high performance, the emission frequencies are estimated using the techniques of
Sequence weighting
Pseudo counts

26. Profile HMM’s
Alignments based on conventional scoring matrices (BLOSUM62) scores all positions in a sequence in an equal manner
Some positions are highly conserved, some are highly variable (more than what is described in the BLOSUM matrix)
Profile HMM’s are ideal suited to describe such position specific variations

27. Finding Distant Members of a Protein Family
A distant cousin of functionally related sequences in a protein family may have weak pairwise similarities with each member of the family and thus fail significance test.
However, they may have weak similarities with many members of the family.
The goal is to align a sequence to all members of the family at once.
Family of related proteins can be represented by their multiple alignment and the corresponding profile.

28. What are Profile HMMs ?
A Profile HMM is a probabilistic representation of a multiple alignment.
A given multiple alignment (of a protein family) is used to build a profile HMM.
This model then may be used to find and score less obvious potential matches of new protein sequences.

29. Sequences of a Protein Family
Sequence profiles
Sequences of a Protein Family
Conserved
Non-conserved
Insertion
ADDGSLAFVPSEF--SISPGEKIVFKNNAGFPHNIVFDEDSIPSGVDASKISMSEEDLLN
TVNGAI--PGPLIAERLKEGQNVRVTNTLDEDTSIHWHGLLVPFGMDGVPGVSFPG---I
-TSMAPAFGVQEFYRTVKQGDEVTVTIT-----NIDQIED-VSHGFVVVNHGVSME---I
IE--KMKYLTPEVFYTIKAGETVYWVNGEVMPHNVAFKKGIV--GEDAFRGEMMTKD---
-TSVAPSFSQPSF-LTVKEGDEVTVIVTNLDE------IDDLTHGFTMGNHGVAME---V
ASAETMVFEPDFLVLEIGPGDRVRFVPTHK-SHNAATIDGMVPEGVEGFKSRINDE----
TVNGQ--FPGPRLAGVAREGDQVLVKVVNHVAENITIHWHGVQLGTGWADGPAYVTQCPI
TKAVVLTFNTSVEICLVMQGTSIV----AAESHPLHLHGFNFPSNFNLVDGMERNTAGVP
Matching any thing but G => large negative score
Any thing can match

30. Example. (SGNH active site)

31. HMM vs. alignment Detailed description of core
Conserved/variable positions
Price for insertions/deletions varies at different locations in sequence
These features cannot be captured in conventional alignments

32. Profile HMM’s X = L1- Y2A3V4R5- I6 P = P1D2P3P4I4P5D6P7 Deletions
Insertions
X = L1- Y2A3V4R5- I6
P = P1D2P3P4I4P5D6P7

33. Building a profile HMM
Multiple alignment is used to construct the HMM model.
Assign each column to a Match state in HMM. Add Insertion and Deletion state.
Estimate the emission probabilities according to amino acid counts in column. Different positions in the protein will have different emission probabilities.
Estimate the transition probabilities between Match, Deletion and Insertion states
The HMM model gets trained to derive the optimal parameters.

34. Paths in Edit Graph and Profile HMM
A path through an edit graph and the corresponding path through a profile HMM

35. Making a Collection of HMM for Protein Families
Use Blast to separate a protein database into families of related proteins
Construct a multiple alignment for each protein family.
Construct a profile HMM model and optimize the parameters of the model (transition and emission probabilities).
Align the target sequence against each HMM to find the best fit between a target sequence and an HMM

36. Application of Profile HMM to Modeling Globin Proteins
Globins represent a large collection of protein sequences
400 globin sequences were randomly selected from all globins and used to construct a multiple alignment.
Multiple alignment was used to assign an initial HMM
This model then get trained repeatedly with model lengths chosen randomly between 145 to 170, to get an HMM model optimized probabilities.

37. How Good is the Globin HMM?
625 remaining globin sequences in the database were aligned to the constructed HMM resulting in a multiple alignment. This multiple alignment agrees extremely well with the structurally derived alignment.
25,044 proteins, were randomly chosen from the database and compared against the globin HMM.
This experiment resulted in an excellent separation between globin and non-globin families.