sequence motifs, information content, logos, and hmm’s morten nielsen, cbs, biocentrum, dtu

Sequence motifs, information content, logos, and HMM’s

Morten Nielsen,CBS, BioCentrum,

DTU

Outline

• What is a binding motif?• How to describe a sequence motif?• Construction of scoring matrices• Sequence motifs and hidden Markov models• Use of HMM• Why are Profile HMM’s better than Anders

Gorms sequence alignments– Or at least PSSM’s

Binding motifs

MHC-I

TAPMHC-II

Anchor positions

MHC class I with peptide

SLLPAIVEL YLLPAIVHI TLWVDPYEV GLVPFLVSV KLLEPVLLL LLDVPTAAV LLDVPTAAV LLDVPTAAVLLDVPTAAV VLFRGGPRG MVDGTLLLL YMNGTMSQV MLLSVPLLL SLLGLLVEV ALLPPINIL TLIKIQHTLHLIDYLVTS ILAPPVVKL ALFPQLVIL GILGFVFTL STNRQSGRQ GLDVLTAKV RILGAVAKV QVCERIPTIILFGHENRV ILMEHIHKL ILDQKINEV SLAGGIIGV LLIENVASL FLLWATAEA SLPDFGISY KKREEAPSLLERPGGNEI ALSNLEVKL ALNELLQHV DLERKVESL FLGENISNF ALSDHHIYL GLSEFTEYL STAPPAHGVPLDGEYFTL GVLVGVALI RTLDKVLEV HLSTAFARV RLDSYVRSL YMNGTMSQV GILGFVFTL ILKEPVHGVILGFVFTLT LLFGYPVYV GLSPTVWLS WLSLLVPFV FLPSDFFPS CLGGLLTMV FIAGNSAYE KLGEFYNQMKLVALGINA DLMGYIPLV RLVTLKDIV MLLAVLYCL AAGIGILTV YLEPGPVTA LLDGTATLR ITDQVPFSVKTWGQYWQV TITDQVPFS AFHHVAREL YLNKIQNSL MMRKLAILS AIMDKNIIL IMDKNIILK SMVGNWAKVSLLAPGAKQ KIFGSLAFL ELVSEFSRM KLTPLCVTL VLYRYGSFS YIGEVLVSV CINGVCWTV VMNILLQYVILTVILGVL KVLEYVIKV FLWGPRALV GLSRYVARL FLLTRILTI HLGNVKYLV GIAGGLALL GLQDCTMLVTGAPVTYST VIYQYMDDL VLPDVFIRC VLPDVFIRC AVGIGIAVV LVVLGLLAV ALGLGLLPV GIGIGVLAAGAGIGVAVL IAGIGILAI LIVIGILIL LAGIGLIAA VDGIGILTI GAGIGVLTA AAGIGIIQI QAGIGILLAKARDPHSGH KACDPHSGH ACDPHSGHF SLYNTVATL RGPGRAFVT NLVPMVATV GLHCYEQLV PLKQHFQIVAVFDRKSDA LLDFVRFMG VLVKSPNHV GLAPPQHLI LLGRNSFEV PLTFGWCYK VLEWRFDSR TLNAWVKVVGLCTLVAML FIDSYICQV IISAVVGIL VMAGVGSPY LLWTLVVLL SVRDRLARL LLMDCSGSI CLTSTVQLVVLHDDLLEA LMWITQCFL SLLMWITQC QLSLLMWIT LLGATCMFV RLTRFLSRV YMDGTMSQV FLTPKKLQCISNDVCAQV VKTDGNPPE SVYDFFVWL FLYGALLLA VLFSSDFRI LMWAKIGPV SLLLELEEV SLSRFSWGAYTAFTIPSI RLMKQDFSV RLPRIFCSC FLWGPRAYA RLLQETELV SLFEGIDFY SLDQSVVEL RLNMFTPYINMFTPYIGV LMIIPLINV TLFIGSHVV SLVIVTTFV VLQWASLAV ILAKFLHWL STAPPHVNV LLLLTVLTVVVLGVVFGI ILHNGAYSL MIMVKCWMI MLGTHTMEV MLGTHTMEV SLADTNSLA LLWAARPRL GVALQTMKQGLYDGMEHL KMVELVHFL YLQLVFGIE MLMAQEALA LMAQEALAF VYDGREHTV YLSGANLNL RMFPNAPYLEAAGIGILT TLDSQVMSL STPPPGTRV KVAELVHFL IMIGVLVGV ALCRWGLLL LLFAGVQCQ VLLCESTAVYLSTAFARV YLLEMLWRL SLDDYNHLV RTLDKVLEV GLPVEYLQV KLIANNTRV FIYAGSLSA KLVANNTRLFLDEFMEGV ALQPGTALL VLDGLDVLL SLYSFPEPE ALYVDSLFF SLLQHLIGL ELTLGEFLK MINAYLDKLAAGIGILTV FLPSDFFPS SVRDRLARL SLREWLLRI LLSAWILTA AAGIGILTV AVPDEIPPL FAYDGKDYIAAGIGILTV FLPSDFFPS AAGIGILTV FLPSDFFPS AAGIGILTV FLWGPRALV ETVSEQSNV ITLWQRPLV

Sequence information

Sequence information

SLLPAIVEL YLLPAIVHI TLWVDPYEV GLVPFLVSV KLLEPVLLL LLDVPTAAV LLDVPTAAV LLDVPTAAVLLDVPTAAV VLFRGGPRG MVDGTLLLL YMNGTMSQV MLLSVPLLL SLLGLLVEV ALLPPINIL TLIKIQHTLHLIDYLVTS ILAPPVVKL ALFPQLVIL GILGFVFTL STNRQSGRQ GLDVLTAKV RILGAVAKV QVCERIPTIILFGHENRV ILMEHIHKL ILDQKINEV SLAGGIIGV LLIENVASL FLLWATAEA SLPDFGISY KKREEAPSLLERPGGNEI ALSNLEVKL ALNELLQHV DLERKVESL FLGENISNF ALSDHHIYL GLSEFTEYL STAPPAHGVPLDGEYFTL GVLVGVALI RTLDKVLEV HLSTAFARV RLDSYVRSL YMNGTMSQV GILGFVFTL ILKEPVHGVILGFVFTLT LLFGYPVYV GLSPTVWLS WLSLLVPFV FLPSDFFPS CLGGLLTMV FIAGNSAYE KLGEFYNQMKLVALGINA DLMGYIPLV RLVTLKDIV MLLAVLYCL AAGIGILTV YLEPGPVTA LLDGTATLR ITDQVPFSVKTWGQYWQV TITDQVPFS AFHHVAREL YLNKIQNSL MMRKLAILS AIMDKNIIL IMDKNIILK SMVGNWAKVSLLAPGAKQ KIFGSLAFL ELVSEFSRM KLTPLCVTL VLYRYGSFS YIGEVLVSV CINGVCWTV VMNILLQYVILTVILGVL KVLEYVIKV FLWGPRALV GLSRYVARL FLLTRILTI HLGNVKYLV GIAGGLALL GLQDCTMLVTGAPVTYST VIYQYMDDL VLPDVFIRC VLPDVFIRC AVGIGIAVV LVVLGLLAV ALGLGLLPV GIGIGVLAAGAGIGVAVL IAGIGILAI LIVIGILIL LAGIGLIAA VDGIGILTI GAGIGVLTA AAGIGIIQI QAGIGILLAKARDPHSGH KACDPHSGH ACDPHSGHF SLYNTVATL RGPGRAFVT NLVPMVATV GLHCYEQLV PLKQHFQIVAVFDRKSDA LLDFVRFMG VLVKSPNHV GLAPPQHLI LLGRNSFEV PLTFGWCYK VLEWRFDSR TLNAWVKVVGLCTLVAML FIDSYICQV IISAVVGIL VMAGVGSPY LLWTLVVLL SVRDRLARL LLMDCSGSI CLTSTVQLVVLHDDLLEA LMWITQCFL SLLMWITQC QLSLLMWIT LLGATCMFV RLTRFLSRV YMDGTMSQV FLTPKKLQCISNDVCAQV VKTDGNPPE SVYDFFVWL FLYGALLLA VLFSSDFRI LMWAKIGPV SLLLELEEV SLSRFSWGAYTAFTIPSI RLMKQDFSV RLPRIFCSC FLWGPRAYA RLLQETELV SLFEGIDFY SLDQSVVEL RLNMFTPYINMFTPYIGV LMIIPLINV TLFIGSHVV SLVIVTTFV VLQWASLAV ILAKFLHWL STAPPHVNV LLLLTVLTVVVLGVVFGI ILHNGAYSL MIMVKCWMI MLGTHTMEV MLGTHTMEV SLADTNSLA LLWAARPRL GVALQTMKQGLYDGMEHL KMVELVHFL YLQLVFGIE MLMAQEALA LMAQEALAF VYDGREHTV YLSGANLNL RMFPNAPYLEAAGIGILT TLDSQVMSL STPPPGTRV KVAELVHFL IMIGVLVGV ALCRWGLLL LLFAGVQCQ VLLCESTAVYLSTAFARV YLLEMLWRL SLDDYNHLV RTLDKVLEV GLPVEYLQV KLIANNTRV FIYAGSLSA KLVANNTRLFLDEFMEGV ALQPGTALL VLDGLDVLL SLYSFPEPE ALYVDSLFF SLLQHLIGL ELTLGEFLK MINAYLDKLAAGIGILTV FLPSDFFPS SVRDRLARL SLREWLLRI LLSAWILTA AAGIGILTV AVPDEIPPL FAYDGKDYIAAGIGILTV FLPSDFFPS AAGIGILTV FLPSDFFPS AAGIGILTV FLWGPRALV ETVSEQSNV ITLWQRPLV

Sequence Information

Sequence Information

Calculate pa at each positionEntropy

Information content

Conserved positions– PV=1, PREST=0 => S=0, I=log(20)

Mutable positions– Paa=1/20 => S=log(20), I=0

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S = − paa

∑ log(pa )

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I = log(20) + paa

∑ log(pa )

Information content

A R N D C Q E G H I L K M F P S T W Y V S I1 0.10 0.06 0.01 0.02 0.01 0.02 0.02 0.09 0.01 0.07 0.11 0.06 0.04 0.08 0.01 0.11 0.03 0.01 0.05 0.08 3.96 0.372 0.07 0.00 0.00 0.01 0.01 0.00 0.01 0.01 0.00 0.08 0.59 0.01 0.07 0.01 0.00 0.01 0.06 0.00 0.01 0.08 2.16 2.163 0.08 0.03 0.05 0.10 0.02 0.02 0.01 0.12 0.02 0.03 0.12 0.01 0.03 0.05 0.06 0.06 0.04 0.04 0.04 0.07 4.06 0.264 0.07 0.04 0.02 0.11 0.01 0.04 0.08 0.15 0.01 0.10 0.04 0.03 0.01 0.02 0.09 0.07 0.04 0.02 0.00 0.05 3.87 0.455 0.04 0.04 0.04 0.04 0.01 0.04 0.05 0.16 0.04 0.02 0.08 0.04 0.01 0.06 0.10 0.02 0.06 0.02 0.05 0.09 4.04 0.286 0.04 0.03 0.03 0.01 0.02 0.03 0.03 0.04 0.02 0.14 0.13 0.02 0.03 0.07 0.03 0.05 0.08 0.01 0.03 0.15 3.92 0.407 0.14 0.01 0.03 0.03 0.02 0.03 0.04 0.03 0.05 0.07 0.15 0.01 0.03 0.07 0.06 0.07 0.04 0.03 0.02 0.08 3.98 0.348 0.05 0.09 0.04 0.01 0.01 0.05 0.07 0.05 0.02 0.04 0.14 0.04 0.02 0.05 0.05 0.08 0.10 0.01 0.04 0.03 4.04 0.289 0.07 0.01 0.00 0.00 0.02 0.02 0.02 0.01 0.01 0.08 0.26 0.01 0.01 0.02 0.00 0.04 0.02 0.00 0.01 0.38 2.78 1.55

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I = log(20) + paa

∑ log(pa )

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S = − paa

∑ log(pa )

Sequence logos

Height of a column equal to I

Relative height of a letter is pHighly useful tool to visualize sequence motifs

High information positions

HLA-A0201

http://www.cbs.dtu.dk/~gorodkin/appl/plogo.html

Characterizing a sequence motif from small data sets

What can we learn?

1. A at P1 favors binding?2. I is not allowed at P9? 3. K at P4 favors binding?4. Which positions are important

for binding?

ALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV

10 MHC restricted peptides

Simple motifs Yes/No rules



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[AGTK]1[LMIV ]2[ANLV ]3 ...[MNRTVL]9

• 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

Simple motifsYes/No rules

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[AGTK]1[LMIV ]2[ANLV ]3 ...[AIFKLV ]7...[MNRTVL]9

• Example

•Two first peptides will not fit the motif

RLLDDTPEV 0.59GLLGNVSTV 0.71ALAKAAAAL 0.47



Extended motifs

Fitness of aa at each position given by P(aa)

Example P1PA = 6/10

PG = 2/10

PT = PK = 1/10

PC = PD = …PV = 0

Problems– Few data– Data redundancy/duplication


Sequence informationRaw sequence counting


Sequence weighting


Poor or biased sampling of sequence spaceExample P1

PA = 2/6

PG = 2/6

PT = PK = 1/6

PC = PD = …PV = 0

}Similar sequencesWeight 1/5

Example RLLDDTPEV 0.59 GLLGNVSTV 0.71 ALAKAAAAL 0.47

Sequence weightingALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV

Pseudo counts


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

A R N D C Q E G H I L K M F P S T W Y V A 0.29 0.03 0.03 0.03 0.02 0.03 0.04 0.08 0.01 0.04 0.06 0.04 0.02 0.02 0.03 0.09 0.05 0.01 0.02 0.07 R 0.04 0.34 0.04 0.03 0.01 0.05 0.05 0.03 0.02 0.02 0.05 0.12 0.02 0.02 0.02 0.04 0.03 0.01 0.02 0.03 N 0.04 0.04 0.32 0.08 0.01 0.03 0.05 0.07 0.03 0.02 0.03 0.05 0.01 0.02 0.02 0.07 0.05 0.00 0.02 0.03 D 0.04 0.03 0.07 0.40 0.01 0.03 0.09 0.05 0.02 0.02 0.03 0.04 0.01 0.01 0.02 0.05 0.04 0.00 0.01 0.02 C 0.07 0.02 0.02 0.02 0.48 0.01 0.02 0.03 0.01 0.04 0.07 0.02 0.02 0.02 0.02 0.04 0.04 0.00 0.01 0.06 Q 0.06 0.07 0.04 0.05 0.01 0.21 0.10 0.04 0.03 0.03 0.05 0.09 0.02 0.01 0.02 0.06 0.04 0.01 0.02 0.04 E 0.06 0.05 0.04 0.09 0.01 0.06 0.30 0.04 0.03 0.02 0.04 0.08 0.01 0.02 0.03 0.06 0.04 0.01 0.02 0.03 G 0.08 0.02 0.04 0.03 0.01 0.02 0.03 0.51 0.01 0.02 0.03 0.03 0.01 0.02 0.02 0.05 0.03 0.01 0.01 0.02 H 0.04 0.05 0.05 0.04 0.01 0.04 0.05 0.04 0.35 0.02 0.04 0.05 0.02 0.03 0.02 0.04 0.03 0.01 0.06 0.02 I 0.05 0.02 0.01 0.02 0.02 0.01 0.02 0.02 0.01 0.27 0.17 0.02 0.04 0.04 0.01 0.03 0.04 0.01 0.02 0.18 L 0.04 0.02 0.01 0.02 0.02 0.02 0.02 0.02 0.01 0.12 0.38 0.03 0.05 0.05 0.01 0.02 0.03 0.01 0.02 0.10 K 0.06 0.11 0.04 0.04 0.01 0.05 0.07 0.04 0.02 0.03 0.04 0.28 0.02 0.02 0.03 0.05 0.04 0.01 0.02 0.03 M 0.05 0.03 0.02 0.02 0.02 0.03 0.03 0.03 0.02 0.10 0.20 0.04 0.16 0.05 0.02 0.04 0.04 0.01 0.02 0.09 F 0.03 0.02 0.02 0.02 0.01 0.01 0.02 0.03 0.02 0.06 0.11 0.02 0.03 0.39 0.01 0.03 0.03 0.02 0.09 0.06 P 0.06 0.03 0.02 0.03 0.01 0.02 0.04 0.04 0.01 0.03 0.04 0.04 0.01 0.01 0.49 0.04 0.04 0.00 0.01 0.03 S 0.11 0.04 0.05 0.05 0.02 0.03 0.05 0.07 0.02 0.03 0.04 0.05 0.02 0.02 0.03 0.22 0.08 0.01 0.02 0.04 T 0.07 0.04 0.04 0.04 0.02 0.03 0.04 0.04 0.01 0.05 0.07 0.05 0.02 0.02 0.03 0.09 0.25 0.01 0.02 0.07 W 0.03 0.02 0.02 0.02 0.01 0.02 0.02 0.03 0.02 0.03 0.05 0.02 0.02 0.06 0.01 0.02 0.02 0.49 0.07 0.03 Y 0.04 0.03 0.02 0.02 0.01 0.02 0.03 0.02 0.05 0.04 0.07 0.03 0.02 0.13 0.02 0.03 0.03 0.03 0.32 0.05 V 0.07 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01 0.16 0.13 0.03 0.03 0.04 0.02 0.03 0.05 0.01 0.02 0.27

The Blosum matrix

Some amino acids are highly conserved (i.e. C), some have a high change of mutation (i.e. I)

• Calculate observed amino acids frequencies fa

• Pseudo frequency for amino acid b

• Example

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gb = faa

∑ ⋅qb |a

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gI = 0.2 ⋅qI |M + 0.1⋅qI |N + ...+ 0.3⋅qI |V + 0.1⋅qI |LgI = 0.2 ⋅0.04 + 0.1⋅0.01+ ...+ 0.3⋅0.18 + 0.1⋅0.17 ≈ 0.09


Pseudo count estimation


Weight on pseudo count

• 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

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pa =α ⋅ fa + β ⋅gaα + β

• Example

• If large, p ≈ f and only the observed data defines the motif

• If small, p ≈ g and the pseudo counts (or prior) defines the motif

is [50-200] normally


Weight on pseudo count

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Sequence weighting and pseudo counts

RLLDDTPEV 0.59GLLGNVSTV 0.71ALAKAAAAL 0.47

P7P and P7S > 0


Position specific weighting

We know that positions 2 and 9 are anchor positions for most MHC binding motifs– Increase weight on high

information positions

Motif found on large data set

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

• qA = 0.070, qW = 0.013

• Finding 6% A is hence not significant, but 6% W highly significant • In nature V is found more often than M, so we must somehow rescale

with the background

A R N D C Q E G H I L K M F P S T W Y V1 0.08 0.06 0.02 0.03 0.02 0.02 0.03 0.08 0.02 0.08 0.11 0.06 0.04 0.06 0.02 0.09 0.04 0.01 0.04 0.082 0.04 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.01 0.11 0.44 0.02 0.06 0.03 0.01 0.02 0.05 0.00 0.01 0.103 0.08 0.04 0.05 0.07 0.02 0.03 0.03 0.08 0.02 0.05 0.11 0.03 0.03 0.06 0.04 0.06 0.05 0.03 0.05 0.074 0.08 0.05 0.03 0.10 0.01 0.05 0.08 0.13 0.01 0.05 0.06 0.05 0.01 0.03 0.08 0.06 0.04 0.02 0.01 0.055 0.06 0.04 0.05 0.03 0.01 0.04 0.05 0.11 0.03 0.04 0.09 0.04 0.02 0.06 0.06 0.04 0.05 0.02 0.05 0.086 0.06 0.03 0.03 0.03 0.03 0.03 0.04 0.06 0.02 0.10 0.14 0.04 0.03 0.05 0.04 0.06 0.06 0.01 0.03 0.137 0.10 0.02 0.04 0.04 0.02 0.03 0.04 0.05 0.04 0.08 0.12 0.02 0.03 0.06 0.07 0.06 0.05 0.03 0.03 0.088 0.05 0.07 0.04 0.03 0.01 0.04 0.06 0.06 0.03 0.06 0.13 0.06 0.02 0.05 0.04 0.08 0.07 0.01 0.04 0.059 0.08 0.02 0.01 0.01 0.02 0.02 0.03 0.02 0.01 0.10 0.23 0.03 0.02 0.04 0.01 0.04 0.04 0.00 0.02 0.25

How to score a sequence to a probability matrix?

• pij describes a motif• The probability that a

peptide fits the motif is

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p(s | model) = ppap

∏

A R N D C Q E G H I L K M F P S T W Y V1 0.08 0.06 0.02 0.03 0.02 0.02 0.03 0.08 0.02 0.08 0.11 0.06 0.04 0.06 0.02 0.09 0.04 0.01 0.04 0.082 0.04 0.01 0.01 0.01 0.01 0.01 0.02 0.02 0.01 0.11 0.44 0.02 0.06 0.03 0.01 0.02 0.05 0.00 0.01 0.103 0.08 0.04 0.05 0.07 0.02 0.03 0.03 0.08 0.02 0.05 0.11 0.03 0.03 0.06 0.04 0.06 0.05 0.03 0.05 0.074 0.08 0.05 0.03 0.10 0.01 0.05 0.08 0.13 0.01 0.05 0.06 0.05 0.01 0.03 0.08 0.06 0.04 0.02 0.01 0.055 0.06 0.04 0.05 0.03 0.01 0.04 0.05 0.11 0.03 0.04 0.09 0.04 0.02 0.06 0.06 0.04 0.05 0.02 0.05 0.086 0.06 0.03 0.03 0.03 0.03 0.03 0.04 0.06 0.02 0.10 0.14 0.04 0.03 0.05 0.04 0.06 0.06 0.01 0.03 0.137 0.10 0.02 0.04 0.04 0.02 0.03 0.04 0.05 0.04 0.08 0.12 0.02 0.03 0.06 0.07 0.06 0.05 0.03 0.03 0.088 0.05 0.07 0.04 0.03 0.01 0.04 0.06 0.06 0.03 0.06 0.13 0.06 0.02 0.05 0.04 0.08 0.07 0.01 0.04 0.059 0.08 0.02 0.01 0.01 0.02 0.02 0.03 0.02 0.01 0.10 0.23 0.03 0.02 0.04 0.01 0.04 0.04 0.00 0.02 0.25



peptide fits the motif is

• The probability that the peptide fits a random model is €

p(s | model) = ppap

∏

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p(s | random) = qap

∏



peptide fits the motif is• The probability that the

peptide fits a random model is

• The ratio of the two gives the odds

• The log gives the score

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p(s | model) = ppap

∏

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p(s | random) = qap

∏

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0 =

ppap

∏

qap

∏=

ppaqap

∏

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S = logppaqa

⎛

⎝ ⎜

⎞

⎠ ⎟

p

∑

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 1 0.6 0.4 -3.5 -2.4 -0.4 -1.9 -2.7 0.3 -1.1 1.0 0.3 0.0 1.4 1.2 -2.7 1.4 -1.2 -2.0 1.1 0.7 2 -1.6 -6.6 -6.5 -5.4 -2.5 -4.0 -4.7 -3.7 -6.3 1.0 5.1 -3.7 3.1 -4.2 -4.3 -4.2 -0.2 -5.9 -3.8 0.4 3 0.2 -1.3 0.1 1.5 0.0 -1.8 -3.3 0.4 0.5 -1.0 0.3 -2.5 1.2 1.0 -0.1 -0.3 -0.5 3.4 1.6 0.0 4 -0.1 -0.1 -2.0 2.0 -1.6 0.5 0.8 2.0 -3.3 0.1 -1.7 -1.0 -2.2 -1.6 1.7 -0.6 -0.2 1.3 -6.8 -0.7 5 -1.6 -0.1 0.1 -2.2 -1.2 0.4 -0.5 1.9 1.2 -2.2 -0.5 -1.3 -2.2 1.7 1.2 -2.5 -0.1 1.7 1.5 1.0 6 -0.7 -1.4 -1.0 -2.3 1.1 -1.3 -1.4 -0.2 -1.0 1.8 0.8 -1.9 0.2 1.0 -0.4 -0.6 0.4 -0.5 -0.0 2.1 7 1.1 -3.8 -0.2 -1.3 1.3 -0.3 -1.3 -1.4 2.1 0.6 0.7 -5.0 1.1 0.9 1.3 -0.5 -0.9 2.9 -0.4 0.5 8 -2.2 1.0 -0.8 -2.9 -1.4 0.4 0.1 -0.4 0.2 -0.0 1.1 -0.5 -0.5 0.7 -0.3 0.8 0.8 -0.7 1.3 -1.1 9 -0.2 -3.5 -6.1 -4.5 0.7 -0.8 -2.5 -4.0 -2.6 0.9 2.8 -3.0 -1.8 -1.4 -6.2 -1.9 -1.6 -4.9 -1.6 4.5

A R N D C Q E G H I L K M F P S T W Y V E 0.06 0.05 0.04 0.09 0.01 0.06 0.30 0.04 0.03 0.02 0.04 0.08 0.01 0.02 0.03 0.06 0.04 0.01 0.02 0.03 G 0.08 0.02 0.04 0.03 0.01 0.02 0.03 0.51 0.01 0.02 0.03 0.03 0.01 0.02 0.02 0.05 0.03 0.01 0.01 0.02 H 0.04 0.05 0.05 0.04 0.01 0.04 0.05 0.04 0.35 0.02 0.04 0.05 0.02 0.03 0.02 0.04 0.03 0.01 0.06 0.02 I 0.05 0.02 0.01 0.02 0.02 0.01 0.02 0.02 0.01 0.27 0.17 0.02 0.04 0.04 0.01 0.03 0.04 0.01 0.02 0.18 L 0.04 0.02 0.01 0.02 0.02 0.02 0.02 0.02 0.01 0.12 0.38 0.03 0.05 0.05 0.01 0.02 0.03 0.01 0.02 0.10 K 0.06 0.11 0.04 0.04 0.01 0.05 0.07 0.04 0.02 0.03 0.04 0.28 0.02 0.02 0.03 0.05 0.04 0.01 0.02 0.03 M 0.05 0.03 0.02 0.02 0.02 0.03 0.03 0.03 0.02 0.10 0.20 0.04 0.16 0.05 0.02 0.04 0.04 0.01 0.02 0.09 F 0.03 0.02 0.02 0.02 0.01 0.01 0.02 0.03 0.02 0.06 0.11 0.02 0.03 0.39 0.01 0.03 0.03 0.02 0.09 0.06

A R N D C Q E G H I L K M F P S T W Y V 0.08 0.05 0.04 0.05 0.02 0.03 0.06 0.07 0.02 0.06 0.10 0.06 0.02 0.04 0.04 0.06 0.05 0.01 0.03 0.07

Example

Calculate the weight matrix based on the following observation (use =50):

Sequence = I

Important. What is ?

€

gb = faa

∑ ⋅qb |a

€


Wij = log(pij/qj)

q

qb|a

Example

So the score is simply the Blosum62 row for amino acid I!!!

This is why is called weight on prior. Our prior knowledge is Blosum. We will only accept a weight matrix different from Blosum if we have many data.

€

gb = faa

∑ ⋅qb |a

€


Wij = log(pij/qj)

A R N D C Q E G H I L K M F P S T W Y 0.05 0.02 0.01 0.02 0.02 0.01 0.02 0.02 0.01 0.27 0.17 0.02 0.04 0.04 0.01 0.03 0.04 0.01 0.02 0.08 0.05 0.04 0.05 0 .02 0.03 0.06 0.07 0.02 0.06 0.10 0.06 0.02 0.04 0.04 0.06 0.05 0.01 -0.45 -1.08 -1.12 -1.12 -0.43 -0.94 -1.12 -1.28 -1.08 1.38 0.53 -0.90 0.39 -0.06 -0.98 -0.82 -0.25 -0.79 -0.44 -1.30 -3.11 -3.23 -3.29 -1.25 -2.71 -3.218 -3.69 -3.13 3.99 1.52 -2.60 1.12 -0.18 -2.82 -2.38 -0.72 -2.28 -1.27

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 1 0.6 0.4 -3.5 -2.4 -0.4 -1.9 -2.7 0.3 -1.1 1.0 0.3 0.0 1.4 1.2 -2.7 1.4 -1.2 -2.0 1.1 0.7 2 -1.6 -6.6 -6.5 -5.4 -2.5 -4.0 -4.7 -3.7 -6.3 1.0 5.1 -3.7 3.1 -4.2 -4.3 -4.2 -0.2 -5.9 -3.8 0.4 3 0.2 -1.3 0.1 1.5 0.0 -1.8 -3.3 0.4 0.5 -1.0 0.3 -2.5 1.2 1.0 -0.1 -0.3 -0.5 3.4 1.6 0.0 4 -0.1 -0.1 -2.0 2.0 -1.6 0.5 0.8 2.0 -3.3 0.1 -1.7 -1.0 -2.2 -1.6 1.7 -0.6 -0.2 1.3 -6.8 -0.7 5 -1.6 -0.1 0.1 -2.2 -1.2 0.4 -0.5 1.9 1.2 -2.2 -0.5 -1.3 -2.2 1.7 1.2 -2.5 -0.1 1.7 1.5 1.0 6 -0.7 -1.4 -1.0 -2.3 1.1 -1.3 -1.4 -0.2 -1.0 1.8 0.8 -1.9 0.2 1.0 -0.4 -0.6 0.4 -0.5 -0.0 2.1 7 1.1 -3.8 -0.2 -1.3 1.3 -0.3 -1.3 -1.4 2.1 0.6 0.7 -5.0 1.1 0.9 1.3 -0.5 -0.9 2.9 -0.4 0.5 8 -2.2 1.0 -0.8 -2.9 -1.4 0.4 0.1 -0.4 0.2 -0.0 1.1 -0.5 -0.5 0.7 -0.3 0.8 0.8 -0.7 1.3 -1.1 9 -0.2 -3.5 -6.1 -4.5 0.7 -0.8 -2.5 -4.0 -2.6 0.9 2.8 -3.0 -1.8 -1.4 -6.2 -1.9 -1.6 -4.9 -1.6 4.5

Scoring a sequence to a weight matrix

RLLDDTPEVGLLGNVSTVALAKAAAAL

Which peptide is most likely to bind?Which peptide second?

11.9 14.7 4.3

0.59 0.71 0.47

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


Prediction accuracy

Pearson correlation 0.45

Predictive performance

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Pearsons correlation

CC 0.45 0.5 0.6 0.65 0.79

Simple Seq.W Seq.W+SCSeq.W+SC+PW

Large dataset

End of first part

Take a deep breathSmile to you neighbor

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

Why hidden?

Model generates numbers– 312453666641

Does not tell which die was used

Alignment (decoding) can give the most probable solution/path (Viterby)– FFFFFFLLLLLL

1:1/62:1/63:1/64:1/65:1/66:1/6Fair

1:1/102:1/103:1/104:1/105:1/106:1/2Loaded

0.95

0.10

0.05

0.9

The unfair casino: Loaded die p(6) = 0.5; switch fair to load:0.05; switch load to fair: 0.1

HMM (a simple example)

ACA---ATG

TCAACTATC

ACAC--AGC

AGA---ATC

ACCG--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)

Core of alignment

.2

.8

.2

ACGT

ACGT

ACGT

ACGT

ACGT

ACGT.8

.8 .8.8

.2.2.2

.2

1

ACGT

.2

.2

.4

1. .4 1. 1.1.

.6.6

.4

HMM construction

ACA---ATG

TCAACTATC

ACAC--AGC

AGA---ATC

ACCG--ATC

• 5 matches. A, 2xC, T, G• 5 transitions in gap region

• C out, G out• A-C, C-T, T out• Out transition 3/5• Stay transition 2/5

ACA---ATG 0.8x1x0.8x1x0.8x0.4x1x1x0.8x1x0.2 = 3.3x10-2

Align sequence to HMM

ACA---ATG 0.8x1x0.8x1x0.8x0.4x1x0.8x1x0.2 = 3.3x10-2

TCAACTATC 0.2x1x0.8x1x0.8x0.6x0.2x0.4x0.4x0.4x0.2x0.6x1x1x0.8x1x0.8 = 0.0075x10-2

ACAC--AGC = 1.2x10-2

AGA---ATC = 3.3x10-2

ACCG--ATC = 0.59x10-2

Consensus:

ACAC--ATC = 4.7x10-2, ACA---ATC = 13.1x10-2

Exceptional:

TGCT--AGG = 0.0023x10-2

Align sequence to HMM - Null model

• Score depends strongly on length

• Null model is a random model. For length L the score is 0.25L

• Log-odds score for sequence S

Log( P(S)/0.25L)• Positive score means

more likely than Null model

ACA---ATG = 4.9

TCAACTATC = 3.0 ACAC--AGC = 5.3AGA---ATC = 4.9ACCG--ATC = 4.6Consensus:ACAC--ATC = 6.7 ACA---ATC = 6.3Exceptional:TGCT--AGG = -0.97

Note!

Model decoding (Viterby)The unfair casino

Example: 1245666

1 2 4 5 6 6 6

F -0.78 -1.58 -2.38 -3.18 -3.98 -4.78 -5.58

L Null -3.08 -3.88 -4.68 -4.78 -5.13 -5.48

FFFFLLL

1:-0.782:-0.783:-0.784:-0.785:-0.786:-0-78

Fair

1:-12:-13:-14:-15:-16:-0.3Loaded

-0.02

-1

-1.3

-0.05Log model

€

2F = −0.78 − 0.02 − 0.78 = −1.58

€

Pl (i +1) = pl (i +1) • maxk

(Pk (i) • akl ) or

log(Pl (i +1) = log(pl (i −1)) + maxk

(log(Pk (i) + log(akl ))

FFFFLLL

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

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

ADDGSLAFVPSEF--SISPGEKIVFKNNAGFPHNIVFDEDSIPSGVDASKISMSEEDLLN TVNGAI--PGPLIAERLKEGQNVRVTNTLDEDTSIHWHGLLVPFGMDGVPGVSFPG---I-TSMAPAFGVQEFYRTVKQGDEVTVTIT-----NIDQIED-VSHGFVVVNHGVSME---IIE--KMKYLTPEVFYTIKAGETVYWVNGEVMPHNVAFKKGIV--GEDAFRGEMMTKD----TSVAPSFSQPSF-LTVKEGDEVTVIVTNLDE------IDDLTHGFTMGNHGVAME---VASAETMVFEPDFLVLEIGPGDRVRFVPTHK-SHNAATIDGMVPEGVEGFKSRINDE----TKAVVLTFNTSVEICLVMQGTSIV----AAESHPLHLHGFNFPSNFNLVDPMERNTAGVPTVNGQ--FPGPRLAGVAREGDQVLVKVVNHVAENITIHWHGVQLGTGWADGPAYVTQCPI

Profile HMM’s

Conserved

Core: Position with < 2 gaps

Deletion

Insertion

Non-conserved

Must have a G Any thing can match

Profile HMM’s

All M/D pairs must be visited once

L1- Y2A3V4R5- I6

P1D2P3P4I4P5D6P7

Example. Sequence profiles

• Alignment of protein sequences 1PLC._ and 1GYC.A• E-value > 1000• Profile alignment

– Align 1PLC._ against Swiss-prot– Make position specific weight matrix from

alignment– Use this matrix to align 1PLC._ against 1GYC.A

• E-value < 10-22. Rmsd=3.3

Example continued

Smith-Waterman score: 53; 26.2% identity in 61 aa overlap

10 20 30 1PLC._ IDVLLGADDGSLAFVPSEFSISPG--EKIV-----FKNNAG :: .: : .:: .: . :... 1GYC.A ILRYQGAPVAEPTTTQTTSVIPLIETNLHPLARMPVPGSPTPGGVDKALNLAFNFNGTNF 280 290 300 310 320 330

40 50 60 70 80 90 1PLC._ FPHNIVFDEDSIPSGVDASKISMSEEDLLNAKGETFEVALSNKGEYSFYCSPHQGAGMVG : .: : ..: .. . ... .::: : 1GYC.A FINNASFTPPTVPVLLQILSGAQTAQDLLPAGSVYPLPAHSTIEITLPATALAPGAPHPF 340 350 360 370 380 390

1PLC._ KVTVN 1GYC.A HLHGHAFAVVRSAGSTTYNYNDPIFRDVVSTGTPAAGDNVTIRFQTDNPGPWFLHCHIDF

400 410 420 430 440 450

Example continued

Score = 97.1 bits (241), Expect = 9e-22 Identities = 13/107 (12%), Positives = 27/107 (25%), Gaps = 17/107 (15%) Query: 3 ADDGSLAFVPSEFSISPGEKI------VFKNNAGFPHNIVFDEDSIPSGVDASKIS 56 F + G++ N+ + +G + +Sbjct: 26 ------VFPSPLITGKKGDRFQLNVVDTLTNHTMLKSTSIHWHGFFQAGTNWADGP 79 Query: 57 MSEEDLLNAKGETFEVAL---SNKGEYSFYCSP--HQGAGMVGKVTV 98 A G +F G + ++ G+ G VSbjct: 80 AFVNQCPIASGHSFLYDFHVPDQAGTFWYHSHLSTQYCDGLRGPFVV 126

Rmsd=3.3 ÅModel redStructure blue

HMM packages

• HMMER (http://hmmer.wustl.edu/)– S.R. Eddy, WashU St. Louis. Freely available.

• SAM (http://www.cse.ucsc.edu/research/compbio/sam.html)– R. Hughey, K. Karplus, A. Krogh, D. Haussler and others, UC Santa

Cruz. Freely available to academia, nominal license fee for commercial users.

• META-MEME (http://metameme.sdsc.edu/)– William Noble Grundy, UC San Diego. Freely available. Combines

features of PSSM search and profile HMM search.

• NET-ID, HMMpro (http://www.netid.com/html/hmmpro.html)– Freely available to academia, nominal license fee for commercial

users.– Allows HMM architecture construction.

• EasyGibbs (http://www.cbs.dtu.dk/biotools/EasyGibbs/)– Webserver for Gibbs sampling of proteins sequences

sequence motifs, information content, logos, and hmm’s morten nielsen, cbs, biocentrum, dtu

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