center for biological sequence analysistechnical university of denmark dtu sequence motifs,...
TRANSCRIPT
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Sequence motifs, information content, logos, and HMM’s
Morten Nielsen,
CBS, BioCentrum,
DTU
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Outline
• Pattern recognition– Regular expression and
probabilities• Information content
– Sequence logos• Multiple alignment and sequence
motifs
• Weight matrix construction– Sequence weighting– Low (pseudo) counts
• Example from the real world• HMM’s and profile HMM’s
– Viterbi decoding– TMHMM (trans-membrane
protein) • Links to HMM packages
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MHC class I with peptideMHC class I with peptide
http://www.nki.nl/nkidep/h4/neefjes/neefjes.htm
Anchor positions
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How to predict MHC binding?
• Structure based– Molecular dynamics– Calculate binding energy explicitly
• Sequence based– Forget about the MHC molecule it self!– Learn binding motif from peptides known to bind MHC
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Sequence informationSLLPAIVEL 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
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Sequence Information
• Calculate pa at each position• Entropy
• 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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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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Sequence logo
• Height of a column equal to I• Relative height of a letter is p• Highly useful tool to visualize sequence
motifs
High information positions
HLA-A0201
http://www.cbs.dtu.dk/~gorodkin/appl/plogo.html
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Characterizing a binding 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
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Simple motifs Yes/No rules
ALAKAAAAM
ALAKAAAAN
ALAKAAAAR
ALAKAAAAT
ALAKAAAAV
GMNERPILT
GILGFVFTM
TLNAWVKVV
KLNEPVLLL
AVVPFIVSV
10 MHC restricted peptides
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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 P3 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
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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
ALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV
10 MHC restricted peptides
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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
ALAKAAAAM
ALAKAAAAN
ALAKAAAAR
ALAKAAAAT
ALAKAAAAV
GMNERPILT
GILGFVFTM
TLNAWVKVV
KLNEPVLLL
AVVPFIVSV
Example: RLLDDTPEV 0.59 GLLGNVSTV 0.71 ALAKAAAAL 0.47
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Sequence information Raw sequence counting
ALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV
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Sequence weighting
ALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV
• Poor or biased sampling of sequence space
• Example P1PA = 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
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Sequence weighting
ALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV
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Pseudo counts
ALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV
• 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
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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)
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• Calculate observed amino acids frequencies fa
• Pseudo frequency for amino acid b
• Example
Pseudo count estimation
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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
ALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV
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ALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV
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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• 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
ALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV
Weight on pseudo count
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Sequence weighting and pseudo counts
RLLDDTPEV 0.59GLLGNVSTV 0.71ALAKAAAAL 0.47
P7p and P7s > 0
ALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV
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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
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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
• PA = 0.070, PW = 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
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How to score a sequence to a probability matrix?
• pij describes a motif
• The probability that a 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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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
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• 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
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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
ALAKAAAAMALAKAAAANALAKAAAARALAKAAAATALAKAAAAVGMNERPILTGILGFVFTMTLNAWVKVVKLNEPVLLLAVVPFIVSV
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Prediction accuracy
Pearson correlation 0.45
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Predictive performance
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End of first part
Take a deep breath
Smile to you neighbor
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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
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Why hidden?
• Model generates numbers– 312453666641
• Does not tell which die was used
• Alignment (decoding) can give the most probable solution/path (Viterby)
– FFFFFFLLLLLL
• Or most probable set of states– FFFFFFLLLLLL
1:1/62:1/63:1/64:1/65:1/66:1/6
Fair
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
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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
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.8
.2
ACGT
ACGT
ACGT
ACGT
ACGT
ACGT.8
.8 .8.8
.2.2.2
.2
1
ACGT .2
.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
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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
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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 = 5.3
AGA---ATC = 4.9
ACCG--ATC = 4.6
Consensus:
ACAC--ATC = 6.7
ACA---ATC = 6.3
Exceptional:
TGCT--AGG = -0.97
Note!
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Model decoding (Viterbi)The unfair casino
Example: 1245666
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
-0.05
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
Log model
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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
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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
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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
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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
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Profile HMM’s
All M/D pairs must be visited once
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ExampleSequence 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
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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 redTemplate blue
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TMHMM (trans-membrane HMM)(Sonnhammer, von Heijne, and Krogh)
Model TM length distribution.Easy in HMM.Difficult in alignment.
Difference in amino acid composition. Easy in HMM. Difficult in alignment.
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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.
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trainanhmm 1.221Copyright (C) 1998 by Anders Krogh
Header {alphabet 123456;}
begin {
trans Fair:0.5 Loaded:0.5;
}
Fair {
trans Fair:0.95 Loaded:0.05;
}
Loaded {
trans Fair:0.1 Loaded:0.9;
letter 6:0.5;
}
1:1/62:1/63:1/64:1/65:1/66:1/6
Fair
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