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 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 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 Sequence Information

Calculate p a at each position Entropy Information content Conserved positions –P V =1, P REST =0 => S=0, I=log(20) Mutable positions –P aa =1/20 => S=log(20), I=0

Information content A R N D C Q E G H I L K M F P S T W Y V S I

Sequence logos 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

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? ALAKAAAA M ALAKAAAA N ALAKAAAA R ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKV V KLNEPVLLL AVVPFIVSV 10 MHC restricted peptides

Simple motifs Yes/No rules ALAKAAAA M ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKV V KLNEPVLLL AVVPFIVSV 10 MHC restricted peptides 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 motifs Yes/No rules Example Two first peptides will not fit the motif RLLDDTPEV 0.59 GLLGNVSTV 0.71 ALAKAAAAL 0.47 ALAKAAAA M ALAKAAAA N ALAKAAAA R ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKV V KLNEPVLLL AVVPFIVSV 10 MHC restricted peptides

Extended motifs Fitness of aa at each position given by P(aa) Example P1 P A = 6/10 P G = 2/10 P T = P K = 1/10 P C = P D = …P V = 0 Problems –Few data –Data redundancy/duplication ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV

Sequence information Raw sequence counting ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV

Sequence weighting ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV Poor or biased sampling of sequence space Example P1 P A = 2/6 P G = 2/6 P T = P K = 1/6 P C = P D = …P V = 0 } Similar sequences Weight 1/5 Example RLLDDTPEV 0.59 GLLGNVSTV 0.71 ALAKAAAAL 0.47

Sequence weighting ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV

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

A R N D C Q E G H I L K M F P S T W Y V A R N D C Q E G H I L K M F P S T W Y V 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 f a Pseudo frequency for amino acid b Example ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV Pseudo count estimation

ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV 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

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 ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV Weight on pseudo count

Sequence weighting and pseudo counts RLLDDTPEV 0.59 GLLGNVSTV 0.71 ALAKAAAAL 0.47 P 7P and P 7S > 0 ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV

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 q A = 0.070, q W = 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 V

How to score a sequence to a probability matrix? p ij describes a motif The probability that a peptide fits the motif is A R N D C Q E G H I L K M F P S T W Y V

How to score a sequence to a probability matrix? p ij describes a motif The probability that a peptide fits the motif is The probability that the peptide fits a random model is

How to score a sequence to a probability matrix? p ij 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

Weight matrices A weight matrix is given as W ij = log(p ij /q j ) –where i is a position in the motif, and j an amino acid. q j 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

A R N D C Q E G H I L K M F P S T W Y V E G H I L K M F A R N D C Q E G H I L K M F P S T W Y V Example Calculate the weight matrix based on the following observation (use  =50): Sequence = I Important. What is  ? W ij = log(p ij /q j ) q q b|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. W ij = log(p ij /q j )

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 Scoring a sequence to a weight matrix RLLDDTPEV GLLGNVSTV ALAKAAAAL Which peptide is most likely to bind? Which peptide second?

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

Prediction accuracy Pearson correlation 0.45

Predictive performance

End of first part Take a deep breath Smile 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 – Does not tell which die was used Alignment (decoding) can give the most probable solution/path (Viterby) –FFFFFFLLLLLL 1:1/6 2:1/6 3:1/6 4:1/6 5:1/6 6:1/6 Fair 1:1/10 2:1/10 3:1/10 4:1/10 5:1/10 6:1/2 Loaded 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

ACGTACGT ACGTACGT ACGTACGT ACGTACGT ACGTACGT ACGTACGT ACGTACGT 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 = x10 -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 = x10 -2

Align sequence to HMM - Null model Score depends strongly on length Null model is a random model. For length L the score is 0.25 L Log-odds score for sequence S Log( P(S)/0.25 L ) 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 = Note!

Model decoding (Viterby) The unfair casino Example: F L Null FFFFLLL 1: : : : : :-0-78 Fair 1:-1 2:-1 3:-1 4:-1 5:-1 6:-0.3 Loaded Log model 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---I IE--KMKYLTPEVFYTIKAGETVYWVNGEVMPHNVAFKKGIV--GEDAFRGEMMTKD--- -TSVAPSFSQPSF-LTVKEGDEVTVIVTNLDE------IDDLTHGFTMGNHGVAME---V ASAETMVFEPDFLVLEIGPGDRVRFVPTHK-SHNAATIDGMVPEGVEGFKSRINDE---- TKAVVLTFNTSVEICLVMQGTSIV----AAESHPLHLHGFNFPSNFNLVDPMERNTAGVP TVNGQ--FPGPRLAGVAREGDQVLVKVVNHVAENITIHWHGVQLGTGWADGPAYVTQCPI Profile HMM’s Conserved Core: Position with < 2 gaps Deletion Insertion Non-conserved Must have a GAny thing can match

Profile HMM’s All M/D pairs must be visited once L1- Y2A3V4R5- I6P1D2P3P4I4P5D6P7L1- Y2A3V4R5- I6P1D2P3P4I4P5D6P7

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 < Rmsd=3.3

Example continued Smith-Waterman score: 53; 26.2% identity in 61 aa overlap PLC._ IDVLLGADDGSLAFVPSEFSISPG--EKIV-----FKNNAG ::.: :.::.:. :... 1GYC.A ILRYQGAPVAEPTTTQTTSVIPLIETNLHPLARMPVPGSPTPGGVDKALNLAFNFNGTNF PLC._ FPHNIVFDEDSIPSGVDASKISMSEEDLLNAKGETFEVALSNKGEYSFYCSPHQGAGMVG :.: :..: ::: : 1GYC.A FINNASFTPPTVPVLLQILSGAQTAQDLLPAGSVYPLPAHSTIEITLPATALAPGAPHPF PLC._ KVTVN 1GYC.A HLHGHAFAVVRSAGSTTYNYNDPIFRDVVSTGTPAAGDNVTIRFQTDNPGPWFLHCHIDF

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: VFPSPLITGKKGDRFQLNVVDTLTNHTMLKSTSIHWHGFFQAGTNWADGP 79 Query: 57 MSEEDLLNAKGETFEVAL---SNKGEYSFYCSP--HQGAGMVGKVTV 98 A G +F G + ++ G+ G V Sbjct: 80 AFVNQCPIASGHSFLYDFHVPDQAGTFWYHSHLSTQYCDGLRGPFVV 126 Rmsd=3.3 Å Model red Structure blue

Class II MHC binding MHC class II binds peptides in the class II antigen presentation pathway Binds peptides of length 9-18 (even whole proteins can bind!) Binding cleft is open Binding core is 9 aa

Gibbs sampler mer peptides ~10 30 combinations Monte Carlo simulations can do it

Gibbs sampler. Prediction accuracy

HMM packages HMMER ( –S.R. Eddy, WashU St. Louis. Freely available. SAM ( –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 ( –William Noble Grundy, UC San Diego. Freely available. Combines features of PSSM search and profile HMM search. NET-ID, HMMpro ( –Freely available to academia, nominal license fee for commercial users. –Allows HMM architecture construction. EasyGibbs ( –Webserver for Gibbs sampling of proteins sequences