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

Morten Nielsen, CBS, BioCentrum, DTU

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**Outline Multiple alignments and sequence motifs**

Weight matrices and consensus sequence Sequence weighting Low (pseudo) counts Information content Sequence logos Mutual information Example from the real world HMM’s and profile HMM’s TMHMM (trans-membrane protein) Gene finding Links to HMM packages

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**Multiple alignment and sequence motifs**

Core Consensus sequence Weight matrices Problems Sequence weights Low counts MLEFVVEADLPGIKA MLEFVVEFALPGIKA MLEFVVEFDLPGIAA YLQDSDPDSFQD ---GSDTITLPCRMKQFINMWQE ---RNQEERLLADLMQNYDPNLR YDPNLRPAERDSDVVNVSLK------ NVSLKLTLTNLISLNEREEA--- ----EREEALTTNVWIEMQWCDYR WCDYRLRWDPRDYEGLWVLR--- --LWVLRVPSTMVWRPDIVLEN IVLENNVDGVFEVALYCNVL- YCNVLVSPDGCIYWLPPAIF PPAIFRSACSISVTYFPFDW---- ********* FVVEFDLPG Consensus

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**Sequences weighting 1 - Clustering**

MLEFVVEADLPGIKA MLEFVVEFALPGIKA MLEFVVEFDLPGIAA YLQDSDPDSFQD ---GSDTITLPCRMKQFINMWQE ---RNQEERLLADLMQNYDPNLR YDPNLRPAERDSDVVNVSLK------ NVSLKLTLTNLISLNEREEA--- ----EREEALTTNVWIEMQWCDYR WCDYRLRWDPRDYEGLWVLR--- --LWVLRVPSTMVWRPDIVLEN IVLENNVDGVFEVALYCNVL- YCNVLVSPDGCIYWLPPAIF PPAIFRSACSISVTYFPFDW---- ********* } Homologous sequences Weight = 1/n (1/3) Consensus sequence YRQELDPLV Previous FVVEFDLPG

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**Sequences weighting 2 - (Henikoff & Henikoff)**

FVVEADLPG 0.37 FVVEFALPG 0.43 FVVEFDLPG 0.32 YLQDSDPDS 0.59 MKQFINMWQ 0.90 LMQNYDPNL 0.68 PAERDSDVV 0.75 LKLTLTNLI 0.85 VWIEMQWCD 0.84 YRLRWDPRD 0.51 WRPDIVLEN 0.71 VLENNVDGV 0.59 YCNVLVSPD 0.71 FRSACSISV 0.75 Waa’ = 1/rs r: Number of different aa in a column s: Number occurrences Normalize so S Waa= 1 for each column Sequence weight is sum of Waa F: r=7 (FYMLPVW), s=4 w’=1/28, w = 0.055 Y: s=3, w`=1/21, w = 0.073 M,P,W: s=1, w’=1/7, w = 0.218 L,V: s=2, w’=1/14, w = 0.109

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**Low count correction Limited number of data**

P1 Limited number of data Poor sampling of sequence space I is not found at position P1. Does this mean that I is forbidden? No! Use Blosum matrix to estimate pseudo frequency of I MLEFVVEADLPGIKA MLEFVVEFALPGIKA MLEFVVEFDLPGIAA YLQDSDPDSFQD -GSDTITLPCRMKQFINMWQE -RNQEERLLADLMQNYDPNLR -----YDPNLRPAERDSDVVNVSLK------ NVSLKLTLTNLISLNEREEA--- --EREEALTTNVWIEMQWCDYR WCDYRLRWDPRDYEGLWVLR--- LWVLRVPSTMVWRPDIVLEN IVLENNVDGVFEVALYCNVL- YCNVLVSPDGCIYWLPPAIF PPAIFRSACSISVTYFPFDW---- *********

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**Low count correction using Blosum matrices**

Every time for instance L/V is observed, I is also likely to occur Estimate low (pseudo) count correction using this approach As more data are included the pseudo count correction becomes less important Blosum62 substitution frequencies # I L V L V NL = 2, NV=2, Neff=12 => fI = (2* *0.1646)/12 = 0.05 pI* = (Neff * pI + b * fI)/(Neff+b) = (12*0 + 10*0.05)/(12+10) = 0.02

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**Information content Information and entropy Shannon information**

Conserved amino acid regions contain high degree of information (high order == low entropy) Variable amino acid regions contain low degree of information (low order == high entropy) Shannon information D = log2(N) + S pi log2 pi (for proteins N=20, DNA N=4) Conserved residue pA=1, pi<>A=0, D = log2(N) ( = 4.3 for proteins) Variable region pA=0.05, pC=0.05, .., D = 0

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**Sequence logo Height of a column equal to D**

MHC class II Logo from 10 sequences Height of a column equal to D Relative height of a letter is pA Highly useful tool to visualize sequence motifs High information position

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**Frequency matrix Frequencies x 100**

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

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**More on Logos Information content Shannon, qi = 1/N = 0.05**

D = S pi log2 (pi/qi) Shannon, qi = 1/N = 0.05 D = S pi log2 (pi) - S pi log2 (1/N) = log2 N - S pi log2 (pi) Kullback-Leibler, qi = background frequency V/L/A more frequent than for instance C/H/W

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**Mutual information ALWGFFPVA ILKEPVHGV ILGFVFTLT LLFGYPVYV GLSPTVWLS**

YMNGTMSQV GILGFVFTL WLSLLVPFV FLPSDFFPS I(i,j) = Saai Saaj P(aai, aaj) * log[P(aai, aaj)/P(aai)*P(aaj)] P(G1) = 2/9 = 0.22, .. P(V6) = 4/9 = 0.44,.. P(G1,V6) = 2/9 = 0.22, P(G1)*P(V6) = 8/81 = 0.10 log(0.22/0.10) > 0

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Mutual information 313 binding peptides 313 random peptides

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**Weight matrices Wij = log(pij/qj)**

Estimate amino acid frequencies from alignment inc. sequence weighting and pseudo counts Now a weight matrix is given as Wij = log(pij/qj) Here 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 Score sequences to weight matrix by looking up and adding L values from matrix

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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 on 528 peptides ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV

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**Example from real life (cont.)**

Raw sequence counting No sequence weighting No pseudo count Prediction accuracy 0.45 Sequence weighting Prediction accuracy 0.5

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**Example from real life (cont.)**

Sequence weighting and pseudo count Prediction accuracy 0.60 Motif found on all data (485) Prediction accuracy 0.79

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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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**HMM (a simple example) Example from A. Krogh**

Core region defines the number of states in the HMM (red) Insertion and deletion statistics is derived from the non-core part of the alignment (blue) ACA---ATG TCAACTATC ACAC--AGC AGA---ATC ACCG--ATC Core of alignment

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**HMM construction ACA---ATG TCAACTATC ACAC--AGC AGA---ATC ACCG--ATC .4**

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 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 0.8x1x0.8x1x0.8x0.4x1x0.8x1x0.2 = 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 = 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

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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-odd score for sequence S Log( P(S)/0.25L) 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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**HMM’s and weight matrices**

Note. In the case of un-gapped alignments HMM’s become simple weight matrices It still might be useful to use a HMM tool package to estimate a weight matrix Sequence weighting Pseudo counts

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**Profile HMM’s Insertion Deletion**

EM55_HUMAN WWQGRVEGSSKESAGLIPSPELQEWRVASMAQSAP--SEAPSCSPFGKKKK-YKDKYLAK CSKP_HUMAN WWQGKLENSKNGTAGLIPSPELQEWRVACIAMEKTKQEQQASCTWFGKKKKQYKDKYLAK KAPB_MOUSE PENLLIDHQGYIQVTDFGFAKRVKG NRC2_NEUCR PENILLHQSGHIMLSDFDLSKQSDPGGKPTMIIGKNGTSTSSLPTIDTKSCIANF EM55_HUMAN HSSIFDQLDVVSYEEVVRLPAFKRKTLVLIGASGVGRSHIKNALLSQNPEKFVYPVPYTT CSKP_HUMAN HNAVFDQLDLVTYEEVVKLPAFKRKTLVLLGAHGVGRRHIKNTLITKHPDRFAYPIPHTT KAPB_MOUSE RTWTLCGTPEYLAPEIILSKGYNKAVDWWALGVLIYEMAAGYPPFFADQPIQIYEKIVSG NRC2_NEUCR RTNSFVGTEEYIAPEVIKGSGHTSAVDWWTLGILIYEMLYGTTPFKGKNRNATFANILRE EM55_HUMAN RPPRKSEEDGKEYHFISTEEMTRNISANEFLEFGSYQGNMFGTKFETVHQIHKQNKIAIL CSKP_HUMAN RPPKKDEENGKNYYFVSHDQMMQDISNNEYLEYGSHEDAMYGTKLETIRKIHEQGLIAIL KAPB_MOUSE KVRFPSHF-----SSDLKDLLRNLLQVDLTKRFGNLKNGVSDIKTHKWFATTDWIAIYQR NRC2_NEUCR DIPFPDHAGAPQISNLCKSLIRKLLIKDENRRLG-ARAGASDIKTHPFFRTTQWALI--R EM55_HUMAN NNGVDETLKKLQEAFDQACSSPQWVPVSWVY CSKP_HUMAN NNEIDETIRHLEEAVELVCTAPQWVPVSWVY KAPB_MOUSE EKCGKEFCEF NRC2_NEUCR ENAVDPFEEFNSVTLHHDGDEEYHSDAYEKR Deletion

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**All M/D pairs must be visited once**

Profile HMM’s All M/D pairs must be visited once

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**TMHMM (trans-membrane HMM) (Sonnhammer, von Heijne, and Krogh)**

Model TM length distribution. Power of HMM. Difficult in alignment.

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**Combination of HMM’s - Gene finding**

Start codon Stop codon x xxxxxxxxATGccc ccc cccTAAxxxxxxxx Inter-genic region Region around start codon Coding region Region around stop codon

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**HMM packages NET-ID, HMMpro (http://www.netid.com/html/hmmpro.html)**

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.

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**Simple Hmmer command hmmbuild --gapmax 0.0 --fast A2.hmmer A2.fsa**

hmmbuild - build a hidden Markov model from an alignment HMMER 2.2g (August 2001) Alignment file: A2.fsa File format: a2m Search algorithm configuration: Multiple domain (hmmls) Model construction strategy: Fast/ad hoc (gapmax 0.0) Null model used: (default) Sequence weighting method: G/S/C tree weights Alignment: #1 Number of sequences: 232 Number of columns: 9 Determining effective sequence number done. [192] Weighting sequences heuristically done. Constructing model architecture done. Converting counts to probabilities done. Setting model name, etc done. [A2.fasta] Constructed a profile HMM (length 9) Average score: bits Minimum score: bits Maximum score: bits Std. deviation: bits hmmbuild --gapmax 0.0 --fast A2.hmmer A2.fsa >HLA-A Example_for_Ligand SLLPAIVEL YLLPAIVHI TLWVDPYEV SXPSGGXGV GLVPFLVSV

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

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