CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Sequence motifs, information content, logos, and HMM’s Morten Nielsen, CBS, BioCentrum, DTU

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Outline Multiple alignment and sequence motifs Weight matrix construction 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Sequences weighting 1 - Clustering (slow, but accurate) 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Sequences weighting 2 - Henikoff & Henikoff (fast) w 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 w aa ’ = 1/rs r: Number of different aa in a column s: Number occurrences Normalize  w aa = 1 for each column Sequence weight is sum of w aa in sequence F: r=7 (FYMLPVW), s=4 w’=1/28, w = Y: s=3, w`=1/21, w = M,P,W: s=1, w’=1/7, w = L,V: s=2, w’=1/14, w = 0.109

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Low count correction MLEFVVEADLPGIKA MLEFVVEFALPGIKA MLEFVVEFDLPGIAA YLQDSDPDSFQD GSDTITLPCRMKQFINMWQE RNQEERLLADLMQNYDPNLR YDPNLRPAERDSDVVNVSLK NVSLKLTLTNLISLNEREEA--- --EREEALTTNVWIEMQWCDYR WCDYRLRWDPRDYEGLWVLR--- LWVLRVPSTMVWRPDIVLEN IVLENNVDGVFEVALYCNVL YCNVLVSPDGCIYWLPPAIF PPAIFRSACSISVTYFPFDW---- ********* Limited number of data Poor sampling of sequence space I is not found at position P1. Does this mean that I can never be found at P1? No! Use Blosum matrix to estimate pseudo frequency of I P1

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Low count correction using Blosum matrices # I L V L V Blosum62 substitution frequencies 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Information content Information and entropy –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 = log 2 (N) +  p i log 2 p i (for proteins N=20, DNA N=4) Conserved residue p A =1, p i<>A =0, D = log 2 (N) ( = 4.3 for proteins) Variable region p A =0.05, p C =0.05,.., D = 0

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Sequence logo Height of a column equal to D Relative height of a letter is p A Highly useful tool to visualize sequence motifs High information positions MHC class I

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU More on logos Information content D =  p i log 2 (p i /q i ) Shannon, q i = 1/N = 0.05 D =  p i log 2 (p i ) -  p i log 2 (1/N) = log 2 N +  p i log 2 (p i ) Kullback-Leibler, q i = background frequency –V/L/A more frequent than for instance C/H/W

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Mutual information P(G 1 ) = 2/9 = 0.22,.. P(V 6 ) = 4/9 = 0.44,.. P(G 1,V 6 ) = 2/9 = 0.22, P(G 1 )*P(V 6 ) = 8/81 = 0.10 log(0.22/0.10) > 0 ALWGFFPVA ILKEPVHGV ILGFVFTLT LLFGYPVYV GLSPTVWLS YMNGTMSQV GILGFVFTL WLSLLVPFV FLPSDFFPS P1P6

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Mutual information 313 binding peptides313 random peptides

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Learning higher order correlation Neural networks can learn higher order correlations! –What does this mean? 0 0 => => => => 0 No linear function can learn this pattern

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU End of first part Take a deep breath Smile to you neighbor

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Weight matrices Estimate amino acid frequencies from alignment including sequence weighting and pseudo counts Construct a weight matrix as W ij = log(p ij /q j ) Here i is a position in the motif, and j an amino acid. q j is the prior 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Weight matrix 2 What are log-odds scores? –Does an monthly income of 2000 $ mean that you are rich? –Depends on where you live In Denmark no In Argentina yes –You must always compare your measured value to a background For proteins the background is either the flat distribution 0.05 or the distribution in Swiss-prot In nature not all amino acids are found equally often –P A = 0.070, P W = –Finding 6% A is hence not significant, but 6% W highly significant

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Scoring sequences to a weight matrix A R N D C Q E G H I L K M F P S T W Y V ILYQVPFSV ALPYWNFAT MTAQWWLDA Which peptide bindes the best? Which peptide second?

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Prediction accuracy Pearson correlation 0.45

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Example (cont.) Raw sequence counting –No sequence weighting –No pseudo count –Prediction accuracy 0.45 Sequence weighting –No pseudo count –Prediction accuracy 0.5 ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Example (cont.) Sequence weighting and pseudo count –Prediction accuracy 0.60 Motif found on all data (485) –Prediction accuracy 0.79 ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU.8.2 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU 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!

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU HMM’s and weight matrices In the case of un-gapped alignments HMM’s become simple weight matrices It still might be useful to apply a HMM tool package to estimate a weight matrix –Sequence weighting –Pseudo counts

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU 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

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU 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 Template blue

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU 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 Insertion Deletion Conserved

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Profile HMM’s All M/D pairs must be visited once

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU TMHMM (trans-membrane HMM) (Sonnhammer, von Heijne, and Krogh) Model TM length distribution. Power of HMM. Difficult in alignment.

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Combination of HMM’s - Gene finding x ccc xxxxxxxxATGccc cccTAAxxxxxxxx Inter-genic region Region around start codon Coding region Region around stop codon Start codon Stop codon

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU 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.

CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU trainanhmm Copyright (C) 1998 by Anders Krogh Header {alphabet ACGT;} begin {trans s1 s2;} S1 {trans s2 End;} S2 {trans s1 End;} End {letter NULL;} B S1 S2 End A 0.25 C 0.25 G 0.25 T 0.25 A 0.25 C 0.25 G 0.25 T 0.25