1. CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Sequence information, logos and Hidden Markov Models Morten Nielsen, CBS, BioCentrum, DTU

2. 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

3. 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 II Logo from 10 sequences http://www.cbs.dtu.dk/~gorodkin/appl/plogo.html

4. CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Sequence information Description of binding motif Example 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

5. CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Sequence information Raw sequence counting ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV

6. CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Sequence weighting ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV

7. CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Pseudo counts Sequence weighting and pseudo count Motif found on more data ALAKAAAAM ALAKAAAAN ALAKAAAAR ALAKAAAAT ALAKAAAAV GMNERPILT GILGFVFTM TLNAWVKVV KLNEPVLLL AVVPFIVSV

8. CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU …and now you cp files from /usr/opt/www/pub/CBS/researchgroups/immunology/intro/HMM/exercise Make weight matrix and logos using –pep2mat -swt 2 -wlc 0 data > mat –mat2logo mat –ghostview logo.ps Include sequence weighting –pep2mat -swt 0 -wlc 0 data > mat –make and view logo –Try the other sequence weighting scheme (clustering) -swt 1. What difference does this make? Include pseudo counts –pep2mat data > mat –make and view logo

9. 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

10. CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Weight matrix predictions Use the program seq2hmm to evaluate the prediction accuracy of your weight matrix –seq2hmm -hmm mat -xs eval.set | grep -v # | args 2,3 | xycorr –What is going on here? By leaving out the -xs option you can generate the scores at each position in the sequence. This is often useful for Neural Network training

11. CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU MHC class II prediction Complexity of problem –Peptides of different length –Weak motif signal Alignment crucial Gibbs Monte Carlo sampler RFFGGDRGAPKRG YLDPLIRGLLARPAKLQV KPGQPPRLLIYDASNRATGIPA GSLFVYNITTNKYKAFLDKQ SALLSSDITASVNCAK PKYVHQNTLKLAT GFKGEQGPKGEP DVFKELKVHHANENI SRYWAIRTRSGGI TYSTNEIDLQLSQEDGQTIE DRB1*0401 peptides

12. CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Gibbs sample algorithm RFFGGDRGAPKRG YLDPLIRGLLARPAKLQV KPGQPPRLLIYDASNRATGIPA GSLFVYNITTNKYKAFLDKQ SALLSSDITASVNCAK PKYVHQNTLKLAT GFKGEQGPKGEP DVFKELKVHHANENI SRYWAIRTRSGGI TYSTNEIDLQLSQEDGQTI Alignment by Gibbs sampler E =  i,j p ij * log( p` ij /q i ) Maximize E using MC Random change in offset Random shift on box position Accept moves to higher E always Accept moves to lower E with decreasing probability

13. CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU Gibbs sampler exercise The file clasII.fsa is a FASTA file containing 50 classII epitopes gibbss_mc -iw -w 1,0,0,1,0,1,0,0,1 -m gibbs.mat classII.fsa –The options -iw and -w 1,0,0,1,0,1,0,0,1 increase matrix weight on important anchor positions in binding motif –Make and view logo Use the matrix to predict classII epitopes –cl2pred -mat gibbs.mat classII.eval.dat | grep -v # | args 4,5 | xycorr –Do you understand what is going on in this command?

14. 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

15. 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

16. CENTER FOR BIOLOGICAL SEQUENCE ANALYSISTECHNICAL UNIVERSITY OF DENMARK DTU.8.2 ACGTACGT ACGTACGT ACGTACGT ACGTACGT ACGTACGT ACGTACGT.8.2 1 ACGTACGT.4 1..4 1..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

17. 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 = 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

18. 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 = -0.97 Note!