1. Sequence motifs, information content, logos, and HMM’s
Morten Nielsen,
CBS, BioCentrum,
DTU

2. 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

3. 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

4. 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

5. 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

6. Low count correction Limited number of dataP1
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----
*********

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. Mutual information
313 binding peptides
313 random peptides

14. 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

15. 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

16. Example from real life (cont.)
Raw sequence counting
No sequence weighting
No pseudo count
Prediction accuracy 0.45
Sequence weighting
Prediction accuracy 0.5

17. Example from real life (cont.)
Sequence weighting and pseudo count
Prediction accuracy 0.60
Motif found on all data (485)
Prediction accuracy 0.79

18. 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

19. 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

20. 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

21. 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

22. 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!

23. 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

24. 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

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

26. TMHMM (trans-membrane HMM) (Sonnhammer, von Heijne, and Krogh)
Model TM length distribution.
Power of HMM.
Difficult in alignment.

27. 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

28. 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.

29. 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

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