# Hidden Markov Models What are the good for? - PowerPoint PPT Presentation

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Hidden Markov Models What are the good for?. Morten Nielsen CBS. Absolutely nothing!. Objectives. Introduce Hidden Markov models and understand that they are just weight matrices with gaps See the beauty of sequence profiles Position specific scoring matrices (PSSMs)

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Hidden Markov Models What are the good for?

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Morten Nielsen

CBS

## Absolutely nothing!

### Objectives

• Introduce Hidden Markov models and understand that they are just weight matrices with gaps

• See the beauty of sequence profiles

• Position specific scoring matrices (PSSMs)

• Understand what biological problems are best described using HMM’s

• And which are not!

What is an HMM

What are they good for?

How to construct an HMM

How to “score” a sequence to an HMM

Viterbi decoding

Profile HMMs

TMHMM

### Markov Models

• A model with no memory

• What I decide depends only on “state” now, not on what I have learned in the past

• No dependence on i-1, i-2 …

### A Markov model?

• No memory

• Model generates numbers

• 312453666641

The unfair casino: Loaded dice p(6) = 0.5; switch fair to load:0.05; switch load to fair: 0.1

0.9

0.95

1:1/6

2:1/6

3:1/6

4:1/6

5:1/6

6:1/6

1:1/10

2:1/10

3:1/10

4:1/10

5:1/10

6:1/2

0.05

0.10

Fair

### Why hidden?

• Model generates numbers

• 312453666641

• Does not tell which dice was used

• Alignment (decoding) can give the most probable solution/path (Viterby)

• FFFFFFLLLLLL

• Or most probable set of states

• FFFFFFLLLLLL

The unfair casino: Loaded dice p(6) = 0.5; switch fair to load:0.05; switch load to fair: 0.1

0.9

0.95

1:1/6

2:1/6

3:1/6

4:1/6

5:1/6

6:1/6

1:1/10

2:1/10

3:1/10

4:1/10

5:1/10

6:1/2

0.05

0.10

Fair

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)

### HMM (a simple example)

Core of alignment

### HMM construction

• 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

TCAACTATC

ACAC--AGC

AGA---ATC

ACCG--ATC

.4

.2

A

C

G

T

.4

.2

.2

.6

.6

.8

A

C

G

T

A

C

G

T

A

C

G

T

.8

A

C

G

T

1

A

C

G

T

A

C

G

T

1.

1.

1.

1.

.4

.8

.2

.8

.2

.2

.2

.8

.2

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=0.0075x10-2

ACAC--AGC =1.2x10-2

Consensus:

ACAC--ATC =4.7x10-2, ACA---ATC =13.1x10-2

Exceptional:

TGCT--AGG =0.0023x10-2

Score depends strongly on length

Null model is a random model. For length L the score is 0.25L

Log-odds score for sequence S

Log( P(S)/0.25L)

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

### Align sequence to HMM - Null model

Note!

Example: 1245666. What was the series of dice used to generate this output?

Log model

-0.05

-0.02

1:-0.78

2:-0.78

3:-0.78

4:-0.78

5:-0.78

6:-0-78

1:-1

2:-1

3:-1

4:-1

5:-1

6:-0.3

-1.3

-1

Fair

### Dynamic programming: computation of scores

T C G C A

T

C

C

A

Any given point in matrix can only be reached from three possible positions (you cannot “align backwards”).

=> Best scoring alignment ending in any given point in the matrix can be found by choosing the highest scoring of the three possibilities.

x

Each new score is found by choosing the maximum of three possibilities. For each square in matrix: keep track of where best score came from.

Fill in scores one row at a time, starting in upper left corner of matrix, ending in lower right corner.

score(x,y-1) - gap-penalty

score(x-1,y-1) + substitution-score(x,y)

score(x-1,y) - gap-penalty

score(x,y) = max

Example: 1245666. What was the series of dice used to generate this output?

Log model

-0.05

-0.02

1:-0.78

2:-0.78

3:-0.78

4:-0.78

5:-0.78

6:-0-78

1:-1

2:-1

3:-1

4:-1

5:-1

6:-0.3

-1.3

-1

Fair

Log model

-0.05

-0.02

1:-0.78

2:-0.78

3:-0.78

4:-0.78

5:-0.78

6:-0-78

1:-1

2:-1

3:-1

4:-1

5:-1

6:-0.3

-1.3

-1

Fair

Log model

-0.05

-0.02

1:-0.78

2:-0.78

3:-0.78

4:-0.78

5:-0.78

6:-0-78

1:-1

2:-1

3:-1

4:-1

5:-1

6:-0.3

-1.3

-1

Fair

### Model decoding (Viterby)

Identify what series of dice was used to generate this output?

Log model

-0.05

-0.02

1:-0.78

2:-0.78

3:-0.78

4:-0.78

5:-0.78

6:-0-78

1:-1

2:-1

3:-1

4:-1

5:-1

6:-0.3

-1.3

-1

Fair

### Model decoding (Viterby)

Series of dice is FFFFLLL

### HMM’s and weight matrices

• In the case of un-gapped alignments HMM’s become simple weight matrices

.4

X

.2

A

C

G

T

.4

.2

.2

.6

.6

.8

A

C

G

T

A

C

G

T

A

C

G

T

.8

A

C

G

T

1

A

C

G

T

A

C

G

T

1.

1.

1.

1.

.4

.8

.2

.8

.2

.2

.2

.8

.2

### HMM construction

.8

A

C

G

T

A

C

G

T

A

C

G

T

.8

A

C

G

T

1

A

C

G

T

A

C

G

T

1.

1.

1.

1.

1.

.8

.2

.8

.2

.2

.2

.8

.2

ACA---ATG sco = 0.8x1x0.8x1x0.8x1x1x1x0.8x1x0.2 = 3.3x10-2 or

Log-sco = log(0.8)+log(0.8)+log(0.8)+log(1)+log(0.8)+log(0.2)

### 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

### HMMs. What are they good for?

• 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

### 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

### What goes wrong when Blast fails?

• Conventional sequence alignment uses a (Blosum) scoring matrix to identify amino acids matches in the two protein sequences

### Alignment scoring matrices

• Blosum62 score matrix. Fg=1. Ng=0?

### Alignment scoring matrices

• Blosum62 score matrix. Fg=1. Ng=0?

• Score =2+6+6+4-1=17

LAGDS

I-GDS

### What goes wrong when Blast fails?

• Conventional sequence alignment uses a (Blosum) scoring matrix to identify amino acids matches in the two protein sequences

• This scoring matrix is identical at all positions in the protein sequence!

EVVFIGDSLVQLMHQC

X

X

X

X

X

X

AGDS.GGGDS

1PLC._

1PLB._

1PLC._

1PMY._

### Sequence profiles

• In reality not all positions in a protein are equally likely to mutate

• Some amino acids (active cites) are highly conserved, and the score for mismatch must be very high

• Other amino acids can mutate almost for free, and the score for mismatch should be lower than the BLOSUM score

• Sequence profiles can capture these differences

Non-conserved

Insertion

Conserved

Deletion

Must have a G

Any thing can match

### Profile HMM’s

TVNGAI--PGPLIAERLKEGQNVRVTNTLDEDTSIHWHGLLVPFGMDGVPGVSFPG---I

-TSMAPAFGVQEFYRTVKQGDEVTVTIT-----NIDQIED-VSHGFVVVNHGVSME---I

IE--KMKYLTPEVFYTIKAGETVYWVNGEVMPHNVAFKKGIV--GEDAFRGEMMTKD---

-TSVAPSFSQPSF-LTVKEGDEVTVIVTNLDE------IDDLTHGFTMGNHGVAME---V

ASAETMVFEPDFLVLEIGPGDRVRFVPTHK-SHNAATIDGMVPEGVEGFKSRINDE----

TKAVVLTFNTSVEICLVMQGTSIV----AAESHPLHLHGFNFPSNFNLVDPMERNTAGVP

Core: Position with < 2 gaps

### HMM vs. alignment

• Detailed description of core

• Conserved/variable positions

• Price for insertions/deletions varies at different locations in sequence

• These features cannot be captured in conventional alignments

1K7C.A

1WAB._

### Profile HMM’s

All M/D pairs must be visited once

L1-Y2A3V4R5-I6

P1D2P3P4I4P5D6P7

### 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 < 10-22. Rmsd=3.3

### Example continued

Score = 97.1 bits (241), Expect = 9e-22

Identities = 13/107 (12%), Positives = 27/107 (25%), Gaps = 17/107 (15%)

F + G++ N+ + +G + +

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

### HMMs. What are they good for II

• Trans membrane helix proteins

### HMMs. What are they good for II

• Transmembrane helix proteins

TMHMM. A. Krogh, 2001

### HMM packages

• HMMER(http://hmmer.wustl.edu/)

• S.R. Eddy, WashU St. Louis. Freely available.

• SAM (http://www.cse.ucsc.edu/research/compbio/sam.html)

• 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 (http://metameme.sdsc.edu/)

• William Noble Grundy, UC San Diego. Freely available. Combines features of PSSM search and profile HMM search.

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