1 Introduction to Bioinformatics 2 Mini Exam 3 3 Mini Exam Take a pencil and a piece of paper Please, not too close to your neighbour There a three

1

Introduction to

Bioinformatics

2

Mini Exam 3

3

Mini Exam

Take a pencil and a piece of paper

Please, not too close to your neighbour

There a three questions. You have in total 15 minutes for writing down short but clear answers

When you are ready please submit your answers to the desk in front

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Mini Exam 3

ANSWERS

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Introduction to Bioinformatics.

LECTURE 4: Hidden Markov Models

* Chapter 4: The boulevard of broken dreams

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Introduction to BioinformaticsLECTURE 4: HIDDEN MARKOV MODELS

4.1 The nose knows

* In 2004 Richard Axel and Linda Buck received the Nobel price for elucidating the olfactory system.

* Odorant Receptors (ORs): sense certain molecules outside the cell and signal inside the cell

* ORs contain 7 transmembrane domains

* OR is single largest gene family in human genome with 1000 genes – same as mice, rat, dog

* Most became pseudogenes – we lost smell due to vision

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4.2 Hidden Markov models

In 1989 Gary Churchill introduced the use of HMM for DNA-segmentation.

CENTRAL IDEAS:

* The string is generated by a system

* The system can be a number of distinct states

* The system can change between states with probability T

* In each state the system emits symbols to the string with

probability E

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4.2 Hidden Markov models

STATE 1 STATE 2

T(1,2)

STATE 3T(2,3)

A: pA

T: pT

C: pC

G: pG

TTCACTGTGAACGATCCGACCAGTACTACG

A: pA

T: pT

C: pC

G: pG

A: pA

T: pT

C: pC

G: pG

ACGTTGCCAAAGCGCTTAT

1111111111111111111111112222222222222333333333333333333333333

s =

h =

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HMM essentials

TRANSITION MATRIX = the probability of a state change:

EMISSION PROBABILITY = symbol probability distribution in a certain state

)|(),( 1 khlhPlkT li

)|(),( khbsPbkE ii

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HMM essentials

INITIAL PROBABILITY of a state :

sequence of the states visited: h

sequence of the generated symbols: s

)(),0( 1 khPkT

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HMM essentials

Probability of the hidden states h:

Probability of generated symbol string s given the hidden states h

),(),(),0()( 1211 nn hhThhThTP h

),(),(),()|( 2211 nn shEshEshEP hs

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HMM essentials

Joint probability of symbol string s and hidden states h:

)()|(),( hhshs PPP

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HMM essentials

Theorem of total probability :

Most likely sequence:

n

jn

j

jjj PPPPHH hh

hhshss )()|(),()(

),(maxarg* hshh

PnH

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EXAMPLE 4.2: Change points in Labda-phage

CG RICH

A: 0.2462C: 0.2476G: 0.2985T: 0.2077

0.9998

AT RICH

A: 0.2700C: 0.2084G: 0.1981T: 0.3236

0.9998

0.0002

0.0002

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EXAMPLE 4.2: Change points in Labda-phage

CG RICH

A: 0.2462C: 0.2476G: 0.2985T: 0.2077

0.9998

AT RICH

A: 0.2700C: 0.2084G: 0.1981T: 0.3236

0.9998

0.0002

0.0002

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4.3 Profile hidden Markov models

* Characterize sets of homologous genes and proteins based on common patterns in their sequence.

* Classis approach: multiple alignments of all elements in the family

* Position Specific Scoring Matrices (PSSM)

* Cannot handle variable lengths or gaps

* Profile HMM (pHHM) can do this

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* See Figure 4.4 for a pHMM for a multiple alignment of:

VIVALASVEGASVIVADA-VI--SVIVADALL--AS

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* Profile HMM (pHMM) allow to summarize the salient features of a protein alignment in one single model

* Also pHMM can be used to produce multiple alignments

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4.4 Finding genes with hidden Markov models

* HMMs are better in detecting genes than sequence alignment

* HMMs can detect introns and exons

* Downside: HMMs are computational much more demanding!

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4.5 Case study: odorant receptors

* The 7-transmembrane (7-TM) G-protein coupled receptors

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EXAMPLE 4.7: odorant receptors

IN

A: 15R: 11...V: 31

P(IN-IN)

OUT

A: 15R: 11...V: 31

P(OUT-OUT)

P(IN-OUT)

P(OUT-IN)

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4.6 Algorithms for HMM computations

Probability of the sequence under the given model is:

the most probable sequence is:

n

jn

j

jjj PPPPHH hh

hhshss )()|(),()(

),(maxarg* hshh

PnH

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The VITERBI Dynamic Programming algorithm

Given a sequence s of length n and an HMM with params (T,E):

1. Create table V of size |H|x(n+1);

2. Initialize i=0; V(0,0)=1; V(k,0)=0 for k>0;

3. For i=1:n, compute each entry using the recursive relation:

V(j,i) = E(j,s(i))*maxk {V(k,i-1)*T(k,j) }

pointer(i,j) = arg maxk {V(k,i-1)*T(k,j) }

4. OUTPUT: P(s,h*) = maxk {V(k,n)}

5. Trace-back: i=n:1, using: h*i-1 = pointer(i, h*i)

6. OUTPUT: h*(n) = maxk {V(k,n)}

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The FORWARD algorithm

Given a sequence s of length n and an HMM with params (T,E):

1. Create table F of size |H|x(n+1);

2. Initialize i=0; F(0,0)=1; V(k,0)=0 for k>0;

3. For i=1:n, compute each entry using the recursive relation:

F(j,i) = E(j,s(i))*∑k {F(k,i-1)*T(k,j) }

pointer(i,j) = arg maxk {V(k,i-1)*T(k,j) }

4. OUTPUT: P(s) = ∑k {F(k,n)}

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The EM (Expectation Maximization) algorithm

Given a sequence s and an HMM with unknown (T,E):

1. Initialize h, E and T;

2. Given s and h estimate E and T just by counting the symbols;

3. Given s, E and T estimate h e.g. with Viterbi-algorithm;

4. Repeat steps 2 and 3 until some criterion is met.

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EXAMPLE:

finding genes with VEIL

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EXAMPLE: finding genes with VEIL

• The Viterbi Exon-Intron Locator (VEIL) was developed by John Henderson, Steven Salzberg, and Ken Fasman at Johns Hopkins University.

• Gene finder with a modular structure:• Uses a HMM which is made up of sub-HMMs each to

describe a different bit of the sequence: upstream noncoding DNA, exon, intron, …

• Assumes test data starts and ends with noncoding DNA and contains exactly one gene.

• Uses biological knowledge to “hardwire” part of HMM, eg. start + stop codons, splice sites.

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The exon sub-model

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Other submodels• The start codon model is very simple:

• The splice junctions are also quite simple and can be hardwired (here is the 5’ splice site):

ExonUpstream a t g

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The overall model

Upstream Start codon Exon

Stop codon

Downstream

3’ splice site 5’ splice siteintron 5’ polyA site

For more details, see J. Henderson, S.L. Salzberg, and K. Fasman (1997) Journal of Computational Biology 4:2, 127-141.

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END of LECTURE 4

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1 Introduction to Bioinformatics 2 Mini Exam 3 3 Mini Exam Take a pencil and a piece of paper Please, not too close to your neighbour There a three