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Applications of Hidden Markov Models

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Applications of Hidden Markov Models

(Lecture for CS397-CXZ Algorithms in Bioinformatics)

March 6, 2004

ChengXiang Zhai

Department of Computer Science

University of Illinois, Urbana-Champaign

- HMM Applications
- Profile HMMs (Classification)
- HMMs for Multiple Sequence Alignment (Pattern discovery)
- HMMs for Gene Finding (Segmentation)

- Special issues in HMMs
- Local Maximas
- Model construction
- Weighting training sequences

- Classification (e.g., Profile HMMs)
- Build an HMM for each class (profile HMMs)
- Classify a sequence using Bayes rule

- Multiple sequence alignment
- Build an HMM based on a set of sequences
- Decode each sequence to find a multiple alignment

- Segmentation (e.g., gene finding)
- Use different states to model different regions
- Decode a sequence to reveal the region boundaries

E.g., Protein families

Assign a family to X

p(X|C) is modeled by a profile HMM built specifically for C

Assuming example sequences are available for C

- Given a set of sequences S={X1, …,Xk}
- Train an HMM, e.g., using Baum-Welch (finding the HMM that maximizes the probability of S)
- Decode each sequence Xi
- Assemble the Viterbi paths to form a multiple alignment (insertions are uncertain)

- Design two types of states
- “Within Gene” States
- “Outside Gene” States

- Use known genes to estimate the HMM
- Decode a new sequence to reveal which part is a gene
- Example software:
- GENSCAN (Burge 1997)
- FGENESH (Solovyev 1997)
- HMMgene (Krogh 1997)
- GENIE (Kulp 1996)
- GENMARK (Borodovsky & McIninch 1993)
- VEIL (Henderson, Salzberg, & Fasman 1997)

Exon HMM Model

Upstream

3’ Splice Site

Start Codon

Exon

Intron

Stop Codon

5’ Splice Site

Downstream

5’ Poly-A Site

- Enter: start codon or intron (3’ Splice Site)
- Exit: 5’ Splice site or three stop codons (taa, tag, tga)

VEIL Architecture

(Slide from N. F. Samatova’s lecture)

It is based on Generalized HMM (GHMM)

Model both strands at once

Other models: Predict on one strand first, then on the other strand

Avoids prediction of overlapping genes on the two strands (rare)

Each state may output a string of symbols (according to some probability distribution).

Explicit intron/exon length modeling

Special sensors for Cap-site and TATA-box

Advanced splice site sensors

Fig. 3, Burge and Karlin 1997

- Local maxima
- Optimal model construction
- Weighting training sequences

- Repeat with different initializations
- Start with the most reasonable initial model
- Simulated annealing (slow down the convergence speed)

Global maxima

Local maxima

Good starting point

Bad starting point

Bayesian model selection:

P(HMM) should prefer simpler models

- Avoid over-counting similar sequences from the same organisms
- Typically compute a weight for a sequence based on an evolutionary tree
- Many ways to incorporate the weights, e.g.,
- Unequal likelihood
- Unequal weight contribution in parameter estimation

- SAM-T98 Tutorial:
- http://www.cse.ucsc.edu/research/compbio/ismb99.tutorial.html

- Pfam
- http://www.sanger.ac.uk/Software/Pfam/