Comp. Genomics

Recitation 911/3/06Gene finding using HMMs & Conservation

Outline

• Gene finding using HMMs• Adding trees to HMMs

• phyloHMM• N-SCAN

• BLAST+ Gene Finding• SGP2

• Examples

3

Markov Sequence Models

• Key: distinguish coding/non-coding statistics• Popular models:

• 6-mers (5th order Markov Model)• Homogeneous/non-homogeneous (reading frame

specific)

• Not sensitive enough for eukaryote genes: exons too short, poor detection of splice junctions

• Simple HMMs can only encode genometric length distributions

• The length of each exon (intron) :

CG © Ron Shamir, 2008 4

Length Distribution

exon intronp q

1-p

1-q

(length ) (1 )kP k p p

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Exon Length Distribution

• The length distribution of introns is ≈ geometric

• For exons, it isn’t: also affected by splicing itself:• Too short (under 50bps): the spliceosomes have no room• Too long (over 300bps): ends have problems finding each

other.• But as usual there are exceptions.

• A different model for exons is needed• A different model is needed for exons.

CG © Ron Shamir, 2008 6

Generalized HMM(Burge & Karlin, J. Mol. Bio. 97 268 78-94)

• Instead of a single char, each state omits a sequence with some length distribution

CG © Ron Shamir, 2008 7

Generalized HMM(Burge & Karlin, J. Mol. Bio. 97 268 78-94)

•Overview:• Hidden Markov states q1,…qn

• State qi has output length distribution fi

• Output of each state can have a separate probabilistic model (weight matrix model, HMM…)

• Initial state probability distribution • State transition probabilities Tij

CG © Ron Shamir, 2008 8

Burge & Karlin JMB 97

GenScan Model

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GenScan model

•states = functional units on a gene•The allowed transitions ensure the

order is biologically consistent.•As an intron may cut a codon, one

must keep track of the reading frame, hence the three I phases:

• phase I0: between codons

• phase I1:: introns that start after 1st base

• phase I2 : introns that start after 2nd base

Phylogenetic HMMs

• Due to Siepel and Haussler• A simple gene-finding HMM looks at

a single Markov process:• Along the sequence: each position is

dependent on the previous position• If we incorporate sequences from

multiple organisms, we can look at another process:• Along the tree: each position is

dependent on its ancestor

Phylogenetic HMMs

• A simple HMM can be thought of as a machine that generates a sequence• Every state omits a single character• Multinomial distribution at every state

• A phyloHMM generates an MSA • Every state omits a single MSA column• Phylogenetic model at every state

Phylogenetic HMMs

Phylogenetic models in phyloHMM

• Defines a stochastic process of substitution• Every position is independent• The following process occurs:

• A character is assigned to the root• The character substitution occur based of

some substitution matrix and based on the branch lengths

• The characters at the leaves of the tree correspond to the MSA column

Phylogenetic models in phyloHMM

• Different models for different states:• Different substitution rates

• E.g., in exons, we’ll see less substitutions

• Different patterns of substitutions• E.g., third position bias in coding sequences

• Different tree topologies• E.g., following recombination

Formally

• S – set of states• Ψ – phylogenetic models (instead of

E in a standard HMM)• A – state transitions• b – initial probabilities

Formally

• Q – substitution rate matrix (e.g., derived from PAM)

• Π – background frequencies• τ – the phylogenetic tree• β – branch lengths

Formally

• - Probability of a column Xi

being omitted by the model ψi

• Can be computed efficiently by Felsenstein’s “pruning algorithm” (recitation 6)

• Joint probability of a path in the HMM and and alignment X

• Viterbi, forward-backward etc. – as usual

Simple phylo-gene-finder

Non-coding

3rd position

• If the parameters are known – Viterbi can be used to find the most probably path – segmentation into coding regions

Phylo-gene-finder is a good idea

• Use of phylogeny is important:• Imposes structure on the substitutions• Weights different pairs differently based

on the evolutionary distance

N-SCAN

• Another phylogeny-HMM-gene-finder• A GHHM that emits MSA columns• Annotates one sequence at a time: the

target sequence• Distinguishes between a target sequence

– T and other informative sequences (Is) that may contain gaps

• States correspond to sequence types in the target sequence

N-SCAN

• Bayesian network instead of a simple evolutionary model

• Accounts for:• 5’ UTRs• Conserved non-coding

• Highly conserved • No “coding” features

SGP-2

• Drawback of the described approaches: require meaningful alignment• Impossible if one of the genomes is not

yet finished• An alignment is not necessary “correct”

SGP-2

• A framework working on two genomes• Idea:

• Use BLAST to identify which positions are more/less conserved

• Feed the BLAST scores into the gene-finding HMM

• The BLAST results serve to modify the scores of the exons.

SGP-2

BACH1

OLIG2

PPM1A

Summary

• Different approaches for gene finding• Adding phylogeny generally helps• But

• What about genes/exons which are specific to humans

• Ape genomes are not (almost) available and too similar

• Phylogenetic help almost essential in more difficult problems• Motif finding (promoter analysis)• Ultraconserved regions with no evident function