CSE182-L9

Gene Finding (DNA signals)Genome Sequencing and

assembly

An HMM for Gene structure

Gene Finding via HMMs

• Gene finding can be interpreted as a d.p. approach that threads genomic sequence through the states of a ‘gene’ HMM. – Einit, Efin, Emid,

– I, IG (intergenic)

Einit

I

Efin

Emid

IG

Note: all links are not shown here

i

Generalized HMMs, and other refinements

• A probabilistic model for each of the states (ex: Exon, Splice site) needs to be described

• In standard HMMs, there is an exponential distribution on the duration of time spent in a state.

• This is violated by many states of the gene structure HMM. Solution is to model these using generalized HMMs.

Length distributions of Introns & Exons

Generalized HMM for gene finding

• Each state also emits a ‘duration’ for which it will cycle in the same state. The time is generated according to a random process that depends on the state.

Forward algorithm for gene finding

j i

qk

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Fk (i) = P qkj<i

∑ (X j ,i) fqk ( j − i +1) alkl∈Q

∑ Fl ( j)

Emission Prob.: Probability that you emitted Xi..Xj in state qk (given by the 5th order markov model)

Forward Prob: Probability that you emitted i symbols and ended up in state qk

Duration Prob.: Probability that you stayedin state qk for j-i+1 steps

De novo Gene prediction: Summary

• Various signals distinguish coding regions from non-coding

• HMMs are a reasonable model for Gene structures, and provide a uniform method for combining various signals.

• Further improvement may come from improved signal detection

DNA Signals

• Coding versus non-coding• Splice Signals• Translation start

ATG

5’ UTR

intron

exon3’ UTR

AcceptorDonor splice siteTranscription start

Translation start

DNA signal example:

• The donor site marks the junction where an exon ends, and an intron begins.

• For gene finding, we are interested in computing a probability – D[i] = Prob[Donor site at position i]

• Approach: Collect a large number of donor sites, align, and look for a signal.

PWMs

• Fixed length for the splice signal.• Each position is generated independently

according to a distribution• Figure shows data from > 1200 donor

sites

321123456321123456AAGAAGGTGTGAGTGAGTCCGCCGGTGTAAGTAAGTGAGGAGGTGTGAGGGAGGTAGTAGGTGTAAGGAAGG

Improvements to signal detection

• Pr[GGGTGTAA] is a donor site? – 0.5*0.5

• Pr[CCGTGTAA] is a donor site?– 0.5*0.5

• Is something wrong with this explanation?

GGGTGTAAGGGTGTAAGGGTGTAAGGGTGTAACCGTGTGGCCGTGTGGCCGTGTGGCCGTGTGG

MDD

• PWMs do not capture correlations between positions• Many position pairs in the Donor signal are correlated

Maximal Dependence Decomposition

• Choose the position i which has the highest correlation score.

• Split sequences into two: those which have the consensus at position i, and the remaining.

• Recurse until <Terminating conditions>– Stop if #sequences is ‘small enough’

MDD for Donor sites

Gene prediction: Summary

• Various signals distinguish coding regions from non-coding

• HMMs are a reasonable model for Gene structures, and provide a uniform method for combining various signals.

• Further improvement may come from improved signal detection

How many genes do we have?

Nature

Science

Alternative splicing

Comparative methods

• Gene prediction is harder with alternative splicing.• One approach might be to use comparative methods to

detect genes• Given a similar mRNA/protein (from another species,

perhaps?), can you find the best parse of a genomic sequence that matches that target sequence• Yes, with a variant on alignment algorithms that penalize

separately for introns, versus other gaps.• There is a genome sequencing project for a different Hirudo

species. You could compare the Hirudo ESTs against the genome to do gene finding.

Comparative gene finding tools

• Procrustes/Sim4: mRNA vs. genomic• Genewise: proteins versus genomic• CEM: genomic versus genomic• Twinscan: Combines comparative and de novo

approach.• Mass Spec related?

– Later in the class we will consider mass spectrometry data.

– Can we use this data to identify genes in eukaryotic genomes? (Research project)

Databases

• RefSeq and other databases maintain sequences of full-length transcripts/genes.

• We can query using sequence.

Course• Sequence Comparison

(BLAST & other tools)• Protein Motifs:

– Profiles/Regular Expression/HMMs

• Discovering protein coding genes– Gene finding HMMs– DNA signals (splice

signals)

• How is the genomic sequence itself obtained?

Protein sequence analysis

ESTs

Gene finding

Silly Quiz

• Who are these people, and what is the occasion?

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Genome Sequencing and Assembly

DNA Sequencing

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• DNA is double-stranded

• The strands are separated, and a polymerase is used to copy the second strand.

• Special bases terminate this process early.

Sequencing

• A break at T is shown here.

• Measuring the lengths using electrophoresis allows us to get the position of each T

• The same can be done with every nucleotide. Fluorescent labeling can help separate different nucleotides

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• Automated detectors ‘read’ the terminating bases.

• The signal decays after 1000 bases.

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Sequencing Genomes: Clone by Clone

• Clones are constructed to span the entire length of the genome.

• These clones are ordered and oriented correctly (Mapping)

• Each clone is sequenced individually

Shotgun Sequencing

• Shotgun sequencing of clones was considered viable

• However, researchers in 1999 proposed shotgunning the entire genome.

Library

• Create vectors of the sequence and introduce them into bacteria. As bacteria multiply you will have many copies of the same clone.

Sequencing

Questions

• Algorithmic: How do you put the genome back together from the pieces? Will be discussed in the next lecture.

• Statistical? • EX: Let G be the length of the genome, and L

be the length of a fragment. How many fragments do you need to sequence?– The answer to the statistical questions had already

been given in the context of mapping, by Lander and Waterman.

Lander Waterman Statistics

G

L€

G = Genome LengthL = Clone LengthN = Number of ClonesT = Required Overlapc = Coverage = LN/Gα = N/Gθ = T/Lσ = 1-θ

Island

LW statistics: questions

• As the coverage c increases, more and more areas of the genome are likely to be covered. Ideally, you want to see 1 island.• Q1: What is the expected number of islands?

• Ans: N exp(-c)• The number

increases at first, and gradually decreases.

Analysis: Expected Number Islands

• Computing Expected # islands.• Let Xi=1 if an island ends at position i,

Xi=0 otherwise.• Number of islands = ∑i Xi

• Expected # islands = E(∑i Xi) = ∑i E(Xi)

Prob. of an island ending at i

• E(Xi) = Prob (Island ends at pos. i)

• =Prob(clone began at position i-L+1

AND no clone began in the next L-T positions)

iL

T

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E(X i) =α 1−α( )L−T

=αe−cσ

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Expected # islands = E(X i) =i

∑ Gαe−cσ = Ne−cσ

LW statistics

• Pr[Island contains exactly j clones]?• Consider an island that has already begun. With

probability e-c, it will never be continued. Therefore• Pr[Island contains exactly j clones]=

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(1− e−cσ ) j−1e−cσ

• Expected # j-clone islands

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=Ne−cσ (1− e−cσ ) j−1e−cσ

Expected # of clones in an island

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ecσ

Why?

Expected length of an island

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Lecσ −1

c

⎛

⎝ ⎜

⎞

⎠ ⎟+ (1−σ )

⎡

⎣ ⎢

⎤

⎦ ⎥