Gene Finding

Finding Genes

• Prokaryotes – Genome under 10Mb– >85% of sequence codes for proteins

• Eukaryotes– Large Genomes (up to 10Gb)– 1-3% coding for vertebrates

Introns

• Humans– 95% of genes have introns– 10% of genes have more than 20 introns– Some have more than 60– Largest Gene (Duchenne muscular dystrophy

locus) spans >2Mb (more than a prokaryote)– Average exon = 150b– Introns can interrupt Open Reading Frame at any

position, even within a codon– ORF finding is not sufficient for Eukaryotic

genomes

Open Reading Frames in Bacteria

• Without introns, look for long open reading frame (start codon ATG, … , stop codon TAA, TAG, TGA)

• Short genes are missed (<300 nucleotides)• Shadow genes (overlapping open reading frames

on opposite DNA strands) are hard to detect• Some genes start with UUG, AUA, UUA and

CUG for start codon• Some genes use TGA to create selenocysteine

and it is not a stop codon

Eukaryotes

• Maps are used as scaffolding during sequencing

• Recombination is used to predict the distance genes are from each other (the further apart two loci are on the chromosome, the more likely they are to be separated by recombination during meiosis)

• Pedigree analysis

Gene Finding in Eukaryotes

• Look for strongly conserved regions• RNA blots - map expressed RNA to DNA• Identification of CPG islands

– Short stretches of CG rich DNA are associated with the promoters of vertebrate genes

• Exon Trapping - put questionable clone between two exons that are expressed. If there is a gene, it will be spliced into the mature transcript

Computational methods

• Signals - TATA box and other sequences– TATA box is found 30bp upstream from about 70%

of the genes

• Content - Coding DNA and non-coding DNA differ in terms of Hexamer frequency (frequency with which specific 6 nucleotide strings are used)– Some organisms prefer different codons for the

same amino acid

• Homology - blast for sequence in other organisms

Genome Browser

• http://genome.ucsc.edu/

• Tables

• Genome browser

Non-coding RNA genes

• Ribosomal rRNA, transfer tRNA can be recognized by stochastic context-free grammars

• Detection is still an open problem

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Hidden Markov Models

(HMMs) • Provide a probabilistic view of a process

that we don’t fully understand

• The model can be trained with data we don’t understand to learn patterns

• You get to implement one for the first lab!!

State Transitions

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Markov Model Example. --x = States of the Markov model -- a = Transition probabilities -- b = Output probabilities -- y = Observable outputs

-How does this differ from a Finite State machine?-Why is it a Markov process?

Example

• Distant friend that you talk to daily about his activities (walk, shop, clean)

• You believe that the weather is a discrete Markov chain (no memory) with two states (rainy, sunny), but you cant observe them directly. You know the average weather patterns

Formal Descriptionstates = ('Rainy', 'Sunny')

observations = ('walk', 'shop', 'clean')

start_probability = {'Rainy': 0.6, 'Sunny': 0.4}

transition_probability = { 'Rainy' : {'Rainy': 0.7, 'Sunny': 0.3}, 'Sunny' : {'Rainy': 0.4, 'Sunny': 0.6}, }

emission_probability = { 'Rainy' : {'walk': 0.1, 'shop': 0.4, 'clean': 0.5}, 'Sunny' : {'walk': 0.6, 'shop': 0.3, 'clean': 0.1}, }

Observations

• Given (walk, shop, clean) – What is the probability of this sequence of

observations? (is he really still at home, or did he skip the country)

– What was the most likely sequence of rainy/sunny days?

MatrixRainy Sunny

walk .6*.1 .4*.6

shop .7*.4 .4*.4 .3*.3 .6*.3

clean .7*.5 .4*.5 .3*.1 .6*.1

Sunny, Rainy, Rainy = (.4*.6)(.4*.4)(.7*.5)

The CpG island problem

• Methylation in human genome– “CG” -> “TG” happens in most places

except “start regions” of genes and within genes

– CpG islands = 100-1,000 bases before a gene starts

• Question– Given a long sequence, how would we find

the CpG islands in it?

Hidden Markov Model

CpG Island

X=ATTGATGCAAAAGGGGGATCGGGCGATATAAAATTTG

OtherOther

How can we identify a CpG island in a long sequence?

Idea 1: Test each window of a fixed number of nucleitidesIdea2: Classify the whole sequence Class label S1: OOOO………….……OClass label S2: OOOO…………. OCC…Class label Si: OOOO…OCC..CO…O…Class label SN: CCCC……………….CC

S*=argmaxS P(S|X)= argmaxS P(S,X)

S*=OOOO…OCC..CO…O

CpG

HMM is just one way of modeling p(X,S)…

A simple HMMParameters

Initial state prob: p(B)= 0.5; p(I)=0.5

State transition prob:p(BB)=0.7 p(BI)=0.3p(IB)=0.5 p(II)=0.5

Output prob:P(a|B) = 0.25,…p(c|B)=0.10…P(c|I) = 0.25 …

P(B)=0.5P(I)=0.5

P(x|B)B I

0.5

0.5P(x|I)

0.7

0.30.5

0.5

P(x|HCpG)=p(x|I)

P(a|I)=0.25P(t|I)=0.25P(c|I)=0.25P(g|I)=0.25

P(x|HOther)=p(x|B)

P(a|B)=0.25P(t|B)=0.40P(c|B)=0.10P(g|B)=0.25

( , , , , )HMM S V B A= Π

( ) : " "i k k ib v prob of generating v at s

A General Definition of HMM

11

{ ,..., } 1N

N ii

π π π=

Π = =∑:i iprob of starting at state sπ

1{ ,..., }MV v v=

1{ ,..., }NS s s=N states

M symbols

Initial state probability:

1

{ } 1 , 1N

ij ijj

A a i j N a=

= ≤ ≤ =∑State transition probability:

1

{ ( )} 1 , 1 ( ) 1M

i k i kk

B b v i N k M b v=

= ≤ ≤ ≤ ≤ =∑

Output probability::ij i ja prob of going s s→

How to “Generate” a Sequence?

B I

0.7

0.30.5

0.5

P(x|B) P(x|I)

P(B)=0.5 P(I)=0.5

B I BB BII I

I I IB BBI I… …

Given a model, follow a path to generate the observations.

model

Sequence

states

P(a|B)=0.25P(t|B)=0.40P(c|B)=0.10P(g|B)=0.25

P(a|I)=0.25P(t|I)=0.25P(c|I)=0.25P(g|I)=0.25

a c g t t …

How to “Generate” a Sequence?

B I

0.7

0.30.5

0.5

P(x|B) P(x|I)

P(B)=0.5 P(I)=0.5

model

Sequence

P(a|B)=0.25P(t|B)=0.40P(c|B)=0.10P(g|B)=0.25

P(a|I)=0.25P(t|I)=0.25P(c|I)=0.25P(g|I)=0.25

a c g t t …

a

B I BII

tgc

0.50.3

P(“BIIIB”, “acgtt”)=p(B)p(a|B) p(I|B)p(c|I) p(I|I)p(g|I) p(I|I)p(t|I) p(B|I)p(t|B)

0.50.50.5

0.40.250.250.250.25

t

HMM as a Probabilistic Model

1 2 1 2 1 1 1 2 1 2 2 1( , ,..., , , ,..., ) ( ) ( | ) ( | ) ( | )... ( | ) ( )T T T T T Tp O O O S S S p S p O S p S S p O S p S S p O S−=

1 2 1 2 1 1( , ,..., ) ( ) ( | )... ( | )T T Tp S S S p S p S S p S S −=

Time/Index: t1 t2 t3 t4 …Data: o1 o2 o3 o4 …

Observation variable: O1 O2 O3 O4 …

Hidden state variable: S1 S2 S3 S4 …

Random variables/process

Sequential data

Probability of observations (incomplete likelihood):

1

1 2 1 2 1,...

( , ,..., ) ( , ,..., , ,... )T

T T TS S

p O O O p O O O S S= ∑

1 2 1 2 1 1 2 2( , ,..., | , ,..., ) ( | ) ( | )... ( | )T T T Tp O O O S S S p O S p O S p O S=

Joint probability (complete likelihood):

State transition prob:

Probability of observations with known state transitions:

Init state distr.

State trans. prob.

Output prob.