Download Gene Finding - Brigham Young University

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
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?
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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 Description
states = ('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?
Matrix
Rainy
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
X=ATTGATGCAAAAGGGGGATCGGGCGATATAAAATTTG
Other
CpG Island
Other
How can we identify a CpG island in a long sequence?
Idea 1: Test each window of a fixed number of nucleitides
Idea2: Classify the whole sequence
Class label S1: OOOO………….……O
Class 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 HMM
0.7
P(B)=0.5
P(I)=0.5
0.5
Parameters
0.3
B
Initial state prob:
p(B)= 0.5; p(I)=0.5
I
P(x|B)
P(x|I)
0.5
State transition prob:
p(BB)=0.7 p(BI)=0.3
p(IB)=0.5 p(II)=0.5
P(x|HOther)=p(x|B)
P(x|HCpG)=p(x|I)
P(a|B)=0.25
P(t|B)=0.40
P(c|B)=0.10
P(g|B)=0.25
P(a|I)=0.25
P(t|I)=0.25
P(c|I)=0.25
P(g|I)=0.25
Output prob:
P(a|B) = 0.25,
…
p(c|B)=0.10
…
P(c|I) = 0.25 …
A General Definition of HMM
HMM  ( S ,V , B, A, )
Initial state probability:
N states
S  {s1 ,..., sN }
  { 1 ,...,  N }
N

i 1
i
1
 i : prob of starting at state si
State transition probability:
M symbols
V  {v1 ,..., vM }
A  {aij }
Output probability:
B  {bi (vk )}
1 i  N, 1 k  M
1  i, j  N
N
a
j 1
aij : prob of going si  s j
M
 b (v )  1
k 1
i
k
bi (vk ) : prob of " generating " vk at si
ij
1
P(x|B)
How to “Generate” a
Sequence?
0.7
P(x|I)
0.5
0.3
P(a|B)=0.25
P(t|B)=0.40
P(c|B)=0.10
P(g|B)=0.25
B
P(B)=0.5
a c g t
B
I
I
I
I
I
I
B
P(a|I)=0.25
P(t|I)=0.25
P(c|I)=0.25
P(g|I)=0.25
I
0.5
t
P(I)=0.5
…
B
model
Sequence
B
I
B
states
B
I
I
B
……
Given a model, follow a path to generate the observations.
How to “Generate” a
Sequence?
P(x|B)
0.7
0.5
0.3
P(a|B)=0.25
P(t|B)=0.40
P(c|B)=0.10
P(g|B)=0.25
B
0.5
a c g t t
0.5
B
0.3
I
0.25
a
0.5
0.25
c
P(a|I)=0.25
P(t|I)=0.25
P(c|I)=0.25
P(g|I)=0.25
I
P(B)=0.5
0.5
I
0.25
g
0.5
Sequence
B
0.25
t
model
P(I)=0.5
…
I
P(x|I)
0.4
t
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)
HMM as a Probabilistic Model
t2
o2
t3
o3
t4 …
o4 …
Observation variable: O1
O2
O3
O4 …
Hidden state variable: S1
S2
S3
S4 …
Time/Index: t1
Data:
o1
Sequential data
Random
variables/
process
State transition prob:
p(S1 , S2 ,..., ST )  p(S1 ) p( S2 | S1 )... p( ST | ST 1 )
Probability of observations with known state transitions:
p(O1 , O2 ,..., OT | S1 , S2 ,..., ST )  p(O1 | S1 ) p(O2 | S2 )... p(OT | ST )
Joint probability (complete likelihood): Init state distr. Output prob.
p(O1 , O2 ,..., OT , S1 , S2 ,..., ST )  p( S1 ) p(O1 | S1 ) p( S2 | S1 ) p(O2 | S2 )... p( ST | ST 1) p(OT ST )
Probability of observations (incomplete likelihood):
p(O1 , O2 ,..., OT )   p(O1 , O2 ,..., OT , S1 ,...ST )
S1 ,...ST
State trans. prob.