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Algorithms for Finding Genes
Rhys Price Jones
Anne R. Haake
There’s something about
Genes
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The human genome consists of about 3
billion base pairs
Some of that can be transcribed and
translated to produce proteins
Most of it does not
What is it that makes some sequences
of DNA encode protein?
The Genetic Code
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Pick a spot in your sequence
Group nucleotides from that point on in
triplets.
Each triplet encodes for an amino acid,
or a “stop”, or a “start”
TGA, TAG, TAA code for “stop”
But there are exceptions!
Complications
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In the 1960s it was thought that a gene
was a linear structure of nucleotides
directly linked in triplets to amino acids
in the resulting protein
This view did not last long with the
discovery in the late 1960s of genes
within genes and overlapping genes
In 1977, split genes were discovered
Introns and Exons
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Most eukaryotic genes are interrupted by
non-coding sections and broken into pieces
called exons. The interrupting sequences are
called introns
Some researchers have used a biological
approach and searched for splicing sites at
intron-exon junctions
Catalogs of splice sites were created in the
1980s
But unreliable
Can you tell if it’s a gene?
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What is it about some sections of DNA that make
them encode for proteins?
Compare
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TTCTTCTCCAAGAGCAGGGCTTAATTCTATGCTTCCAGGCGAAAGACTGC
ATGGCTAACAAAGCAACGCCTAACACATTCCTAAGCAATTGGCTTGCACC
GTCTTCCCGAGGGTGTTTCTCCAATGGAAAGAGGCGTCGCTGGGCACCC
GCCGGGAACGGCCGGGTGACCACCCGGTCATTGTGAACGGAAGTTTCG
AGA
Is there anything that distinguishes the second from
the first?
We’ll return to this issue
Before we embark on the
biological problem
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We will look at an easier analogy
Sometimes called the Crooked Casino
Basic idea:
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sequence of values generated by one or
more processes
from the values, try to deduce which
process produced which parts of the
sequence
A useful analogy
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The loaded die
I rolled a die 80 times and got
2363662651611344141666324264633142224
2145353556233136631321454662631116546
622542
Some of the time it was a fair die
Some of the time the die produced 6s half the
time and 1-5 randomly the rest of the time
Confession
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(append (fair 20) (loaded 10) (fair 20)
(loaded 10) (fair 20))
(define fair
(lambda (n)
(if (zero? n) '() (cons (1+ (random 6)) (fair (1- n))))))
(define loaded
(lambda (n)
(if (zero? n)
'()
(cons (if (< (random 2) 1) 6 (1+ (random 5))) (loaded (1- n))))))
2363662651611344141666324264633142224
2145353556233136631321454662631116546
622542
There are no computer
algorithms to recognize genes
reliably
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Statistical approaches
Similarity-based approaches
Others
Similarity Methods
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Searching sequences for regions that have
the “look and feel” of a gene (Dan Gusfield)
An early step is the investigation of ORFs
(in Eukaryotes) look for possible splicing sites
and try to assemble exons
Combine sequence comparison and database
search, seeking similar genes
Statistical Approaches
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Look for features that appear frequently in genes but
not elsewhere
As for the loaded die sequence above, that is not
100% reliable
But then, what is? This is Biology and it’s had billions
of years to figure out how to outfox us!
If you want to learn about nature, to appreciate
nature, it is necessary to understand the language
that she speaks in. She offers her information only in
one form; we are not so unhumble as to demand
that she change before we pay any attention. (R.
Feynman)
Relative Frequency of Stop
Codons
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3 of the possible 64 nucleotide triplets are
stop codons
We would thus expect stop codons to form
approximately 5% of any stretch of random
DNA, giving an average distance between
stop codons of about 20 codons
Very long stretches of triplets containing no
stop codons (long ORFs) might, therefore,
indicate gene possibilities
Rather like looking for regions
where my die was fair
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By seeking a shortage of 6s
Similarly, there is (organism-specific) codon
bias of various kinds, and this can be
exploited by gene-finders
People and programs have looked for such
bias features as:
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regularity in codon frequencies
regularity in bicodon frequencies
periodicity
homogeneity vs. complexity
CpG Islands
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CG dinucleotides are often written CpG to
avoid confusion with the base pair C-G
In the human genome CpG is a rarer bird
than would be expected in purely random
sequences (there are chemical reasons for
this involving methylation)
In the start regions of many genes, however,
the methylation process is suppressed, and
CpG dinucleotides appear more frequently
than elsewhere
Rather like looking for
stretches where my die was
loaded
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By seeking a plethora of 6s
But now we’ll look for high incidences
of CpG
How can we detect shortage
or plethora of CpGs?
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Markov Models
Assume that the next state depends
only on the previous state
If the states are x1 x2 ... xn
We have a matrix of probabilities pij
pij is the probability that state xj will
follow xi
Transition matrices
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CpG islands
A
C
A 18 27
C 17 37
G 16 34
T
8 35
G
43
27
37
38
T
12
19
13
18
elsewhere
A
C
A 30 20
C 32 30
G 25 25
T 18 24
G
28
8
30
29
T
21
30
20
29
(adapted from Durbin et al, 1998)
How do we get those
numbers?
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empirically
lots of hard wet and dry lab work
We can think of these numbers as
parameters of our model
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later we’ll pay more attention to model
parameters
For our loaded die example
we have
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0 means non-6
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loaded
0
6
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0
50
50
unloaded
0
0
83
6
83
6
50
50
6
17
17
Discrimination
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Given a sequence x we can calculate a log odds score that it was
generated by one of two models.
S(x) = log (P(x | model A) / P(x | model B))
= sum of log((prob xi-1 to xi in A) / (prob xi-1 to xi in B))
Demonstration
(define beta
(lambda (x y)
(cond
((and (= x
((and (= x
((and (< x
((and (< x
6)
6)
6)
6)
(<
(=
(<
(=
y
y
y
y
6))
6))
6))
6))
(log
(log
(log
(log
(/
(/
(/
(/
.83
.17
.83
.17
.5)))
.5)))
.5)))
.5))))))
(define s
(lambda (l)
(cond
((null? (cdr l)) 0)
(else (+ (beta (car l) (cadr l)) (s (cdr l)))))))
Similar Analysis for CpG
Islands
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Visit the code
(show mary)
(show gene)
(scorecpg mary)
(scorecpg gene)
Sliding Window
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(slidewindow 20 mary)
(show (classify mary))
Hidden Markov Models
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The Markov model we have just seen could be used for locating
CpG islands
For example you could calculate the log odds score of a moving
window of, say 50 nucleotides
Hidden Markov Models try to combine the two models in a
single model
For each state, say x, in the Markov model, we imagine two
states xA and xB for the two models A and B
Both new states “emit” the same character
But we don’t know whether it was CA or CB that “emitted” the
nucleotide C
HMMs
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Hidden Markov Models are so prevalent in
bioinformatics, we’ll just refer to them as HMMs
Given
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a sequence of “emitted signals” -- the observed sequence
and a matrix of transition probabilities and emission
probabilities
For a path of hidden states, calculate the conditional
probability of the sequence given the path
Then try to find an optimal path for the sequence
such that the conditional probability is maximized
HMM “combines” Markov
Models
A+
27
17
16
C+
34
27
43
8
18
35
G+
37
38
13
12
19
T+
29
21
T-
37
18
30
20
29
30
A-
18
25
32
28
G30
8
24
25
20
30
C-
Must be able to move
between models
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Figure out these transition probabilities
A+
C+
G+
T+
TGA-
C-
Add a begin and an end state
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and figure even more transition
probabilities
A+
C+
G+
T+
B
E
TGA-
C-
Basic Idea
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Each state emits a nucleotide (except B and
E)
A+ and A- both emit A
C+ and C- both emit C
You know the sequence of emissions
You don’t know the exact sequences of states
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Was it A+ C+ C+ G- that produced ACCG
Or was it A- C- C+ G-
You want to find the most likely sequence
Parameters of the HMM
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How do we know the transition probabilities
between hidden states?
 empirical, hard lab work
 as above for the CpG island transition
probabilities
 imperfect data will lead to imperfect model
Is there an alternative?
Machine Learning
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Grew out of other disciplines, including statistical
model fitting
Tries to automate the process as much as possible
 use very flexible models
 lots of parameters
 let the program figure them out
Based on ...
 known data and properties
 training sets
Induction and inference
Bayesian Modeling
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Understand the hypotheses (model)
Assign prior probabilities to the
hypotheses
Use Bayes’ theorem (and the rest of
“probability calculus”) to evaluate
posterior probabilities for the
hypotheses in light of actual data
Neural Networks
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Very flexible
Inputs
Thresholds
Weights
Output
Variations:
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additional layers
loops
Training Neural Networks
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Need set of inputs and desired outputs
Run the network with a given input
Compare to desired output
Adjust weights to improve
Repeat...
Training HMMs
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Similar idea
Begin with guesses for the parameters
of the HMM
Run it on your training set, and see how
well it predicts whatever you designed it
for
Use the results to adjust the parameters
Repeat...
Hope that
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When you provide brand new inputs
The trained network will produce useful
outputs
Some gene finder programs
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GRAIL – neural net discriminant
Genie – HMM
GENSCAN – “Semi Markov Model”
GeneParser – neural net
FGENEH etc (Baylor) – Classification by Linear Discrimination
Analysis (LDA) a well-known statistical technique
GeneID – rule-based