Alignment scoring matrices and evolution
ORF Graphs: types of edges
ATG  TAG (single exon gene)
ATG  GT (initial coding exon)
GT  AG (intron)
AG  GT (internal exon)
AG  TAG (terminal coding exon)
TAG  ATG (intergenic region)
Conceptual framework for
gene finding with ORF graphs
1. Given an input sequence S, compute the ORF
graph G for S.
2. Score the vertices and edges in G using some
scoring strategy or function, f.
3. Extract the highest-scoring valid parse  from G
according to f.
Common assumptions
• No overlapping genes
– reasonably safe
• No nested genes
– reasonably safe
• No partial genes
– limiting; needs to be relaxed for real gene
finders
Common assumptions (continued)
• No non-canonical splice sites or start
codons
– GTG, TTG common start sites in bacteria
– GC-AG and AT-AC introns present in plants
and animals
• No frame shifts or sequencing errors
– OK for finished sequence
Common assumptions (continued)
• Optimal parse only
– useful, but if we allow the gene finder more
guesses it may do better
• Constraints on exon/intron lengths
– max sizes needed for practical reasons
– but, human introns can be >100,000 bp
– for now we just miss those
Common assumptions (continued)
• No split start/stop codons
– introns can occur right in the middle of an
ATG or TAG/TGA/TAA!
– (most of) today’s gene finders will miss
these
• No alternative splicing
– some species have an average of 2
alternative splicing products per gene
– researchers actively working on this
Common assumptions (continued)
• No selenocysteine codons
– encoded by TGA
• No ambiguity codes
– R = purine = A or G
– Y = pyrimidine = C or T
– other codes for all possible ambiguous
base calls
The (Eukaryotic) Gene Prediction Problem
exons
ATG…..GT…..AG…………GT….AG……..TAG
UTR
UTR
introns
Gene prediction is the problem of parsing a sequence into
nonoverlapping coding segments (CDSs) consisting of exons separated
by introns. Untranslated regions (UTR) are rarely predicted.
This parsing problem can be visualized as one of choosing the best
path through the graph of all open reading frames (ORFs):
slide courtesy of Bill Majoros
Some Eukaryotic Gene-finding Programs
GenScan
TwinScan
Genie
SGP2
TWAIN
Augustes
JIGSAW
VEIL
GrailEXP
SNAP
GenomeScan
FGenesH
SLAM
GlimmerHMM
EuGène
Unveil
Morgan
Exonomy
GeneZilla
DoubleScan
SGP1
GlimmerM
GeneMark
HMMgene
Grail
Phat
GAZE
gray boxes = developed in Salzberg lab
slide courtesy of Bill Majoros
Similarities Between Gene-finding Programs
slide courtesy of Bill Majoros
Gene Finding Strategies
Gene finding programs can be classified into several types:
(1) ad hoc. These apply an ad hoc scoring function to the set of all
ORFs and then predict only those ORFs scoring above a predefined
threshold. Examples are GRAIL and GlimmerM.
(2) probabilistic. These adopt a rigorous probabilistic model of
sequence structure and choose the most probable parse according to
that probabilistic model. Examples are GenScan and GeneZilla.
(3) homology-based. These utilize evidence in the form of homology.
These can be either ad hoc (eg., GrailEXP) or probabilistic (eg.,
TwinScan, Slam, Twain).
(4) combiners. These combine multiple forms of evidence, such as the
predictions of other gene finders, and use ad hoc methods to arrive at a
consensus prediction. Examples include Ewan Birney’s Ensembl and
Jonathan Allen’s JIGSAW.
slide courtesy of Bill Majoros
Probabilistic Gene Finders
Review of Probability Theory
P(x) denotes the probability of event x occurring. P(x)=0.25 means, for
example, that x occurs 25% of the time. P(x)=1 implies that the event x is
certain to occur. P(x)=0 implies that x cannot occur.
The probability of events x and y both occurring is denoted by:
P(x, y) or P(x  y)
(joint probability)
P(x | y) denotes the probability of event x occurring, given that y has
occurred, or given that y is a true statement. If P(y)≠0 then:
P(x | y) = P(x, y) / P(y)
(conditional probability)
so that:
P(x, y) = P(x | y) × P(y)
(multiplication rule)
If x and y are independent then:
P(x, y) = P(x) × P(y),  P(x | y) = P(x).
(independence)
slide courtesy of Bill Majoros
Review of Probability Theory
If x and y are mutually exclusive (i.e., can’t both happen), then:
(the addition rule)
P(x  y) = P(x) + P(y).
If an experiment is guaranteed to yield one of a set of mutually exclusive
events {x1,x2,…,xn} then
n
Σ P(x ) = 1
i=1
(partitioning rule)
i
If a set of events {x1,x2,…,xn} are all pairwise mutually independent then:
n
P(x1, x2, …, xn) = Π P(xi)
(independence)
i=1
PM(x)=P(x|M) is an estimate of P(x) according to model M. (prob. model)
slide courtesy of Bill Majoros
Ab initio Gene Finding = Modeling
Computational gene prediction is generally carried out as follows:
1. We formulate a mathematical model M which describes some
method for generating DNA sequences and their gene structures. That
is, M generates pairs of the form (S, ) for sequence S and gene
structure .
2. Using a set T of known genes, we customize or “train” the model so
that the sequences and gene structures which M generates have the
same statistical properties as the real genes in T.
3. Given an un-annotated sequence S, we pretend that M generated S,
even though we know that it did not. (Evolution and the cellular
machinery generated it, not our model!)
4. Since we assume that M generated S, we can determine precisely how
likely it is for M to have generated it—i.e., the precise intron/exon
boundaries that M would have imposed while it was generating S.
slide courtesy of Bill Majoros
A Model Generates Sequences and Gene Structures
The underlying model of a gene finder generates both sequences and
their gene structures. These can be denoted as pairs of the form
(S,) for sequence S and gene structure .
gene structure
M
exon 1
exon 2
exon 3
AGCTAGCAGTCGATCATGGCATTATCGGCCGTAGTACGTAGCAGTAGCTAGTAGCAGTCGATAGTA
sequence
slide courtesy of Bill Majoros
The Model Parameters Affect the Model’s Output
The parameters to M determine the statistical properties of the
sequences and gene models which it generates (both the structural
properties of the gene models and frequences of individual bases).
M
AGCTAGCAGTCGATCATGGCATTATCGGCCGTAGTACGTAGCAGTAGCTAGTAGCAGTCGATAGTA
6,23,843,924…
M
TAGGCTCTATTAGCGCTATGCTACGTTATATTCTGATGTGTGATCGTATCTATATATCGATCTAGG
45,2,8214,32…
M
CCCTATCGCGCGCGCGCTATCACACACACTACGCGTCATTATCTTACTGAGCGCGCGCTATCGTAT
11,413,7,235,8…
slide courtesy of Bill Majoros
Tuning the Model to Obtain Optimal Behavior
The parameters to M can be tuned to make its outputs most similar
to the set of known genes:
known
AGCTAGCAGTCGATCATGGCATTATCGGCCGTAGTACGTAGCAGTAGCTAGTAGCAGTCGATAGTA
M
modify
parms
predicted
CGCGCTATCGATCGATCATCTGCGATCGTATATGCTACGGTCGTAGCTAGCTGATCGATCGATCGC
6,23,843,924…
AGCTAGCAGTCGATCATGGCATTATCGGCCGTAGTACGTAGCAGTAGCTAGTAGCAGTCGATAGTA
M
Still
dissimilar
TGCTGCTATATGCTACGAGCATCTAGCTGACTTATCGCGCGCTAGCTAGCATCGATCGATCTAGCG
45,2,8214,32…
modify
parms
AGCTAGCAGTCGATCATGGCATTATCGGCCGTAGTACGTAGCAGTAGCTAGTAGCAGTCGATAGTA
M
11,413,7,235,8…
similar
AGCTTTCAGTCGATCCCGGCATTATCGGCCGTAGCCCGTAGGGGTAGCTAGTACGCATCGATAGTA
slide courtesy of Bill Majoros
Using the Model to Predict Gene Structure
Given an input sequence, we can ask what gene structure the model
is most likely to have generated at the same time that it generated
that sequence:
parameter file
Gene Finder XYZ
11,413,7,235,8…
M
sequence S
AGCTAGTACG…
Suppose M was invoked
1,000,000,000,000,000,000
(Si,i) times. Collect those pairs
(Si,i) where Si=S. Among
those pairs, which gene
structure  is most
common? Emit that .
gene structure 
argmax

P ( | S )
(maximum a
posteriori, MAP)
slide courtesy of Bill Majoros