Gene Finding 1 Exons

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Gene Finding 1 Exons

• http//compbio.uchsc.edu/hunter/bioi7711

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Annotation of Genomic Sequence

• Given the sequence of a genome, we would like to
  be able to identify
• Genes
• Exon boundaries splice sites
• Beginning and end of translation
• Alternative splicings
• Regulatory elements (e.g. promoters)
• Only certain way to do this is experimentally,
  but computational methods can achieve reasonable
  accuracy quickly, and help direct experimental
  approaches.

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Eukaryotic gene structure
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Gene Prediction

• There is no (yet known) perfect method for
  finding genes. All approaches rely on combining
  various weak signals together
• Find elements of a gene
• coding sequences (exons)
• promoters and start signals
• poly-A tails and downstream signals
• Assemble into a consistent gene model
• Use of homologous sequences

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Exon Finding

• Essence of any gene annotation scheme for
  Eukaryotic organisms is exon finding. Simplest
  task, and vital precondition.
• Although information from up- and down- stream
  regions can help, most exon finding approaches
  try to discriminate between exon and non-exon
  sequence.
• Discrimination problems are widely studied in
  statistical inference and machine learning

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ORFs

• ORF Open Reading Frame. Region of sequence
  that has the potential to be translated into a
  protein.
• Six possible reading frames (3 starts x 2
  strands)
• Starts with a atg (met)
• Ends with a stop codon (taa, tag or tga).
• No intervening stop codons
• Not all ORFs are exons, but all exons must be in
  an ORF.

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How to identify ORFs that are exons?

• Observed length distribution is non-random
• Long ORFs more likely to be exons
• Proposed 12 part mixture model of length
  distributions
• Signatures of exons
• CpG islands
• intron splice junctions
• (hexa)nucleotide frequencies
• Signatures of non-exons (repeats, ALUs, etc.)
• Compatibility with surrounding sequence other
  exons (e.g. consistent reading frame)

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CpG Islands

• CpG islands are regions of sequence that have a
  high proportion of CG dinucleotide pairs (p is a
  phoshodiester bond linking them)
• CpG islands are present in the promoter and
  exonic regions of approximately 40 of mammalian
  genes
• Other regions of the mammalian genome contain few
  CpG dinucleotides and these are largely
  methylated
• Definition sequences of gt500 bp with
• GC ? 55
• Observed(CpG)/Expected(CpG) ? 0.65

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Splice junctions

• Most Eukaryotic introns have a consensus splice
  signal GU at the beginning (donor), AG at the
  end (acceptor).
• Variation does occur in the splice sites
• Many AGs and GTs are not splice sites.
• Database of experimentally validated human splice
  sites http//www.ebi.ac.uk/thanaraj/splice.html

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Hexanucleotide frequencies

• Amino acid distributions are biased e.g. p(A) gt
  p(C)
• Pairwise distributions also biasede.g.
  p(AT)/p(A)p(T) gt p(AC)/p(A)p(C)
• Nucleotides that code for preferred amino acids
  (and AA pairs) occur more frequently in coding
  regions than in non-coding regions.
• Codon biases (per amino acid)
• Hexanucleotide distributions that reflect those
  biases indicate coding regions.

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Issues in 6mer frequency

• Sliding window across all 6 reading frames.
• Significance of a score?
• In order to get good statistics on hexamer
  frequencies in an ORF, it has to be long
• Amino acid dimer (and nucleotide hexamer)
  frequencies vary by organism.
• Using frequencies from one organism (or a
  consensus) for another gives a noisier signal yet.

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General challenges

• Short exons are hard to find, but not uncommon.
  Shortest human exon is 3bp!
• First and last exons are particularly difficult
• No bounding intron, so no splice site signal
  (although start and end codons are related
  signals)
• Generally contain non-coding sequence as well as
  coding sequence, so hexamer signals are diluted.
• Alternative splicing means that there are
  multiple true solutions for some genes.

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Probabilistic framework

• We can express all of these weak signals as
  probabilities
• P(exon length)
• P(exon hexamer composition)
• P(exon CpG content)
• P(exon adjacent splice signals)
• etc. etc.
• How to combine them?
• Need to know dependency structure!
• Empirical versus theoretical approaches

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Inductive Learning

• The inference of general rules from a set of
  examples a classic problem in CS, statistics...
• Training examples
• Must be representative (random is best) and
  labeled
• Need an adequate number
• Sometimes benefit from positive and negative
  instances
• Representation (what aspects of examples?)
• Kind of rule to be induced (e.g. linear)
• Algorithm for induction...

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Representation

• Most important aspect of inductive learning
• Most common fixed length feature vector.
• Feature observable value related to task
• Fixed length vector a particular list of
  features which has the same meaning from example
  to example
• Some feature sets (like sequences) have variable
  length or can have variable meaning
• Can translate by sliding window
• Need all the relevant features and not too many
  irrelevant ones (for amount of data)

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HEXON/FEX

• Early, simple approach. Linear discriminant
  analysis (LDA).
• Training set (exons and non-exons)
• Set of features (for internal exons)
• donor/acceptor site recognizers
• octonucleotide preferences for coding region
• octonucleotide preferences for intron interiors
  on either side
• Rule to be induced linear combination of
  features.
• Moderately accurate

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Linear Discriminant Analysis

• Imagine we set a pseudovariable Y to be 1 when
  an example is an exon, and -1 otherwise
• Let the F features in the vector be Xi, i?F
• Do multiple regression over the examples to
  calculate the least squares fit of coefficients a
  and ci to
• For new examples to be tested, if Y gt 0, then
  call it an exon.

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Linear discrimination picture
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HMM for exons

• Large, internal exons only
• Training sequences
• Initial training on 100 nucleotides of intron
• Followed by 100-200 (avg 142) nucleotides of exon
• Followed by 100 nucleotides of intron.
• Found a composition periodicity of size 10,
  apparently due to position in nucleosome.

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Exon HMM periodicity

• Donor and acceptorare clear, as is G rich
  region near donor

10 state circular HMM probability is nearly as
high as linear model!
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GRAIL

• Similar approach to FEX, but different feature
  list, and a neural network to combine features.
• First, uses about 30 manually derived rules to
  exclude impossible candidates (95!)
• Then neural network with these features
• Coding probability (from hexamers)
• GC composition
• length
• splice site signal strength measure
• intron score for adjacent regions

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Neural Networks

• Method for inducing non-linear predictive
  combinations from examples
• Metaphor to real neurons.

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How do NN's work?

• Each node has a value, and each arc a weight
• Values of input nodes are set by each example
• Non-input node are the weighted sum of their
  inputs put through a "squashing" function

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Using a NN for prediction

• Each layer gets inputs only from the layer below
  it, and gives output only to the layer above it.
  A feed forward topology.
• Given the weights and input values, start with
  the inputs and work forward to an output.
• Output node can be normalized to 0-1 for
  probability
• Input to each node is a linear combination, but
  output is non-linear.
• Combination of non-linear combinations can
  approximate a very large number of functions.

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NN discrimination picture
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Where do weights come from?

• Have training examples with known outputs.
• Use the "backpropagation" algorithm
• Start with small random weights
• For each example, use feed forward to calculate
  the predicted outcome.
• Calculate the error (difference between predicted
  and actual outcome) and change the weights to
  reduce the amount of error.
• Repeat.

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How to change the weights

• Calculate an error term for each node
• For the output node, error term (e) target (t)
  output (o)
• Let the derivative of the squashing function be f
  '. Define the error signal to be f '(sum of
  inputs) e
• For non-output nodes, the error term is the sum
  of all of the error signals in the layer above,
  multiplied by the weights connecting them to the
  node.
• ?wierror term ni LWhere ni is the input on
  that weight

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Weight change picture
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?wf '(sum) e ni L
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Neural Network Training Summary

• Calculating the partial derivative of each weight
  with respect to the total error, and moving the
  weight a little bit in the direction that reduces
  error
• A minimization in error space.
• Generally, convergence to a local minimum in
  training error space gives good performance.
• But...

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Overfitting!

• If there are too many weights for the number of
  training examples, or training goes on too long,
  generalization performance will be poor.

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Overfitting picture
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Feature 2
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More on Neural Networks

• Neural Network FAQ (programs, tutorials, etc.)
  ftp//ftp.sas.com/pub/neural/FAQ.html
• Different squashing functions have different
  generalization, e.g. radial basis functions.
• Can add "momentum" term to minimization to avoid
  oscillations
• Other minimization techniques (e.g. conjugate
  gradient descent) can give faster / better
  convergence and eliminate rate parameter

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MZEF

• Michael Zhang's Exon Finder
• Uses more nuanced view of exon (12 different
  categories)
• Fancier models of end regions (e.g. splice sites)
• Quadratic Discrimination Analysis
• Similar to LDA, but more complex function allows
  for curved discrimination surfaces
• Better accuracy than either LDA or NN's in a
  third party comparison.

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QDA picture
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Feature 2
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Readings

• Mount, ch 8, pp. 337-357. Most of this section
  describes Prokaryotic gene identification, which
  is a much easier task. Note that an HMM achieves
  very good accuracy at it.
• Michael Zhang, Computational Prediction of
  Eukaryotic Protein Coding Genes. Nature Reviews
  Genetics 3 698-709. (2002)