Diapositiva 1

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• Developing computational methodologies

• for genome transcript mapping

Daniela Bianchi, Raffaele Calogero, Brunello
Tirozzi
Department of Physics, University La Sapienza
Bioinformatics and Genomics Unit, Turin
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Structure of the thesis
Aim of the thesis
Understanding the mechanisms underlying
transcription expression modulation
I have investigated the efficacy of Kohonen
algorithm

• Part 1.
• Transcription expression clustering
• Part 2
• Promoter structure analysis

I have addressed the problem of motifs detection
in putative promoter regions
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WHAT DOES IT MEAN GENE CLUSTERING?

• It means to divide the interval, to which the
  expression levels of genes belong, into an
  optimal partition.

The partition is optimal if the associated global
classification error E is minimal
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CLASSIFICATION

• Let I a partition of the interval (0,A) in N
  disjoint intervals.
• Let ?i i 1,N, the centers of such
  intervals.
• Then a given gene is classified ?i if x Ii.
• The classification error is

x-?i
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KOHONEN NETWORK

• It is an artificial neural network with a single
  layer of neurons.
• Each neuron is associated with a weight ?i, the
  center of atom Ii.
• The number of neurons is equal to the number of
  atoms.
• When an input pattern x is presented to the
  network this input is mapped to the neuron with
  the closest weigth. The weight changes during
  the learning process and tends to the values of
  the distribution of the input data.

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LEARNING OF KOHONEN NETWORK

• A data point x is presented to the network and
  all the differences
• ?i (0)- x
• are computed
• The winner neuron is chosen, in such way it is
  the neuron v with minimal difference
• ?v (0)- x
• The weight of this neuron is changed, or in some
  case the weigths of neighboring neurons are
  changed.
• This procedure is repeated with another input
• At the end of process the set of input data is
  partitioned in disjoint sets (the clusters) and
  the weights associated with neurons are the
  values of the centers of partition s groups (the
  fixed values which the weights converge).

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UPDATE RULE

• Each weight vector is updated by

?i(n1) ?i(n) ?(n) G (i,v) ( ?(n1) - ?i(n) )
where 0?(n)lt 1 and ?(n) ?(n1)
?(n) is called the learning parameter and it is
basic for the algorithm convergence G (i,v) is
called the neighborhood function of the winner
and determines the width of the activation area
near the winner
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NEIGHBORHOOD FUNCTION (1/2)

• A convenient choice is

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NEIGHBORHOOD FUNCTION (2/2)
Another choice is
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THE ORDER

• Remembering that for order configuration in one
  dimension means

The Kohonen network has the property of order
If Kohonen learning algorithm applied to one
dimensional configuration of weights converges,
the configuration orders itself at a certain step
of the process. The same order is preserved at
each subsequent step of the algorithm.
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THE PARAMETER ? (n)
The convergence of Kohonen algorithm strongly
depends on the rate of decay of the learning
parameter ?(n)
I have seen numerically that the there is no
convergence ( in mean o not almost everywhere)
I have seen numerically that the there is
convergence in mean (but not almost everywhere)
I have seen numerically that the there is
convergence almost everywhere
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Parameter of neighborhood function

• The convergence of the Kohonen algorithm depends
  also on the values of parameters concerning the
  neighborhood function

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Numerical analysis (1/3)

• I run the algorithm 1000 times
• I used sets of uniformly distributed data in
  (0,1) containing 4000, 10000,20000,30000,60000,12
  0000,150000,250000 elements
• The procedure was done for all the mentioned ?(n)
  and both ? and h.

I had 1000 cases of weights limit values at the
end of the algorithm running
Results the mean value of these cases converged
to the center of the optimal partition of the
interval (0,1) for the previous mentioned ?(n)
and both ? and h.
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Numerical analysis (2/3)
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Numerical analysis (3/4)
The average error of limit weights with respect
to the exact values of the centers decreases on
increasing the number of iterations using ? the
error decreases more quickly.
The almost everywhere convergence of the
algorithm is obtained
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Numerical analysis (4/4)
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APPLICATIONS

• I applied Kohonen network to microarrays data
  generated using a breast cancer mouse model.
• Data were derived by the paper Quaglino et al.
  JCI 2004.
• The authors studied the effect of HER2 DNA
  vaccination to halt breast cancer progression in
  BALB-neuT mice. A small set of genes (34) only
  associated to the transcriptional profile of the
  vaccinated mice was identified by hierarchical
  agglomerative clustering.

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RESULTS
Using this approach I identified 34 genes
described in the paper and I also managed to
identify a subset of other vaccination specific
genes (25) that could not be discovered using the
clustering approach described in paper of
Quaglino.

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Conclusion
(FIRST PART)

• Kohonen network in one dimension converges
  almost everywhere for appropriate learning
  parameters and that makes it powerful and more
  adaptable
• It has the drawback of the choice of number of
  clusters
• The Kohonen algorithm in more than one dimension
  works well but there exists only a sufficient
  proof of the convergence

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Promoter structure analysis
It is basic to define the most likely
transcription factor binding locations on the
promoter
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Binding site models

• Matrix representation
• Position weight matrix
• Energy matrix
• String-based representation
• Consensus sequence

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Position weight matrix (1/2)
Every element of matrix is the number of times
each nucleotide is found at every position of an
alignment
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Position weigth matrix (2/2)

• From this matrix
• Position specific frequency matrix (PSFM)
• Log-odds matrix
• Information content

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Searching binding sites

• De novo method
• Novel motifs which are enriched are found
• Scanning method
• Using a given motif model a genome sequence is
  scanned to find more motif matches

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Motif detection
To find instances of a given motif I have used a
PSFM and a higher order background model.
A higher background model means that a DNA
sequence can be generated with a Markov model of
order m
Observation this type of score is log likelihood
ratio of observing the data given a motif model
versus a model of DNA background. Therefore a
high score at a specific position suggests high
degree of the presence of motif in that
particular location of DNA sequence
I have computed score as
Where
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Statistical significance of scores (1/2)

• Is the score unlikely to have arisen by chance?

To answer it is necessary to know the p-value of
the score x
P-value of the score x
(score of the match of the motif with a given DNA
sequence)
If the p-value is very low the motif is
significantly represented in the DNA sequence
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Statistical signficance of scores (2/2)
P-value of the score of the motif match with a
random sequence (identically independent model,
iid all the position in the sequence have the
same distributions and are independent of each
other)
It is a good approach to reduce the number of
false positive matches of the motif
It does not give the right information on the
over representation of the motif in a given DNA
sequence
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Extreme theory value

• Extreme value theory (EVT) provides a framework
  to formalize the study of behaviour in the tails
  of a distribution. EVT allows us to use extreme
  observations to measure the density in the tail.

Peak over threshold (POT) Analysis of large
observations which exceed a high threshold
The problem is to estimate the distribution
function Fu Fu(y)P(X-uyXgtu)P(YyXgtu),
0yxF-u

yx-u, xF right endpoint
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Applications

• I have applied the mentioned studies to a set of
  promoter regions of human DNA (2836 sequences)
  containg at least one regulatory estrogen
  responsive element (ERE).

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Preliminary analysis (1/2)

• Making histograms, box-plots,tests for normality

The data set is not normally distributed but its
distribution tends towards the gaussian
distribution
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Preliminary analysis (2/2)

• Analysis on random sequences ( all positions
  have the same letter distribution and are
  independet of each other)

The distribution of the sum of iid variables over
0,a is

• I have checked
• the normality
• type of extreme value distribution
• the Von Mises condition

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Results

• Focusing the attention on detection one ERE at
  once
• the distribution of maximum of scores using
  random sequences is almost like a Weibull
  distribution (only 2/100 are not like a Weibull)
• the distribution of maximum of scores using DNA
  sequences is mainly like a Weibull. There are
  413/2836 score sequences which are like a Frechet
  and 13 which are Gumbel.

I show the result of
These genes have been proved to contain at least
one ERE by ChIP
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Results
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Results
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Results
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Results

• Detection of two EREs

I have applied the same procedure mentioned
previously considering also the distance between
the two EREs

• Only for some particular distances I have
  detected a couple of EREs
• The position for one of the two EREs of the
  couple is the same position found biologically.
• A relatevely high homology is conserved for the
  mouse ortholog in the 3 genes
• Only for the DVL1 gene the high homology is
  conserved for the three orthologs ( mouse, rat,
  dog)

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Conclusion (1/2)

• I have improved the detection of motifs
• Using a higher order of background
• Computing scores for two or three motifs
• Using POT on both DNA and random sequences
• Testing the pvalue

The model fits well it is able to detect those
gene validated by ChIP and which are considered
in literature containing at least one ERE.
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Conclusion (2/2)

• Problems
• Analyzing more than three motifs the model
  creates files with critic dimension.

• Future work
• Detecting different motifs
• Implementing new biologically results in the
  model
• Implementing a single routine in R

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The End
Thanks to Prof. B.Tirozzi Prof. R. Calogero The
laboratory of bioinformatic in Orbassano