Whole Genome Assembly Microarray analysis

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Whole Genome AssemblyMicroarray analysis
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Mate Pairs

• Mate-pairs allow you to merge islands (contigs)
  into super-contigs

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Super-contigs are quite large

• Make clones of truly predictable length. EX 3
  sets can be used 2Kb, 10Kb and 50Kb. The
  variance in these lengths should be small.
• Use the mate-pairs to order and orient the
  contigs, and make super-contigs.

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Problem 3 Repeats
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Repeats Chimerisms

• 40-50 of the human genome is made up of
  repetitive elements.
• Repeats can cause great problems in the assembly!
• Chimerism causes a clone to be from two different
  parts of the genome. Can again give a completely
  wrong assembly

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Repeat detection

• Lander Waterman strikes again!
• The expected number of clones in a Repeat
  containing island is MUCH larger than in a
  non-repeat containing island (contig).
• Thus, every contig can be marked as Unique, or
  non-unique. In the first step, throw away the
  non-unique islands.

Repeat
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Detecting Repeat Contigs 1 Read Density

• Compute the log-odds ratio of two hypotheses
• H1 The contig is from a unique region of the
  genome.
• The contig is from a region that is repeated at
  least twice

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Detecting Chimeric reads

• Chimeric reads Reads that contain sequence from
  two genomic locations.
• Good overlaps G(a,b) if a,b overlap with a high
  score
• Transitive overlap T(a,c) if G(a,b), and G(b,c)
• Find a point x across which only transitive
  overlaps occur. X is a point of chimerism

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Contig assembly

• Reads are merged into contigs upto repeat
  boundaries.
• (a,b) (a,c) overlap, (b,c) should overlap as
  well. Also,
• shift(a,c)shift(a,b)shift(b,c)
• Most of the contigs are unique pieces of the
  genome, and end at some Repeat boundary.
• Some contigs might be entirely within repeats.
  These must be detected

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Creating Super Contigs
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Supercontig assembly

• Supercontigs are built incrementally
• Initially, each contig is a supercontig.
• In each round, a pair of super-contigs is merged
  until no more can be performed.
• Create a Priority Queue with a score for every
  pair of mergeable supercontigs.
• Score has two terms
• A reward for multiple mate-pair links
• A penalty for distance between the links.

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Supercontig merging

• Remove the top scoring pair (S1,S2) from the
  priority queue.
• Merge (S1,S2) to form contig T.
• Remove all pairs in Q containing S1 or S2
• Find all supercontigs W that share mate-pair
  links with T and insert (T,W) into the priority
  queue.
• Detect Repeated Supercontigs and remove

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Repeat Supercontigs

• If the distance between two super-contigs is not
  correct, they are marked as Repeated
• If transitivity is not maintained, then there is
  a Repeat

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Filling gaps in Supercontigs
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Consenus Derivation Assembly

• Summary
• Do an all pairs prefix-suffix alignment.
  (Speedup using k-mer hashing).
• Construct a graph of overlapping alignments.
• Break the graph into unique regions (Number of
  clones similar to prediction using LW), and
  repeat/chimeric regions. Each such unique
  region is called a contig.
• Merge contigs into super-contigs using mate-pair
  links
• For each contig, construct a multiple alignment,
  and consensus sequence.
• Pad the consensus sequence using NNs.

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Summary

• Once controversial, whole genome shotgun is now
  routine
• Human, Mouse, Rat, Dog, Chimpanzee..
• Many Prokaryotes (One can be sequenced in a day)
• Plant genomes Arabidopsis, Rice
• Model organisms Worm, Fly, Yeast
• WGS must be followed up with a finishing effort.
• A lot is not known about genome structure,
  organization and function.
• Comparative genomics offers low hanging fruit.

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Biol. Data analysis Review
Assembly
Protein Sequence Analysis
Sequence Analysis/ DNA signals
Gene Finding
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Other static analysis is possible
Genomic Analysis/ Pop. Genetics
Assembly
Protein Sequence Analysis
Sequence Analysis
Gene Finding
ncRNA
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A Static picture of the cell is insufficient

• Each Cell is continuously active,
• Genes are being transcribed into RNA
• RNA is translated into proteins
• Proteins are PT modified and transported
• Proteins perform various cellular functions
• Can we probe the Cell dynamically?
• Which transcripts are active?
• Which proteins are active?
• Which proteins interact?

Gene Regulation
Proteomic profiling
Transcript profiling
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Micro-array analysis
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The Biological Problem

• Two conditions that need to be differentiated,
  (Have different treatments).
• EX ALL (Acute Lymphocytic Leukemia) AML (Acute
  Myelogenous Leukima)
• Possibly, the set of genes over-expressed are
  different in the two conditions

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Supplementary fig. 2. Expression levels of
predictive genes in independent dataset. The
expression levels of the 50 genes most highly
correlated with the ALL-AML distinction in the
initial dataset were determined in the
independent dataset. Each row corresponds to a
gene, with the columns corresponding to
expression levels in different samples. The
expression level of each gene in the independent
dataset is shown relative to the mean of
expression levels for that gene in the initial
dataset. Expression levels greater than the mean
are shaded in red, and those below the mean are
shaded in blue. The scale indicates standard
deviations above or below the mean. The top panel
shows genes highly expressed in ALL, the bottom
panel shows genes more highly expressed in AML.
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Gene Expression Data

• Gene Expression data
• Each row corresponds to a gene
• Each column corresponds to an expression value
• Can we separate the experiments into two or more
  classes?
• Given a training set of two classes, can we build
  a classifier that places a new experiment in one
  of the two classes.

s1
s2
s
g
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Three types of analysis problems

• Cluster analysis/unsupervised learning
• Classification into known classes (Supervised)
• Identification of marker genes that
  characterize different tumor classes

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Supervised Classification Basics

• Consider genes g1 and g2
• g1 is up-regulated in class A, and down-regulated
  in class B.
• g2 is up-regulated in class A, and down-regulated
  in class B.
• Intuitively, g1 and g2 are effective in
  classifying the two samples. The samples are
  linearly separable.

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Basics

• With 3 genes, a plane is used to separate
  (linearly separable samples). In higher
  dimensions, a hyperplane is used.

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Non-linear separability

• Sometimes, the data is not linearly separable,
  but can be separated by some other function
• In general, the linearly separable problem is
  computationally easier.

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Formalizing of the classification problem for
micro-arrays
v

• Each experiment (sample) is a vector of
  expression values.
• By default, all vectors v are column vectors.
• vT is the transpose of a vector
• The genes are the dimension of a vector.
• Classification problem Find a surface that will
  separate the classes

vT
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Formalizing Classification

• Classification problem Find a surface
  (hyperplane) that will separate the classes
• Given a new sample point, its class is then
  determined by which side of the surface it lies
  on.
• How do we find the hyperplane? How do we find the
  side that a point lies on?

1 2 3 4 5 6
1
2
g1
3
1 .9 .8 .1 .2 .1
g2
.1 0 .2 .8 .7 .9
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Basic geometry

• What is x2 ?
• What is x/x
• Dot product?

x(x1,x2)
y
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Dot Product
x

• Let ? be the unit vector.
• ? 1
• Recall that
• ?Tx x cos ?
• What is ?Tx if x is orthogonal (perpendicular)
  to ??
• How do we specify a hyperplane?

?
?
?Tx x cos ?
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Hyperplane

• How can we define a hyperplane L?

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Points on the hyperplane

• Consider a hyperplane L defined by unit vector ?,
  and distance ?0
• Notes
• For all x ? L, xT? must be the same, xT? ?0
• For any two points x1, x2,
• (x1- x2)T ?0

x2
x1
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Hyperplane properties

• Given an arbitrary point x, what is the distance
  from x to the plane L?
• D(x,L) (?Tx - ?0)
• When are points x1 and x2 on different sides of
  the hyperplane?

x
?0
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Separating by a hyperplane

• Input A training set of ve -ve examples
• Goal Find a hyperplane that separates the two
  classes.
• Classification A new point x is ve if it lies
  on the ve side of the hyperplane, -ve otherwise.
• The hyperplane is represented by the line
• x-?0?1x1?2x20

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Error in classification

• An arbitrarily chosen hyperplane might not
  separate the test. We need to minimize a
  mis-classification error
• Error sum of distances of the misclassified
  points.
• Let yi1 for ve example i, yi-1 otherwise.
• Other definitions are also possible.

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Gradient Descent

• The function D(?) defines the error.
• We follow an iterative refinement. In each step,
  refine ? so the error is reduced.
• Gradient descent is an approach to such iterative
  refinement.

D(?)
D(?)
?
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Rosenblatts perceptron learning algorithm
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Classification based on perceptron learning

• Use Rosenblatts algorithm to compute the
  hyperplane L(?,?0).
• Assign x to class 1 if f(x) gt 0, and to class 2
  otherwise.

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Perceptron learning

• If many solutions are possible, it does no choose
  between solutions
• If data is not linearly separable, it does not
  terminate, and it is hard to detect.
• Time of convergence is not well understood

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Linear Discriminant analysis

• Provides an alternative approach to
  classification with a linear function.
• Project all points, including the means, onto
  vector ?.
• We want to choose ? such that
• Difference of projected means is large.
• Variance within group is small

?
x2
-
x1
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LDA Contd
Fisher Criterion
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Maximum Likelihood discrimination

• Suppose we knew the distribution of points in
  each class.
• We can compute Pr(x?i) for all classes i, and
  take the maximum

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ML discrimination

• Suppose all the points were in 1 dimension, and
  all classes were normally distributed.

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ML discrimination recipe

• We know the distribution for each class, but not
  the parameters
• Estimate the mean and variance for each class.
• For a new point x, compute the discrimination
  function gi(x) for each class i.
• Choose argmaxi gi(x) as the class for x