Tumors and Large Scale DNA Damage

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Tumors and Large Scale DNA Damage

• Tumors are characterized by large-Scale DNA
  damage
• In this paper we consider characterization of
  large scale structural changes such as deletion,
  inversion .

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Methods for Detecting Structural Changes
Deletion
Insertion
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Method I PCR-array

• Base on Ion-channel sensor' principle proposed
  by Sugawara et al 1987
• Idea
• DNA is electrochemically inactive
• the interaction of target DNA and a specific
  protein was monitored by measuring redox peak
  currents on cyclic voltammogram of redox-active
  species

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Method I PCR-array
When a target DNA duplex having a mismatch site
was captured by the MutS protein on the
electrode, the electrostatic repulsion arose
between polyanionic DNA duplexes and
negatively-charged ferrocyanide/ferricyanide
redox couple ions.
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Method II FISH

• FISH Fluorescence in Situ Hybridization
• Step 1 Use fluorescent probes which bind only to
  those parts of the chromosome with which they
  show a high degree of sequence similarity
• Step 2 Fluorescence microscopy can be used to
  find out where the fluorescent probe bound to the
  chromosome.

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Method II FISH
Specific Molecules that absorb energy at a
specific wavelength and emit it at different
wavelength
FISH uses a Fluorescence Microscope that is based
on phenomena of fluorescence and phosphorescence
instead of, or in addition to, reflection and
absorption to detect gene mutation.
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New Method?

• Problem with current methods
• Assume Homogeneous population of cells
• Fail if heterogeneous mix?
• FISH is to cumbersome and not accurate

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New Method? Polymerase Chain Reaction
Can we take advantage of this technique to
amplify interested region?
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New Method? PAMP Primer Approximation
Multiplex PCR
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New Method? PAMP
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PAMP Constraints/Problem

• Constraint
• Cover the region of the interest
• Primers should not be farther than 1kb
• Primers should not dimerize with each other
• Primer must satisfy physico-chemical
  characteristics to allow polymerase reaction
• Problem Optimize the amount of sequence space
  which can be covered suing a fixed primer density

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Sketching the Problem
Constraint Matrix
A
B
C
Nodes that have constraints are connected to each
other
Distance Matrix
Weight is distance beyond allowed max 0, DAB
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Summarizing the problem

• There are n variables
• Some variables may conflict w. each other
• We would like to have neighboring variables
  placed as closely as possible to each other, not
  necessarily too close
• Penalty max 0, (distance 10kb)

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Complexity?

• Is it similar to Max2-SAT problem?

A Clause is a set of values given an
assignment Clause1 X1C1 S1C1, S1C2,
Variables can be set of assignment X1S1, X1
S1,
NP Hard?
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Solution I

• Can we characterize the problem linearly?

A series of linear constraints on two variables
produces a region of possible values for those
variables. Solvable problems will have a feasible
region in the shape of a simple polygon.
Integer Linear Programming
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ILP
What should we do if the answer is not Integer?
Add more LP constraint to force solutions to be
close to integer
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PAMP in ILP
For conflicting primers
When both primers are selected
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CSP (Constraint Satisfaction Programming)

• X x1,x2,,xn
• xi ? d(xi).
• c ? C
• specifies which values of the variables are
  compatible with each other.
• Filtering in CSP?
• Arc-consistency is a filtering method applied for
  reducing search space.

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CSP, filtering?

• Can we learn from failures?
• ABC ? Fail
• ABC ? Fail
• Thus AB ? Fail