Algorithms for Smoothing Array CGH data

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Algorithms forSmoothing Array CGH data
Kees Jong (VU, CS and Mathematics) Elena
Marchiori (VU, Computer Science) Aad van der
Vaart (VU, Mathematics) Gerrit Meijer
(VUMC) Bauke Ylstra (VUMC) Marjan Weiss (VUMC)
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Tumor Cell
Chromosomes of tumor cell
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CGH Data
? C o p y
Clones/Chromosomes ?
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Naïve Smoothing
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Discrete Smoothing
Copy numbers are integers
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Why Smoothing ?

• Noise reduction
• Detection of Loss, Normal, Gain, Amplification
• Breakpoint analysis

• Recurrent (over tumors) aberrations may indicate
• an oncogene or
• a tumor suppressor gene

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Is Smoothing Easy?

• Measurements are relative to a reference sample
• Printing, labeling and hybridization may be
  uneven
• Tumor sample is inhomogeneous

• vertical scale is relative
• do expect only few levels

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Smoothing example
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Problem Formalization

• A smoothing can be described by
• a number of breakpoints
• corresponding levels
• A fitness function scores each smoothing
  according to fitness to the data
• An algorithm finds the smoothing with the highest
• fitness score.

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Smoothing
breakpoints
variance
levels
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Fitness Function

• We assume that data are a realization of a
  Gaussian noise process and use the maximum
  likelihood criterion adjusted with a penalization
  term for taking into account model complexity

We could use better models given insight in
tumor pathogenesis
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Fitness Function (2)
CGH values x1 , ... , xn
breakpoints 0 lt y1lt lt yN lt xN levels m1, . .
., mN error variances s12, . . ., sN2
likelihood
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Fitness Function (3)
Maximum likelihood estimators of µ and s 2
can be found explicitly
Need to add a penalty to log likelihood
to control number N of breakpoints
penalty
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Algorithms

• Maximizing Fitness is computationally hard
• Use genetic algorithm local search to find
  approximation to the optimum

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Algorithms Local Search

• choose N breakpoints at random
• while (improvement)
• - randomly select a breakpoint
• - move the breakpoint one position to
  left
• or to the right

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Genetic Algorithm

• Given a population of candidate smoothings
• create a new smoothing by
• - select two parents at random from population
• - generate offspring by combining parents
• (e.g. uniform crossover or union)
• - apply mutation to each offspring
• - apply local search to each offspring
• - replace the two worst individuals with the
  offspring

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Experiments

• Comparison of
• GLS
• GLSo
• Multi Start Local Search (mLS)
• Multi Start Simulated Annealing (mSA)
• GLS is significantly better than the other
  algorithms.

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Comparison to Expert
algorithm
expert
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Relating to Gene Expression
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Relating to Gene Expression
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Algorithms forSmoothing Array CGH data
Kees Jong (VU, CS and Mathematics) Elena
Marchiori (VU, CS) Aad van der Vaart (VU,
Mathematics) Gerrit Meijer (VUMC) Bauke Ylstra
(VUMC) Marjan Weiss (VUMC)
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(No Transcript)
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Conclusion

• Breakpoint identification as model fitting to
  search for most-likely-fit model given the data
• Genetic algorithms local search perform well
• Results comparable to those produced by hand by
  the local expert
• Future work
• Analyse the relationship between Chromosomal
  aberrations and Gene Expression

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Example of a-CGH Tumor
? V a l u e
Clones/Chromosomes ?
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a-CGH vs. Expression

• a-CGH
• DNA
• In Nucleus
• Same for every cell
• DNA on slide
• Measure Copy Number Variation

• Expression
• RNA
• In Cytoplasm
• Different per cell
• cDNA on slide
• Measure Gene Expression

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Breakpoint Detection

• Identify possibly damaged genes
• These genes will not be expressed anymore
• Identify recurrent breakpoint locations
• Indicates fragile pieces of the chromosome
• Accuracy is important
• Important genes may be located in a region with
  (recurrent) breakpoints

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Experiments

• Both GAs are Robust
• Over different randomly initialized runs
  breakpoints are (mostly) placed on the same
  location
• Both GAs Converge
• The individuals in the pool are very similar
• Final result looks very much like (mean error
  0.0513) smoothing conducted by the local expert

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Genetic Algorithm 1 (GLS)

• initialize population of candidate solutions
  randomly
• while (termination criterion not satisfied)
• - select two parents using roulette wheel
• - generate offspring using uniform crossover
• - apply mutation to each offspring
• - apply local search to each offspring
• - replace the two worst individuals with the
  offspring

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Genetic Algorithm 2 (GLSo)

• initialize population of candidate solutions
  randomly
• while (termination criterion not satisfied)
• - select 2 parents using roulette wheel
• - generate offspring using OR crossover
• - apply local search to offspring
• - apply join to offspring
• - replace worst individual with offspring

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Fitness function (2)
CGH values x1 , ... , xn
breakpoints 0 lt y1lt lt yN lt xN
levels m1, . . ., mN
error variances s12, . . ., sN2
likelihood