Fusing Results from Microarray Experiments

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Fusing Results from Microarray Experiments

• Matt.Boardman_at_dal.ca
• http//www.cs.dal.ca/boardman

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Summary

• Primary paper
• Gilks et al, Fusing microarray experiments with
  multivariate regression, Bioinformatics, 2005.
• The basic idea
• Microarray experiments are subject to noise and
  variation
• Regression model fuses data from several
  microarray tests
• Unique visualization!
• Application
• Rustici et al, Periodic gene expression program
  of the fission yeast cell cycle, Nature
  Genetics, 2004.

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Agenda

• Introduction to Microarrays
• Regression Model
• Experimental Procedures
• Visualization of Results
• Project Proposal

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DNA Transcription to mRNA
Orengo et al, Figure 1.1
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DNA Microarrays

• A microarray is a collection of thousands of
  small test locations, arranged in a 1 x 3
  array.
• Each test location has a small fragment of DNA,
  called a probe (about 20-70 bases), which
  corresponds to a particular gene.
• Fragments of mRNA (recently transcribed messenger
  RNA) from a test subject bind to each probe.
• We measure the quantity of mRNA that sticks to
  each probe, to determine how much mRNA for that
  gene is present in the sample.

http//www.agilent.com/about/newsroom/lsca/imageli
brary/index_2003.html
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DNA Microarrays

• Flash demo
• http//www.bio.davidson.edu/Courses/genomics/chi
  p/chipQ.html

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DNA Microarrays

• Slide Manufacturers
• Agilent (HP spinoff)
• Amersham Codelink
• Corning CMT GAPS II
• Erie Sciences Gold Seal

• Scanner Manufacturers
• Affymetrix
• Agilent
• Applied Precision
• Asper Biotech
• Axon
• Molecular Devices
• National Instruments
• Vidar
• Commercial Software
• Axon/GenePix
• GeneExplorer
• Iobion-Stratagene/GeneTraffic
• Rosetta Resolver
• Spotfire
• SGI/GeneSpring

http//microarrays.ucsd.edu/biogem/resources/image
s/agilent_scanner.jpg
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DNA Microarrays

• Sources of error
• gene-specific dye bias
• probe design and manufacturing
• heterogeneity in source material (The Fly!)
• glass surface abnormalities (warpage, curvature)
• variations in glass thickness
• slide movement within scanner
• slide manufacturing quality
• mRNA deterioration
• Remedies
• daily calibration
• dynamic autofocus (Agilent)
• software fixes (e.g. normalization)
• repeat, repeat, repeat

http//www.moleculardevices.com/pages/instruments/
gn_genepix4000.html
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Multivariate Regression Model

• Microarray test repetition
• Different laboratories
• Different slides / scanners / software
• Different procedures for sample preparation
• Authors propose a new model to combine data from
  multiple microarray tests
• No need to infer the causes of error
• Automatically filter out noise and artefacts
• Iteratively weight each test based on quality of
  results
• Avoid polluting high-quality results with lower
  quality data
• Deliver fused and cleaned dataset for further
  analysis

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Multivariate Regression Model

• Let
• N be the number of microarray tests
• m be the number of genes in each microarray
• n be the number of hypothetical cell types under
  test
• Note
• Typically m N
• We dont know n, but we assume n lt N

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Multivariate Regression Model
Gilks et al, Equation 1

• Where
• D is the matrix of observations the actual
  microarray tests
• X is a matrix of weights, uniquely designed for
  each experiment
• C is the ideal, perfect microarray test with no
  variation or noise
• e contains unknown residual errors and noise
• So
• D are the warped, noisy observations of the
  perfect microarray test C

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Experiment Periodic Cell-Cycles in Yeast

• Question
• Which genes are involved in cell reproduction in
  yeast?
• Schizosaccharomyces pombe (fission yeast)
• Nine experiments were designed in order to
  synchronize the cell cycles in yeast
• centrifugal elutriation
• cdc25 block-release
• combinations of both methods
• Microarrays taken every 15 minutes, for roughly
  two cell cycles (about 5.5 hours)

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Experiment Periodic Cell-Cycles in Yeast

• Goal
• Fuse these nine different experiments into one
  ideal
• Result will be a set of microarray results for
  one cell-cycle
• Problem
• Different synchronization methods ? different
  cell-cycles
• Experiments are not exactly in phase with each
  other
• Experiments result in different cell-cycle
  lengths

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Experiment Periodic Cell-Cycles in Yeast

• These nine experiments produce N178 microarray
  tests
• Each microarray test has m407 genes
• Selected since they are identified as periodic in
  cell-cycle
• 136 of these show significant changes during
  cycle
• Define an ideal cell-cycle, divided into n10
  fusion times
• Each microarray test will be at a different
  angle in the ideal cycle
• The coefficients in X are chosen to weight the
  relevance of each microarray test to each of the
  fusion times

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Experiment Periodic Cell-Cycles in Yeast

• How are the coefficients in X chosen?
• Suppose microarray test h occurs at ?h in the
  cell-cycle
• Linear interpolation
• Find the two fusion times on either side of ?h
• Weight each one according to how close they are
  to ?h
• The other fusion times for h have a zero weight
• How is this done? We dont know ?h !
• Algorithm assumes initial weight values, then
  iteratively updates according to resulting
  generalization error
• Authors claim convergence of these weights within
  3 or 4 iterations, but continue through 10
  iterations in their results for precision

See Gilks et al, Equation 7
See Gilks et al, Equation 6
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Experiment Periodic Cell-Cycles in Yeast

• Now use the DXCe model to estimate C
• But how do we know the answer we get is correct?
• Need a technique to visualize the results!

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Singular Value Decomposition (SVD)

• A technique in linear algebra
• Commonly used to solve systems of linear
  equations
• Also used for linear least-squares problems, or
  curve fitting
• The authors use SVD to find the two eigenvectors
  of a matrix which exhibit the highest variation
• i.e. the most variable components of a matrix
• not part of the actual model, just used for
  visualization
• Similar in purpose to PCA (Principal Components
  Analysis), which identifies the components with
  highest variance
• For more information on SVD and PCA with
  bioinformatics applications, see Wall et al.

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Gilks et al, Figure 1
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Closeup of experiment cdc25-1
Ten fusion times are evenly spaced at p/5
radian intervals in the cycle.
Gilks et al, Figure 2
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Peppered Fried Egg Plot
? Fusion Times
? Fusion Times
Specific Genes
Specific Genes
Cell-Cycleness
Cell-Cycleness
Gene Density
Gene Density
Fusion times are evenly spaced at intervals of
p/5 radians. Longer arrows indicate more
variability in gene expression levels at this
fusion time.
The pepper represents the periodic activation
of particular genes. Larger radius from the
origin indicates more cell-cycle dependence.
The boundary of the yolk represents the average
radius from the origin of all genes, at each
point in the cell cycle.
The boundary of the egg white represents the
average gene density, at each point in the cell
cycle.
Gilks et al, Figure 4
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Multivariate Regression Model

• Possible difficulties with proposed algorithm?
• Assumes linear relationships for simplicity of
  algorithm
• Note the linear interpolation in our choice of X
  coefficients
• Microarray tests which fail to cohere with the
  generality of results will be downweighted
  automatically, as part of the algorithm
• In other words, the majority wins what if the
  majority of experiments have been conducted
  poorly?
• Difference in coverage over cell-cycle
• Some parts of the cell-cycle have many
  contributors, others few
• Treatment of missing data KNN (K Nearest
  Neighbors)
• However, these imputed data points have the
  same weight in the algorithm as the measured data
  points
• Doesnt address some significant sources of
  error, such as gene-specific dye bias
• Most microarray experiments use the same dyes,
  Cy3 and Cy5

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Project Proposal

• Can we use different methods to obtain similar
  results?
• SVM regression (Support Vector Machines)?
• To model the ideal, noise-free microarray test at
  any point in cycle
• ICA (Independent Components Analysis)?
• Identify contributions from n different cell
  types and a noise component
• Simulated Annealing (a stochastic optimization
  method)?
• Identify the best cell-cycle synchronization
  points
• Why SVM regression?
• Ability to generalize from a low number of
  samples
• Detect non-linear relationships (paper assumes
  linear!)
• Why ICA?
• Computationally complex, but requires no
  assumptions about underlying data or noise models
  (we dont need to know n!)

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References

• Primary Paper
• W.R.Gilks, B.D.M.Tom, A.Brazma, Fusing
  microarray experiments with multivariate
  regression, Bioinformatics, 21(Suppl.
  2)137143, 2005.
• Experimental Procedures
• G.Rustici, J.Mata, K.Kivinen, P.Lió, C.J.Penkett,
  G.Burns, J.Hayles, A.Brazma, P.Nurse, J.Bähler,
  Periodic gene expression program of the fission
  yeast cell cycle, Nature Genetics,
  36(8)809817, 2004.
• Microarrays
• Wikipedia Contributors, DNA microarray,
  (http//en.wikipedia.org/wiki/CDNA_microarray),
  2006.
• A.M.Campbell, DNA microarray methodology Flash
  animation, Department of Biology, Davidson
  College, Davidson, NC, (http//www.bio.davidson.ed
  u/Courses/genomics/chip/chipQ.html), 2001.
• C.A.Orengo, D.T.Jones, J.M.Thornton,
  Bioinformatics Genes, Proteins Computers, New
  York Springer-Verlag, pp.218228, 2003.
• Singular Value Decomposition (SVD)
• W.H.Press, S.A.Teukolsky, W.T.Vetterling,
  B.P.Flannery, Numerical Recipes in C The Art of
  Scientific Computing, 2nd ed., Cambridge
  University Press, pp.5970, 1992.
• M.E.Wall, A.Rechtsteiner, L.M.Rocha."Singular
  value decomposition and principal component
  analysis". In A Practical Approach to Microarray
  Data Analysis, D.P.Berrar, W.Dubitzky, M.Granzow,
  eds., pp. 91109, Kluwer Norwell, MA, 2003.
• Support Vector Machines (SVM)
• K.P.Bennett, C.Campbell, Support vector
  machines Hype or hallelujah? SIGKDD
  Explorations, 2(2)113, 2000.
• A.J.Smola, B.Schölkopf, A tutorial on support
  vector regression, Statistics and Computing,
  14(3)199222, 2004.
• V.N.Vapnik, The Nature of Statistical Learning
  Theory, 2nd ed., New York Springer-Verlag, 1999.
• Independent Components Analysis (ICA)
• A.Hyvärinen, Survey on independent components
  analysis, Neural Computing Surveys, 294128,
  1999.

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Support Vector Machines

• SVM use statistical machine learning
• Constrained optimization problem
• Objective Find a hyperplane which
  maximizes margin
• Higher dimensional mappings provide flexibility
• Non-separable data a tradeoff to allow
  misclassification some points in order to improve
  generalization performance (cost parameter)
• Non-linear SVM (Polynomial, Sigmoid, Gaussian
  kernels)

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Support Vector Machines

• The importance of data normalization (centre and
  scale)
• The importance of free-parameter selection

Dataset from MLDB Iris Plant Database
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e-Tube Support Vector Regression
Bennet et al, Figure 12

• Can we use e-SVR for outlier detection?
• i.e. identify contributing samples which are
  outside the e boundary, remove them, and retrain
  the model
• Missing data can we include the number of
  missing data points as another input variable for
  the SVM model?

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Independent Components Analysis

• ICA attempts to find the true underlying signals
  from multiple observations of a mix of signals
• Finds signals which are as statistically
  independent from one another as possible blind
  source separation
• Different to PCA, which identifies the measured
  signals with highest variance
• For example, consider a hypothetical political
  debate
• Martin and Harper are speaking at the same time
• two omnidirectional microphones listening to both
  speakers
• ICA can isolate each speakers voice!
• For a demo http//www2.ele.tue.nl/ica99/realworl
  d.html

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Independent Components Analysis Test
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Independent Components Analysis Samples
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Independent Components Analysis Results
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Cell-cycle for Selected Genes
Gilks et al, Figure 5