Microarrays

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Microarrays
Carsten Daub www.mpimp-golm.mpg.de daub_at_mpimp-golm
.mpg.de
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Microarrays
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Microarrays

• Short Introduction to Microarray Technology
• The data matrix
• Distance metrics
• Clustering techniques
• Relevance of networks

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Microarrays
DNA
Cell
RNA Polymerase
mRNA
labeled Nucleotides
Reverse Transcriptase




















labeled cDNA
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Microarrays

• The conentration of labels in the cDNA is
  measured!
• Assumptions for interpretation of Microarray
  data
• mRNA is stable over time until cDNA is
  transcribed
• The concentration of cDNA equals the concentraton
  of mRNA
• The labeled nucleotides are inserted
  statistically
• The labels are often flourophors with a cyanine
  structure

cy3
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Microarrays
labeled cDNA as probe


















target

• cDNA Microarrays
• Immobilisation of whole cDNA
• cDNA is obtained via becteria
• Spotted by inkjet technology
• cDNA libraries are needed

• oligonucleotide Microarrays
• Immobilisation of characteristc sequences
• Sequences are designed
• Sequences are synthesized on the chip
• Several commercial products are available

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Comparing two situations
cDNA Microarrays


















Situation A treated probe
Situation B wild type
A reference is needed to compare data from
different arrays.) Mixture of A and B is spotted
Extraction of intensities with picture analysis
software
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Comparing two situations

• 0 lt ratio lt Inf.
• Inf. lt log2(ratio) lt Inf.
• where
• log2(ratio) gt 0 increase
• log2(ratio) lt 0 decrease

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Absolute Intensities
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Data Matrix
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Data Normalisation

• Background noise
• The background is determined around each spot
• Some spots are left empty to determin background
• There are several different procedures to
  substract background
• The background around a point is substracted for
  that point
• The average background is substracted from each
  point
• A background profile is determined for the whole
  array can also be used to determin systematical
  errors of array

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Data Normalisation

• Correct for
• Differences in labelling and detection
  efficiencies
• Differences in quantity of initial mRNA
• Some widely used techniques
• Total intensity normalisation
• Assumption Quantity of initial mRNA is similar
  for both labelled samples
• Total integrated intensities are equal for both
  samples
• Re-scale intensities for each gene
• Normalisation using regression techniques
• Normalisation using ratio statistics

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Data Normalisation

• Some widely used techniques (continued)
• Normalisation using regression techniques
• Assumption mRNA derived from closely related
  samples is used
• Scatterplot of int(Cy5) vs. int(Cy3) has a
  diagonal part with slope 1
• Re-scale intensities for each gene
• Local regression techniques also available for
  non-linear scatterplots
• Normalisation using ratio statistics
• Confidence limits are calculated via statistics

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Data Normalisation
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Data Normalisation
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Undefined values

• Gene expression datasets often contain undefined
  values.
• The background and the signal give similar
  intensity
• Surface of the chip is not planar (cDNA chips)
• The probe is not properly fixed on the chip
• hybridistion step didnt work properly
• Probe was not washed away properly
• Undefined values can be
• Discarted -gt leads to problems in data analysis
• Replaced with averages of rows/columns
• Replaced by zero

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Similarity of Genes

• Co-regulated genes show a similar behaviour
• There exists no a priori definition of similarity
• Different similarity measures are used
• Different patterns are seen with different
  similarity measures

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Similarity of Genes

• Example
• An expression vector is defined for each gene
• The expression values are the dimensions (x1,x2,
  ..., xn) in expression space
• Each gene is represented as one
• n-dimensional point in expression space
• Two genes with similar expression behaviour are
  spatially nearby
• Similarity is inverse proportional to spatial
  distance

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Similarity of Genes

• Example (continued)
• Different clustering algorithms can be applied to
  find clusters of genes

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Similarity of Experiments

• Instead of clustering genes it is also possible
  to cluster experiments
• Each experiment is regarded as experiment
  vector in the experiment space

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Visualisation of Data Matrix

• The data matrix can be visualised to get an
  impression of gene expression behaviour.
• The order of genes in data matrix can be
  reorganised for better recognition of expression
  patterns.

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Distance Metrics

• For clustering algorithms the calculation of a
  distance between gene vectors or experiment
  vectors is a necessary step
• Distances metrics can be classified as
• Metric distances
• Semi-metric distances
• Metric distances
• dab gt 0
• dab dba
• daa 0
• dab lt dac dca
• Semi-metric distances obey 1) to 3), fail in 4)

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Distance Metrics
Minkowski distance If q 1, d is Manhattan
distance (semi-metric distance) If q 2, d is
Euclidean distance (metric distance)
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Distance Metrics
Pearson correlation coefficient (semi-metric
distance)
-1 lt d(i,j) lt 1
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Distance Metrics
Rank-ordered Pearson correlation coefficient -gt
Spearman (semi-metric distance)
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Distance Metrics
Other variations of Pearsons correlation
coefficient Uncentered Pearson
correlation (semi-metric distance)
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Distance Metrics
Entropy based distances Mutual
Information (semi-metric distance)

• Mutual Information (MI) is a statistical
  representation of the correlation of two signals
  A and B.
• MI is a measure of the additional information
  known about one expression pattern when given
  another.
• MI is not based on linear models and can
  therefore also see non-linear dependencies (see
  picture).

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Clustering Techniques

• Several classification criteria of clustering
  algorithms exist with regard to
• Clustering result hierarchical not
  hierarchical
• Clustering process divisive - agglomerative
• Clustering criterion sequential - global

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Clustering Techniques
Hierarchical clustering
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Clustering Techniques
Hierarchical clustering phylogenetic tree
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Clustering Techniques

• Hierarchical clustering
• Various hierarchical clustering algorithms exist
• Single-linkage clustering, nearest-neighbour
• Complete-linkage, furthest-neighbour
• Average-linkage, unweighted pair-group method
  average (UPGMA)
• Weighted-pair group average, UPGMA weighted by
  cluster sizes
• Within-groups clustering
• Wards method
• ...

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Clustering Techniques

• k-means clustering
• The number of clusters k has to be chosen in
  advance)
• Initial position of cluster centers is random)
• For each data point the (euclidean) distance to
  each cluster center is calculated
• Each data point is assigned to its nearest
  cluster
• Cluster centers are shifted to the center of data
  points assigned to this cluster center
• Step 3. 5. is iterated until cluster centers
  are not shifted anymore

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Clustering Techniques
k-means clustering (continued) A reasonable
number of cluster centers k can be estimated
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Clustering Techniques
k-means clustering (continued) The initial
position of cluster centers can be estimated by
the distribution of the data vectors
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Clustering Techniques

• Principal Component Analysis (PCA)
• Singular value decomposition (SVD)
• Reduction of effective dimensionality of
  gene-expression space
• by (linear) combination of initial dimensions
• Mathematically complex

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Clustering Techniques

• No clustering technique is better than another
• Different clustering techniques have shown to
  lead to reasonable results depending on the
  measured data
• Organism
• Tissue
• Experimental condition, e.g. mutants or time
  course experiments
• Distance metric used

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Visualisation
Visualisation in clusters
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Relevance of Networks

• There is now abolute measure for quality of
  clusters
• Biological relevance of clusters can be checked
  with biochemical knowlegde
• Functional classifications are provided by some
  databases, e.g. MIPS (http//gsf.mips.de)
• Genes in clusters can be checked if a majority is
  annotated to one or a few functional classes

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Conclusion

• Microarrays measure the concentration of mRNA
• Several assumptions are made in the progress of
  analysis
• Biological
• Numerical
• Experimental conditions are important!
• Different distances matrics combined with
  different clustering algorithms can leed to
  completely different results

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Software Sources

• AFM (Array File Maker) from Samuel Lunenfeld
  Research Institute, Mount Sinai Hospital
  (Toronto) http//www.mshri.on.ca/tyers/software.h
  tml
• AMADA (Analyzing Microarray Data) from Univ of
  Hong Kong http//web.hku.hk/xxia/software/AMADA.
  htm
• ANOVA programs for microarray data from
  Churchill's group at Jackson Lab
  http//www.jax.org/research/churchill/software/an
  ova/index.html
• CLUSFAVOR (CLUSter and Factor Analysis using
  Varimax Orthogonal Rotation), from Baylor
  http//mbcr.bcm.tmc.edu/genepi/
• CLUSTER, TREEVIEW from Eisen's lab at Lawrence
  Berkeley National Lab http//rana.lbl.gov/EisenSo
  ftware.htm also, http//www.microarrays.org/softw
  are.html
• D-CHIP specifically for Affymetrix chip data,
  from Wong's lab at Biostatistic Department,
  Harvard University http//www.dchip.org
• GENE-CLUSTER Whitehead Institute (registration
  is required). A commercial version of this
  program is also developed, at Affymetrix
  http//www.genome.wi.mit.edu/MPR/software.html
• J-EXPRESS Univ of Bergen, Norway
  http//www.ii.uib.no/bjarted/jexpress/index.html
  
• ONTO-EXPRESS Wayne Univ http//vortex.cs.wayne.
  edu/Projects.html
• PAGE (PAtterns from Gene Expression) from U
  Penn. http//www.cbil.upenn.edu/PaGE/
• PLAID from Owen's lab at Stanford Univ.
  http//www-stat.stanford.edu/owen/plaid/
• SAM (significance analysis of microarrays) from
  Tibshirani's group at Stanford Univ.
  http//www-stat.stanford.edu/tibs/SAM/index.html
  
• SAM (significance of array measurement) from
  Institute for Systems Biology http//www.systemsb
  iology.org/VERAandSAM/
• SMA (Statistic for Microarray Analysis, in R or
  S-PLUS subroutines) from Speed's lab at
  Statistics Department of UC Berkeley
  http//www.stat.berkeley.edu/users/terry/zarray/S
  oftware/smacode.html
• SVDMAN from Los Alamos National Laboratory
  http//public.lanl.gov/mewall/svdman/
• TREE-ARRANGE and TREEPS from Univ Waterloo
  http//monod.uwaterloo.ca/downloads/treearrange/
• VERA (variability and error assessment) from
  Institute for Systems Biology http//www.systemsb
  iology.org/VERAandSAM/
• XCLUSTER from Sherlock's lab of Genetics
  Department of Stanford Univ http//genome-www.sta
  nford.edu/sherlock/cluster.html

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Literature

• Sessions at Pacific Symposium on
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• Gene Regulation Networks - a Finite State Linear
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• A. J. Butte, I. S. Kohane. 2000. Mutual
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• B Dutilh. 1999. Gene Networks from Microarray
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• P D'Haeseleer, S. Liang, R. Somogyi. 2000.
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• P D'haeseleer, S. Liang, R. Somogyi. 1999. Gene
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