September 24, 2003 Microarray data analysis. Many of the images in this powerpoint presentation are...
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September 24, 2003 Microarray data analysis
September 24, 2003 Microarray data analysis. Many of the images in this powerpoint presentation are from Bioinformatics and Functional Genomics by Jonathan
Many of the images in this powerpoint presentation are from
Bioinformatics and Functional Genomics by Jonathan Pevsner (ISBN
0-471-21004-8). Copyright 2003 by John Wiley & Sons, Inc.John
Wiley & Sons, Inc These images and materials may not be used
without permission from the publisher. We welcome instructors to
use these powerpoints for educational purposes, but please
acknowledge the source. The book has a homepage at
http://www.bioinfbook.orghttp://www.bioinfbook.org Including
hyperlinks to the book chapters. Copyright notice
Slide 3
Microarray data analysis begin with a data matrix (gene
expression values versus samples) Page 190
Slide 4
Microarray data analysis begin with a data matrix (gene
expression values versus samples) Page 190 Typically, there are
many genes (>> 10,000) and few samples (~ 10)
Slide 5
Microarray data analysis begin with a data matrix (gene
expression values versus samples) Preprocessing Inferential
statisticsDescriptive statistics Page 190
Slide 6
Microarray data analysis: preprocessing Observed differences in
gene expression could be due to transcriptional changes, or they
could be caused by artifacts such as: different labeling
efficiencies of Cy3, Cy5 uneven spotting of DNA onto an array
surface variations in RNA purity or quantity variations in washing
efficiency variations in scanning efficiency Page 191
Slide 7
Microarray data analysis: preprocessing The main goal of data
preprocessing is to remove the systematic bias in the data as
completely as possible, while preserving the variation in gene
expression that occurs because of biologically relevant changes in
transcription. A basic assumption of most normalization procedures
is that the average gene expression level does not change in an
experiment. Page 191
Slide 8
Data analysis: global normalization Global normalization is
used to correct two or more data sets. In one common scenario,
samples are labeled with Cy3 (green dye) or Cy5 (red dye) and
hybridized to DNA elements on a microrarray. After washing, probes
are excited with a laser and detected with a scanning confocal
microscope. Page 192
Slide 9
Data analysis: global normalization Global normalization is
used to correct two or more data sets Example: total fluorescence
in Cy3 channel = 4 million units Cy 5 channel = 2 million units
Then the uncorrected ratio for a gene could show 2,000 units versus
1,000 units. This would artifactually appear to show 2-fold
regulation. Page 192
Slide 10
Data analysis: global normalization Global normalization
procedure Step 1: subtract background intensity values (use a blank
region of the array) Step 2: globally normalize so that the average
ratio = 1 (apply this to 1-channel or 2-channel data sets) Page
192
Slide 11
Microarray data preprocessing Some researchers use housekeeping
genes for global normalization Visit the Human Gene Expression
(HuGE) Index: www.HugeIndex.org Page 192
Slide 12
Scatter plots Useful to represent gene expression values from
two microarray experiments (e.g. control, experimental) Each dot
corresponds to a gene expression value Most dots fall along a line
Outliers represent up-regulated or down-regulated genes Page
193
Slide 13
Scatter plot analysis of microarray data Page 193
Slide 14
Brain Astrocyte Fibroblast Differential Gene Expression in
Different Tissue and Cell Types
Slide 15
expression level high low up down Expression level (sample 1)
Expression level (sample 2) Page 193
Slide 16
Page 195 Log-log transformation
Slide 17
Scatter plots Typically, data are plotted on log-log
coordinates Visually, this spreads out the data and offers symmetry
raw ratiolog 2 ratio time behavior valuevalue t=0basal1.00.0 t=1hno
change1.00.0 t=2h2-fold up2.01.0 t=3h2-fold down0.5-1.0 Page 194,
197
Slide 18
expression level high low up down Mean log intensity Log ratio
Page 196
Slide 19
SNOMAD converts array data to scatter plots http://snomad.org
2-fold Log 10 (Ratio ) Mean ( Log 10 ( Intensity ) ) EXP CON EXP
CON EXP > CON EXP < CON 2-fold Linear-linear plot Log-log
plot Page 196-197
Slide 20
SNOMAD corrects local variance artifacts 2-fold Log 10 ( Ratio
) Mean ( Log 10 ( Intensity ) ) robust local regression fit
residual EXP > CON EXP < CON Corrected Log 10 ( Ratio )
[residuals] Mean ( Log 10 ( Intensity ) ) Page 196-197
Slide 21
SNOMAD describes regulated genes in Z-scores Corrected Log 10 (
Ratio ) Mean ( Log 10 ( Intensity ) ) 2-fold Locally estimated
standard deviation of positive ratios Z= 1 Z= -1 Locally estimated
standard deviation of negative ratios Local Log 10 ( Ratio )
Z-Score Mean ( Log 10 ( Intensity ) ) Z= 5 Z= -5 Corrected Log 10 (
Ratio ) Mean ( Log 10 ( Intensity ) ) 2-fold Z= 2 Z= 1 Z= -1 Z= -2
Z= 5 Z= -5
Slide 22
Inferential statistics Inferential statistics are used to make
inferences about a population from a sample. Hypothesis testing is
a common form of inferential statistics. A null hypothesis is
stated, such as: There is no difference in signal intensity for the
gene expression measurements in normal and diseased samples. The
alternative hypothesis is that there is a difference. We use a test
statistic to decide whether to accept or reject the null
hypothesis. For many applications, we set the significance level to
p < 0.05. Page 199
Slide 23
Inferential statistics A t-test is a commonly used test
statistic to assess the difference in mean values between two
groups. t = = Questions Is the sample size (n) adequate? Are the
data normally distributed? Is the variance of the data known? Is
the variance the same in the two groups? Is it appropriate to set
the significance level to p < 0.05? Page 199 x 1 x 2 difference
between mean values variability (noise)
Slide 24
Inferential statistics ParadigmParametric testNonparametric
Compare two unpaired groupsUnpaired t-testMann-Whitney test Compare
two paired groupsPaired t-testWilcoxon test Compare 3 orANOVA more
groups Page 198-200
Slide 25
Inferential statistics Is it appropriate to set the
significance level to p < 0.05? If you hypothesize that a
specific gene is up-regulated, you can set the probability value to
0.05. You might measure the expression of 10,000 genes and hope
that any of them are up- or down-regulated. But you can expect to
see 5% (500 genes) regulated at the p < 0.05 level by chance
alone. To account for the thousands of repeated measurements you
are making, some researchers apply a Bonferroni correction. The
level for statistical significance is divided by the number of
measurements, e.g. the criterion becomes: p < (0.05)/10,000 or p
< 5 x 10 -6 Page 199
Descriptive statistics Microarray data are highly dimensional:
there are many thousands of measurements made from a small number
of samples. Descriptive (exploratory) statistics help you to find
meaningful patterns in the data. A first step is to arrange the
data in a matrix. Next, use a distance metric to define the
relatedness of the different data points. Two commonly used
distance metrics are: -- Euclidean distance -- Pearson coefficient
of correlation 203
Slide 30
Page 205 Data matrix (20 genes and 3 time points from Chu et
al.)
Slide 31
Page 205 3D plot (using S-PLUS software) t=0t=0.5 t=2.0
Slide 32
Descriptive statistics: clustering Clustering algorithms offer
useful visual descriptions of microarray data. Genes may be
clustered, or samples, or both. We will next describe hierarchical
clustering. This may be agglomerative (building up the branches of
a tree, beginning with the two most closely related objects) or
divisive (building the tree by finding the most dissimilar objects
first). In each case, we end up with a tree having branches and
nodes. Page 204
Divisive clustering a b c d e a,b d,e c,d,e a,b,c,d,e 43210
tree is constructed Page 206
Slide 43
divisive agglomerative a b c d e a,b d,e c,d,e a,b,c,d,e 43210
43210 Page 206
Slide 44
Page 205
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Page 207
Slide 46
1 1 12 Page 207 Agglomerative and divisive clustering sometimes
give conflicting results, as shown here
Slide 47
Cluster and TreeView Page 208
Slide 48
Cluster and TreeView clustering PCASOMK means Page 208
Slide 49
Cluster and TreeView Page 208
Slide 50
Cluster and TreeView Page 208
Slide 51
Slide 52
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Slide 54
Page 209 Two-way clustering of genes (y-axis) and cell lines
(x-axis) (Alizadeh et al., 2000)
Slide 55
Self-organizing maps (SOM) To download GeneCluster:
http://www.genome.wi.mit.edu/MPR/software.html
Slide 56
Self-organizing maps (SOM) One chooses a geometry of
'nodes'-for example, a 3x2 grid
http://www.genome.wi.mit.edu/MPR/SOM.html Page 210
Slide 57
Self-organizing maps (SOM) The nodes are mapped into
k-dimensional space, initially at random and then successively
adjusted. Page 210
Slide 58
Self-organizing maps (SOM) Page 211
Slide 59
Unlike k-means clustering, which is unstructured, SOMs allow
one to impose partial structure on the clusters. The principle of
SOMs is as follows. One chooses an initial geometry of nodes such
as a 3 x 2 rectangular grid (indicated by solid lines in the figure
connecting the nodes). Hypothetical trajectories of nodes as they
migrate to fit data during successive iterations of SOM algorithm
are shown. Data points are represented by black dots, six nodes of
SOM by large circles, and trajectories by arrows.
Slide 60
Self-organizing maps (SOM) Neighboring nodes tend to define
'related' clusters. An SOM based on a rectangular grid thus is
analogous to an entomologist's specimen drawer in which adjacent
compartments hold similar insects.
Slide 61
Two pre-processing steps essential to apply SOMs 1. Variation
Filtering: Data were passed through a variation filter to eliminate
those genes showing no significant change in expression across the
k samples. This step is needed to prevent nodes from being
attracted to large sets of invariant genes. 2. Normalization: The
expression level of each gene was normalized across experiments.
This focuses attention on the 'shape' of expression patterns rather
than absolute levels of expression.
Slide 62
Principal component axis #2 (10%) Principal component axis #1
(87%) PC#3: 1% C3 C4 C2 C1 N2 N3 N4 P1 P4 P2 P3 Lead (P) Sodium (N)
Control (C) Legend Principal components analysis (PCA), an
exploratory technique that reduces data dimensionality,
distinguishes lead-exposed from control cell lines
Slide 63
An exploratory technique used to reduce the dimensionality of
the data set to 2D or 3D For a matrix of m genes x n samples,
create a new covariance matrix of size n x n Thus transform some
large number of variables into a smaller number of uncorrelated
variables called principal components (PCs). Principal components
analysis (PCA) Page 211
Slide 64
Principal components analysis (PCA): objectives to reduce
dimensionality to determine the linear combination of variables to
choose the most useful variables (features) to visualize
multidimensional data to identify groups of objects (e.g.
genes/samples) to identify outliers Page 211
