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Microarray data analysis

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Gene Expression - Microarrays
Misha Kapushesky
European Bioinformatics Institute, EMBL
St. Petersburg, Russia
May 2010
Compare gene expression
in this cell type…
…after viral
infection
…relative
to a knockout
…in samples
from patients
…after drug
treatment
…at a later
developmental time
…in a different
body region
Gene expression is context-dependent,
and is regulated in several basic ways
• by region (e.g. brain versus kidney)
• in development (e.g. fetal versus adult tissue)
• in dynamic response to environmental signals
(e.g. immediate-early response genes)
• in disease states
• by gene activity
Page 297
Outline: microarray data analysis
Gene expression
Microarrays
Preprocessing
normalization
scatter plots
Inferential statistics
t-test
ANOVA
Exploratory (descriptive) statistics
distances
clustering
principal components analysis (PCA)
Microarrays: tools for gene expression
A microarray is a solid support (such as a membrane
or glass microscope slide) on which DNA of known
sequence is deposited in a grid-like array.
Page 312
Microarrays: tools for gene expression
The most common form of
microarray is used to measure
gene expression. RNA is isolated
from matched samples
of interest. The RNA is typically
converted to cDNA,
labeled with fluorescence (or
radioactivity), then hybridized
to microarrays in order to
measure the expression levels
of thousands of genes.
Measuring RNA abundances
ostolop@ebi.ac.uk
How it works
Complementary hybridization:
- Put a part of the gene sequence on the array
- convert mRNA to cDNA using reverse transcriptase
ostolop@ebi.ac.uk
Spotted Arrays
• Robot puts little spots of DNA on glass slides
• Each spot is a DNA analog of the mRNA we
want to detect
ostolop@ebi.ac.uk
Spotted Arrays
• Two channel technology for comparing two
samples – relative measurements
• Two mRNA samples (reference, test) are reverse
transcribed to cDNA, labeled with fluorescent
dyes (Cy3, Cy5) and allowed to hybridize to array
ostolop@ebi.ac.uk
Spotted Arrays
• Read out two images by scanning array with lasers,
one for each dye
ostolop@ebi.ac.uk
Oligonucleotide Arrays
• One channel technology – absolute measurements
• Instead of putting entire genes on array, put multiple
oligonucleotide probes: short, fixed length DNA
sequences (25-60 nucleotides)
• Oligos are synthesized in situ
• Affymetrix uses a photolithography process,
similar to that used to make semiconductor chips
• Other technologies available (e.g. mirror arrays)
ostolop@ebi.ac.uk
Oligonucleotide Arrays
• For each gene, construct a probeset – a set of
n-mers to specific to this gene
ostolop@ebi.ac.uk
Advantages of microarray experiments
Fast
Data on >20,000 transcripts within weeks
Comprehensive
Entire yeast or mouse genome on a chip
Flexible
Custom arrays can be made
to represent genes of interest
Easy
Submit RNA samples to a core facility
Cheap?
Chip representing 20,000 genes for $300
Disadvantages of microarray experiments
Cost
■Some researchers can’t afford to do
appropriate numbers of controls, replicates
RNA
в– The final product of gene expression is protein
significance ■“Pervasive transcription” of the genome is
poorly understood (ENCODE project)
в– There are many noncoding RNAs not yet
represented on microarrays
Quality
control
в– Impossible to assess elements on array surface
в– Artifacts with image analysis
в– Artifacts with data analysis
в– Not enough attention to experimental design
в– Not enough collaboration with statisticians
Sample
acquisition
Data
acquisition
Data
analysis
Data
confirmation
Biological insight
Stage 1: Experimental design
Stage 2: RNA and probe preparation
Stage 3: Hybridization to DNA arrays
Stage 4: Image analysis
Stage 5: Microarray data analysis
Stage 6: Biological confirmation
Stage 7: Microarray databases
Stage 1: Experimental design
[1] Biological samples: technical and biological replicates:
determine the data analysis approach at the outset
[2] RNA extraction, conversion, labeling, hybridization:
except for RNA isolation, routinely performed at core facilities
[3] Arrangement of array elements on a surface:
randomization can reduce spatially-based artifacts
Page 314
Stage 2: RNA preparation
For Affymetrix chips, need total RNA (about 5 ug)
Confirm purity by running agarose gel
Measure a260/a280 to confirm purity, quantity
One of the greatest sources of error in microarray
experiments is artifacts associated with RNA isolation;
appropriately balanced, randomized experimental
design is necessary.
Stage 3: Hybridization to DNA arrays
The array consists of cDNA or oligonucleotides
Oligonucleotides can be deposited by photolithography
The sample is converted to cRNA or cDNA
(Note that the terms “probe” and “target” may refer to the
element immobilized on the surface of the microarray, or
to the labeled biological sample; for clarity, it may be
simplest to avoid both terms.)
Stage 4: Image analysis
RNA transcript levels are quantitated
Fluorescence intensity is measured with a
scanner.
Differential Gene Expression on a cDNA Microarray
Control
Rett
a B Crystallin
is over-expressed
in Rett Syndrome
Fig. 8.21
Page 319
Fig. 8.21
Page 319
Stage 5: Microarray data analysis
Hypothesis testing
• How can arrays be compared?
• Which RNA transcripts (genes) are regulated?
• Are differences authentic?
• What are the criteria for statistical significance?
Clustering
• Are there meaningful patterns in the data (e.g. groups)?
Classification
• Do RNA transcripts predict predefined groups, such as
disease subtypes?
Page 318
Stage 6: Biological confirmation
Microarray experiments can be thought of as
“hypothesis-generating” experiments.
The differential up- or down-regulation of specific RNA
transcripts can be measured using independent assays
such as
-- Northern blots
-- polymerase chain reaction (RT-PCR)
-- in situ hybridization
Page 320
Stage 7: Microarray databases
There are two main repositories:
Gene Expression Omnibus (GEO) at NCBI
ArrayExpress at the European Bioinformatics
Institute (EBI)
Microarray Overview I
Microtiter Plate
Microbial
ORFs
Design PCR Primers
Microarray Slide
(with 60,000 or more
spotted genes)
+
PCR Products
Eukaryotic
Genes
Select cDNA clones
PCR Products
Many different plates
containing different genes
For each plate set,
many identical replicas
Microarray Overview II
Measure
Fluorescence
in 2 channels
red/green
Control
Test
Prepare Fluorescently
Labeled Probes
Hybridize,
Wash
Analyze the data
to identify
patterns of
gene expression
Affymetrix GeneChipв„ў Expression Analysis
Hybridize and
wash chips
Scan chips
Control
Analyze
Test
Obtain RNA
Samples
Prepare
Fluorescently
Labeled
Probes
PM
MM
Microarray Expression Analysis
Tissue
Selection
Differential
State/Stage
Selection
RNA Preparation
and Labeling
Competitive
Hybridization
Gene
Spots
on an
Array
Fluorescence
Intensity
Expression
Measurement
Steps in the Process
Select array elements and annotate them
Build a database to manage stuff
Print arrays and manage the lab
Hybridize and analyze images; manage data
Analyze hybridization data and get results
MIAME
In an effort to standardize microarray data presentation
and analysis, Alvis Brazma and colleagues at 17
institutions introduced Minimum Information About a
Microarray Experiment (MIAME). The MIAME framework
standardizes six areas of information:
в–єexperimental design
в–єmicroarray design
в–єsample preparation
в–єhybridization procedures
в–єimage analysis
в–єcontrols for normalization
Visit http://www.mged.org
Interpretation of RNA analyses
The relationship of DNA, RNA, and protein:
DNA is transcribed to RNA. RNA quantities and
half-lives vary. There tends to be a low positive
correlation between RNA and protein levels.
The pervasive nature of transcription:
The Encyclopedia of DNA Elements (ENCODE)
project identified functional features of genomic
DNA, initially in 30 megabases (1% of the human
genome). One of its observations was the
“pervasive nature of transcription”: the vast majority
of DNA is transcribed, although the function is
unknown.
Outline: microarray data analysis
Gene expression
Microarrays
Preprocessing
normalization
scatter plots
Inferential statistics
t-test
ANOVA
Exploratory (descriptive) statistics
distances
clustering
principal components analysis (PCA)
Microarray data analysis
• begin with a data matrix (gene expression values
versus samples)
genes
(RNA
transcript
levels)
Microarray data analysis
• begin with a data matrix (gene expression values
versus samples)
Typically, there are
many genes
(>> 20,000) and
few samples (~ 10)
Fig. 9.1
Page 333
Microarray data analysis
• begin with a data matrix (gene expression values
versus samples)
Preprocessing
Inferential statistics
Descriptive statistics
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
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.
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.
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.
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)
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
Differential Gene Expression
in Different Tissue and Cell Types
Fibroblast
Brain
Astrocyte
Astrocyte
Expression level (sample 2)
high
low
Expression level (sample 1)
Log-log
transformation
Scatter plots
Typically, data are plotted on log-log coordinates
Visually, this spreads out the data and offers symmetry
time
t=0
t=1h
t=2h
t=3h
behavior
basal
no change
2-fold up
2-fold down
raw ratio
value
1.0
1.0
2.0
0.5
log2 ratio
value
0.0
0.0
1.0
-1.0
expression level
low
high
Log ratio
up
down
Mean log intensity
You can make these plots in Excel…
…but for many bioinformatics applications use R.
Visit http://www.r-project.org to download it.
There are limits to what you
can measure
The Limits of log-ratios: The space we explore
The Limits of log-ratios: The space we explore
The Limits of log-ratios: The space we explore
Good Data
Bad Data from Parts Unknown
Each “pin group” is colored differently
Gary Churchill
Lowess Normalization
Why LOWESS?
A
SD =
0.346
1. Intensity-dependent structure
2. Data not mean centered at log2(ratio) = 0
Ratio Cy3/Cy5 for the same RNA
sorted from least most expressed
LOWESS Results
Affymetrix Chips
Mismatch (MM) probes
• MM probes are used to measure background
signals due to non-specific sources and
scanner offset.
• Using a MM probe as an estimate of
background seems wrong and often the MM
signal >= the PM signal
• Some would claim that subtraction of the
mismatch probe adds noise for little gain.
Computing expression summaries: a
three-step process
• Background/Signal adjustment
• Normalization (can happen at the probe-pair or
the probe-set level).
• Summarization of probe-pairs into probe-set or
gene level information
Background/Signal Adjustment
• A method which does some or all of the following
Corrects for background noise, processing effects
Adjusts for cross hybridization
Adjust estimated expression values to fall on proper scale
• Probe intensities are used in background adjustment
to compute correction (unlike cDNA arrays where area
surrounding spot might be used)
Normalization Methods
• Complete data (no reference chip, information
from all arrays used)
Quantile normalization (Bolstadt al 2003)
• Baseline (normalized using reference chip)
Scaling (Affymetrix)
Non linear (Li-Wong)
Summarization
• Reduce the 11-20 probe intensities on each array to a
single number for gene expression
• Main Approaches
Single chip
• AvDiff (Affymetrix) – no longer recommended for use due to
many flaws
• Mas5.0 (Affymetrix) –use a 1 step Tukey biweight to combine
the probe intensities in log scale
Multiple Chip
•MBEI (Li-Wong dChip) –a multiplicative model
•RMA –a robust multi-chip linear model fit on the log scale
Robust multi-array analysis (RMA)
• Developed by Rafael Irizarry (Dept. of Biostatistics), Terry
Speed, and others
• Available at www.bioconductor.org as an R package
• Also available in various software packages (including
Partek, www.partek.com and Iobion Gene Traffic)
• See Bolstad et al. (2003) Bioinformatics 19;
Irizarry et al. (2003) Biostatistics 4
There are three steps:
[1] Background adjustment based on a normal plus
exponential model (no mismatch data are used)
[2] Quantile normalization (nonparametric fitting of signal
intensity data to normalize their distribution)
[3] Fitting a log scale additive model robustly. The model is
additive: probe effect + sample effect
GCRMA
• GC-RMA is a modified version of RMA that models
intensity of probe level data as a function of GC-content
• expect to see higher intensity values for probes that are GC
rich due to increased binding
M
M
A
A
After RMA (a normalization
procedure), the median is near zero,
and skewing is corrected.
Scatterplots display the effects of
normalization.
vsn: variance stabilizing normalization
• Variance depends on signal intensity
in microarray data
• A transformation can be found after
which the variance is approximately
constant
• Like the logarithm at the upper end
of, approximately linear at the lower
end
• Also incorporates the estimation of
"normalization" parameters (shift and
scale)
• Assumes that less than half of the
genes on the arrays are differentially
transcribed across the experiment.
vsn: post-normalization plot
Histograms of raw
intensity values for 14
arrays (plotted in R)
before and after RMA
was applied.
log signal intensity
log signal intensity
array
array
log intensity
RMA can adjust for the effect of GC content
GC content
Robust multi-array analysis (RMA)
RMA offers a large increase in precision (relative to
Affymetrix MAS 5.0 software).
log expression SD
precision
MAS 5.0
RMA
average log expression
Robust multi-array analysis (RMA)
RMA offers comparable accuracy to MAS 5.0.
observed log expression
accuracy
log nominal concentration
Outline: microarray data analysis
Gene expression
Microarrays
Preprocessing
normalization
scatter plots
Inferential statistics
t-test
ANOVA
Exploratory (descriptive) statistics
distances
clustering
principal components analysis (PCA)
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 a to p < 0.05.
Analyzing expression data
Question: for each of my 20,000 transcripts, decide
whether it is significantly regulated in some disease.
control
disease
[1] Obtain a matrix of genes (rows) and expression values columns.
Here there are 20,000 rows of genes of which the first six are shown.
There are three control samples and three disease samples. Calculate
the mean value for each gene (transcript) for the controls and the
disease (experimental) samples.
Analyzing expression data
[2] Calculate the ratios of control versus disease.
Also note that some ratios, such as 2.00, appear to be dramatic while
others are not. Some researchers set a cut-off for changes of interest
such as two-fold.
A significant
difference
Probably
not
Inferential statistics
A t-test is a commonly used test statistic to assess
the difference in mean values between two groups.
t=
x1 – x2
SE
=
difference between mean values
variability (standard error
of the difference)
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?
Inferential statistics
A t-test is a commonly used test statistic to assess
the difference in mean values between two groups.
t=
x1 – x2
SE
=
difference between mean values
variability (standard error
of the difference)
Notes
• t is a ratio (it thus has no units)
• We assume the two populations are Gaussian
• The two groups may be of different sizes
• Obtain a P value from t using a table
• For a two-sample t test, the degrees of freedom is N - 2.
• For any value of t, P gets smaller as df gets larger
Analyzing expression data
[3] Perform a t-test. Hypothesis is that the
transcript in the disease group is up (or down)
relative to controls.
Analyzing expression data
[3] Note the results: you can have…
a small p value (<0.05) with a big ratio difference
a small p value (<0.05) with a trivial ratio difference
a large p value (>0.05) with a big ratio difference
a large p value (>0.05) with a trivial ratio difference
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
The Bonferroni correction is generally considered to be too
conservative.
Inferential statistics: false discovery rate
The false discovery rate (FDR) is a popular multiple
corrections correction. A false positive (also called a type
I error) is sometimes called a false discovery.
The FDR equals the p value of the t-test times the
number of genes measured (e.g. for 10,000 genes and a
p value of 0.01, there are 100 expected false positives).
You can adjust the false discovery rate. For example:
FDR # regulated transcripts
0.1
100
0.05
45
0.01
20
# false discoveries
10
3
1
Would you report 100 regulated transcripts of which 10
are likely to be false positives, or 20 transcripts of which
one is likely to be a false positive?
Inferential statistics: other methods used
• t-test for two sample groups, SAM and t-tests with
permutation testing
• ANOVA for multiple factors
• Linear models with Bayesian moderation of variance
Smyth G. (2004) “Linear Models and Empirical Bayes Methods for
Assessing Differential Expression in Microarray Experiments”
• Simultaneous inference: multivariate t-distributions for
simultaneous confidence intervals
Hsu et al. (1996) “Multiple Comparisons: Theory and Methods”
Hsu et al. (2006) “Screening for Differential Gene Expressions from
Microarray Data”
p value (treated versus control)
A volcano plot displays both p values and fold change
log fold change (treated/untreated)
Outline: microarray data analysis
Gene expression
Microarrays
Preprocessing
normalization
scatter plots
Inferential statistics
t-test
ANOVA
Exploratory (descriptive) statistics
distances
clustering
principal components analysis (PCA)
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
What is a cluster?
A cluster is a group that has homogeneity
(internal cohesion) and separation (external
isolation). The relationships between objects
being studied are assessed by similarity or
dissimilarity measures.
samples (time points)
genes
Data matrix
(20 genes and
3 time points
from Chu et al.,
1998)
Software: SPLUS package
t=2.0
t=0.5
t=0
3D plot (using S-PLUS softwar
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 355
log2(cy5/cy3)
Distance Is Defined by a Metric
3
0
-3
Distance Metric:
Euclidean Pearson*
D
1.4
-0.05
D
6.0
+1.00
log2(cy5/cy3)
Distance is Defined by a Metric
2
0
-2
Distance Metric:
Euclidean Pearson(r*-1)
D
1.4
-0.90
D
4.2
-1.00
Distance Matrix
Gene1
Gene2
Gene3
Gene4
Gene5
Gene6
0
1.5
1.2
0.25
0.75
1.4
1.5
0
1.3
0.55
2.0
1.5
1.2
1.3
0
1.3
0.75
0.3
0.25
0.55
1.3
0
0.25
0.4
0.75
2.0
0.75
0.25
0
1.2
Gene6
Gene5
Gene4
Gene3
Gene2
Gene1
Once a distance metric has been selected, the starting point for all
clustering methods is a “distance matrix”
1.4
1.5
0.3
0.4
1.2
0
The elements of this matrix are the pair-wise distances. Note that the
matrix is symmetric about the diagonal.
Agglomerative clustering
0
1
2
3
a
b
a,b
c
d
e
Adapted from Kaufman and Rousseeuw (1990)
4
Agglomerative clustering
0
1
2
a
b
a,b
c
d
e
d,e
3
4
Agglomerative clustering
0
1
2
3
a
b
a,b
c
d
e
c,d,e
d,e
4
Agglomerative clustering
0
1
2
3
4
a
b
a,b
a,b,c,d,e
c
d
e
c,d,e
d,e
…tree is constructed
Divisive clustering
a,b,c,d,e
4
3
2
1
0
Divisive clustering
a,b,c,d,e
c,d,e
4
3
2
1
0
Divisive clustering
a,b,c,d,e
c,d,e
d,e
4
3
2
1
0
Divisive clustering
a,b
a,b,c,d,e
c,d,e
d,e
4
3
2
1
0
Divisive clustering
a
b
a,b
a,b,c,d,e
c
c,d,e
d
d,e
e
4
3
2
1
0
…tree is constructed
agglomerative
0
1
2
3
4
a
b
a,b
a,b,c,d,e
c
c,d,e
d
d,e
e
4
3
2
1
0
divisive
Adapted from Kaufman and Rousseeuw (1990)
1
12
Agglomerative and
divisive clustering
sometimes give conflicting
results, as shown here
1
12
Agglomerative Linkage Methods
Linkage methods are rules or metrics that return
a value that can be used to determine which
elements (clusters) should be linked.
Three linkage methods that are commonly used
are:
Single Linkage
Average Linkage
Complete Linkage
(HCL-6)
Single Linkage
Cluster-to-cluster distance is defined as the minimum distance
between members of one cluster and members of the another
cluster. Single linkage tends to create �elongated’ clusters with
individual genes chained onto clusters.
DAB = min ( d(ui, vj) )
where u пѓЋпЂ A and v пѓЋпЂ B
for all i = 1 to NA and j = 1 to NB
DAB
(HCL-7)
Average Linkage
Cluster-to-cluster distance is defined as the average distance
between all members of one cluster and all members of another
cluster. Average linkage has a slight tendency to produce clusters of
similar variance.
DAB = 1/(NANB) SпЂ S ( d(ui, vj) )
where u пѓЋпЂ A and v пѓЋпЂ B
for all i = 1 to NA and j = 1 to NB
DAB
(HCL-8)
Complete Linkage
Cluster-to-cluster distance is defined as the maximum distance
between members of one cluster and members of the another
cluster. Complete linkage tends to create clusters of similar size and
variability.
DAB = max ( d(ui, vj) )
where u пѓЋпЂ A and v пѓЋпЂ B
for all i = 1 to NA and j = 1 to NB
DAB
(HCL-9)
Comparison of Linkage Methods
Single
Average
Complete
Two-way
clustering
of genes (y-axis)
and cell lines
(x-axis)
(Alizadeh et al.,
2000)
x2
A
a2
Euclidean distance
1
b2
B
a’2
A’
Angle distance
0.5
Chord distance
b’2
B’
a
пЃў
пЃ§
0.5
1
a’1
b’1
1.5
a1
x1
b1
K-Means/Medians Clustering – 1
1. Specify number of clusters, e.g., 5.
2. Randomly assign genes to clusters.
G1
G2
G3
G4
G5
G6
G7
G8
G9
G10
G11
G12
G13
K-Means/Medians Clustering – 2
3. Calculate mean/median expression profile of each cluster.
4. Shuffle genes among clusters such that each gene is now in the
cluster whose mean expression profile (calculated in step 3) is
the closest to that gene’s expression profile.
G3
G11
G6
G1
G8
G4
G7
G5
G2
G10
G9 G12
G13
5. Repeat steps 3 and 4 until genes cannot be shuffled around any
more, OR a user-specified number of iterations has been
reached.
k-means is most useful when the user has an a priori hypothesis about the
number of clusters the genes should belong to.
K-Means / K-Medians Support (KMS)
Because of the random initialization of K-Means/K-Means,
clustering results may vary somewhat between successive runs on
the same dataset. KMS helps us validate the clustering results
obtained from K-Means/K-Medians.
Run K-Means / K-Medians multiple times.
The KMS module generates clusters in which the member genes
frequently group together in the same clusters (“consensus
clusters”) across multiple runs of K-Means / K-Medians.
The consensus clusters consist of genes that clustered together
in at least x% of the K-Means / Medians runs, where x is the
threshold percentage input by the user.
Principal components analysis (PCA)
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): 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
http://www.okstate.edu/artsci/botany/ordinate/PCA.htm
http://www.okstate.edu/artsci/botany/ordinate/PCA.htm
http://www.okstate.edu/artsci/botany/ordinate/PCA.htm
http://www.okstate.edu/artsci/botany/ordinate/PCA.htm
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12
High-throughput methods beyond microarrays
ostolop@ebi.ac.uk
RNA-seq
• Sequencing technology is making fast progress
• Idea: sequencing is so cheap that we can sequence
mRNA molecules directly
“Digital Gene Expression”
ostolop@ebi.ac.uk
RNA-seq
ostolop@ebi.ac.uk
(a) After two rounds of poly(A) selection, RNA
is fragmented to an average length of 200
nt by magnesium-catalyzed hydrolysis and
then converted into cDNA by random
priming. The cDNA is then converted into a
molecular library for Illumina/Solexa 1G
sequencing, and the resulting 25-bp reads
are mapped onto the genome. Normalized
transcript prevalence is calculated with an
algorithm from the ERANGE package.
(b) Primary data from mouse muscle RNAs
that map uniquely in the genome to a 1-kb
region of the Myf6 locus, including reads
that span introns. The RNA-Seq graph
above the gene model summarizes the
quantity of reads, so that each point
represents the number of reads covering
each nucleotide, per million mapped reads
(normalized scale of 0–5.5 reads).
(c) Detection and quantification of differential
expression. Mouse poly(A)-selected RNAs
from brain, liver and skeletal muscle for a
20-kb region of chromosome 10 containing
Myf6 and its paralog Myf5, which are
muscle specific. In muscle, Myf6 is highly
expressed in mature muscle, whereas Myf5
is expressed at very low levels from a small
number of cells. The specificity of RNA-Seq
is high: Myf6 expression is known to be
highly muscle specific, and only 4 reads out
of 71 million total liver and brain mapped
reads were assigned to the Myf6 gene
model.
RNA-seq
ostolop@ebi.ac.uk
Acknowledgements
• This presentation uses slides/graphics from:
J. Pevsner (Johns Hopkins, http://www.bioinfbook.org)
J. Quackenbush (DFCI, Harvard)
C. Dewey (Wisconsin, http://www.biostat.wisc.edu/bmi576)
ostolop@ebi.ac.uk
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