Download Analysis of Expression Array Results

Clustering Gene Expression Data
DNA Microarrays Workshop
Feb. 26 – Mar. 2, 2001 ,UNIL & EPFL, Lausanne
Gaddy Getz, Weizmann Institute, Israel
• Gene Expression Data
• Clustering of Genes and Conditions
• Methods
– Agglomerative Hierarchical: Average Linkage
– Centroids: K-Means
– Physically motivated: Super-Paramagnetic Clustering
• Coupled Two-Way Clustering
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Gene Expression Technologies
• DNA Chips (Affymetrix) and MicroArrays can measure
mRNA concentration of thousands of genes simultaneously
• General scheme: Extract RNA, synthesize labeled cDNA,
Hybridize with DNA on chip.
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Single Experiment
• After hybridization
– Scan the Chip and obtain an image file
– Image Analysis (find spots, measure signal and noise)
Tools: ScanAlyze, Affymetrix, …
• Output File
– Affymetrix chips: For each gene a reading proportional
to the concentrations and a present/absent call.
(Average Difference, Absent Call)
– cDNA MicroArrays: competing hybridization of target
and control. For each gene the log ratio of target and
control. (CH1I-CH1B, CH2I-CH2B)
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Preprocessing: From one experiment to many
• Chip and Channel Normalization
– Aim: bring readings of all experiments to be on the
same scale
– Cause: different RNA amounts, labeling efficiency and
image acquisition parameters
– Method: Multiply readings of each array/channel by a
scaling factor such that:
• The sum of the scaled readings will be the same for all arrays
• Find scaling factor by a linear fit of the highly expressed genes
– Note: In multi-channel experiments normalize each
channel separately.
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Preprocessing: From one experiment to many
Colon cancer data (Alon et. al.)
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• Filtering of Genes
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– Remove genes that are
absent in most
600
experiments
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– Remove genes that are constant in all
1000
experiments
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– Remove genes with low readings which are not
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reliable.
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Genes
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2000
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Experiments
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Noise and Repeats
log – log plot
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•
•
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>90% 2 to 3 fold
Multiplicative noise
Repeat experiments
Log scale
dist(4,2)=dist(2,1)
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We canSupervised
ask many
Methods questions?
(use predefined labels)
• Which genes are expressed differently in two
known types of conditions?
• What is the minimal set of genes needed to
distinguish one type of conditions from the others?
• Which genes behave similarly in the experiments?
• How many different types of conditions are there?
Unsupervised Methods
(use only the data)
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Unsupervised Analysis
• Goal A: Find groups of genes that have correlated
expression profiles.
These genes are believed to belong to the same
biological process and/or are co-regulated.
• Goal B: Divide conditions to groups with similar
gene expression profiles.
Example: divide drugs according to their effect on
gene expression.
Clustering Methods
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What is clustering?
• Input: N data points, Xi, i=1,2,…,N in a D
dimensional space.
• Goal: Find “natural” groups or clusters.
Data point of same cluster – “more similar”
• Note: number of clusters also to be determined
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Clustering is ill-posed
• Problem specific definitions
• Similarity: which points should be
considered close?
– Correlation coefficient
– Euclidean distance
• Resolution: specify/hierarchical results
• Shape of clusters: general, spherical.
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Similarity Measure
• Similarity measures
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–
–
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Centered Correlation
Uncentered Correlation
Absolute correlation
Euclidean
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Need to define the distance between the
new cluster and the other clusters.
Single Linkage:
distance between closest pair.
Agglomerative Hierarchical Clustering
Complete Linkage: distance between farthest pair.
Average
Linkage:
average
Distance between
joined
clustersdistance between all pairs
or distance between cluster centers
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The dendrogram induces a linear ordering
of the data points
Dendrogram
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Agglomerative Hierarchical Clustering
• Results depend on distance update method
– Single Linkage: elongated clusters
– Complete Linkage: sphere-like clusters
• Greedy iterative process
• NOT robust against noise
• No inherent measure to choose the clusters
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Centroid Methods - K-means
•Start with random position of K
centroids.
•Iteratre until centroids are stable
•Assign points to centroids
•Move centroids to center
of assign points
Iteration = 0
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Centroid Methods - K-means
•Start with random position of K
centroids.
•Iteratre until centroids are stable
•Assign points to centroids
•Move centroids to center
of assign points
Iteration = 1
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Centroid Methods - K-means
•Start with random position of K
centroids.
•Iteratre until centroids are stable
•Assign points to centroids
•Move centroids to center
of assign points
Iteration = 1
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Centroid Methods - K-means
•Start with random position of K
centroids.
•Iteratre until centroids are stable
•Assign points to centroids
•Move centroids to center
of assign points
Iteration = 3
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Centroid Methods - K-means
• Result depends on initial centroids’ position
• Fast algorithm: compute distances from data
points to centroids
• No way to choose K.
• Example: 3 clusters / K=2, 3, 4
• Breaks long clusters
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Super-Paramagnetic Clustering (SPC)
M.Blatt, S.Weisman and E.Domany (1996) Neural Computation
• The idea behind SPC is based on the physical
properties dilute magnets.
• Calculating correlation between magnet
orientations at different temperatures (T).
T=Low
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Super-Paramagnetic Clustering (SPC)
M.Blatt, S.Weisman and E.Domany (1996) Neural Computation
• The idea behind SPC is based on the physical
properties dilute magnets.
• Calculating correlation between magnet
orientations at different temperatures (T).
T=High
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Super-Paramagnetic Clustering (SPC)
M.Blatt, S.Weisman and E.Domany (1996) Neural Computation
• The idea behind SPC is based on the physical
properties dilute magnets.
• Calculating correlation between magnet
orientations at different temperatures (T).
T=Intermediate
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Super-Paramagnetic Clustering (SPC)
• The algorithm simulates the magnets behavior at a range of
temperatures and calculates their correlation
• The temperature (T) controls the resolution
• Example: N=4800 points in D=2
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Output of SPC
A function (T) that peaks
when stable clusters break
Size of largest clusters as
function of T
Dendrogram
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Stable clusters
“live” for large T
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Choosing a value for T
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Advantages of SPC
• Scans all resolutions (T)
• Robust against noise and initialization calculates collective correlations.
• Identifies “natural” () and stable clusters (T)
• No need to pre-specify number of clusters
• Clusters can be any shape
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Many clustering methods applied
to expression data
• Agglomerative Hierarchical
– Average Linkage (Eisen et. al., PNAS 1998)
• Centroid (representative)
– K-Means (Golub et. al., Science 1999)
– Self Organized Maps (Tamayo et. al., PNAS 1999)
• Physically motivated
– Deterministic Annealing (Alon et. al., PNAS 1999)
– Super-Paramagnetic Clustering (Getz et. al., Physica A 2000)
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Available Tools
• M. Eisen’s programs for clustering and display of
results (Cluster, TreeView)
– Predefined set of normalizations and filtering
– Agglomerative, K-means, 1D SOM
• Matlab
– Agglomerative, public m-files.
• Dedicated software packages (SPC)
• Web sites: e.g. http://ep.ebi.ac.uk/EP/EPCLUST/
• Statistical programs (SPSS, SAS, S-plus)
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Colon cancer data (normalized genes)
Back to gene expression data
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• 2 Goals: Cluster Genes and Conditions
• 2 independent clustering:
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600
Genes
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– Genes represented as vectors of expression in
all conditions 1200
1400
– Conditions are represented
as vectors of
expression of all 1600
genes
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0.2
0
-0.2
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-0.4
2000
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Experiments
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First clustering - Experiments
1. Identify tissue classes (tumor/normal)
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Second Clustering - Genes
2. Find Differentiating And Correlated Genes
Ribosomal proteins
Cytochrome C
metabolism
HLA2
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Two-way
Clustering
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Coupled Two-Way Clustering (CTWC)
G. Getz, E. Levine and E. Domany (2000) PNAS
• Why use all the genes to represent conditions and all
conditions to represent genes?
Different structures emerge when clustering
sub-matrices.
• New Goal: Find significant structure in subsets of the
data matrix.
• A non-trivial task – exponential number of subsets.
• Recently we proposed a heuristic to solve this
problem.
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CTWC of colon cancer data
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(A)
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(B)
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Biological Work
• Literature search for the genes
• Genomics: search for common regulatory
signal upstream of the genes
• Proteomics: infer functions.
• Design next experiment – get more data to
validate result.
• Find what is in common with sets of
experiments/conditions.
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Summary
• Clustering methods are used to
– find genes from the same biological process
– group the experiments to similar conditions
• Different clustering methods can give different
results. The physically motivated ones are more
robust.
• Focusing on subsets of the genes and conditions
can uncover structure that is masked when using
all genes and conditions
www.weizmann.ac.il/physics/complex/compphys
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