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Microarray Technology and
Data Analysis
(November 28, 2007)
slides assembled by Dong-Guk Shin and J Peter Gogarten
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Introduction to MicroarrayTechnology
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Two color microarrays:
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two conditions
two labels for cDNA
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develop slide with mRNAs
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make images, one for each probe
fuse in computer
hybridize mixture of both probes to printed glass slides
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An alternative is to synthesize the DNA directly onto the matrix (slides from Affymetrix)
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created through photolithography
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on cell in array
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hybridization to labeled RNA from sample
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result of hybridization to array
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Experimental design and sources for variation
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Biological Variation -
Rules of thumb:
•Biological Replicates are a must!
•As many biological replicates as you can afford!
•Cell population as homogeneous as possible!
Sample Processing
Variation
Array & Environment
Variation
Technical Variation
Effect Size
“One characteristic common to all biological material is that it varies.”
Finney, 1953
E.g.: Two mice in two different cages
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Control of Experiment Variance
Degree of Replication
•Robustness of the method Spot replication•Dye Swap array replication•Robustness of the biological assay
•Absolute Transcript frequency/signal intensity Sample replication•Relative Transcript frequency associated with the biological effect Sample replication
•Cellular sample composition Sample replication
“If I had to replicate my experiments, I could only do half as much.”Botstein, 1999
Biological Replication •Biological variance 0 •High accuracy experiment•Biological and technical variation
are confounded•Measurement precision decreased
Technical Replication •Technical variance 0
•High Precision experiment
•Technical Replication: Estimation of technical Variation•biological effect inaccurate
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Statistical Analysis and Design
Single Color•Post hoc comparison
Two Color•Direct comparison
•Indirect comparison
• Post Hoc Design– 2 data point/gene/condition
• Loop Design (Balanced)– biological and technical variation
not confounded– 8 datapoints/gene/condition
• Reference Design (Unbalanced)– biological and technical variation
not confounded– Reference overrepresented– 4 data point/gene/condition
The number of independent data points is a function of the comparison design:
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Pooling
from http://discover.nci.nih.gov/microarrayAnalysis/Experimental.Design.jsp
A reference design: the red and green arrows represent chips.
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A loop design: arrows represent chips with samples labeled as indicated.
A saturated design w/o dye swap
A design for a comparative study of the effect of a treatment on two biological strains with replicates and a few dye swaps
from http://discover.nci.nih.gov/microarrayAnalysis/Experimental.Design.jsp
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Topic 2Data Preprocessing
• Background Correction
• Normalization
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Background Correction
• None– DNA vs Substrate– No Imputation/Offset
• Local– Negative Signal Intensities
likely– Imputation/Offset required
• Global– Negative Signal Intensities
likely– Imputation/Offset required
• Moving Minimum – 3x3 spot average background– Negative Signal Intensities
likely– Imputation/Offset required
• Edwards– log-linear interpolation of
background intensities– Background Intensity insensitive– Test for Imputation
• Norm-Exp– regression based background
estimation using Signal to Noise ratios
– Background Intensity sensitive– No Imputation
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Normalization
Background correction
Expression ratio: Ti= Ri/Gi
log2(ratio) log2(1) = 0, log2(2) = 1, log2(1/2) = 1, log2(4) = 2, log2(1/4) = 2
total intensity normalization: If one has a large random sample of genes most of which remain unchanged, one could normalize so that the mean ratio (T) for all spots is 1. (for the log2Ti correction this corresponds to a subtraction of a constant. see http://www.nature.com/cgi-taf/DynaPage.taf?file=/ng/journal/v32/n4s/full/ng1032.html&filetype=pdf )
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Cond.2a
Cond.2b
Cond.2c
Cond.1a
Cond.1b
Cond.1c
Comparison Synth. Image Scatterplot Ratiohistogram
Two Color Analytical Plots
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typical depiction ratio versus intensity (log R +log G)
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From: http://www.nature.com/cgi-taf/DynaPage.taf?file=/ng/journal/v32/n4s/full/ng1032.html&filetype=pdf
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after locally weighted linear regression analysis
From: http://www.nature.com/cgi-taf/DynaPage.taf?file=/ng/journal/v32/n4s/full/ng1032.html&filetype=pdf
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Beware
Any data adjustment, even if it performed as sophisticated or industrious as possible, cannot convert low quality data into high quality data.
Data adjustment always removes a part of the biology.
!!Use it as sparingly as possible!!
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Filtering Data
From: http://www.nature.com/cgi-taf/DynaPage.taf?file=/ng/journal/v32/n4s/full/ng1032.html&filetype=pdf
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Outliers in the original data (in red) are excluded from the remainder of the data (blue) selected on the basis of a two-standard-deviation cut on the replicates.
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Statistical Methods for Identifying Differentially Expressed Genes in Replicated Microarray Experiments
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Sample 1 Sample 2 Sample M
Gene 1Gene 2
Gene N
Expression Profile
Expression
Signature
Gene Expression Data represented as N x M Matrix
N rows correspond to the N genes.
M columns correspond to the M samples (microarray experiments).
Each column = a sample or a replicate
Example:Four replicate spots per array produces four column R/G ratio.
If four replicate arrays are used,It will produce a 16 column matrix.Or 32 if R and G values are putseparately.
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Student’s Test Statistics
99% 95% 68% of all samples
H0: The groups are not different
Naïve solution: do t-test for each gene.Multiplicity Problem: The probability of error increases. (Bonferoni correction too conservative!)
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Linear Models for Microarray DataPackage to analyze MA data. Good plot capabilities.
Significance Analysis of Microarrays
semi-parametric hierarchical (SPH) mixture model
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Significance Analysis of Microarrays (SAM)
uses balanced permutations (sample versus control intensities “re-labeling”) to generate an expectation for the comparison
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Volcano plotscompare significance (Y-axis) against effect (x
axis)•The plot compares significance determinations obtained with MAANOVA (MicroArray ANalysis Of VAriance) •On the plot, the y-axis value is -log10(P-value) for the F1 test. The x-axis value is proportional to the fold changes. •A horizontal line represents the significance threshold of the F1 test. •Blue dots: EE genes•Green dots: F3 •Orange dots: Fs •F2 (In example graph, F2 tests
were not run.)
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Microarray Data: Clustering
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ClusteringAssign n similar objects to groups
Example: green/ red data points were generated from two different normal distributions
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Why cluster genes?• Identify groups of possibly co-regulated genes • Identify temporal or spatial gene expression patterns
Why cluster experiments/samples? • Detect experimental artifacts/bad hybridizations• Identify new classes of biological samples (e.g. tumor subtypes)
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To Do Clustering You Need …C
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Distance measure (Example: Intra-Cluster Distances for hierarchical clustering)
• Euclidean:
• Manhattan:
• Correlation:
gene expression # 1: x = (x1, …, xn),
gene expression # 2: y = (y1, …, yn)
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Cluster Algorithm/Method (1) Hierarchical(2) Parametric (Partitioning)
To Do Clustering You Also Need …
Basic Idea•small within-cluster distances• large between-cluster distances
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1 5 2 3 4
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Agglomerative
Hierarchical Clustering
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Copyright ©1998 by the National Academy of Sciences
Eisen, Michael B. et al. (1998) Proc. Natl. Acad. Sci. USA 95, 14863-14868
Hierarchical clustering
Clustered display of data from time course of serum stimulation of primary human fibroblasts (grown in culture and deprived of serum for 48 hr, serum was added back and samples taken at time 0, 15 min, 30 min, 1 hr, 2 hr, 3 hr, 4 hr, 8 hr, 12 hr, 16 hr, 20 hr, 24 hr). All measurements are relative to time 0. Genes were selected for this analysis if their expression level deviated from time 0 by at least a factor of 3.0 in at least 2 time points. Each gene is represented by a single row of colored boxes; each time point is represented by a single column. Labeled clusters contain multiple genes involved in (A) cholesterol biosynthesis, (B) the cell cycle, (C) the immediate-early response, (D) signaling and angiogenesis, and (E) wound healing and tissue remodeling. These clusters also contain named genes not involved in these processes and numerous uncharacterized genes.
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Volcano Plot and Heatmaps
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Parametric Clustering (partitioning)
• K-Means• K-Medoids (PAM)• SOM• Fuzzy-C Means
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Partitioning Algorithms: Basic Concept
• Partitioning method: Construct a partition of a database D of n objects into a set of k clusters
• Given a k, find a partition of k clusters that optimizes the chosen partitioning criterion– Global optimal: exhaustively enumerate all partitions
– Heuristic methods: k-means and k-medoids algorithms
– k-means (MacQueen’67): Each cluster is represented by the center of the cluster
– k-medoids or PAM (Partition around medoids) (Kaufman & Rousseeuw’87): Each cluster is represented by one of the objects in the cluster
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The K-Means Clustering Method
• Given k, the k-means algorithm is implemented in 4 steps:– Partition objects into k nonempty subsets– Compute seed points as the centroids of the clusters of the
current partition. The centroid is the center (mean point) of the cluster.
– Assign each object to the cluster with the nearest seed point. – Go back to Step 2, stop when no more new assignment.
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Parametric or Hierarchical (Non-Parametric)?
Parametric:Advantages
Optimal for certain criteria.
Genes automatically assigned to clusters
Disadvantages
Need initial k;
Often require long computation times.
Every gene is assigned to a cluster.
HierarchicalAdvantages
Faster computation.
Visual Representation.
Disadvantages
Unrelated genes are eventually joined
Rigid, cannot correct later for erroneous decisions made earlier.
Hard to define clusters.
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Meta Analyses of MA data:Go AnalysisPathway Analysis
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To do:
For Friday
–Read chapter 18
–Browse through http://jura.wi.mit.edu/bio/education/bioinfo/lecture10-color.pdf and
–http://www.nature.com/cgi-taf/DynaPage.taf?file=/ng/journal/v32/n4s/full/ng1032.html&filetype=pdf
For Monday:
–Refresh your memory on McRobot and Bayesian analyses
–Go through quiz 8 (will be posted Friday/Saturday, due following Wednesday)