Microarray Technology and

Data Analysis

(November 28, 2007)

slides assembled by Dong-Guk Shin and J Peter Gogarten

Introduction to MicroarrayTechnology

Two color microarrays:

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two conditions

two labels for cDNA

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)

created through photolithography

on cell in array

hybridization to labeled RNA from sample

result of hybridization to array

Experimental design and sources for variation

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

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

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:

Pooling

from http://discover.nci.nih.gov/microarrayAnalysis/Experimental.Design.jsp

A reference design: the red and green arrows represent chips.

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

Topic 2Data Preprocessing

• Background Correction

• Normalization

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

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

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!!

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.

Statistical Methods for Identifying Differentially Expressed Genes in Replicated Microarray Experiments

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.

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!)

Linear Models for Microarray DataPackage to analyze MA data. Good plot capabilities.

Significance Analysis of Microarrays

semi-parametric hierarchical (SPH) mixture model

Significance Analysis of Microarrays (SAM)

uses balanced permutations (sample versus control intensities “re-labeling”) to generate an expectation for the comparison

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.)

Microarray Data: Clustering

ClusteringAssign n similar objects to groups

Example: green/ red data points were generated from two different normal distributions

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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Distance measure (Example: Intra-Cluster Distances for hierarchical clustering)

• Euclidean:

• Manhattan:

• Correlation:

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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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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.

Volcano Plot and Heatmaps

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Parametric Clustering (partitioning)

• K-Means• K-Medoids (PAM)• SOM• Fuzzy-C Means

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

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.

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.

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)