BioInfoSummer, ANU, December 2003

Challenges in the Analysis of GeneChip Microarray data

Sue WilsonCMA & CBiS, MSI

ANU

Outline

I Introduction to/ Summary of GeneChip technology

II Challenges* Relationship between I and mRNA* Design* Analysis* Others, including normalisation and multiple testing

Microarray technologyfor RNA expression

profiling

Largely encompasses 2 different technologies:

1. Spotted cDNA/oligo arrays

2. Short oligonucleotide arrays (Affymetrix’s GeneChip)

Other gene expression assay technologies include:

a. macroarrays

b. Serial analysis of gene expression (SAGE)

c. Long oligonucleotide arrays (Agilent Inkjet)

d. Fibre optic arrays (Illumina)

•Defining differences (1. & 2.) include:Genomic material used to make the array,How this material is placed on the array. Both have implications for

Design of experiments.

(Essentially) Shared Features

• HybridizationGenetic material fixed to array - ProbeLabeled c*NA - Target

• Obtaining TargetExtract RNA, reverse transcribe -> cDNA (Spotted - tag with fluorescent dye Oligo GeneChip - biotin-labelled cRNA from cDNA)

• Wash excess c*NA from array (Oligo GeneChip - stain with fluorescent molecule)

• Scan

(Essentially) Shared Features, C’td

The Data• Signal & Background

Image analysis• Transform?

(Essentially) Shared Features, C’td

The Data, c’td• Normalization & scaling

To remove differences between arrays that may be due to the following reasons: * biological - background, sample treatment * biochemical and molecular biology - buffers, enzymes,

reaction conditions * technological - GeneChip & wafer quality, hybridization

conditions

• Replication# & level - technical vs biological;

depends on question/s being addressed

(Essentially) Shared Features, C’td

‘Uncontrolled experimental variables may be introduced at any step in the wet laboratory workup of microarray experiments and may add to observed variances from array to array.’

HV Baker, Stat. Sci., 2003At design stage, important to recognise where UEVs may

be; often unavoidable. Potential sources vary with application. Eg, clinical studies for GE differences between tumour and normal tissue. UEVs may include age, sex, diet, diurnal variations in GE, type of anesthetic used, time from tissue removal to RNA stabilisation, method of RNA isolation, etc.; analogous for laboratory animals except that some of these UEVs can be controlled.

Differential recovery of specific cell types from tissue may bias the GE profile observed for a particular tissue type.

Affymetrix GeneChip technology (Summary)

• Short (25 mer) Oligonucleotides

• 40-60k DNA oligos on ~ 2.5 cm2 glass surface.

• Technology combines oligonucleotide synthesis with photolithographic computer chip technology.

• The oligonucleotides are synthesized on the slide.

A probe set = 11-20 PM, MM pairs

There may be 5,000-100,000 probe sets per chip

Spotted vs. Affymetrix arrays

Spotted cDNA arrays| Affymetrix arrays

One probe / gene (EST) 11-20 probe pairs /gene

Probes of varying length

Probes are 25-mers

2 target samples / array 1 target sample / array

Oligonucleotide chips

• The manufacturing of GeneChip® probe arrays is a combination of photolithography and combinatorial chemistry. See: Affymetrix Technology [on www]

Oligonucleotide chips

Affy Image analysis

• Raw data, DAT image files -> CEL files• Each probe cell: 10x10 pixels• Gridding: estimate location of probe cell

centres• Signal:

- Reduce -> 8x8 pixels (outer 36 removed)- The probe cell signal is the 75th percentile of 64 values

• Background: Average of lowest 2% probe cell values is subtracted

Log 2 Equal color scaling

Saturation

Examples of laser saturation and chip

defects

Chip Defects

HistogramsExamples of laser

saturation and chip defects

Saturation

Chip Defects

QC (C’td)

Glynne et al (2000) Nature

Expression measures• Many expression measures are based

on differences PM - MMThe intention is to correct for background and NSB; Problem: MM also may measure ‘signal’.

• Many use just PM• Many summarise over probes (e.g.

Affy), others use the probe level data• …

What do we want to measure?Gene “Expression” (GE) / Gene activity[“perfect” Gene Specific Binding (GSB)]

What do we actually measure?Signal intensity (I) of indirectly labeled probes. This is often “massaged” to obtain a summary value termed “(gene) expression measurement”.

What is the relationship between(i) GE and I ?(ii) actual concentration and observed I ?

What else may be affecting I besides GSB?

• Non specific binding (NSB)• Physical chemistry

efficiency of oligo-probes as target binders varies; truncated probes (<25mer).

• Saturation• Labelling & Probe density may interfere with

binding• Probe:probe interactions• A target may bridge two probes, or a probe

may be only partially accessible• Desorption during washing• Imaging• …

Affymetrix Latin Square Experiment Concentrations

“14 Genes”

20 C

hips

4 Replicates

4 Replicates

Transcri

pt

37777_at

684_at 1597_at

38734_at

39058_at

36311_at

36889_at

1024_at

36202_at

36085_at

40322_at

407_at

1091_at

1708_at

Expts

1 2 3 4 5 6 7 8 9 10 11 12 13 14

A 0 0.25 0.5 1 2 4 8 16 32 64 128 0 512 1024

B 0.25 0.5 1 2 4 8 16 32 64 128 256 0.25 1024 0

C 0.5 1 2 4 8 16 32 64 128 256 512 0.5 0 0.25

D 1 2 4 8 16 32 64 128 256 512 1024 1 0.25 0.5

E 2 4 8 16 32 64 128 256 512 1024 0 2 0.5 1

F 4 8 16 32 64 128 256 512 1024 0 0.25 4 1 2

G 8 16 32 64 128 256 512 1024 0 0.25 0.5 8 2 4

H 16 32 64 128 256 512 1024 0 0.25 0.5 1 16 4 8

I 32 64 128 256 512 1024 0 0.25 0.5 1 2 32 8 16

J 64 128 256 512 1024 0 0.25 0.5 1 2 4 64 16 32

K 128 256 512 1024 0 0.25 0.5 1 2 4 8 128 32 64

L 256 512 1024 0 0.25 0.5 1 2 4 8 16 256 64 128

M, N, O,

P

512 1024 0 0.25 0.5 1 2 4 8 16 32 512 128 256

Q, R, S, T

1024 0 0.25 0.5 1 2 4 8 16 32 64 1024 256 512

14 C

once

ntra

tion

leve

ls

Probe Response curves for the 14 spiked-in genes

PM MM

Outlier

PM Fitted values

Hyperbolic Response Functions Michaelis-Menton curve in enzyme kinetics

MM Fitted values

PM Fitted values

MM Fitted values

Langmuir Adsorption Model

Assume:1. (Adsorption) Target mRNA attaches to probes at a

rate proportional to concentration of specific target mRNA and fraction of unoccupied probes

2. (Desorption) Target mRNA detaches from probes at a rate proportional to fraction of occupied probes

→ At equilibrium, intensity I(x) at target concentration x follows “Langmuir Isotherm”:

Kx

bxIxI

++= 0)(

I(x)

x

Kx

bxIxI

++= 0)(

0I

bI +0

bI2

10 +

0 K

Raw data from .cel files

Affy spike-in experiment

Gene 37777_at

Red = PMBlack = MM

Raw data from .cel files

Affy spike-in experiment

Gene 37777_at

Red = PMBlack = MM

Model for Ip

GLM: Hyperbolic response function, gamma error

Affy spike-in experiment

Gene 37777_at

Red = PMBlack = MM

Implications

X Saturation to a single value (Held et al, 2003)

NB Hekstra et al (2003) removed ~30% of data!

PM-MM - Approximately linear for relatively small concentration levels.

Fold ChangeIt can be shown that all methods give estimated

fold changes that are biased below the true values. This bias increases with concentration due to saturation of the signal.

Estimating concentration(i) Estimate I0 , b, K, using, say, nucleotide

sequence for each probe

(ii) From observed I(x), estimate x, separately for each probe

(iii) Find median

Bootstrap at probe level & repeat (i), (ii), (iii).

Plot estimated concentration versus real concentration (log scale) for 12 genes, and 95% coverage.

• Individual probes have very different responses depending on their nucleotide sequence!

• Temperature, pH, wafer effects, time to reach equilibrium etc. also important.

• Role (and usefulness) of MMs is not clear.• Sips model (replace x & K by x & K ) was

not overall statistically significant.

- Estimating absolute concentration values from I data still under development

Understanding GE microarray data• Spotted cDNA?

Relationship between measured intensities (or log ratios) and concentration of mRNA???

• NB (i) The key to understanding is that Signal Intensity (of indirectly labelled probe/target & interactions) is many steps away from what is being measured - gene expression.

• (ii) Sample is not a single cell, but a population of cells whose homogeneity may be very questionable.

Design• We do not understand, as well as we would like for

the purposes of design, the different sources of variation in gene expression.

General Reviews: * Maindonald, Pittelkow & Wilson (2003)

in Goldstein (Ed.); see

cbis.anu.edu.au/microarray_site.html

* Yang & Speed (2003) in Speed (Ed.)

Another problem underpinning analysis

Nxv, N>>v Nxv, N<<v

Small N, large v

BiplotGraphical Display of a

Rank 2 matrix

Rao, 1965Gabriel, 1971 Biometrika

Inner Product

Proportional

Zero entries

Z GTC=

Column Effects

=

Ro

w E

ffec

tsz

Biplot - Microarray Data

Factorization metric in which to represent the data.

Approximation of Z by a matrix of rank 2

SVD

Choice of ZExpression level transformations ? (logs)

Row (chip) standardizing? (Scaling, Normalization)

Column (gene) mean correcting or standardization?

Gene selection (filtering) ?

Z GTC=

GR-1 TCRT=

Approximate Biplot

Eckhart and Young 1939Good 1969

•Minimizes ΣiΣj(zij-z(k)ij)2

•Goodness of Fit is

Σki=1i

2/Σri=1i

2

•cols of V = right singular vectors

= eigenvectors of ZtZ

•cols of U = left singular vectors

= eigenvectors of ZZt

= diag0

= diageigenvalues)

1

2

12

u1 u2

v2

v1

GTCZ =

Z(2) = U(2)(2)V(2)T

GE-biplotFactorization

Z=CGT= (UVT• If =0, C= U and GT=VT

Then if Z is mean corrected

and C= NcU and G=(1/Nc)VT

GGT= Sg

Matrix Z

•Log 2 expression level

•Chips - standardized

•Genes - mean corrected

Display

•Chips - vectors with annotation.

•Genes - points or symbols

Focus: Similarity of up down regulation.Variant of the h-plotCorsten and Gabriel (1976)

Goodness of Fit variances

Σki=1i

4/Σri=1i

4

Simulation StudyMultiplicative model

‘True’ expression values

low (1), medium (3), or high (9)

• 27 genes• 3 treatment groups• 3 replicates

Treatment Groups

Samples

T3 T2 T3E

xpre

ssio

n le

vel

low

high

Every combination

Gene

Matrix Z

1. Log 2 expression level

2. Chips - standardized

3. Genes - mean corrected

Goodness of fit .98

Note

Chips

Replicates

Different treatments

Genes

•Similar up down regulation

•Non responding genes

Some InterpretationsGenes• Euclidean distance• Cosine of the angleChips• Mahalanobis

Distance

Inner products• zij = ci

Tgj

• Difference vectors zij-zij' = ci

T(gj-gj')

zij-zi'j = (ciT- ci'

T)gj

Leukaemia Training Data SetData 38 x 7129

•11 Acute Lymphoblastic Leukaemia (ALL)

• 27 Acute Myeloid Leukaemia (AML).

• 8 T-cells

• 19 B-cells

•Pre-processing steps as described in Dudoit et al (2002)

•Thresholding : floor 100 ceiling 16000

•Filtering : max/min ≤ 5 and max-min ≤ 100

•3030 genes

•Censored dataGolub, T.R., Slonim, D.K., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J.P., Coller, H., Loh, M.L., Downing, J.R., Caligiuri, M.A., Bloomfield, C.D., Lander, E.S., 1999. Molecular classification of cancer: Class discovery and class prediction by gene expression profiling. Science, 286, 531-537.

Leukaemia Data (3030 genes)

Golub et al.

Dudoit et al.

Ge et al.

Korenberg

Kiiveri

Goodness of Fit

I2= .59

10% Most varying genesGoodness of Fit

I2= .72

Gene Selection

GeneRaVE(Kiiveri, 2003)

1. The biplot is a useful visualization tool for microarray data

Simultaneous plotting of the genes and chips on the same plot

2. Many types of biplots

• Factorization

• Rank 2 approximation

• Matrix

3. GE-Biplot

• Log 2, Chip standardized, gene centered

• Factorization

• Plotting the chips as vectors and the genes as symbols

• Annotation

See cbis.anu.edu.au/microarray_site.html

Summary

Normalisation

Ad hocEffect? - Removing “signal”?Use in many applications

questionable

Gene Filtering

Ad hoc

Multiple testing

Neyman-Pearson framework vs Fisherian

FWE vs FDR

Open questions; see Dudoit et al (2003) Statistical Science, p.100–1

Multiple (vs Single) gene analyses

E.g. pairs PC2 ~ 106 comparisons

Set of genes change (e.g. with treatment)

Do gene networks/ biochemical pathways change?

Systems biology

Combining GE microarray data with phenotypic (e.g. clinical)

data

E.g. Survival analysis

+ Genotypic data

Design, Analysis & Interpretation of Microarray

Experiments

o These topics are still in their infancy

o Entirely satisfactory solutions still elude us - even to simple problems - let alone complex challenges!

Acknowledgements:Acknowledgements:

Yvonne Pittelkow

Conrad Burden

John Maindonald

http://cbis.anu.edu.au/

Spotted: Campbell’s animation

http://www.bio.davidson.edu/courses/genomics/chip/chip.htmlOligo

QuickTime™ and aCinepak decompressorare needed to see this picture.