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From colored speckles to expression values. o quality control / optimization o calibration and error modeling o data transformations o software Wolfgang Huber Dep. of Molecular Genome Analysis DKFZ Heidelberg. samples: mRNA from tissue biopsies, cell lines. probes:

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from colored speckles to expression values
From colored speckles to expression values

o quality control / optimizationo calibration and error modelingo data transformationso software

Wolfgang Huber

Dep. of Molecular Genome


DKFZ Heidelberg



mRNA from

tissue biopsies,

cell lines


gene-specific DNA strands


tissue A

tissue B

tissue C

























a microarray slide
a microarray slide

Slide: 25x75 mm

4x4 or 8x4 sectors

17...38 rows and columns per sector

ca. 4600…46000


Spot-to-spot: ca. 150-350 mm

sector: corresponds

to one print-tip


sample: RNA (cDNA) hybridized to the array, aka target, mobile substrate.

probe: DNA spotted on the array, aka spot, immobile substrate.

sector: rectangular matrix of spots printed using the same print-tip (or pin)

plate: set of 384 (768) spots printed with DNA from the same microtitre plate of clones


channel: data from one color (Cy3 = cyanine 3 = green, Cy5 = cyanine 5 = red).

batch: collection of microarrays with the same probe layout and quality

raw data

Image Analysis

Raw data
  • scanner signal
  • 2D image:
  • 5 or 10 mm spatial resolution,
      • 16 bit (65536) dynamic range per channel
  • ca. 30-50 pixels per probe (60 mm spot size)
  • 40 MB per array

spot intensities

2 numbers per probe (~100-300 kB)

… auxiliaries: background, area, std dev, …

image analysis

R and G for each spot on the array.

Image analysis

1. Addressing. Estimate location of spot centers.

2. Segmentation. Classify pixels as foreground (signal) or background.

  • 3. Information extraction. For
  • each spot on the array and each
  • dye
    • foreground intensities;
    • background intensities;
    • quality measures.
local background

---- GenePix

---- QuantArray

---- ScanAlyze

affymetrix files
Affymetrix files

Main software from Affymetrix:

MAS - MicroArray Suite.

DAT file: Image file, ~107 pixels, ~50 MB.

CEL file: probe intensities, ~400k numbers

CDF file: Chip Description File. Describes which probes go in which probe sets (genes, gene fragments, ESTs).

affymetrix image analysis
Affymetrix image analysis

DAT image files  CEL files

Each probe cell: 10x10 pixels.

Gridding: estimate location of cell centers.


Remove outer 36 pixels  8x8 pixels.

Probe cell signal, PM or MM, is the 75th percentile of the 8x8 pixel values.

Background: Average of the lowest 2% probe cells is taken as the background value and subtracted.

Compute also quality values.

data and notation
Data and notation

PMijg, MMijg= Intensity for perfect match and mismatch probe j for gene g in chip i.

i = 1,…, n one to hundreds of chips

j = 1,…, J usually 16 or 20 probe pairs

g= 1,…, G 8…20,000 probe sets.


calibrate (normalize) the measurements from different chips (samples)

summarize for each probe set the probe level data, i.e., 20 PM and MM pairs, into a single expression measure.

compare between chips (samples) for detecting differential expression.

spot or probe intensity data
spot or probe intensity data

n one-color arrays (Affymetrix, nylon)

two-color spotted arrays

Probes (genes)

conditions (samples)

spot intensities are not mrna concentrations
Spot intensities are not mRNA concentrations

The point is not that these steps are ‘not perfect’; it is that they may vary from array to array, experiment to experiment.

sources of variation



o similar effect on many


o corrections can be estimated from data

o too random to be ex-plicitely accounted for

o “noise”


Error model

Sources of variation

amount of RNA in the biopsy

efficiencies of

-RNA extraction

-reverse transcription



PCR yield

DNA quality

spotting efficiency,

spot size

cross-/unspecific hybridization

stray signal

measured intensity of probe k in sample i
measured intensity of probe k in sample i



actual abundance

aik, bik all unknown: need to approximately determine from data


quantity of interest


No non-linear terms:

Saturation can be avoided in the experiments.

Data from well-performed experiments shows no evidence for gross deviations from affine linearity.

The flexibility (and complexity) lies in the number of parameters: twice the number of data points!

parameters must not all be independent

make simplifiying assumptions, reduce the number of independent parameters to manageable size

Quality control: verify that assumptions hold for the data at hand

Normalization, calibration: estimate parameters for the data at hand

Error modeling: control the error bars both of measured yik and of estimated normalization parameters aik,bik


bi per-sample

normalization factor

bk sequence-wise

labeling efficiency

log hik ~ N(0,s22)

“multiplicative noise”

ai per-sample offset

Lik local background provided by image analysis

eik ~ N(0, bi2s12)

“additive noise”

A typical set of assumptions

discussion and possible extensions
Discussion and possible extensions

Sequence-wise factors bkneed not be explicitely determined if only interested in relative expression levels

The assumptions bring down the number of parameters to 2*d - the rest is modeled as noise.

Array calibration terms ai, bi same for all probes on array - could extend to include print-tip or plate effects

Probe affinities bk same for all arrays - could extend to include batch effects


= normalization

=parameter estimation of model parameters

o data heteroskedastic variance stabilizing data transformation

o maximum likelihood estimator

o model holds for genes that are unchanged; differentially transcribed genes act as outliers.

o heavy-tailed data distributions

robust variant of ML estimator, à la Least Trimmed Sum of Squares regression.

o works up to breakdown point of 50%

gene expression measures
Gene expression measures

o average over multiple probes

e.g. Affymetrix GeneChip MAS 4.0: trimmed mean

o sort dj = PMj -MMj

o exclude highest and lowest value

o J := those pairs within 3 standard deviations of the average

gene expression measures mas 5 0
Gene expression measures: MAS 5.0

Instead of MM, use "repaired" version CT

CT = MM if MM<PM

= PM / "typical log-ratio" if MM>=PM

"Signal" =

Tukey.Biweight (log(PM-CT))

(… median)

Tukey Biweight: B(x) = (1 – x2/c2)2 if |x|<c, 0 otherwise

expression measures li wong
Expression measures: Li & Wong

dChip fits a model for each gene


  • qi: expression index for gene i
  • fj: probe sensitivity

o estimate qi by maximum likelihood.

o need at least 10 or 20 chips.

Current version works with PMs only.

rma method irizarry speed et al 2002
RMA method: Irizarry, Speed et al. (2002)

o Estimate one global background value b=mode(MM). Otherwise ignore MM.

o Assume: PM = Ytrue + b

Estimate Y0 from PM and b as a conditional expectation E[strue|PM, b].

o Use log2(Y).

o Nonparametric nonlinear calibration ('quantile normalization') across a set of chips.

rma expression measures
RMA expression measures

AvDiff – type:

with A a set of “suitable” pairs.

Li-Wong – type:

robust estimation of ai: median polish (iterative: successively remove row and column medians and accumulate terms until the process stabilizes).



affy Affymetrix pre-processing


marrayInput two-color slides

vsn calibration and variance


o open-source („reproducible research“)

o based on R (biggest statistics library in the


quality control
Quality control

verify the assumptions that underly the


+error model

visualization, diagnostic plots

some examples what can go wrong




usual assumption for spotted arrays:

total brightness =

specific part (from labeled sample cDNA)

+ background brightness (adjacent to spot)




usual assumption for Affymetrix arrays:

PM intensity =

+ specific part (from labeled sample cDNA)

MM intensity


From: R. Irizarry et al., Biostatistics 2002

pcr plates
PCR plates

Scatterplot, colored by PCR-plate

Two RZPD Unigene II filters (cDNA nylon membranes)


spotting pin quality decline

after delivery of 5x105 spots

after delivery of 3x105 spots

H. Sueltmann DKFZ/MGA

spatial effects
spatial effects

R Rb R-Rbcolor scale by rank

another array: print-tip

color scale ~ log(G)

color scale ~ rank(G)

spotted cDNA arrays, Stanford-type


Batches: array to array differences dij = madk(hik -hjk)

arrays i=1…63; roughly sorted by time

coefficient of variation
Coefficient of variation

cDNA slide

data from

H. Sueltmann


Density representation of the scatterplot

(76,000 clones, RZPD Unigene-II filters)


Normalization for cDNA microarray data: a robust composite method addressing single and multiple slide systematic variation. YH Yang, S Dudoit, P Luu, DM Lin, V Peng, J Ngai and TP Speed.  Nucl. Acids Res. 30(4):e15, 2002.

Variance Stabilization Applied to Microarray Data Calibration and to the Quantification of Differential Expression. W.Huber, A.v.Heydebreck, H.Sültmann, A.Poustka, M.Vingron. Bioinformatics, Vol.18, Supplement 1, S96-S104, 2002.

A Variance-Stabilizing Transformation for Gene Expression Microarray Data. BP Durbin, JS Hardin, DM Hawkins, DM Rocke. Bioinformatics, Vol.18, Suppl. 1, S105-110.

Exploration, Normalization, and Summaries of High Density Oligonucleotide Array Probe Level Data. RA Irizarry, B Hobbs, F Collin, YD Beazer-Barclay, KJ Antonellis, U Scherf, TP Speed (2002). Biostatistics.

A more complete list of references is in:

Elementary analysis of microarray gene expression data. W. Huber, A. von Heydebreck, M. Vingron, manuscript.


UMC Leiden

Judith Boer

Bioconductor Project

Robert Gentleman

Sandrine Dudoit

Rafael Irizarry

Laurent Gautier

MPI Molekulare Genetik

Anja von Heydebreck

Martin Vingron

Tim Beißbarth

Uni Heidelberg

Günther Sawitzki

DKFZ Heidelberg

Annemarie Poustka

Holger Sültmann

Frank Bergmann

Andreas Buneß

Katharina Finis

Florian Haller

Patrick Herde

Yvonne Keßler

Jörg Schneider

Anke Schroth

Klaus Steiner

Stephanie Süß

Markus Vogt

Friederike Wilmer

… and

many more!