1. 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

2. microarrays samples: mRNA from tissue biopsies, cell lines probes: gene-specific DNA strands 2.93 1.67 0.72 0.6 5.8 1.12 tissue B 3.314.2MCAM 0.671.32LAMA4 0.120.01CASP4 1.02.2ALDH4 1.81.1VIM 2.120.02ErbB2 tissue Ctissue A detection

3. 4x4 or 8x4 sectors 17...38 rows and columns per sector ca. 4600…46000 probes/array sector: corresponds to one print-tip a microarray slide Slide: 25x75 mm Spot-to-spot: ca. 150-350  m

4. Terminology 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 slide, array channel: data from one color (Cy3 = cyanine 3 = green, Cy5 = cyanine 5 = red). batch: collection of microarrays with the same probe layout and quality

5. 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  m spot size) 40 MB per array Image Analysis spot intensities 2 numbers per probe (~100-300 kB) … auxiliaries: background, area, std dev, …

6. 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. R and G for each spot on the array.

7. Local background ---- GenePix ---- QuantArray ---- ScanAlyze

8. Oligonucleotide chips

9. Affymetrix files Main software from Affymetrix: MAS - MicroArray Suite. DAT file: Image file, ~10 7 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).

10. Affymetrix image analysis DAT image files  CEL files Each probe cell: 10x10 pixels. Gridding: estimate location of cell centers. Signal: Remove outer 36 pixels  8x8 pixels. Probe cell signal, PM or MM, is the 75 th 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.

11. Data and notation PM ijg, MM ijg = Intensity for perfect match and mismatch probe j for gene g in chip i. i = 1,…, none to hundreds of chips j = 1,…, J usually 16 or 20 probe pairs g = 1,…, G 8…20,000 probe sets. Tasks: 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.

12. spot or probe intensity data two-color spotted arrays Probes (genes) n one-color arrays (Affymetrix, nylon) conditions (samples)

13. Spot intensities are not mRNA concentrations o tissue contamination o clone identification and mapping o image segmentation o RNA degradation o PCR yield, contamination o signal quantification o amplification efficiency o spotting efficiency o ‘background’ correction o reverse transcription efficiency o DNA-support binding o hybridization efficiency and specificity o other array manufacturing- related issues The point is not that these steps are ‘not perfect’; it is that they may vary from array to array, experiment to experiment.

14. Sources of variation amount of RNA in the biopsy efficiencies of -RNA extraction -reverse transcription -labeling -photodetection PCR yield DNA quality spotting efficiency, spot size cross-/unspecific hybridization stray signal CalibrationError model Systematic o similar effect on many measurements o corrections can be estimated from data Stochastic o too random to be ex- plicitely accounted for o “noise”

15. measured intensity of probe k in sample i unspecificgainactual abundance a ik, b ik all unknown: need to approximately determine from data

16. Implications 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 y ik and of estimated normalization parameters a ik, b ik data quantity of interest

17. a i per-sample offset L ik local background provided by image analysis  ik ~ N(0, b i 2 s 1 2 ) “additive noise” b i per-sample normalization factor b k sequence-wise labeling efficiency log  ik ~ N(0,s 2 2 ) “multiplicative noise” A typical set of assumptions

18. Discussion and possible extensions Sequence-wise factors b k need 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 a i, b i same for all probes on array - could extend to include print-tip or plate effects Probe affinities b k same for all arrays - could extend to include batch effects

19. Calibration = 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%

20. Gene expression measures o average over multiple probes e.g. Affymetrix GeneChip MAS 4.0: trimmed mean o sort d j = PM j -MM j o exclude highest and lowest value o J := those pairs within 3 standard deviations of the average

21. 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 – x 2 /c 2 ) 2 if |x|<c, 0 otherwise

22. Expression measures: Li & Wong dChip fits a model for each gene where –  i : expression index for gene i –  j : probe sensitivity o estimate  i by maximum likelihood. o need at least 10 or 20 chips. Current version works with PMs only.

23. RMA method: Irizarry, Speed et al. (2002) o Estimate one global background value b=mode(MM). Otherwise ignore MM. o Assume: PM = Y true + b Estimate Y  0 from PM and b as a conditional expectation E[s true |PM, b]. o Use log 2 (Y). o Nonparametric nonlinear calibration ('quantile normalization') across a set of chips.

24. RMA expression measures AvDiff – type: with A a set of “suitable” pairs. Li-Wong – type: robust estimation of a i : median polish (iterative: successively remove row and column medians and accumulate terms until the process stabilizes).

25. software www.bioconductor.org packages: affyAffymetrix pre-processing (CEL, CDF) marrayInputtwo-color slides vsncalibration and variance stabilization o open-source („reproducible research“) o based on R (biggest statistics library in the world)

26. Quality control verify the assumptions that underly the + calibration + error model  visualization, diagnostic plots  some examples what can go wrong

27. Background usual assumption for spotted arrays: total brightness = specific part (from labeled sample cDNA) +background brightness (adjacent to spot) ?

28. log(PM/MM) 0 From: R. Irizarry et al., Biostatistics 2002 Background usual assumption for Affymetrix arrays: PM intensity = +specific part (from labeled sample cDNA) MM intensity

29. Scatterplot, colored by PCR-plate Two RZPD Unigene II filters (cDNA nylon membranes) PCR plates

31. PCR plates: boxplots

32. array batches

33. print-tip effects

34. spotting pin quality decline after delivery of 3x10 5 spots after delivery of 5x10 5 spots H. Sueltmann DKFZ/MGA

35. spatial effects R RbR-Rb color scale by rank spotted cDNA arrays, Stanford-type another array: print-tip color scale ~ log(G) color scale ~ rank(G)

36. Batches: array to array differences d ij = mad k (h ik -h jk ) arrays i=1…63; roughly sorted by time

37. Coefficient of variation cDNA slide data from H. Sueltmann

38. Density representation of the scatterplot (76,000 clones, RZPD Unigene-II filters)

39. Three-way comparisons

40. References 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. http://biosun01.biostat.jhsph.edu/~ririzarr/papers/index.html A more complete list of references is in: Elementary analysis of microarray gene expression data. W. Huber, A. von Heydebreck, M. Vingron, manuscript. http://www.dkfz-heidelberg.de/abt0840/whuber/

41. Acknowledgements 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! MPI Molekulare Genetik Anja von Heydebreck Martin Vingron Tim Beißbarth Uni Heidelberg Günther Sawitzki UMC Leiden Judith Boer Bioconductor Project Robert Gentleman Sandrine Dudoit Rafael Irizarry Laurent Gautier