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array of plenty - results from a 4 base resolution yeast genome tiling array. Wolfgang Huber Lars Steinmetz European Molecular Biology Laboratory. Genechip S. cerevisiae Tiling Array. 4 bp tiling path over complete genome (12 Mio basepairs, 16 chromosomes) Sense and Antisense strands
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array of plenty - results from a 4 base resolution yeast genome tiling array Wolfgang Huber Lars Steinmetz European Molecular Biology Laboratory
Genechip S. cerevisiae Tiling Array 4 bp tiling path over complete genome (12 Mio basepairs, 16 chromosomes) Sense and Antisense strands 6.5·106 oligonucleotides 5 mm feature size Chips manufactured by Affymetrix Application + analysis by L. Steinmetz (EMBL/Stanford Genome Center) and W. Huber (EMBL/EBI)
3,039,046 perfect match probes 7,359 splice junction probes 127,813 YJM789 polymorphism probes 16,271 Tag3 barcode probes The first complete genome on one array
Samples Genomic DNA Poly-A RNA (double enriched) from exponential growth in rich media Total RNA from exponential growth in rich media 3 replicates each
before Probe specific affinity normalization after
Probe-specific affinity normalization si probe-sequence specific affinity. Estimation: geometric mean of intensities from DNA hybridization bi =b(si ) probe-sequence specific background. Estimation: for strata of probes with similar si, estimate b through location estimator of distribution of intergenic probes, then interpolate to obtain continuous b(s)
Segmentation Two obvious options: Smoothing (e.g. running median) and thresholding: simple, but estimates of change points will be biased and depend on expression level Hidden Markov Model (HMM): but our “states” come from a continuum! Fiddly. Our solution: Fit a piecewise constant function change point
The model t1,…, tS: change points Y: normalized intensities x: genomic coordinates mk: level of k-th segment
Model fitting Minimize t1,…, tS: change points J: number of replicate arrays
Maximization Naïve optimization has complexity ns, where n≈105 and s≈103. Fortunately, there is a dynamic programming algorithm with complexity ≈n2: F. Picard et al. A statistical approach for array CGH data analysis. BMC Bioinformatics 6 (2005) Implementation: W. Huber, Bioconductor packagetilingArray
Piecewise linear models strucchangepackage by Achim Zeileis TU Vienna (CRAN): - more general piecewise linear models - confidence intervals Confidence intervals based on asymptotic theory of Bai+Perron (2003) Dynamic programming algorithm has been around since mid 1970s. Context: mostly econometrics
Confidence Intervals Di level difference Qi no. data points / unit t Wi error variance (allowing serial correlations) true and estimated change points Vi(s) appropriately scaled and shifted Wiener process (Brownian motion) Bai and Perron, J. Appl. Econometrics 18 (2003)
Model selection criteria model family has just one parameter: no. of segments
Novel Transcripts Potential antisense regulator
Defining Expressed Transcripts Segments not overlapping any annotated features Segments overlapping annotated features Normal distribution
Expressed Features 5646 ORFs with ≥ 7 probes 5306 (94%) above background in poly-A RNA 5192 (92%) in total RNA (FDR=0.001) untranscribed: meiosis, sporulation poly-A RNA: 9356k of 11360k (82.4%) total RNA: 8786k (77.2%) Both: 9612k (84.3%) … of which not annotated: 1559k (13.7%) annotated total: 8997k of 12071k (74.5%) Fraction of transcribed basepairs
Novel transcripts Basis: multiple alignment of 4 yeast genomes: S.cerevisiae, S.bayanus, S.mikatae, S.paradoxus. Kellis et al. Nature (2003) Conservation analysis: fraction of segments for which there is a multiple alignment; total tree length Codon signature: 3-periodicity of mutation frequencies novel transcribed segments untranscribed << annotated transcripts. with Lee Bofkin, Nick Goldman
Antisense transcripts • microtubule-mediated nuclear migration • cell separation during cytokinesis • cell wall • single-stranded RNA binding (all 5: NAB2, NAB3, NPL3, PAB1, SGN1) • (p<2x10-16)
Bioconductor package tilingArray contains Picard’s segmentation algorithm Along-chromosome plots To do: better user-interface and documentation
Data will be publically available from EBI's microarray database ArrayExpress www.ebi.ac.uk/arrayexpress
Conclusions o Conventional microarrays: measure transcript levels o High resolution tiling arrays: also transcript structure introns, exons, alternative transcription start sites partial degradation novel transcripts annotation errors o Probe-response normalization: make signal comparable across probes. o Simple segmentation algorithm o Well-developed theory, accurate estimation of change-points, including confidence intervals o Software - available as part of Bioconductor (http://www.bioconductor.org, also: CEL file import, normalization, further statistical testing)
Acknowledgements Oleg Sklyar Jörn Tödling Raeka Aiyar EMBL-GE & Stanford: Lior David Marina Granovskaia Robert Gentleman Rafael Irizarry Vince Carey Ben Bolstad Lars Steinmetz