Low Abundance Genes. DNA Microarrays. Log Transformation? Basic Idea. Mining for Low-abundance Transcripts in Microarray Data. Exploratory Methods

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1 Mining for Low-abundance Transcripts in Microarray Data Yi Lin 1, Samuel T. Nadler 2, Alan D. Attie 2, Brian S. Yandell 1,3 1 Statistics, 2 Biochemistry, 3 Horticulture, University of Wisconsin-Madison September 2 Basic Idea DNA microarrays present tremendous opportunities to understand complex processes Transcription factors and receptors expressed at low levels, missed by most other methods Analyze low expression genes with normal scores Robustly adapt to changing variability across average expression levels Basis for clustering and other exploratory methods Data-driven p-value sensitive to low abundance & changes in variability with gene expression DNA Microarrays 1-1, items per chip cdna, oligonucleotides, proteins dozens of technologies, changing rapidly expose live tissue from organism mrna cdna hybridize with chip read expression signal as intensity (fluorescence) design considerations compare conditions across or within chips worry about image capture of signal Low Abundance Genes background adjustment remove local geography comparing within and between chips negative values after adjustment low abundance genes virtually absent in one condition could be important genes: transcription factors, receptors large measurement variability early technology (bleeding edge) prevalence across genes on a chip -2% per chip 1-5% across multiple conditions Log Transformation? tremendous scale range in mean intensities 1-1 fold common concentrations of chemicals (ph) fold changes have intuitive appeal looks pretty good in practice want transformed data to be roughly normal easy to test if no difference across conditions looking for genes that are outliers beyond edge of bell shaped curve provide formal or informal thresholds Exploratory Methods Clustering methods (Eisen 1998, Golub 1999) Self-organizing maps (Tamayo 1999) search for genes with similar changes across conditions do not determine significance of changes in expression require extensive pre-filtering to eliminate low intensity modest fold changes may detect patterns unrelated to fold change comparison of discrimination methods (Dudoit 2) 1

2 Confirmatory Methods ratio-based decisions for 2 conditions (Chen 1997) constant variance of ratio on log scale, use normality anova (Kerr 2, Dudoit 2) handles multiple conditions in anova model constant variance on log scale, use normality Bayesian inference (Newton 2, Tsodikov 2) Gamma-Gamma model variance proportional to squared intensity error model (Roberts 2, Hughes 2) variance proportional to squared intensity transform to log scale, use normality. acquire data Q, B 1. adjust for background A=Q B 2. rank order genes R=rank(A)/(n+1) 3. normal scores N=qnorm(R) 4. contrast conditions Y=N 1 N 2 Y = contrast 7. standardize Z= Y center spread 6. center & spread X = mean 5. mean intensity X=mean(N) Normal Scores Procedure adjusted expression A = Q B rank order R = rank(a) / (n+1) normal scores N = qnorm( R ) average intensity X = (N 1 +N 2 )/2 difference Y = N 1 N 2 variance Var(Y X) σ 2 (X) standardization S = [Y µ(x)]/σ(x) Motivate Normal Scores natural transformation to normality is log(a) background intensity B = bd +ω B measured with error ω attenuation d may depend on condition gene measurement Q = [αexp(g+h+ε)+b]d+ω Q gene signal g degree of hybridization h: intrinsic noise ε (variance may depend on g) attenuation α (depends thickness of sample, etc.) subtract background: A = Q B adjusted measurements A = dαexp(g+h+ε)+δ symmetric measurement error δ=ω B ω Q Motivate Normal Scores (cont.) adjusted measurements: A = Q B = dαg+δ log expression level: log(g) = g+h+ε gene signal g confounded with hybridization h unless hybridization h independent of condition G is observed if no measurement error δ no dye or array effect (no attenuation dα) no background intensity natural under this model to consider N=log(G) normal scores almost as good Robust Center & Spread genes sorted based on X partitioned into many (about 4) slices containing roughly the same number of genes slices summarized by median and MAD MAD = median absolute deviation robust to outliers (e.g. changing genes) MAD ~ same distribution across X up to scale MAD i = σ i Z i, Z i ~ Z, i = 1,,4 log(mad i ) = log(σ i ) + log( Z i ) median ~ same idea 2

3 Robust Center & Spread MAD ~ same distribution across X up to scale log(mad i ) = log(σ i ) + log( Z i ), I = 1,,4 regress log(mad i ) on X i with smoothing splines smoothing parameter tuned automatically generalized cross validation (Wahba 199) globally rescale anti-log of smooth curve Var(Y X) σ 2 (X) can force σ 2 (X) to be decreasing similar idea for median E(Y X) µ(x) Motivation for Spread log expression level: log(g) = g+h+ε hybridization h negligible or same across conditions intrinsic noise ε may depend on gene signal g compare two conditions 1 and 2 Y = N 1 N 2 log(g 1 ) log(g 2 ) = g 1 g 2 + ε 1 -ε 2 no differential expression: g 1 =g 2 =g Var(Y g) = σ 2 (g) g X suggests condition on X instead, but: Var(Y X) not exactly σ 2 (X) cannot be determined without further assumptions Simulation of Spread Recovery 1, genes: log expression Normal(4,2) 5% altered genes: add Normal(,2) no measurement error, attenuation estimate robust spread Robust Spread Estimation Estimate of Spread Q-Q Plot spread Sample Quantiles mean expression Bonferroni-corrected p-values standardized normal scores S = [Y µ(x)]/σ(x) ~ Normal(,1)? genes with differential expression more dispersed Zidak version of Bonferroni correction p = 1 (1 p 1 ) n 13, genes with an overall level p =.5 each gene should be tested at level 1.95*1-6 differential expression if S > 4.62 differential expression if Y µ(x) > 4.62σ(X) too conservative? weight by X? Dudoit (2) Simulation Study simulations with two conditions 1, genes g 1,g 2 ~ Normal(4,2) for nonchanging genes 5% with differential expression g c ~ Normal(4,2) + Normal(3-rank(X)/(n+1),1/2) up- or down-regulated with probability 1/2 intrinsic noise ε ~ Normal(,.5) attenuation α = 1 measurement error variance =, 1, 2, 5, 1, 2 3

4 Comparison of Methods 5 differential expression for two conditions Newton (2) J Comp Biol Gamma-Gamma-Bernouli model Bayesian odds of differential expression Chen (1997) constant ratio of expressions underlying log-normality 1 normal scores (Lin 2) some (unknown) transformation to normality robust, smooth estimate of spread & center Bonferroni-style p-values Capturing Changed Genes: Noise.2 Fold Change 1. Fold Change Capturing Changed Genes: No Noise No Noise: Average Intensity.5 E. coli with IPTG-b Comparison with E. coli Data Normal Scores IPTG-b Cy3/Cy5 ratio ~15 genes at low abundance including key genes Cy3/Cy5 ratio 1 e-3 1 e-1 1 e+3 Bayesian odds of differential expression IPTG-b known to affect only a few genes Raw IPTG-b 4,+ genes (whole genome) Newton (2) J Comp Biol Noise 1: Average Intensity 5. Number of Changed Genes Captured Success in Capture 1 e-2 1 e+ Mean Intensity 1 e Mean Intensity 2. 4

5 Diabetes & Obesity Study 13,+ gene fragments (11,+ genes) oligonuleotides, Affymetrix gene chips mean(pm) - mean(nm) adjusted expression levels six conditions in 2x3 factorial lean vs. obese B6, F1, BTBR mouse genotype adipose tissue influence whole-body fuel partitioning might be aberrant in obese and/or diabetic subjects Nadler (2) PNAS Low Abundance Obesity Genes low mean expression on at least 1 of 6 conditions negative adjusted values ignored by clustering routines transcription factors I-κB modulates transcription - inflammatory processes RXR nuclear hormone receptor - forms heterodimers with several nuclear hormone receptors regulation proteins protein kinase A glycogen synthase kinase-3 roughly 1 genes 9 new since Nadler (2) PNAS Table 1. Genes Differentially Expressed with Obesity as Identified by the Normal Scores Procedure Accesion # Description Obese/Lean Lean/Obese Average p-value aa68251 Mus musculus Dp1l1 mrna for polyposis locus protein 1-like 1 (TB2 protein-like ) x93999 M.musculus Gal beta-1,3-galnac-specific GalNAc alpha-2,6-sialyltransferase gene w45955 No significant homologies U16297 Mus musculus cytochrome B561 (mcyt) X72862* M.musculus gene for beta-3-adrenergic receptor X12521 Mouse mrna for transition protein 1 TP aa No significant homologies AA62269 Mus musculus protamine AA Mus musculus transition protein 1 (Tnp1) X63349 M.musculus tyrosinase-related protein AA11671 Mus musculus serum response factor (Srf) AA15229 Mus musculus hepsin (Hpn) aa26714 No significant homologies aa48365 Mus musculus mrna for SRp25 nuclear protein j5663 Mouse vas deferens androgen related protein (MVDP) w49331 No significant homologies J2935 Mouse camp-dependent protein kinase type II regulatory subunit aa195 No significant homologies m3181 Mouse 2,3 -cyclic-nucleotide 3 -phosphodiesterase AA33381 No significant homologies aa No significant homologies u2883 Mus musculus Balb/c mammary-derived growth inhibitor (MDGI) AA No significant homologies D14883 Mouse C33/R2/IA W36455 Mus musculus adipsin (Adn) m2751 Mus musculus protamine X8796 M.musculus brevican AA48974 No significant homologies ET63455 Mus musculus serum amyloid A-4 protein (Saa4) X6526 M.musculus mrna for GTP-binding protein AA Similar to Rat S6 kinase ET6236 CALCIUM-DEPENDENT PHOSPHOLIPASE A2 PRECURSOR w64688 No significant homologies AA3587 No significant homologies AA Mus musculus hippocalcin-like 1 (Hpcal1) w1922 No significant homologies w48392 similar X7518 Id4 helix-loop-helix protein AA Sequence withdrawn X99143 M.musculus hair keratin, mhb AA similar to Human ras-related protein rab W1926 Mus musculus mrna for ubiquitin like protein AA13862 Similar to Human hqp J4179 Mouse chromatin nonhistone high mobility group protein (HGM-I(Y)) X355 Mouse gene exon 2 for serum amyloid A (SAA) 3 protein U957 Mus musculus p21 (Waf1) AA2399 Mus musculus dutpase u7746 Mus musculus anaphylatoxin C3a receptor x66224 M.musculus retinoid X receptor-beta AA Mus musculus protein tyrosine phosphatase (Ptpn16) W85163 Mus musculus migration inhibitory factor Low Abundance Genes for Obesity Obese vs. Lean Microarray ANOVAs Kerr (2) gene by condition interaction N ijk = gene i + condition j + gene*condition ij + rep error ijk conditions organized in factorial design experimental units may be whole or part of array genes are random effects focus on outliers (BLUPs), not variance components gene*condition ij = differential expression allow variance to depend on gene i main effect replication to improve precision, catch gross errors Average Intensity for Obesity 5

6 Microarray Random Effects variance component for non-changing genes robust estimate of MS(G*C) using smoothed MAD rescale normal score response N by spread σ(x) look for differential expression or use clustering methods variance component for replication robust estimate of MSE using smoothed MAD look for outliers = gross errors Obesity Genotype Main Effects Obesity Dominance Obesity Additive Microarray QTLs condition may be genotype whole organism or pattern of genes genotype may be inferred rather than known exactly N ijk = gene i + QTL j + gene*qtl ij + individual ijk QTL genotype depends on flanking markers mixture model across possible QTL genotypes single vs. multiple QTL single QTL may influence numerous genes epistasis = inter-genic interaction modification of biochemical pathway(s) 6