Use of Mixture Model in a genome-wide DNA microarray-based genetic screen for components of the NHEJ Pathway in Yeast Rafael A. Irizarry Department of Biostatistics, JHU

Damaged DNA Rad50p/Mre11p/Xrs2p Yku70p/Yku80p (DNA-PK ) DNA end binding Lig4p/Lif1p Ligation Nucleolytic processing Repaired DNA

kanR A Transformation into deletion pool Select for Ura + transformants Genomic DNA preparation Circular pRS416 PCR Cy5 labeled PCR productsCy3 labeled PCR products Oligonucleotide array hybridization B EcoRI linearized PRS416 NHEJ Defective MCS CEN/ARS URA3 ttaa aatt CEN/ARS URA3 UPTAG DOWNTAG

Data 5718 mutants 3 replicates on each slide 5 Haploid slides, 4 Diploid slides Haploids are divided into 2 downtags, 3 uptag (2 of which replicate uptags) Diploids are divided into 3 uptags (2 of which are replicates) and 2 uptags

Which mutants are NHEJ defective? Find mutants defective for transformation with linear DNA Dead in linear transformation (green) Alive in circular transformation (red) Look for spots with large log(R/G)

Improvement to usual approach Take into account that some mutants are dead and some alive Use a statistical model to represent this Mixture model? With ratio’s we lose information about of R and G separately Look at them separately (absolute analysis)

Warning Absolute analyses can be dangerous for competitive hybridization slides We must be careful about “spot effect” Big R or G may only mean the spot they where on had large amounts of cDNA Look at some facts that make us feel safer

Correlation between replicates R1 R2 R3 G1 G2 G3 R R R G G G

Correlation between red, green, haploid, diplod, uptag, downtag RHD RHU RDD RDU GHD GHU GDD GDU RHD RHU RDD RDU GHD GHU GDD GDU

BTW The mean squared error across slides is about 3 times bigger than the mean squared error within slides

Mixture Model We use a mixture model that assumes: There are three classes: –Dead –Marginal –Alive Normally distributed with same correlation structure from gene to gene

Random effect justification Each x = (r1,…,r5,g1,…,g5) will have the following effects: Individual effect: same mutant same expression (replicates are alike) Genetic effect: same genetics same expression PCR effect : expect difference in uptag, downtag

Does it fit?

What can we do now that we couldn’t do before? Define a t-test that takes into account if mutants are dead or not when computing variance For each gene compute likelihood ratios comparing two hypothesis: alive/dead vs.dead/dead or alive/alive

QQ-plot for new t-test

Better looking than others

1 YMR106C a a YOR005C a d YLR265C a m YDL041W a m YIL012W a a YIL093C a a YIL009W a a YDL042C a d YIL154C m m YNL149C m d YBR085W a a YBR234C m d YLR442C a a 100

Acknowledgements Siew Loon Ooi Jef Boeke Forrest Spencer Jean Yang