1. 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 rafa@jhu.edu

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

4. 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

5. 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

6. 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)

12. 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)

18. 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

19. Correlation between replicates R1 R2 R3 G1 G2 G3 R1 1.00 0.95 0.95 0.94 0.90 0.90 R2 0.95 1.00 0.96 0.90 0.95 0.91 R3 0.95 0.96 1.00 0.91 0.92 0.95 G1 0.94 0.90 0.91 1.00 0.96 0.96 G2 0.90 0.95 0.92 0.96 1.00 0.97 G3 0.90 0.91 0.95 0.96 0.97 1.00

20. Correlation between red, green, haploid, diplod, uptag, downtag RHD RHU RDD RDU GHD GHU GDD GDU RHD 1.00 0.59 0.56 0.32 0.95 0.58 0.54 0.37 RHU 0.59 1.00 0.38 0.56 0.58 0.95 0.40 0.58 RDD 0.56 0.38 1.00 0.58 0.54 0.39 0.92 0.64 RDU 0.32 0.56 0.58 1.00 0.33 0.53 0.58 0.89 GHD 0.95 0.58 0.54 0.33 1.00 0.62 0.56 0.39 GHU 0.58 0.95 0.39 0.53 0.62 1.00 0.41 0.58 GDD 0.54 0.40 0.92 0.58 0.56 0.41 1.00 0.73 GDU 0.37 0.58 0.64 0.89 0.39 0.58 0.73 1.00

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

22. 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

23. 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

24. Does it fit?

26. 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

27. QQ-plot for new t-test

28. Better looking than others

32. 1 YMR106C 9.5 47 69.2 a a 100 2 YOR005C 19.7 35 44.9 a d 100 3 YLR265C 6.1 32 35.8 a m 100 4 YDL041W 10.4 32 35.6 a m 100 5 YIL012W 12.2 31 21.7 a a 100 6 YIL093C 4.8 29 30.8 a a 100 7 YIL009W 5.6 29 -23.5 a a 100 8 YDL042C 12.9 29 32.1 a d 100 9 YIL154C 1.8 28 91.3 m m 82 10 YNL149C 1.7 27 93.4 m d 71 11 YBR085W 2.5 26 -15.8 a a 84 12 YBR234C 1.7 26 87.5 m d 75 13 YLR442C 6.1 26 -100.0 a a 100

33. Acknowledgements Siew Loon Ooi Jef Boeke Forrest Spencer Jean Yang