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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
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Damaged DNA
Rad50p/Mre11p/Xrs2p
Yku70p/Yku80p(DNA-PK )DNA end binding
Lig4p/Lif1pLigation
Nucleolytic processing
Repaired DNA
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kanRA
Transformation into deletion pool
Select for Ura+ transformantsGenomic DNA preparation
Circular pRS416
PCRCy5 labeled PCR products Cy3 labeled PCR products
Oligonucleotide array hybridization
B
EcoRI linearized PRS416
NHEJ Defective
MCS
CEN/ARS
URA3 ttaaaatt
CEN/ARS
URA3
UPTAG DOWNTAG
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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
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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)
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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)
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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
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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
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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 0.37RHU 0.59 1.00 0.38 0.56 0.58 0.95 0.40 0.58RDD 0.56 0.38 1.00 0.58 0.54 0.39 0.92 0.64RDU 0.32 0.56 0.58 1.00 0.33 0.53 0.58 0.89GHD 0.95 0.58 0.54 0.33 1.00 0.62 0.56 0.39GHU 0.58 0.95 0.39 0.53 0.62 1.00 0.41 0.58GDD 0.54 0.40 0.92 0.58 0.56 0.41 1.00 0.73GDU 0.37 0.58 0.64 0.89 0.39 0.58 0.73 1.00
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BTW
The mean squared error across slides is about 3 times bigger than the mean squared error within slides
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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
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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
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Does it fit?
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Does it fit?
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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
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QQ-plot for new t-test
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Better looking than others
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1 YMR106C 9.5 47 69.2 a a 1002 YOR005C 19.7 35 44.9 a d 1003 YLR265C 6.1 32 35.8 a m 1004 YDL041W 10.4 32 35.6 a m 1005 YIL012W 12.2 31 21.7 a a 1006 YIL093C 4.8 29 30.8 a a 1007 YIL009W 5.6 29 -23.5 a a 1008 YDL042C 12.9 29 32.1 a d 1009 YIL154C 1.8 28 91.3 m m 8210 YNL149C 1.7 27 93.4 m d 7111 YBR085W 2.5 26 -15.8 a a 8412 YBR234C 1.7 26 87.5 m d 7513 YLR442C 6.1 26 -100.0 a a 100
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Acknowledgements
• Siew Loon Ooi
• Jef Boeke
• Forrest Spencer
• Jean Yang