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

Damaged DNA

Rad50p/Mre11p/Xrs2p

Yku70p/Yku80p(DNA-PK )DNA end binding

Lig4p/Lif1pLigation

Nucleolytic processing

Repaired DNA

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

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

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

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

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?

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 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

Acknowledgements

• Siew Loon Ooi

• Jef Boeke

• Forrest Spencer

• Jean Yang