Some thoughts of the design of cDNA microarray experiments Terry Speed & Yee HwaYang, Department of Statistics UC Berkeley MGED IV Boston, February 14, 2002

Some aspects of design Layout of the array –Which cDNA sequence to print? Library Controls –Spatial position Allocation of samples to the slides –Different design layout A vs B : Treatment vs control Multiple treatments Factorial Time series –Other considerations Replication Physical limitations: the number of slides and the amount of material Extensibility - linking

Some issues to consider before designing cDNA microarray experiments Scientific Aims of the experiment Specific questions and priorities between them. How will the experiments answer the questions posed? Practical (Logistic) Types of mRNA samples: reference, control, treatment, mutant, etc Amount of material. Count the amount of mRNA involved in one channel of hybridization as one unit. The number of slides available for the experiment. Other Information The experimental process prior to hybridization: sample isolation, mRNA extraction, amplification, labelling,… Controls planned: positive, negative, ratio, etc. Verification method: Northern, RT-PCR, in situ hybridization, etc.

Natural design choice Case 1: Meaningful biological control (C) Samples: Liver tissue from four mice treated by cholesterol modifying drugs. Question 1: Genes that respond differently between the T and the C. Question 2: Genes that responded similarly across two or more treatments relative to control. Case 2: Use of universal reference. Samples: Different tumor samples. Question: To discover tumor subtypes. C T1 T2T3T4 T1T1 Ref T2T2 T n-1 TnTn

Treatment vs Control Two samples e.g. KO vs. WT or mutant vs. WT TC TRef C Direct Indirect  2 /22222 average (log (T/C))log (T / Ref) – log (C / Ref )

Caveat The advantage of direct over indirect comparisons was first pointed out by Churchill & Kerr, and in general, we agree with the conclusion. However, you can see in the last M vs A plot that the difference is not a factor of 2, as theory predicts. Why? A likely explanation is that the assumption that log(T/Ref) and log(C/Ref) are uncorrelated is not valid, and so the gains are less than predicted. The reason for the correlation is less obvious, but there are a number of possibilities. One is that we use mRNA from the same extraction; another is that we didn‘t dye-swap with the two indirect comparisons, but did when we replicated the direct comparison. The answer is not yet clear.

Labeling 3 sets of self – self hybridization: (cerebellum vs cerebellum) Data 1 and Data 2 were labeled together and hybridized on two slides separately. Data 3 were labeled separately. Data 1 Data 2 Data 3

Olfactory bulb experiment: 3 sets of Anterior vs Dorsal performed on different days #10 and #12 were from the same RNA isolation and amplification #12 and #18 were from different dissections and amplifications All 3 data sets were labeled separately before hybridization Extraction

I) Common Reference II) Common reference III) Direct comparison Number of Slides Ave. variance Units of material A = B = C = 1A = B = C = 2 Ave. variance One-way layout: one factor, k levels CB A ref CBA CBA

I) Common Reference II) Common reference III) Direct comparison Number of Slides N = 3N=6N=3 Ave. variance20.67 Units of materialA = B = C = 1A = B = C = 2 Ave. variance10.67 One-way layout: one factor, k levels CB A ref CBA CBA For k = 3, efficiency ratio (Design I / Design III) = 3. In general, efficiency ratio = 2k / (k-1). However, remember the assumption!

Design I Design III A B C A Ref BC Illustration from one experiment Box plots of log ratios: we are still ahead!

CTL OSM EGF OSM & EGF Factorial experiments Treated cell lines Possible experiments Here we are interested not in genes for which there is an O or an E effect, but in which there is an O  E interaction, i.e. in genes for which log(O&E/O)-log(E/C) is large or small.

Other examples of factorial experiments Suppose we have tumor T and standard cells S from the same tissue, and are interested in the impact of radiation R on gene expression. In general, genes for which log(RT/T) and log(RS/S) are large or small, will be less interesting to us than those for which log(RT/T) - log(RS/S) are large or small, i.e. those with large interactions. Next, suppose that our interest is in comparing gene expression in two mutants, say M and M’, at two developmental stages, E and P say. Then we are probably more interested in those genes for which the temporal pattern in the two mutants differ, than in the patterns themselves, i.e. interest focusses on genes for which log(ME/MP)-log(M’E/M’P) is large or small, again the ones with large interactions.

IndirectA balance of direct and indirect I)II)III)IV) # Slides N = 6 Main effect A NA Main effect B Interacti on A.B x 2 factorial: some design options C A.BBA B C A B C A B C A Table entry: variance (assuming all log ratios uncorrelated)

Design choices in time series. Entry: variance t vs t+1t vs t+2t vs t+3 Ave T1T2T2T3T3T4T1T3T2T4T1T4 N=3A) T1 as common reference B) Direct Hybridization N=4C) Common reference D) T1 as common ref + more E) Direct hybridization choice F) Direct Hybridization choice T2 T3 T4 T1 T2 T3 T4 T1 Ref T2 T3 T4 T1 T2T3T4T1 T2T3T4T1 T2 T3 T4 T1

M1.WT.P11 M1.MT.P21 M1.MT.P11 M1.WT.P21M1.WT.P1 M1.MT.P1 Mutant 1 (M1) Mutant 2 (M2) M2.WT.P11 M2.MT.P21 M2.MT.P11 M2.WT.P21 M2.WT P1 M2.MT.P1 Question: Seek genes that are changing over time and are different in MT vs WT. Analysis: Looking at the interaction effect between time and type. An recently designed factorial experiment

Summary The balance of direct and indirect comparisons in a given context should be determined by optimizing the precision of the estimates among comparisons of interest, subject to the scientific and physical constraints of the experiment.

Acknowledgments Jean Yee Hwa Yang Sandrine Dudoit Gary Glonek (Adelaide) Ingrid Lönnstedt (Uppsala) John Ngai’s Lab (Berkeley) Jonathan Scolnick Cynthia Duggan Vivian Peng Moriah Szpara Percy Luu Elva Diaz Dave Lin (Cornell)

Some web sites: Technical reports, talks, software etc. Statistical software R (“GNU’s S”) Packages within R environment: -- SMA (statistics for microarray analysis) Spot