Gordon Smyth, Natalie Thorne and James Wettenhall
The
Walter and Eliza Hall Institute of Medical Research
29 October 2003
Limma is a package for the analysis of gene expression microarray data, especially the use of linear models for analysing designed experiments and the assessment of differential expression. Limma provides the ability to analyse comparisons between many RNA targets simultaneously. The normalization and data analysis functions are for two-colour spotted microarrays. The linear model and differential expression functions apply to all microarrays including Affymetrix and other multi-array oligonucleotide experiments.
The Bioconductor packages marrayClasses, marrayInput and marrayNorm provide alternative functions for reading and normalizing spotted microarray data. If you are using limma in conjunction with these packages, see Section 10. The package affy provides functions for reading and normalizing Affymetrix microarray data. If you are using the affy package, see Sections 7.2 and 11.
This tutorial was prepared using R Version 1.8.0 for Windows and limma version 1.3.0. The latest version of limma is always available from
http://www.bioconductor.org under
"Developmental Packages" or from
http://bioinf.wehi.edu.au/limma/. If you
are using Windows, you can install the last official Bioconductor release of limma from the drop-down menu
in R, simply
select Packages then Install package(s) from Bioconductor....
Note however that this is updated only once every 6 months. The data sets used in the
case study examples can be downloaded from
http://bioinf.wehi.edu.au/marray/genstat2002/. Help with limma is available
by sending questions or problems to
bioconductor@stat.math.ethz.ch.
This guide describes limma as a command-driven package. A menu-driven interface called limmaGUI is also available to most commonly used functions in limma. LimmaGUI is available from http://bioinf.wehi.edu.au/limmaGUI. Although using limmaGUI is easy, installing limmaGUI is at the time of writing a job for an IT professional or for a very experienced computer user because it depends on tck/tk extensions which are not part of standard R.
R is a program for statistical computing. It is a command-driven language meaning that you have to type commands into it rather than pointing and clicking. A good way to get started is to type
help.start()
at the R prompt or, if you're using Windows, to follow the drop-down menu [Help > Html help]. Following the links [Packages > limma] from the html help page will lead you to the contents page of help topics for commands in limma.
Before you can use any limma commands you have to load the package by typing
library(limma)
at the R prompt. You can get help on any function in any loaded package by typing ? and the function name at the R prompt, for example
?read.maimages
for detailed help on the read.maimages function. Anything that you create in
R is an "object". Objects might include data sets, variables, functions,
anything at all. For example
x <- 2
will create a variable x and will assign it the value 2. At any
stage of your R session you can type
objects()
to get a list of all the objects you have created. You see show the contents
of any object by typing the name of the object at the prompt, for example either of the
following commands will print out the contents of x:
show(x) x
We hope that you can use limma without having to spend a lot of time learning about the R language itself but a little knowledge in this direction will be very helpful, especially when you want to do something not explicitly provided for in limma or in the other Bioconductor packages. For more details about the R language see An Introduction to R which is available from the online help.
For those who want to see very quickly what a limma analysis might look like for cDNA data, here is a quick analysis of four replicate arrays (including two dye-swaps). The data has been scanned using an Axon scanner, producing a Gene Allocation List (GAL) file, and then the intensities have been captured from the images using SPOT software. The GAL file and the image analysis files are in the current working directory of R. For more detail about the data see the Swirl Data example below.
> files <- dir(pattern="*.spot") # Get the names of the files containing the intensity data
> RG <- read.maimages(files, source="spot") # Read in the data
> RG$genes <- readGAL() # Read in GAL file containing gene names
> RG$printer <- getLayout(RG$genes) # Set printer layout information
> MA <- normalizeWithinArrays(RG) # Print-tip group loess normalization
> MA <- normalizeBetweenArrays(MA) # Scale normalization between arrays, optional
> fit <- lmFit(MA, design=c(-1,1,-1,1)) # Estimate all the fold changes by fitting a linear model.
# The design matrix indicates which arrays are dye-swaps
> fit <- eBayes(fit) # Apply Bayesian smoothing to the standard errors (very important!)
> options(digits=3)
> topTable(fit, n=30, adjust="fdr") # Show the top 30 genes, control false discovery rate
Block Row Column ID Name M A t P.Value B
3721 8 2 1 control BMP2 -2.21 12.1 -21.1 0.000357 7.96
1609 4 2 1 control BMP2 -2.30 13.1 -20.3 0.000357 7.78
3723 8 2 3 control Dlx3 -2.18 13.3 -20.0 0.000357 7.71
1611 4 2 3 control Dlx3 -2.18 13.5 -19.6 0.000357 7.62
8295 16 16 15 fb94h06 20-L12 1.27 12.0 14.1 0.002067 5.78
7036 14 8 4 fb40h07 7-D14 1.35 13.8 13.5 0.002067 5.54
515 1 22 11 fc22a09 27-E17 1.27 13.2 13.4 0.002067 5.48
5075 10 14 11 fb85f09 18-G18 1.28 14.4 13.4 0.002067 5.48
7307 14 19 11 fc10h09 24-H18 1.20 13.4 13.2 0.002067 5.40
319 1 14 7 fb85a01 18-E1 -1.29 12.5 -13.1 0.002067 5.32
2961 6 14 9 fb85d05 18-F10 -2.69 10.3 -13.0 0.002067 5.29
4032 8 14 24 fb87d12 18-N24 1.27 14.2 12.8 0.002067 5.22
6903 14 2 15 control Vox -1.26 13.4 -12.8 0.002067 5.20
4546 9 14 10 fb85e07 18-G13 1.23 14.2 12.8 0.002067 5.18
683 2 7 11 fb37b09 6-E18 1.31 13.3 12.4 0.002182 5.02
1697 4 5 17 fb26b10 3-I20 1.09 13.3 12.4 0.002182 4.97
7491 15 5 3 fb24g06 3-D11 1.33 13.6 12.3 0.002182 4.96
4188 8 21 12 fc18d12 26-F24 -1.25 12.1 -12.2 0.002209 4.89
4380 9 7 12 fb37e11 6-G21 1.23 14.0 12.0 0.002216 4.80
3726 8 2 6 control fli-1 -1.32 10.3 -11.9 0.002216 4.76
2679 6 2 15 control Vox -1.25 13.4 -11.9 0.002216 4.71
5931 12 6 3 fb32f06 5-C12 -1.10 13.0 -11.7 0.002216 4.63
7602 15 9 18 fb50g12 9-L23 1.16 14.0 11.7 0.002216 4.63
2151 5 2 15 control vent -1.40 12.7 -11.7 0.002216 4.62
3790 8 4 22 fb23d08 2-N16 1.16 12.5 11.6 0.002221 4.58
7542 15 7 6 fb36g12 6-D23 1.12 13.5 11.0 0.003000 4.27
4263 9 2 15 control vent -1.41 12.7 -10.8 0.003326 4.13
6375 13 2 15 control vent -1.37 12.5 -10.5 0.004026 3.91
1146 3 4 18 fb22a12 2-I23 1.05 13.7 10.2 0.004242 3.76
157 1 7 13 fb38a01 6-I1 -1.82 10.8 -10.2 0.004242 3.75
We assume that an experiment has been conducted with one or more microarrays, all printed with the same library of probes. Each array has been scanned to produce a TIFF image. The TIFF images have then been processed using an image analysis program such a ArrayVision, ImageGene, GenePix, QuantArray or SPOT to acquire the red and green foreground and background intensities for each spot. The spot intensities have then been exported from the image analysis program into a series of text files. There should be one file for each array or, in the case of Imagene, two files for each array.
You will need to have (i) a file which describes the probes, often called the Gene List, and (ii) the image analysis output files. It most cases it is also desirable to have a Targets File which describes which RNA sample was hybridized to each channel of each array. A further optional file is the Spot Types file which identifies special probes such as control spots.
Let files be a character vector containing the names of the
image analysis output files. The foreground and background intensities can be
read into an RGList object using a command of the form
RG <- read.maimages(files, source="<imageanalysisprogram>", path="<directory>")
where <imageanalysisprogram> is the name of the image analysis
program and <directory> is the full path of the directory
containing the files. If the files are in the current R working directory then
the argument path can be omitted; see the help entry for
setwd for how to set the current working directory. For example, if the files are SPOT output and
have common extension "spot" then they can
be read using
files <- dir(pattern="*\\.spot") RG <- read.maimages(files, source="spot")
The object files is then a character vector containing all the
spot file names in alphabetical order. If the files are GenePix output files and have extension "gpr" then they
can be read using
files <- dir(pattern="*\\.gpr") RG <- read.maimages(files, source="genepix")
Consult the help entry for read.maimages to see which other
image analysis programs are supported. Files are assumed by default to be
tab-delimited. If the files use a different separator this may be specified
using the sep= argument. For example if the Genepix files were
comma-separated (csv) then the read command would be
RG <- read.maimages(files, source="genepix", sep=",")
What should you do if your image analysis program is not currently supported by limma? If your output files are of a standard format, you can supply the column names corresponding to the intensities yourself. For example,
RG <- read.maimages(files, columns=list(Rf="F635 Mean",Gf="F532 Mean",Rb="B635 Median",Gb="B532 Median"))
is exactly equivalent to the earlier command with source="genepix".
"Standard format" means here that there is a unique column name identifying each
column of interest and that there are no lines in the file following the last
line of data. Header information at the start of the file is ok.
It is a good idea to look at your data to check that it has been read in correctly. Type
show(RG)
to see a print out the first few lines of data. Also try
summary(RG$R)
to see a five-number summary of the red intensities for each array, and so on.
It is possible to read the data in several steps. If RG1 and
RG2 are two data sets corresponding to different sets of arrays
then
RG <- cbind(RG1, RG2)
will combine them into one large data set. Data sets can also be subsetted.
For example RG[,1] is the data for the first array while
RG[1:100,] is the data on the first 100 genes.
It is desirable to use the image analysis to compute a weight for each spot between 0 and 1 which indicates the reliability of the acquired intensities at that spot. For example, if the SPOT image analysis program is used and the size of an ideal perfectly circular spot is known to be 100 pixels, then one might use
> RG <- read.maimages(files,source="spot",wt.fun=wtarea(100))
The function wtarea(100) gives full weight to spots with area
100 pixels and down-weights smaller and larger spots. Spots which have zero area
or are more than twice the ideal size are given zero weight. This will create a
component called weights in the RG list. The weights will be used
automatically by functions such as normalizeWithinArrays which operate on
the RG-list.
With GenePix data
> RG <- read.maimages(files,source="genepix",wt.fun=wtflags(0.1))
will give weight 0.1 to any spot which receives a negative flag from the GenePix program.
Computing quality weights depends on the image analysis program. Consult the
help entry QualityWeights to see what quality weight functions are
available.
Although not necessary to use limma it is usually a good idea to construct a targets file which lists the RNA target hybridized to each channel of each array. The Targets File is normally in tab-delimited text format. The file should contain a row for each microarray. It should contain FileName column, giving the file from image-analysis containing raw foreground and background intensities for each slide, a Cy3 column giving the RNA type reverse transcribed and labelled with Cy3 dye for that slide (e.g. Wild Type) and a Cy5 column giving the RNA type reverse transcribed and labelled with Cy5 dye for that slide. For ImaGene files, the FileName column is split into a FileNameCy3 column and a FileNameCy5. As well as the essential columns, you can have a Name column giving an alternative slide name to the default name, "Slide n", where n is the SlideNumber and you can have a Date column, listing the date of the hybridization, and as many extra columns as you like, as long as the column names are unique.
Some examples are shown below.
The ImaGene Targets file below shows the special case of the ImaGene image-processing software which gives two (tab-delimited text) output files for each slide, one for the Cy3 (Green) channel and one for the Cy5 (Red) channel. So instead of having a single FileName column, there are two file name columns: a FileNameCy3 column and a FileNameCy5 column.
The Date column is optional and is not currently used in limma.
A Name column can be included, giving each array a name which can be used for plotting. In this case, a short name
is used so that a boxplot of all sixteen arrays can be plotted with labels for all arrays along the horizontal axis. If
no Name column is given, then a default name will be given to each slide, e.g. "Slide 1".
The Targets file below is from an experiment with four different RNA sources. The main Targets file is not shown. The one below is used to analyse the spiked-in scorecard controls. Spike-in controls will generally be analysed separately from genes because the follow different rules, e.g. for genes, the log-ratio between A and B plus the log-ratio between B and C should equal the log-ratio between A and C, but for scorecard controls, all three log (red/green) ratios may be the same.
The Targets
File can be read using readTargets(). The file can have any name
but the default name is Targets.txt. Very often the targets file
will be first thing read because it contains the image analysis output file
names, e.g.,
> targets <- readTargets() > RG <- read.maimages(targets$FileName)
If the arrays have been scanned with an Axon scanner, then the gene names will be available in a GenePix Array List (GAL) file. If the GAL file has extension "gal" and is in the current working directory, then it may be read into a data.frame by
> RG$genes <- readGAL()
The print layout of the arrays can be extracted from the GAL by
> RG$printer <- getLayout(RG$genes)
Non-Genepix gene lists can be read into R using the function read.table
from R base. If you have Imagene or SMD image analysis output, then the gene
list will be extracted from the image analysis output files by read.images.
The Spot Types file (another tab-delimited text file) is optional but it is very useful in distinguishing between genes, controls and blanks when using the Color-Coded M A Plot (with legend) feature. Certain spot types (e.g. scorecard controls) can be excluded from a linear model fit if desired. For a given spot type, e.g. "Ratio_control_*", spot sub-types "Ratio_control_1", "Ratio_control_2" can be determined automatically to give a series of box-plots comparing the moderated t-statistics or B statistics (log odds of differential expression) between the controls, which may help in deciding which genes are truly differentially expressed, i.e. what moderated t statistic is significant.
Every SpotType must have a SpotType column, for which each entry should be unique. It must also have an ID column, a Name column and a default Color column. The rows of the SpotTypes file should be read as a list of rules (in order) for defining spot types. First, we say everything is a gene, then we rename certain spots according to what is find in the ID or Name column of the GAL file. The color given here is just a suggested color to associate with the spot type.
Again, do not change the capitalization or spelling of the column names and do not insert extra spaces.
Here is a short spot types file.
The spot types file below defines the scorecard control spots. The asterisks are wildcards which can represent anything.
You can read the spot types files using readSpotTypes(). For example, if the file has the default name SpotTypes.txt you can use
> spottypes <- readSpotTypes()
The spot types file is used by the spotStatus() function to set the status of each spot on the array, for example
> RG$genes$Status <- spotStatus(spottypes)
It is advisable to display your data in various ways as a quality check and to check for unexpected effects. We recommend an imageplot of the raw log-ratios and an MA-plot of the raw data for each array as a minimum routine displays. See the Swirl data case study for examples.
Limma implements a range of normalization methods for spotted microarrays. Smyth and Speed (2003) describe of the mostly commonly used methods. Most of the examples given in this manual use print-tip loess normalization as the major method. Print-tip loess normalization is performed by
> MA <- normalizeWithinArrays(RG)
By default, limma will subtract the background from the foreground
intensities as part of the normalization process using
normalizeWithinArrays so there is no need for any special action on the
part of users. If you want to over-ride this default background correct, for
example to ensure that all the corrected intensities are positive, then use the
backgroundCorrect function. For example use
> RG <- backgroundCorrect(RG, method="minimum")
to reset zero or negative intensities to half the value of the minimum value
of the positive intensities. No further background correction will be performed
when normalizeWithinArrays is used subsequently to normalize the
intensities.
Limma contains some more sophisticated normalization methods. Normalization of absolute expression levels as well as just log-ratios is covered in Section 11 at the end of this guide.
The package limma uses an approach called linear models to analyse designed microarray experiments. This approach allows very general experiments to be analysed just as easily as a simple replicated experiment. The approach is outlined in Smyth (2003) and Yang and Speed (2002). The approach requires one or two matrices to be specified. The first is the design matrix which indicates in effect which RNA samples have been applied to each array. The second is the contrast matrix which specifies which comparisons you would like to make between the RNA samples. For very simple experiments, you may not need to specify the contrast matrix.
If you have data from Affymetrix experiments, from single-channel spotted microarrays or from spotted microarrays using a common reference, then linear modeling is the same a ordinary analysis of variance or multiple regression except that a model is fitted for every gene. With data of this type you can create design matrices as one would do for ordinary modeling with univariate data. If you have data from spotted microarrays using a direct design, i.e., a connected design with no common reference, then the linear modeling approach is very powerful but the creation of the design matrix may require more statistical knowledge.
For statistical analysis and assessing differential expression, limma uses an empirical Bayes method to moderate the standard errors of the estimated log-fold changes. This results in more stable inference and improved power, especially for experiments with small numbers of arrays (Smyth, 2003). For arrays with within-array replicate spots, limma uses a pooled correlation method to make full use of the duplicate spots (Smyth et al, 2003).
Affymetrix data will usually be normalized using the affy package. We will
assume here that the data is available as an exprSet object called
eset. Such an object will have an slot containing the log-expression
values for each gene on each array which can be extracted using exprs(eset). Affymetrix and
other single-channel microarray data may be analysed very much like ordinary
linear models or anova models. The difference with microarray data is that it is
almost always necessary to extract particular contrasts of interest and so
the standard parametrizations provided for factors in R are not usually adequate.
There are many ways to approach the analysis of a complex experiment in limma. A straightforward strategy is to set up the simplest possible design matrix and then to extract from the fit the contrasts of interest.
Suppose that there are three RNA sources to be compared.
Suppose that the first three arrays are hybridized with RNA1, the next two with
RNA2 and the next three with RNA3. Suppose that all pair-wise comparisons
between the RNA sources are of interest. We assume that the data has been
normalized and stored in an exprSet object, for example by
> data <- ReadAffy() > eset <- rma(data)
An appropriate design matrix can be created and a linear model fitted using
> design <- model.matrix(~ -1+factor(c(1,1,1,2,2,3,3,3)))
> colnames(design) <- c("group1", "group2", "group3")
> fit <- lmFit(eset, design)
To make all pair-wise comparisons between the three groups the appropriate contrast matrix can be created by
> contrast.matrix <- makeContrasts(group2-group1, group3-group3, group3-group1, levels=design) > fit2 <- contrasts.fit(fit, contrast.matrix) > fit2 <- eBayes(fit2)
A list of top genes differential expressed in group2 versus group1 can be obtained from
> topTable(fit2, coef=1, adjust="fdr")
You may classify each gene according to the three pair-wise comparisons using
> clas <- classifyTests(fit2)
A Venn diagram showing numbers of genes significant in each comparison can be obtained from
> vennDiagram(clas)
Now consider two-color microarray experiments in which a common reference has
been used on all the arrays. Such experiments can be analysed very similarly to
Affymetrix experiments except that allowance must be made for dye-swaps. The
simplest method is to setup the design matrix using the designMatrix()
function and the targets file. As an example, we consider part of an experiment
conducted by Jöelle Michaud, Catherine Carmichael and Dr Hamish Scott at the
Walter and Eliza Hall Institute to compare the effects of transcription factors
in a human cell line. The targets file is as follows:
> targets <- readTargets("runxtargets.txt")
> targets
SlideNumber Cy3 Cy5
1 2144 EGFP AML1
2 2145 EGFP AML1
3 2146 AML1 EGFP
4 2147 EGFP AML1.CBFb
5 2148 EGFP AML1.CBFb
6 2149 AML1.CBFb EGFP
7 2158 EGFP CBFb
8 2159 CBFb EGFP
9 2160 EGFP AML1.CBFb
10 2161 AML1.CBFb EGFP
11 2162 EGFP AML1.CBFb
12 2163 AML1.CBFb EGFP
13 2166 EGFP CBFb
14 2167 CBFb EGFP
In the experiment, green fluorescent protein (EGFP) has been used as a common reference. An adenovirus system was used to transport various transcription factors into the nuclei of HeLa cells. Here we consider the transcription factors AML1, CBFbeta or both. A simple design matrix was formed and a linear model fit:
> design <- designMatrix(targets,ref="EGFP") > design AML1 AML1.CBFb CBFb 1 1 0 0 2 1 0 0 3 -1 0 0 4 0 1 0 5 0 1 0 6 0 -1 0 7 0 0 1 8 0 0 -1 9 0 1 0 10 0 -1 0 11 0 1 0 12 0 -1 0 13 0 0 1 14 0 0 -1 > fit <- lmFit(RG, design)
It is of interest to compare each of the transcription factors to EGFP and also to compare the combination transcription factor with AML1 and CBFb individually. An appropriate contrast matrix was formed as follows:
> contrast.matrix <- makeContrasts(AML1,CBFb,AML1.CBFb,AML1.CBFb-AML1,AML1.CBFb-CBFb,levels=design)
> contrast.matrix
AML1 CBFb AML1.CBFb AML1.CBFb - AML1 AML1.CBFb - CBFb
AML1 1 0 0 -1 0
AML1.CBFb 0 0 1 1 1
CBFb 0 1 0 0 -1
The linear model fit can now be expanded and empirical Bayes statistics computed:
> fit2 <- contrasts.fit(fit, contrasts.matrix) > fit2 <- eBayes(fit2)
Two-colour designs without a common reference require the most statistical knowledge to choose the appropriate design matrix. As an example, we consider an experiment conducted by Dr Mireille Lahoud at the Walter and Eliza Hall Institute to compare gene expression in three different populations of dendritric cells (DC).
This experiment involved six cDNA microarrays in three dye-swap pairs, with each pair used to compare two DC types. The design is shown diagrammatically above. The targets file was as follows:
> targets SlideNumber FileName Cy3 Cy5 1 12 ml12med.spot CD4 CD8 2 13 ml13med.spot CD8 CD4 3 14 ml14med.spot DN CD8 4 15 ml15med.spot CD8 DN 5 16 ml16med.spot CD4 DN 6 17 ml17med.spot DN CD4
There are many valid choices for a design matrix for such an experiment and no single correct choice. We chose to setup the design matrix as follows:
> design <- cbind("CD8-CD4"=c(1,-1,1,-1,0,0),"DN-CD4"=c(0,0,-1,1,1,-1))
> rownames(design) <- removeExt(targets$FileName)
> design
CD8-CD4 DN-CD4
ml12med 1 0
ml13med -1 0
ml14med 1 -1
ml15med -1 1
ml16med 0 1
ml17med 0 -1
In this design matrix, the CD8 and DN populations have been compared back to the CD4 population. The coefficients estimated by the linear model will correspond to the log-ratios of CD8 vs CD4 (first column) and DN vs CD4 (second column). After appropriate normalization of the expression data, a linear model was fit using
> fit <- lmFit(MA, design, ndups=2)
The use of ndups is to specify that the arrays contained
duplicates of each gene, see Section 9.
The linear model can now be interrogated to answer any questions of interest. For this experiment it was of interest to make all pairwise comparisons between the three DC populations. This was accomplished using the contrast matrix
> contrast.matrix <- cbind("CD8-CD4"=c(1,0),"DN-CD4"=c(0,1),"CD8-DN"=c(1,-1))
> rownames(contrast.matrix) <- colnames(design)
> contrast.matrix
CD8-CD4 DN-CD4 CD8-DN
CD8-CD4 1 0 1
DN-CD4 0 1 -1
The contrast matrix can be used to expand the linear model fit and then to compute empirical Bayes statistics:
> fit2 <- constrast.fit(fit, contrast.matrix) > fit2 <- eBayes(fit2)
In this section we consider a case study in which two RNA sources are compared directly on a set of replicate or dye-swap arrays. The case study includes reading in the data, data display and exploration, as well as normalization and differential expression analysis. The analysis of differential expression is analogous to a classical one-sample test of location for each gene.
In this example we assume that the data is provided as a GAL file called
fish.gal and raw SPOT output files and that these files are in the
current working directory.
Background. The experiment was carried out using zebrafish as a model organism to study the early development in vertebrates. Swirl is a point mutant in the BMP2 gene that affects the dorsal/ventral body axis. The main goal of the Swirl experiment is to identify genes with altered expression in the Swirl mutant compared to wild-type zebrafish.
The hybridizations. Two sets of dye-swap experiments were performed making a total of four replicate hybridizations. Each of the arrays compares RNA from swirl fish with RNA from normal ("wild type") fish. The experimenters have prepared a tab-delimited targets file called "SwirlSamples.txt" which describes the four hybridizations:
> targets <- readTargets("SwirlSample.txt")
> targets
SlideNumber FileName Cy3 Cy5 Date
1 81 swirl.1.spot swirl wild type 2001/9/20
2 82 swirl.2.spot wild type swirl 2001/9/20
3 93 swirl.3.spot swirl wild type 2001/11/8
4 94 swirl.4.spot wild type swirl 2001/11/8
We see that slide numbers 81, 82, 93 and 94 were used to make the arrays. On slides 81 and 93, swirl RNA was labelled with green (Cy3) dye and wild type RNA was labelled with red (Cy5) dye. On slides 82 and 94, the labelling was the other way around.
Each of the four hybridized arrays was scanned on an Axon scanner to produce
a TIFF image, which was then processed using the image analysis software SPOT.
The data from the arrays are stored in the four output files listed under
FileName. Now we read the intensity data into an RGList
object in R. The default for SPOT output is that Rmean and Gmean
are used as foreground
intensities and morphR and morphG are used as
background intensities:
> RG <- read.maimages(targets$FileName, source="spot")
Read swirl.1.spot
Read swirl.2.spot
Read swirl.3.spot
Read swirl.4.spot
> RG
An object of class "RGList"
$R
swirl.1 swirl.2 swirl.3 swirl.4
[1,] 19538.470 16138.720 2895.1600 14054.5400
[2,] 23619.820 17247.670 2976.6230 20112.2600
[3,] 21579.950 17317.150 2735.6190 12945.8500
[4,] 8905.143 6794.381 318.9524 524.0476
[5,] 8676.095 6043.542 780.6667 304.6190
8443 more rows ...
$G
swirl.1 swirl.2 swirl.3 swirl.4
[1,] 22028.260 19278.770 2727.5600 19930.6500
[2,] 25613.200 21438.960 2787.0330 25426.5800
[3,] 22652.390 20386.470 2419.8810 16225.9500
[4,] 8929.286 6677.619 383.2381 786.9048
[5,] 8746.476 6576.292 901.0000 468.0476
8443 more rows ...
$Rb
swirl.1 swirl.2 swirl.3 swirl.4
[1,] 174 136 82 48
[2,] 174 133 82 48
[3,] 174 133 76 48
[4,] 163 105 61 48
[5,] 140 105 61 49
8443 more rows ...
$Gb
swirl.1 swirl.2 swirl.3 swirl.4
[1,] 182 175 86 97
[2,] 171 183 86 85
[3,] 153 183 86 85
[4,] 153 142 71 87
[5,] 153 142 71 87
8443 more rows ...
The arrays. The microarrays used in this experiment were printed with 8448 probes (spots), including 768 control spots. The array printer uses a print head with a 4x4 arrangement of print-tips and so the microarrays are partitioned into a 4x4 grid of tip groups. Each grid consists of 22x24 spots that were printed with a single print-tip. The gene name associated with each spot is recorded in a GenePix array list (GAL) file:
> RG$genes <- readGAL("fish.gal")
> RG$genes[1:30,]
Block Row Column ID Name
1 1 1 1 control geno1
2 1 1 2 control geno2
3 1 1 3 control geno3
4 1 1 4 control 3XSSC
5 1 1 5 control 3XSSC
6 1 1 6 control EST1
7 1 1 7 control geno1
8 1 1 8 control geno2
9 1 1 9 control geno3
10 1 1 10 control 3XSSC
11 1 1 11 control 3XSSC
12 1 1 12 control 3XSSC
13 1 1 13 control EST2
14 1 1 14 control EST3
15 1 1 15 control EST4
16 1 1 16 control 3XSSC
17 1 1 17 control Actin
18 1 1 18 control Actin
19 1 1 19 control 3XSSC
20 1 1 20 control 3XSSC
21 1 1 21 control 3XSSC
22 1 1 22 control 3XSSC
23 1 1 23 control Actin
24 1 1 24 control Actin
25 1 2 1 control ath1
26 1 2 2 control Cad-1
27 1 2 3 control DeltaB
28 1 2 4 control Dlx4
29 1 2 5 control ephrinA4
30 1 2 6 control FGF8
The 4x4x22x24 print layout also needs to be set. The easiest way to do this is to infer it from the GAL file:
> RG$printer <- getLayout(RG$genes)
Image plots. It is interesting to look at the variation of background values over the array. Consider image plots of the red and green background for the first array:
> imageplot(log2(RG$Rb[,1]), RG$printer, low="white", high="red") > imageplot(log2(RG$Gb[,1]), RG$printer, low="white", high="green")
Image plot of the un-normalized log-ratios or M-values for the first array:
> MA <- normalizeWithinArrays(RG, method="none") > imageplot(MA$M[,1], RG$printer, zlim=c(-3,3))
The imageplot function lies the slide on its side, so the first print-tip group is bottom left
in this plot. We can see a red
streak across the middle two grids of the 3rd row caused by a scratch or dust on
the array. Spots which are affected by
this artefact will have suspect M-values. The streak also shows up as darker
regions in the background plots.
MA-plots. An MA-plot plots the log-ratio of R vs G against the overall intensity of each spot. The log-ratio is represented by the M-value, M = log2(R)-log2(G), and the overall intensity by the A-value, A = log2(R)+log2(G). Here is the MA-plot of the un-normalized values for the first array:
> plotMA(MA)
The red streak seen on the image plot can be seen as a line of spots in the upper right of this plot. Now we plot the individual MA-plots for each of the print-tip groups on this array, together with the loess curves which will be used for normalization:
> plotPrintTipLoess(MA)
Normalization. Print-tip loess normalization:
> MA <- normalizeWithinArrays(RG) > plotPrintTipLoess(MA)
We have normalized the M-values with each array. A further question is whether normalization is required between the arrays. The following plot shows overall boxplots of the M-values for the four arrays.
> boxplot(MA$M~col(MA$M),names=colnames(MA$M))
There is some evidence that the different arrays have different spreads of M-values, so we will scale normalize between the arrays.
> MA <- normalizeBetweenArrays(MA) > boxplot(MA$M~col(MA$M),names=colnames(MA$M))
Linear model. Now estimate the average M-value for each gene. We do this by fitting a simple linear model for each gene. The negative numbers in the design matrix indicate the dye-swaps.
> design <- c(-1,1,-1,1)
> fit <- lmFit(MA,design)
> fit
An object of class "MArrayLM"
$coefficients
[1] -0.3943421 -0.3656843 -0.3912506 -0.2505729 -0.3432590
8443 more elements ...
$stdev.unscaled
[1] 0.5 0.5 0.5 0.5 0.5
8443 more elements ...
$sigma
[1] 0.3805154 0.4047829 0.4672451 0.3206071 0.2838043
8443 more elements ...
$df.residual
[1] 3 3 3 3 3
8443 more elements ...
$method
[1] "ls"
$design
[,1]
[1,] -1
[2,] 1
[3,] -1
[4,] 1
$genes
Block Row Column ID Name
1 1 1 1 control geno1
2 1 1 2 control geno2
3 1 1 3 control geno3
4 1 1 4 control 3XSSC
5 1 1 5 control 3XSSC
8443 more rows ...
$Amean
[1] 13.46481 13.67631 13.42665 10.77730 10.88446
8443 more elements ...
In the above fit object, coefficients is the average M-value for
each gene and sigma is the sample standard deviations for each
gene. Ordinary t-statistics for comparing mutant to wt could be computed by
> ordinary.t <- fit$coef / fit$stdev.unscaled / fit$sigma
We prefer though to use empirical Bayes moderated t-statistics which are computed below. Now create an MA-plot of the average M and A-values for each gene.
> M <- fit$coef > A <- fit$Amean > plot(A,M,pch=16,cex=0.1) > abline(0,0,col="blue")
Empirical Bayes analysis. We will now go on and compute empirical Bayes statistics for differential expression. The moderated t-statistics use sample standard deviations which have been shrunk towards a pooled standard deviation value.
> fit <- eBayes(fit) > qqt(fit$t,df=fit$df.prior+fit$df.residual,pch=16,cex=0.1) > abline(0,1)
Visually there seems to be plenty of genes which are differentially
expressed. We will obtain a summary table of some key statistics for the top genes.
> options(digits=3)
> topTable(fit,number=30,adjust="fdr")
Block Row Column ID Name M A t P.Value B
3721 8 2 1 control BMP2 -2.21 12.1 -21.1 0.000357 7.96
1609 4 2 1 control BMP2 -2.30 13.1 -20.3 0.000357 7.78
3723 8 2 3 control Dlx3 -2.18 13.3 -20.0 0.000357 7.71
1611 4 2 3 control Dlx3 -2.18 13.5 -19.6 0.000357 7.62
8295 16 16 15 fb94h06 20-L12 1.27 12.0 14.1 0.002067 5.78
7036 14 8 4 fb40h07 7-D14 1.35 13.8 13.5 0.002067 5.54
515 1 22 11 fc22a09 27-E17 1.27 13.2 13.4 0.002067 5.48
5075 10 14 11 fb85f09 18-G18 1.28 14.4 13.4 0.002067 5.48
7307 14 19 11 fc10h09 24-H18 1.20 13.4 13.2 0.002067 5.40
319 1 14 7 fb85a01 18-E1 -1.29 12.5 -13.1 0.002067 5.32
2961 6 14 9 fb85d05 18-F10 -2.69 10.3 -13.0 0.002067 5.29
4032 8 14 24 fb87d12 18-N24 1.27 14.2 12.8 0.002067 5.22
6903 14 2 15 control Vox -1.26 13.4 -12.8 0.002067 5.20
4546 9 14 10 fb85e07 18-G13 1.23 14.2 12.8 0.002067 5.18
683 2 7 11 fb37b09 6-E18 1.31 13.3 12.4 0.002182 5.02
1697 4 5 17 fb26b10 3-I20 1.09 13.3 12.4 0.002182 4.97
7491 15 5 3 fb24g06 3-D11 1.33 13.6 12.3 0.002182 4.96
4188 8 21 12 fc18d12 26-F24 -1.25 12.1 -12.2 0.002209 4.89
4380 9 7 12 fb37e11 6-G21 1.23 14.0 12.0 0.002216 4.80
3726 8 2 6 control fli-1 -1.32 10.3 -11.9 0.002216 4.76
2679 6 2 15 control Vox -1.25 13.4 -11.9 0.002216 4.71
5931 12 6 3 fb32f06 5-C12 -1.10 13.0 -11.7 0.002216 4.63
7602 15 9 18 fb50g12 9-L23 1.16 14.0 11.7 0.002216 4.63
2151 5 2 15 control vent -1.40 12.7 -11.7 0.002216 4.62
3790 8 4 22 fb23d08 2-N16 1.16 12.5 11.6 0.002221 4.58
7542 15 7 6 fb36g12 6-D23 1.12 13.5 11.0 0.003000 4.27
4263 9 2 15 control vent -1.41 12.7 -10.8 0.003326 4.13
6375 13 2 15 control vent -1.37 12.5 -10.5 0.004026 3.91
1146 3 4 18 fb22a12 2-I23 1.05 13.7 10.2 0.004242 3.76
157 1 7 13 fb38a01 6-I1 -1.82 10.8 -10.2 0.004242 3.75
The top gene is BMP2 which is significantly down-regulated in the Swirl zebrafish, as it should be because the Swirl fish are mutant in this gene. Other positive controls also appear in the top 50 genes in terms.
In the table, t is the empirical Bayes moderated t-statistic, the
corresponding P-values have been adjusted to control the false discovery rate
and B is the empirical Bayes log odds of differential expression. Beware that
the Benjamini and Hochberg method used to control the false discovery rate
assumes independent statistics which we do not have here (see help(p.adjust)).
> ord <- order(fit$lods,decreasing=TRUE) > top30 <- ord[1:30] > plot(A,M,pch=16,cex=0.1) > text(A[top30],M[top30],labels=MA$genes[top30,"Name"],cex=0.8,col="blue")
In this section we consider a case study where two RNA sources are compared through a common reference RNA. The analysis of the log-ratios involves a two-sample comparison of means for each gene.
In this example we assume that the data is available as an RG list in the
data file ApoAI.RData.
Background. The data is from a study of lipid metabolism by Callow et al (2000). The apolipoprotein AI (ApoAI) gene is known to play a pivotal role in high density lipoprotein (HDL) metabolism. Mice which have the ApoAI gene knocked out have very low HDL cholesterol levels. The purpose of this experiment is to determine how ApoAI deficiency affects the action of other genes in the liver, with the idea that this will help determine the molecular pathways through which ApoAI operates.
Hybridizations. The experiment compared 8 ApoAI knockout mice with 8 normal C57BL/6 ("black six") mice, the control mice. For each of these 16 mice, target mRNA was obtained from liver tissue and labelled using a Cy5 dye. The RNA from each mouse was hybridized to a separate microarray. Common reference RNA was labelled with Cy3 dye and used for all the arrays. The reference RNA was obtained by pooling RNA extracted from the 8 control mice.
| Number of arrays | Red | Green |
| 8 | Normal "black six" mice | Pooled reference |
| 8 | ApoAI knockout | Pooled reference |
This is an example of a single comparison experiment using a common reference. The fact that the comparison is made by way of a common reference rather than directly as for the swirl experiment makes this, for each gene, a two-sample rather than a single-sample setup.
> load("ApoAI.RData")
> objects()
[1] "design" "genelist" "layout" "RG"
> RG$R[1:4,]
c1 c2 c3 c4 c5 c6 c7 c8 k1 k2 k3
1 2765.58 1768.22 1440.54 763.06 2027.94 864.05 958.68 644.58 747.11 1388.79 1588.76
2 2868.43 2277.18 1599.92 1238.33 1513.43 1079.33 1228.66 757.33 1930.25 2093.00 1369.81
3 1236.32 1546.84 2639.45 999.48 3689.67 1505.20 785.10 994.86 753.52 1300.00 1301.61
4 383.62 532.50 323.55 585.14 250.74 566.58 409.18 417.79 829.82 402.84 513.91
k4 k5 k6 k7 k8
1 1280.17 1881.72 1733.53 1170.84 1512.45
2 1071.17 3218.58 2451.04 1605.00 1700.82
3 3292.26 1149.23 3424.30 1901.06 2200.82
4 459.69 391.09 601.00 438.03 507.25
> MA <- normalizeWithinArrays(RG,layout)
> boxplot(MA$M~col(MA$M),names=colnames(RG$R))
The differences in scale are moderate, so we won't scale normalize between arrays.
Now we can go on to estimate the fold change between the two groups. In this case the design matrix has two columns. The coefficient for the second column estimates the parameter of interest, the log-ratio between knockout and control mice.
> design
Control-Ref KO-Control
c1 1 0
c2 1 0
c3 1 0
c4 1 0
c5 1 0
c6 1 0
c7 1 0
c8 1 0
k1 1 1
k2 1 1
k3 1 1
k4 1 1
k5 1 1
k6 1 1
k7 1 1
k8 1 1
> fit <- lm.series(MA$M,design)
> fit$coef[1:5,]
Control-Ref KO-Control
[1,] -0.6595 0.6393
[2,] 0.2294 0.6552
[3,] -0.2518 0.3342
[4,] -0.0517 0.0405
[5,] -0.2501 0.2230
> eb <- ebayes(fit)
> options(digits=3)
> toptable(coef=2,number=15,genelist=genelist[,1:6],fit=fit,eb=eb,adjust="fdr")
GridROW GridCOL ROW COL NAME TYPE M t P.Value B
2149 2 2 8 7 ApoAI,lipid-Img cDNA -3.166 -23.98 3.05e-11 14.927
540 1 2 7 15 EST,HighlysimilartoA cDNA -3.049 -12.96 5.02e-07 10.813
5356 4 2 9 1 CATECHOLO-METHYLTRAN cDNA -1.848 -12.44 6.51e-07 10.448
4139 3 3 8 2 EST,WeaklysimilartoC cDNA -1.027 -11.76 1.21e-06 9.929
1739 2 1 7 17 ApoCIII,lipid-Img cDNA -0.933 -9.84 1.56e-05 8.192
2537 2 3 7 17 ESTs,Highlysimilarto cDNA -1.010 -9.02 4.22e-05 7.305
1496 1 4 15 5 est cDNA -0.977 -9.00 4.22e-05 7.290
4941 4 1 8 6 similartoyeaststerol cDNA -0.955 -7.44 5.62e-04 5.311
947 1 3 8 2 EST,WeaklysimilartoF cDNA -0.571 -4.55 1.77e-01 0.563
5604 4 3 1 18 cDNA -0.366 -3.96 5.29e-01 -0.553
4140 3 3 8 3 APXL2,5q-Img cDNA -0.420 -3.93 5.29e-01 -0.619
6073 4 4 5 4 estrogenrec cDNA 0.421 3.91 5.29e-01 -0.652
1337 1 4 7 14 psoriasis-associated cDNA -0.838 -3.89 5.29e-01 -0.687
954 1 3 8 9 Caspase7,heart-Img cDNA -0.302 -3.86 5.30e-01 -0.757
563 1 2 8 17 FATTYACID-BINDINGPRO cDNA -0.637 -3.81 5.30e-01 -0.839
Notice that the top gene is ApoAI itself which is heavily down-regulated. Theoretically the M-value should be minus infinity for ApoAI because it is the knockout gene. Several of the other genes are closely related. The top eight genes here were confirmed by independent assay subsequent to the microarray experiment to be differentially expressed in the knockout versus the control line.
> plot(fit$coef[,2],eb$lods[,2],pch=16,cex=0.1,xlab="Log Fold Change",ylab="Log Odds",main="KO vs Control") > ord <- order(eb$lods[,2],decreasing=TRUE) > top8 <- ord[1:8] > text(fit$coef[top8,2],eb$lods[top8,2],labels=substring(genelist[top8,"NAME"],1,5),cex=0.8,col="blue")
This case study considers a more involved analysis in which the sources of
RNA have a factorial structure. In this example we assume that data is available as an
RGList.
Background. This is a case study examining the development of certain neurons in wild-type and weaver mutant mice from Diaz et al (2002). The weaver mutant affects cerebellar granule neurons, the most numerous cell-type in the central nervous system. Weaver mutant mice are characterized by a weaving gait. Granule cells are generated in the first postnatal week in the external granule layer of the cerebellum. In normal mice, the terminally differentiated granule cells migrate to the internal granule layer but in mutant mice the cells die before doing so, meaning that the mutant mice have strongly reduced numbers of cells in the internal granule layer. The expression level of any gene which is specific to mature granule cells, or is expressed in response to granule cell derived signals, is greatly reduced in the mutant mice.
Tissue dissection and RNA preparation. At each time point (P11 = 11 days postnatal and P21 = 21 days postnatal) cerebella were isolated from two wild-type and two mutant littermates and pooled for RNA isolation. RNA was then divided into aliquots and labelled before hybridizing to the arrays. (This means that different hybridizations are biologically related through using RNA from the same mice, although we will ignore this here. See Yang and Speed (2002) for a detailed discussion of this issue in the context of this experiment.)
Hybridizations. We have just four arrays each comparing two out of the four treatment combinations of time (11 days or 21 days) by genotype (wild-type or mutant). This has the structure of a 2x2 factorial experiment.
> objects() [1] "designIA" "designMt" "gal" "layout" "RG" "Targets" > Targets FileName Name Cy5 Cy3 1 cb.1.spot P11WT.P11MT P11WT P11MT 2 cb.2.spot P11MT.P21MT P11MT P21MT 3 cb.3.spot P21MT.P21WT P21MT P21WT 4 cb.4.spot P21WT.P11WT P21WT P11WT > MA <- normalizeWithinArrays(RG,layout) > boxplot(MA$M~col(MA$M),names=Targets$Name)
First we consider a classical interaction parametrization.
> designIA
TimeWt Mutant11 I/A
P11WT.P11MT 0 -1 0
P11MT.P21MT -1 0 -1
P21MT.P21WT 0 1 1
P21WT.P11WT 1 0 0
TimeWt is late vs early time for the wild-type mice. Mutant11 is mutant vs wild-type at the early time. The third column estimates the interaction between time and genotype.
> fitIA <- lm.series(MA$M,designIA)
> ebIA <- ebayes(fitIA)
> options(digits=3)
> toptable(coef="I/A",n=10,genelist=gal,fit=fitIA,eb=ebIA,adjust="fdr")
ID Name M t P.Value B
7737 RIKEN Z6801 6.49 12.95 0.886 -4.03
780 RIKEN Z636 6.57 12.67 0.886 -4.03
4063 RIKEN Z3559 6.41 12.37 0.886 -4.03
3627 Control L1 6.08 11.89 0.886 -4.03
3084 RIKEN Z2652 4.88 9.38 1.000 -4.04
16230 Control T7/SP6 7- Vrg2 6.00 9.12 1.000 -4.05
12537 RIKEN Z11025 5.03 9.03 1.000 -4.05
2866 RIKEN Z2506 4.19 8.46 1.000 -4.05
11430 Control T7/SP6 5- msx 1 3.31 6.40 1.000 -4.08
15590 RIKEN Z13718 3.17 5.88 1.000 -4.10
With only four arrays there is only one residual df for the linear model, so even large M-values and t-statistics are not significant after adjusting for multiple testing. There are differentially expressed genes here, although it is difficult to confirm it from the four arrays that we are using for this exercise.
Consider another parametrization.
> designMt
Mutant11 Mutant21 TimeMt
P11WT.P11MT -1 0 0
P11MT.P21MT 0 0 -1
P21MT.P21WT 0 1 0
P21WT.P11WT 1 -1 1
Here Mutant21 is mutant vs wild-type at the later time and TimeMt is late vs early time for the mutant mice.
> fitMt <- lm.series(MA$M,designMt) > ebMt <- ebayes(fitMt) > plot(fitMt$coef[,"Mutant11"],fitMt$coef[,"Mutant21"],pch=16,cex=0.1,xlab="Mutant11",ylab="Mutant21") > sel <- abs(ebMt$t[,"Mutant11"])>4 | abs(ebMt$t[,"Mutant21"])>4 > points(fitMt$coef[sel,"Mutant11"],fitMt$coef[sel,"Mutant21"],col="blue")
This scatterplot allows the genes to be visually clustered according to
whether they are differentially expressed in the mutant at the two times.
We will now collate the results of the two fits.
> fit <- fitIA
> fit$coefficients <- cbind(fitMt$coef,fitIA$coef)
> fit$coefficients <- fit$coef[,c(1,2,4,3,6)]
> fit$coef[1:5,]
Mutant11 Mutant21 TimeWt TimeMt I/A
[1,] -0.5396 0.1670 1.3362 2.043 0.7066
[2,] 0.2481 0.8601 -0.9112 -0.299 0.6120
[3,] -1.1368 -0.5642 -0.0119 0.561 0.5726
[4,] -1.0166 -0.5837 0.0837 0.517 0.4329
[5,] 0.0135 0.0614 0.3701 0.418 0.0479
> fit$stdev.unscaled <- cbind(fitMt$std,fitIA$std)
> fit$stdev.unscaled <- fit$std[,c(1,2,4,3,6)]
> fit$std[1:5,]
Mutant11 Mutant21 TimeWt TimeMt I/A
[1,] 0.866 0.866 0.866 0.866 1
[2,] 0.866 0.866 0.866 0.866 1
[3,] 0.866 0.866 0.866 0.866 1
[4,] 0.866 0.866 0.866 0.866 1
[5,] 0.866 0.866 0.866 0.866 1
> eb <- ebayes(fit)
> heatdiagram(abs(eb$t),fit$coef,"Mutant21",names=gal$Name)
This heat diagram shows the expression profiles for all genes judged to be differentially expressed (|t| > 4) with respect to Mutant21. The genes are sorted from left to right in terms of their coefficients for Mutant21, with red meaning up-regulation and green meaning down-regulation. It is especially interesting to see that genes which are up-regulated (red) in the mutant at 21 days are those which have decreasing expression in the wild-type over time, and those which are down-regulated (green) in the mutant are those which increase over time in the wild-type. The mutant is not participating in normal development between 11 and 21 days in respect of these genes.
In this section we consider a case study in which all genes (ESTs and controls) are printed more than once on the array. This means that there is both within-array and between-array replication for each gene. The structure of the experiment is therefore essentially a randomized block experiment for each gene. The approach taken here is to estimate a common correlation for all the genes for between within-array duplicates. The theory behind the approach is explained in Smyth, Michaud and Scott (2003). This approach assumes that all genes are replicated the same number of times on the array and that the spacing between the replicates is entirely regular.
In this example we assume that the data is available as an RG list.
Background. This data is from a study of transcription factors critical to B cell maturation by Lynn Corcoran and Wendy Dietrich at the WEHI. Mice which have a targeted mutation in the Bob (OBF-1) transcription factor display a number of abnormalities in the B lymphocyte compartment of the immune system. Immature B cells that have emigrated from the bone marrow fail to differentiate into full fledged B cells, resulting in a notable deficit of mature B cells.
Arrays. Arrays were printed with expressed sequence tags (ESTs) from the National Institute of Aging 15k mouse clone library, plus a range of positive, negative and calibration controls. The arrays were printed using a 48 tip print head and 26x26 spots in each tip group. Data from 24 of the tip groups are given here. Every gene (ESTs and controls) was printed twice on each array.
Hybridizations. A retrovirus was used to add Bob back to a Bob deficient cell line. Two RNA sources were compared using 2 dye-swap pairs of microarrays. One RNA source was obtained from the Bob deficient cell line after the retrovirus was used to add GFP ("green fluorescent protein", a neutral protein). The other RNA source was obtained after adding both GFP and Bob protein. RNA from Bob+GFP was labelled with Cy5 in arrays 2 and 4, and with Cy3 in arrays 1 and 4.
> objects() [1] "design" "gal" "layout" "RG" > design [1] -1 1 -1 1 > gal[1:40,] Library Name 1 Control cDNA1.500 2 Control cDNA1.500 3 Control Printing.buffer 4 Control Printing.buffer 5 Control Printing.buffer 6 Control Printing.buffer 7 Control Printing.buffer 8 Control Printing.buffer 9 Control cDNA1.500 10 Control cDNA1.500 11 Control Printing.buffer 12 Control Printing.buffer 13 Control Printing.buffer 14 Control Printing.buffer 15 Control Printing.buffer 16 Control Printing.buffer 17 Control cDNA1.500 18 Control cDNA1.500 19 Control Printing.buffer 20 Control Printing.buffer 21 Control Printing.buffer 22 Control Printing.buffer 23 Control Printing.buffer 24 Control Printing.buffer 25 Control cDNA1.500 26 Control cDNA1.500 27 NIA15k H31 28 NIA15k H31 29 NIA15k H32 30 NIA15k H32 31 NIA15k H33 32 NIA15k H33 33 NIA15k H34 34 NIA15k H34 35 NIA15k H35 36 NIA15k H35 37 NIA15k H36 38 NIA15k H36 39 NIA15k H37 40 NIA15k H37
Although there are only four arrays, we have a total of eight spots for each gene, and more for the controls. Naturally the two M-values obtained from duplicate spots on the same array are highly correlated. The problem is how to make use of the duplicate spots in the best way. The approach taken here is to estimate the spatial correlation between the adjacent spots using REML and then to conduct the usual analysis of the arrays using generalized least squares.
First normalize the data using print-tip loess regression.
> MA <- normalizeWithinArrays(RG,layout)
Now estimate the spatial correlation. We estimate a correlation term by REML for each gene, and then take a trimmed mean on the atanh scale to estimate the overall correlation. This command takes a lot of time, perhaps as much as an hour for a series of arrays.
> cor <- dupcor.series(MA$M,design,ndups=2) # This is a very slow computation! > cor$cor [1] 0.571377 > boxplot(cor$cor.genes)
> fit <- gls.series(MA$M,design,ndups=2,correlation=0.571377)
> eb <- ebayes(fit)
> genenames <- uniquegenelist(gal[,"Name"],ndups=2)
> toptable(number=30,genelist=genenames,fit=fit,eb=eb,adjust="fdr")
Name M t P.Value B
1 H34599 0.4035865 13.053838 0.0004860773 7.995550
2 H31324 -0.5196599 -12.302094 0.0004860773 7.499712
3 H33309 0.4203320 12.089742 0.0004860773 7.352862
4 H3440 0.5678168 11.664229 0.0004860773 7.049065
5 H36795 0.4600335 11.608550 0.0004860773 7.008343
6 H3121 0.4408640 11.362917 0.0004860773 6.825927
7 H36999 0.3806754 11.276571 0.0004860773 6.760715
8 H3132 0.3699805 11.270201 0.0004860773 6.755881
9 H32838 1.6404839 11.213454 0.0004860773 6.712681
10 H36207 -0.3930972 -11.139510 0.0004860773 6.656013
11 H37168 0.3909476 10.839880 0.0005405097 6.421932
12 H31831 -0.3738452 -10.706775 0.0005405097 6.315602
13 H32014 0.3630416 10.574797 0.0005405097 6.208714
14 H34471 -0.3532587 -10.496483 0.0005405097 6.144590
15 H37558 0.5319192 10.493157 0.0005405097 6.141856
16 H3126 0.3849980 10.467091 0.0005405097 6.120389
17 H34360 -0.3409371 -10.308779 0.0005852911 5.988745
18 H36794 0.4716704 10.145670 0.0006399135 5.850807
19 H3329 0.4125222 10.009042 0.0006660758 5.733424
20 H35017 0.4337911 9.935639 0.0006660758 5.669656
21 H32367 0.4092668 9.765338 0.0006660758 5.519781
22 H32678 0.4608290 9.763809 0.0006660758 5.518423
23 H31232 -0.3717084 -9.758581 0.0006660758 5.513778
24 H3111 0.3693533 9.745794 0.0006660758 5.502407
25 H34258 0.2991668 9.722656 0.0006660758 5.481790
26 H32159 0.4183633 9.702614 0.0006660758 5.463892
27 H33192 -0.4095032 -9.590227 0.0007130533 5.362809
28 H35961 -0.3624470 -9.508868 0.0007205823 5.288871
29 H36025 0.4265827 9.503974 0.0007205823 5.284403
30 H3416 0.3401763 9.316136 0.0008096722 5.111117
> plot(fit$coef,eb$lods,xlab="Log2 Fold Change",ylab="Log Odds",pch=16,cex=0.1)
The packages marrayClasses, marrayInput, marrayNorm and marrayTools are
designed to read and normalize cDNA data. The marrayNorm package provides some
normalization methods which are not provided by limma. Normalization using marrayNorm will produce a
data object
of class marrayNorm. Suppose that you have an marrayNorm
object called N. The data may be converted into an MAList
suitable for further manipulation in limma using
> MA <- as.MAList(N)
Even without conversion, the marrayNorm object may be used
directly in the lmFit function in limma, for example
fit <- lmFit(N, design)
after which one proceeds exactly as in previous sections.
Note that there are no facilities for importing marrayRaw
objects into limma. This means that, if you have read your data into R using the
marrayInput package, you should use marrayNorm rather than limma for
normalization. After normalization, you are free to use limma for analysis of
differential expression.
Normalization of Affymetrix data using functions in the package affy
will produce a data object of class exprSet or of AffyBatch
which inherits from exprSet. Objects of class exprSet may be used
directly in the lmFit function in limma. Let eset be the
exprSet object. A linear model may be fitted using
fit <- lmFit(eset, design)
See Section 7.2 for more details.
We provide a short background on the topic of single-channel normalization for two color arrays. Throughout this section the ApoAI data set will be used to demonstrate single-channel normalization.
Load the ApoAI data and perform background correction
on the RGList data object:
> load("ApoAI.RData")
> RG.b <-backgroundCorrect(RG,method="minimum")
cDNA (or oligo) microarrays compare the gene expression between two different sources of RNA for thousands of genes simultaneously. In general, the log-ratio of spot intensities for the red and green channels form the primary data used for downstream analysis. Thus traditional normalization methods, which remove systematic variation in microarray data, focus on adjusting the log-ratios within each slide. However sometimes it is desirable to work with single-channel (log-intensity) data rather than the log-ratios and so new techniques for normalizing such single-channel data have been investigated. In the current literature there has been limited attention given to single-channel normalization despite many groups basing their entire analyses on single channel data. Single- channel data display a higher level of systematic variation than that observed in log-ratio data.
For example below are imageplots of the log-intensity
single-channels and the log-ratio for a single array from the ApoAI
data set. (The imageplots below are based on non-normalised
background corrected data). Clearly some of the systematic spatial variation is
cancelled out by forming the log-ratio. This is just a simple
demonstration of how M-values are less noisy than single-channels.
> imageplot(log(RG.b$R[,4],2), layout, low="white", high="red")
> imageplot(log(RG.b$G[,4],2), layout, low="white", high="green")
> imageplot(log(MA.n$M[,4],2), layout, low="white", high="blue")
It should be noted that analysing log-ratios corresponds to doing all analysis on the basis of within-array contrasts while the single-channel approach gives the possibility of recovering information from the between-array variation. This should only be considered after careful single- channel normalization to remove uncontrolled systematic effects at the array level. Yang and Thorne (2003) provides an outline of the motivations for performing single-channel (log-intensity) analysis. We currently perform single-channel normalization using a quantile method based on Bolstad et al.'s quantile normalization of high density oligonucleotide data). In the following we demonstrate within-slide and between-slide single-channel normalization routines. We use the ApoAI data set to illustrate the methods.
We perform the normalization of single-channel data using methods
in the normalizeWithinArrays and
normalizeBetweenArrays functions.
Note that RG.b contains unlogged single-channel
intensities and normalizeWithinArrays expects its input
RGlist to be unlogged. There is an argument
log.transform=F which needs to be implemented if the
RGlist supplied is already logged. The following command
creates an MAList containing non-normalized background
corrected values.
> MA.n <-normalizeWithinArrays(RG.b,layout,method="n")
Next we normalize the M-values via the default within array
normalization of printtiploess (we could have use the
method loess instead, but we find that
printtiploess is often a good choice since it acts as a proxy
for spatial normalization of the Mvalues.
> MA.p <-normalizeWithinArrays(RG.b,layout)
At any stage we can recover the RGList of normalized
single-channels using RG.MA. RG.MA(MA.p)
would give us within-array only normalized single-channels. Next we
perform between array normalization of the single-channels. We use the
function normalizeBetweenArrays which takes and returns
an MAList. normalizeBetweenArrays forms an RG matrix when implementing the quantile
normalization method on the single-channels; and although it returns
an MAList the single-channel normalised values can be
obtained by using the function RG.MA. We show how to
implement the following between array normalization methods
respectively, quantile normalization between all single-channels
only (q); quantile normalization after printtiploess
normalization within arrays (pq); quantile normalization
between the arrays on the Aq values which is then
combined with the within array printtiploess normalization
Mp to give MpAq . Notice that for
MpAq we have mixed and matched different within and between
array normlizations to create a simultaneous within and between
array single-channel normalization method.
> MA.q <- normalizeBetweenArrays(MA.n, method="quantile")
> MA.pq <- normalizeBetweenArrays(MA.p, method="quantile")
> MA.Aq <- normalizeBetweenArrays(MA.n, method="Aquantile")
> MA.MpAq <- new("MAList", list(M=MA.p$M, A=MA.Aq$A))
We find that pq and MpAq work quite well. Next we
show some plots of the single-channel log-intensity densities which
illustrate the results of the different single-channel normalization methods. We use the function plotDensities which will
take either an RGList or an MAList . The
form of the call is: plotDensities(object, log.transform = FALSE, arrays = NULL, singlechannels = NULL,
groups = NULL, col = NULL).
The default usage of plotDensities results in red/green coloring of the densities.
Without any background correction there is a significant difference between the red and green single-channel intensity distributions:
> plotDensities(RG, log.transform=TRUE)
> plotDensities(RG.b, log.transform=TRUE)
> plotDensities(MA.n)
Printtiploess makes the single-channels within arrays
similar:
> plotDensities(MA.p)
All the single-channels have the same distribution.
> plotDensities(MA.q, col="black")
> plotDensities(MA.pq, col="black")
MpAq gives very similar results as pq.
> plotDensities(MA.MpAq)
Thanks to Yee Hwa Yang and Sandrine Dudoit for the first three data sets. The Swirl zebrafish data were provided by Katrin Wuennenburg-Stapleton from the Ngai Lab at UC Berkeley. Thanks to Lynn Corcoran for the Bob Mutant data.