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Analyzing Illumina® Bead Summary Gene Expression Data

This example shows how to analyze Illumina BeadChip gene expression summary data using MATLAB® and Bioinformatics Toolbox™ functions.

Introduction

This example shows a number of ways to import and analyze gene expression data from the Illumina BeadChip microarray platform. The data set in the example is from the study of gene expression profiles of human spermatogenesis by Platts et al., 2007. The expression levels were measured on Illumina Sentrix Human 6 (or WG6) BeadChips.

Each Illumina WG6 BeadChip contains six identical arrays with 47,293 unique probes. Illumina's BeadStudio™ software outputs the summarized expression levels for each bead type on the arrays on the BeadChip. The output from the BeadStudio software can be either a text file or an Excel® file.

Both raw and normalized Illumina expression data are available on the Gene Expression Omnibus (GEO) database Web site: http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE6967.

The data from most microarray gene expression experiments usually consists of four components: experiment data values, sample information, feature annotations, and information about the experiment. You will work with the data from the experiment, construct each of the four components, assemble them into an ExpressionSet object, and find the differentially expressed genes. For more examples about the ExpressionSet class, see Working with Objects for Microarray Experiment Data.

Importing Experiment Data from the GEO Database

Samples were hybridized on three Illumina Sentrix Human 6 (or WG6) BeadChips in the experiment. Use the getgeodata function to retrieve the GEO Series data, GSE6967, and read it into the MATLAB Workspace as a structure, TNGEOData. You can also download the raw Illumina summary data files of the GSE6967 record via FTP from the GEO database.

TNGEOData = getgeodata('GSE6967')
TNGEOData = 

    Header: [1x1 struct]
      Data: [47293x13 bioma.data.DataMatrix]

The TNGEOData structure contains Header and Data fields. The Header field has two fields, Series and Samples, containing a description of the experiment and samples respectively. The Data field contains a DataMatrix of normalized summary expression levels from the experiment.

Determine the number of samples in the experiment.

nSamples = numel(TNGEOData.Header.Samples.geo_accession)
nSamples =

    13

Inspect the sample titles from the Header.Samples field.

TNGEOData.Header.Samples.title'
ans = 

    'Teratozoospermic individual: Sample T2'
    'Teratozoospermic individual: Sample T1'
    'Teratozoospermic individual: Sample T6'
    'Teratozoospermic individual: Sample T4'
    'Teratozoospermic individual: Sample T8'
    'Normospermic individual: Sample N11'
    'Teratozoospermic individual: Sample T3'
    'Teratozoospermic individual: Sample T7'
    'Teratozoospermic individual: Sample T5'
    'Normospermic individual: Sample N6'
    'Normospermic individual: Sample N12'
    'Normospermic individual: Sample N5'
    'Normospermic individual: Sample N1'

For simplicity, extract the sample labels from the sample titles.

sampleLabels = cellfun(@(x) char(regexp(x, '\w\d+', 'match')),...
                TNGEOData.Header.Samples.title, 'UniformOutput',false)
sampleLabels = 

  Columns 1 through 9

    'T2'    'T1'    'T6'    'T4'    'T8'    'N11'    'T3'    'T7'    'T5'

  Columns 10 through 13

    'N6'    'N12'    'N5'    'N1'

Importing Expression Data from Illumina BeadStudio Summary Files

Raw, non-normalized summary data was deposited as supplementary data for the GSE6967 record in the GEO database. Download the supplementary file GSE6967_RAW.tar. Unzip the file to access the 13 text files produced by the BeadStudio software, which contain the raw, non-normalized bead summary values.

There is one file for each array (or each sample). Inside each file is a line of column headers followed by a data matrix with 47,293 rows. Each row corresponds to a different target probe (gene) in the experiment. The matrix contains the summarized expression values (Avg_Signal), standard error of the bead replicates (BEADSTDEV), number of beads used (Avg_NBEADS) and a detection score, which estimates the confidence limit of detection of a target probe from the samples hybridized on the BeadChip. The column header information also includes the Sentrix chip IDs and sample IDs placed on each array.

The raw data text files are named with their GSM accession numbers. For this example, construct the file names of the text data files using the path where the text files are located.

rawDataFiles = cell(1,nSamples);
for i = 1:nSamples
    rawDataFiles {i} = [TNGEOData.Header.Samples.geo_accession{i} '.txt'];
end

Modify this line to contain the path and directory to which you extracted the data files.

rawDataPath = fullfile('C:', 'Examples', 'illuminagedemo', 'GSE6967')
rawDataPath =

C:\Examples\illuminagedemo\GSE6967

Use the ilmnbsread function to read one of the summary files and inspect the returned structure.

rawData =ilmnbsread(fullfile(rawDataPath, rawDataFiles{1}))
rawData = 

             Header: [1x1 struct]
           TargetID: {47293x1 cell}
        ColumnNames: {1x8 cell}
               Data: [47293x8 double]
    TextColumnNames: {}
           TextData: {}

Inspect the column names in the rawData structure.

rawData.ColumnNames'
ans = 

    'MIN_Signal-1412091085_A'
    'AVG_Signal-1412091085_A'
    'MAX_Signal-1412091085_A'
    'NARRAYS-1412091085_A'
    'ARRAY_STDEV-1412091085_A'
    'BEAD_STDEV-1412091085_A'
    'Avg_NBEADS-1412091085_A'
    'Detection-1412091085_A'

Determine the number of target probes.

nTargets = size(rawData.Data, 1)
nTargets =

       47293

Read the non-normalized expression values (Avg_Signal), the detection confidence limits and the Sentrix chip IDs from the 13 summary data files. The gene expression values are identified with Illumina probe target IDs.

rawMatrix = bioma.data.DataMatrix(zeros(nTargets, nSamples),...
                                  rawData.TargetID, sampleLabels);
detectionConf = bioma.data.DataMatrix(zeros(nTargets, nSamples),...
                                      rawData.TargetID, sampleLabels);
chipIDs = categorical([]);

You can specify the columns to read from the data file.

for i = 1:nSamples
    rawData =ilmnbsread(fullfile(rawDataPath, rawDataFiles{i}),...
                                'COLUMNS', {'AVG_Signal', 'Detection'});
    chipIDs(i) = regexp(rawData.ColumnNames(1), '\d*', 'match', 'once');
    rawMatrix(:, i) = rawData.Data(:, 1);
    detectionConf(:,i) = rawData.Data(:,2);
end

There are three Sentrix BeadChips used in the experiment. Inspect the Illumina Sentrix BeadChip IDs in chipIDs and determine the number of samples hybridized on each chip.

summary(chipIDs)
     1412091085      1412091086      1477791158 
              6               4               3 

sampleLabels(chipIDs=='1412091085')
sampleLabels(chipIDs=='1412091086')
sampleLabels(chipIDs=='1477791158')
ans = 

    'T2'    'T1'    'T6'    'T4'    'T8'    'N11'


ans = 

    'T3'    'T7'    'T5'    'N6'


ans = 

    'N12'    'N5'    'N1'

Six samples (T2, T1, T6, T4, T8 and N11) were hybridized to six arrays on the first chip, four samples (T3, T7, T5 and N6) on the second chip, and three samples (N12, N5, and N1) on the third chip.

Normalizing the Expression Data

Use a boxplot to view the raw expression levels of each sample in the experiment.

logRawExprs = log2(rawMatrix);
maboxplot(logRawExprs,'ORIENTATION', 'horizontal')
ylabel('Sample Labels')
xlabel('log2(Expression Value)')
title('Before Normalization')

The difference in intensities between samples on the same chip and samples on different chips does not seem too large. The first BeadChip, containing samples T2, T1, T6, T4, T8 and N11, seems to be slightly more variable than others.

Using MA and XY plots to do a pairwise comparison of the arrays on a BeadChip can be informative. On an MA plot, the average of the expression levels of two arrays (A) are plotted on the x axis, and the difference in the measurement (M) on the y axis. An XY plot is a scatter plot of one array against another. In this example, you will use the helper function maxyplot to plot MAXY plots for a pairwise comparison of the three arrays on the first chip hybridized with teratozoospermic samples (T2, T1 and T6).

Note: You can also use the mairplot function to create the MA or IR (Intensity/Ratio) plots for comparison of specific arrays.

inspectIdx = 1:3;
maxyplot(rawMatrix, inspectIdx)
suptitle('Before Normalization')

In an MAXY plot, the MA plots for all pairwise comparisons are in the upper-right corner. In the lower-left corner are the XY plots of the comparisons. The MAXY plot shows the two arrays, T1 and T2, to be quite similar, while different from the other array, T6.

The expression boxplots and MAXY plots reveal that, there are differences in expression levels within chips and between chips; hence, the data requires normalization. Use the quantilenorm function to apply quantile normalization to the raw data.

Note: You can also try invariant set normalization using the mainvarsetnorm function.

normExprs = rawMatrix;
normExprs(:, :) = quantilenorm(rawMatrix.(':')(':'));
log2NormExprs = log2(normExprs);

Display and inspect the normalized expression levels in a boxplot.

figure;
maboxplot(log2NormExprs,'ORIENTATION', 'horizontal')
ylabel('Sample Labels')
xlabel('log2(Expression Value)')
title('After Quantile Normalization')

Display and inspect the MAXY plot of the three arrays (T2, T1 and T6) on the first chip after the normalization.

maxyplot(normExprs, inspectIdx)
suptitle('After Quantile Normalization')

Many of the genes in this study are not expressed, or have only small variability across the samples. Remove these genes using non-specific filtering.

Use the genelowvalfilter function to filter out genes with very low absolute expression values.

[mask, log2NormExprs] = genelowvalfilter(log2NormExprs);
detectionConf = detectionConf(mask, :);

Use the genevarfilter function to filter out genes with a small variance across samples.

[mask, log2NormExprs] = genevarfilter(log2NormExprs);
detectionConf = detectionConf(mask, :);

Importing Feature Metadata from a BeadChip Annotation File

Microarray manufactures usually provide annotations of a collection of features for each type of chip. The chip annotation files contain metadata such as the gene name, symbol, NCBI accession number, chromosome location and pathway information. Before assembling an ExpressionSet object for the experiment. Obtain the annotations about the features or probes on the BeadChip. You can download the Human_WG-6.csv annotation file for Sentrix Human 6 (or WG6) BeadChips from the Support page at the Illumina web site and save the file locally. Read the annotation file into MATLAB as a dataset array. Modify this line to contain the path and directory to which you downloaded the annotation file.

annotPath = fullfile('C:', 'Examples', 'illuminagedemo', 'Annotation');
WG6Annot = dataset('xlsfile', fullfile(annotPath, 'Human_WG-6.csv'));

Inspect the properties of this dataset array.

get(WG6Annot)
       Description: ''
    VarDescription: {}
             Units: {}
          DimNames: {'Observations'  'Variables'}
          UserData: []
          ObsNames: {}
          VarNames: {1x13 cell}

Get the names of variables describing the features on the Sentrix Human 6 BeadChips.

fDataVariables = get(WG6Annot, 'VarNames')
fDataVariables = 

  Columns 1 through 5

    'Search_key'    'Target'    'ProbeId'    'Gid'    'Transcript'

  Columns 6 through 10

    'Accession'    'Symbol'    'Type'    'Start'    'Probe_Sequence'

  Columns 11 through 13

    'Definition'    'Ontology'    'Synonym'

Check the number of probe target IDs in the annotation file.

numel(WG6Annot.Target)
ans =

       47296

Because the expression data in this example is only a small set of the full expression values, you will work with only the features in the DataMatrix object log2NormExprs. Find the matching features in log2NormExprs and WG6Annot.Target.

[commTargets, fI, WGI] =intersect(rownames(log2NormExprs), WG6Annot.Target);

Building an ExpressionSet Object - Experiment Data Values

You can store the preprocessed expression values and detection limits of the annotated probe targets as an ExptData object.

fNames = rownames(log2NormExprs);
TNExptData = bioma.data.ExptData({log2NormExprs(fI, :), 'ExprsValues'},...
                                 {detectionConf(fI, :), 'DetectionConfidences'})
TNExptData = 

Experiment Data:
  42313 features,  13 samples
  2 elements
  Element names: ExprsValues, DetectionConfidences

Building an ExpressionSet Object - Sample Information

The sample data in the Header.Samples field of the TNGEOData structure can be overwhelming and difficult to navigate through. From the data in Header.Samples field, you can gather the essential information about the samples, like the sample titles, GEO sample accession numbers, etc., in the experiment, and store the sample data as a MetaData object.

Retrieve the descriptions about sample characteristics.

sampleChars = cellfun(@(x) char(regexp(x, '\w*tile', 'match')),...
               TNGEOData.Header.Samples.characteristics_ch1, 'UniformOutput',false)
sampleChars = 

  Columns 1 through 5

    'Infertile'    'Infertile'    'Infertile'    'Infertile'    'Infertile'

  Columns 6 through 10

    'Fertile'    'Infertile'    'Infertile'    'Infertile'    'Fertile'

  Columns 11 through 13

    'Fertile'    'Fertile'    'Fertile'

Create a dataset array to store the sample data you just extracted.

sampleDS = dataset({TNGEOData.Header.Samples.geo_accession', 'GSM'},...
                   {strtok(TNGEOData.Header.Samples.title)', 'Type'},...
                   {sampleChars', 'Characteristics'}, 'obsnames', sampleLabels')
sampleDS = 

           GSM                Type                      Characteristics
    T2     'GSM160620'        'Teratozoospermic'        'Infertile'    
    T1     'GSM160621'        'Teratozoospermic'        'Infertile'    
    T6     'GSM160622'        'Teratozoospermic'        'Infertile'    
    T4     'GSM160623'        'Teratozoospermic'        'Infertile'    
    T8     'GSM160624'        'Teratozoospermic'        'Infertile'    
    N11    'GSM160625'        'Normospermic'            'Fertile'      
    T3     'GSM160626'        'Teratozoospermic'        'Infertile'    
    T7     'GSM160627'        'Teratozoospermic'        'Infertile'    
    T5     'GSM160628'        'Teratozoospermic'        'Infertile'    
    N6     'GSM160629'        'Normospermic'            'Fertile'      
    N12    'GSM160630'        'Normospermic'            'Fertile'      
    N5     'GSM160631'        'Normospermic'            'Fertile'      
    N1     'GSM160632'        'Normospermic'            'Fertile'      

Store the sample metadata as an object of the MetaData class, including a short description for each variable.

TNSData = bioma.data.MetaData(sampleDS,...
    {'Sample GEO accession number',...
    'The spermic type of individual whoes sample was collected ',...
    'Sample individual fertility characteristics'})
TNSData = 

Sample Names:
    T2, T1, ...,N1 (13 total)
Variable Names and Meta Information:
                       VariableDescription                                             
    GSM                'Sample GEO accession number'                                   
    Type               'The spermic type of individual whoes sample was collected '    
    Characteristics    'Sample individual fertility characteristics'                   

Building an ExpressionSet Object - Feature Annotations

The collection of feature metadata for Sentrix Human 6 BeadChips is large and diverse. Select information about features that are unique to the experiment and save the information as a MetaData object. Extract annotations of interests, for example, Accession and Symbol.

fIdx = ismember(fDataVariables, {'Accession', 'Symbol'});
featureAnnot = WG6Annot(WGI, fDataVariables(fIdx));
featureAnnot = set(featureAnnot, 'ObsNames', WG6Annot.Target(WGI));

Create a MetaData object for the feature annotation information with brief descriptions about the two variables of the metadata.

WG6FData = bioma.data.MetaData(featureAnnot, ...
            {'Accession number of probe target', 'Gene Symbol of probe target'})
WG6FData = 

Sample Names:
    GI_10047089-S, GI_10047091-S, ...,hmm9988-S (42313 total)
Variable Names and Meta Information:
                 VariableDescription                   
    Accession    'Accession number of probe target'    
    Symbol       'Gene Symbol of probe target'         

Building an ExpressionSet Object - Experiment Information

Most of the experiment descriptions in the Header.Series field of the TNGEOData structure can be reorganized and stored as a MIAME object, which you will use to assemble the ExpressionSet object for the experiment.

TNExptInfo = bioma.data.MIAME(TNGEOData)
TNExptInfo = 

Experiment Description:
  Author name: Adrian,E,Platts
David,J,Dix
Hector,E,Chemes
Kary,E,Thompson
Robert,,Goodrich
John,C,Rockett
Vanesa,Y,Rawe
Silvina,,Quintana
Michael,P,Diamond
Lillian,F,Strader
Stephen,A,Krawetz
  Laboratory: Wayne State University
  Contact information: Stephen,A,Krawetz
  URL: http://compbio.med.wayne.edu
  PubMedIDs: 17327269
  Abstract: A 82 word abstract is available. Use the Abstract property.
  Experiment Design: A 61 word summary is available. Use the ExptDesign property.
  Other notes: 
    'ftp://ftp.ncbi.nlm.nih.gov/pub/geo/DATA/supplementary/series/GSE6967/G...'

Building an ExpressionSet Object - Assembling the ExpressionSet Object

Now that you've created all the components, you can create an object of the ExpressionSet class to store the expression values, sample information, chip feature annotations and description information about this experiment.

TNExprSet = bioma.ExpressionSet(TNExptData, 'sData', TNSData,...
                                            'fData', WG6FData,...
                                            'eInfo', TNExptInfo)
TNExprSet = 

ExpressionSet
Experiment Data: 42313 features, 13 samples
  Element names: Expressions, DetectionConfidences
Sample Data:
    Sample names:     T2, T1, ...,N1 (13 total)
    Sample variable names and meta information: 
        GSM: Sample GEO accession number
        Type: The spermic type of individual whoes sample was collected 
        Characteristics: Sample individual fertility characteristics
Feature Data:
    Feature names:     GI_10047089-S, GI_10047091-S, ...,hmm9988-S (42313 total)
    Feature variable names and meta information: 
        Accession: Accession number of probe target
        Symbol: Gene Symbol of probe target
Experiment Information: use 'exptInfo(obj)'

Note: The ExprsValues element in the ExptData object, TNExptData, is renamed to Expressions in TNGeneExprSet.

You can save an object of ExpressionSet class as a MAT file for further data analysis.

save TNGeneExprSet TNExprSet
clear all

Profiling Gene Expression - Grouping Samples

Load the experiment data saved from the previous section. You will find differentially expressed genes between the teratozoospermia and normal samples.

load TNGeneExprSet

Group samples into two variables: Tz, consisting of eight teratozoospermia samples, and Ns, consisting of five normospermic reproductive samples. From the expression data of all 13 samples, extract the data of the two different groups.

TNSamples = sampleNames(TNExprSet);
Tz = strncmp(TNSamples, 'T', 1);
Ns = strncmp(TNSamples, 'N', 1);
nTz = sum(Tz)
nNs = sum(Ns)
nTz =

     8


nNs =

     5

Profiling Gene Expression - Permutation T-tests

To identify the differential changes in the levels of transcripts in normospermic Ns and teratozoospermic Tz samples, compare the gene expression values between the two groups of data: Tz and Ns.

TNExprs = expressions(TNExprSet);
TzData = TNExprs(:,Tz);
NsData = TNExprs(:,Ns);
meanTzData = mean(TzData,2);
meanNsData = mean(NsData,2);
groupLabels = [TNSamples(Tz), TNSamples(Ns)];

Perform a permutation t-test using the mattest function to permute the columns of the gene expression data matrix of TzData and NsData. Note: Depending on the sample size, it may not be feasible to consider all possible permutations. Usually, a random subset of permutations are considered in the case of a large sample size.

Use the nchoosek function in Statistics Toolbox™ to determine the number of all possible permutations of the samples in this example.

perms = nchoosek(1:nTz+nNs, nTz);
nPerms = size(perms,1)
nPerms =

        1287

Use the PERMUTE option of the mattest function to compute the p-values of the 1,287 permutations.

pValues = mattest(TzData, NsData, 'Permute', nPerms);

You can also compute the differential score from the p-values using this anonymous function [1].

diffscore = @(p, avgTest, avgRef) -10*sign(avgTest - avgRef).*log10(p);

The differential score of 13 corresponds to a p-value of 0.05, the differential score of 20 corresponds to a p-value of 0.01, and the differential score of 30 corresponds to a p-value of 0.001. A positive differential score represents up regulation, while a negative score represents down regulation.

diffScores = diffscore(pValues, meanTzData, meanNsData);

Determine the number of genes considered to have a differential score greater than 20. Note: You may get a different number of genes due to the permutation test outcome.

sum(diffScores > 20)
ans =

        3743

sum(diffScores < -20)
ans =

        3035

Profiling Gene Expression - Estimating FDR

In multiple hypothesis testing, which simultaneously tests the null hypothesis of thousands of genes from microarray expression data, each test has a specific false positive rate, or a false discovery rate (FDR) (Storey et al., 2003). Estimate the FDR and q-values for each test using the mafdr function.

figure;
[pFDR, qValues] = mafdr(pValues, 'showplot', true);
diffScoresFDRQ = diffscore(qValues, meanTzData, meanNsData);

Determine the number of genes with an absolute differential score greater than 20. Note: You may get a different number of genes due to the permutation test and the bootstrap outcomes.

sum(abs(diffScoresFDRQ)>=20)
ans =

        3135

Profiling Gene Expression - Differential Gene Expression

Plot the -log10 of p-values against fold changes in a volcano plot.

diffStruct = mavolcanoplot(TzData, NsData, qValues,...
                                   'pcutoff', 0.01, 'foldchange', 5);

Note: From the volcano plot UI, you can interactively change the p-value cutoff and fold-change limit, and export differentially expressed genes.

Determine the number of differentially expressed genes.

nDiffGenes = numel(diffStruct.GeneLabels)
nDiffGenes =

   451

Get the list of up-regulated genes for the Tz samples compared to the Ns samples.

up_genes = diffStruct.GeneLabels(diffStruct.FoldChanges > 0);
nUpGenes = length(up_genes)
nUpGenes =

   223

Get the list of down-regulated genes for the Tz samples compared to the Ns samples.

down_genes = diffStruct.GeneLabels(diffStruct.FoldChanges < 0);
nDownGenes = length(down_genes)
nDownGenes =

   228

Extract a list of differentially expressed genes.

diff_geneidx = zeros(nDiffGenes, 1);
for i = 1:nDiffGenes
    diff_geneidx(i) = find(strncmpi(TNExprSet.featureNames, ...
                            diffStruct.GeneLabels{i}, length(diffStruct.GeneLabels{i})), 1);
end

You can get the subset of experiment data containing only the differentially expressed genes.

TNDiffExprSet = TNExprSet(diff_geneidx, groupLabels);

PCA and Clustering Analysis of Significant Gene Profiles

Principal component analysis (PCA) on differentially expressed genes shows linear separability of the Tz samples from the Ns samples.

PCAScore = pca(TNDiffExprSet.expressions);

Display the coefficients of the first and sixth principal components.

figure;
plot(PCAScore(:,1), PCAScore(:,6), 's', 'MarkerSize',10, 'MarkerFaceColor','g');
hold on
text(PCAScore(:,1)+0.02, PCAScore(:,6), TNDiffExprSet.sampleNames)
plot([0,0], [-0.5 0.5], '--r')
ax = gca;
ax.XTick = [];
ax.YTick = [];
ax.YTickLabel = [];
title('PCA Mapping')
xlabel('Principal Component 1')
ylabel('Principal Component 6')

You can also use the interactive tool created by the mapcaplot function in the Bioinformatics Toolbox to perform principal component analysis.

mapcaplot((TNDiffExprSet.expressions)')

Perform unsupervised hierarchical clustering of the significant gene profiles from the Tz and Ns groups using correlation as the distance metric to cluster the samples.

sampleDist = pdist(TNDiffExprSet.expressions','correlation');
sampleLink = linkage(sampleDist);
figure;
dendrogram(sampleLink, 'labels', TNDiffExprSet.sampleNames,'ColorThreshold',0.5)
ax = gca;
ax.YTick = [];
ax.Box = 'on';
title('Hierarchical Sample Clustering')

Use the clustergram function to create the hierarchical clustering of differentially expressed genes, and apply the colormap redbluecmap to the clustergram.

cmap = redbluecmap(9);
cg = clustergram(TNDiffExprSet.expressions,'Colormap',cmap,'Standardize',2);
addTitle(cg,'Hierarchical Gene Clustering')

You can also add column color markers to distinguish the two groups.

colAnnot.Labels = TNDiffExprSet.sampleNames;
colAnnot.Colors = {'g','g','g','g','g','g','g','g','r','r','r','r', 'r'};
cg.ColumnLabelsColor = colAnnot;
cg.LabelsWithMarkers = true;

Clustering of the most differentially abundant transcripts clearly partitions teratozoonspermic (Tz) and normospermic (Ns) spermatozoal RNAs.

References

[1] Platts, A.E., et al., "Success and failure in human spermatogenesis as revealed by teratozoospermic RNAs", Human Molecular Genetics, 16(7):763-73, 2007.

[2] Storey, J.D. and Tibshirani, R., "Statistical significance for genomewide studies", PNAS, 100(16):9440-5, 2003.

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