Downloading the read counts

Readers wishing to reproduce the analysis presented in this article can either download the matrix of read counts from GEO or recreate the read count matrix from the raw sequence counts. We will present first the analysis using the downloaded matrix of counts. At the end of this article we will present the R commands needed to recreate this matrix.

The following commands download the genewise read counts for the GEO series GSE60450. The zipped tab-delimited text file GSE60450_Lactation-GenewiseCounts.txt.gz will be downloaded to the working R directory:

> FileURL <- paste(
+   "http://www.ncbi.nlm.nih.gov/geo/download/?acc=GSE60450",
+   "format=file",
+   "file=GSE60450_Lactation-GenewiseCounts.txt.gz",
+   sep="&")
> download.file(FileURL, "GSE60450_Lactation-GenewiseCounts.txt.gz")

The counts can then be read into a data.frame in R:

> GenewiseCounts <- read.delim("GSE60450_Lactation-GenewiseCounts.txt.gz",
+                              row.names="EntrezGeneID")
> colnames(GenewiseCounts) <- substring(colnames(GenewiseCounts),1,7)
> dim(GenewiseCounts)

[1] 27179    13

> head(GenewiseCounts)

          Length MCL1.DG MCL1.DH MCL1.DI MCL1.DJ MCL1.DK MCL1.DL MCL1.LA
497097      3634     438     300      65     237     354     287       0
100503874   3259       1       0       1       1       0       4       0
100038431   1634       0       0       0       0       0       0       0
19888       9747       1       1       0       0       0       0      10
20671       3130     106     182      82     105      43      82      16
27395       4203     309     234     337     300     290     270     560
          MCL1.LB MCL1.LC MCL1.LD MCL1.LE MCL1.LF
497097          0       0       0       0       0
100503874       0       0       0       0       0
100038431       0       0       0       0       0
19888           3      10       2       0       0
20671          25      18       8       3      10
27395         464     489     328     307     342

The row names of GenewiseCounts are the Entrez Gene Identifiers. The first column contains the length of each gene, being the total number of bases in exons and UTRs for that gene. The remaining 12 columns contain read counts and correspond to rows of targets.

The edgeR package stores data in a simple list-based data object called a DGEList. This object is easy to use as it can be manipulated like an ordinary list in R, and it can also be subsetted like a matrix. The main components of a DGEList object are a matrix of read counts, sample information in the data.frame format and optional gene annotation. We enter the counts into a DGEList object using the function DGEList in edgeR:

> library(edgeR)
> y <- DGEList(GenewiseCounts[,-1], group=group,
+              genes=GenewiseCounts[,1,drop=FALSE])
> options(digits=3)
> y$samples

              group lib.size norm.factors
MCL1.DG    B.virgin 23227641            1
MCL1.DH    B.virgin 21777891            1
MCL1.DI  B.pregnant 24100765            1
MCL1.DJ  B.pregnant 22665371            1
MCL1.DK B.lactating 21529331            1
MCL1.DL B.lactating 20015386            1
MCL1.LA    L.virgin 20392113            1
MCL1.LB    L.virgin 21708152            1
MCL1.LC  L.pregnant 22241607            1
MCL1.LD  L.pregnant 21988240            1
MCL1.LE L.lactating 24723827            1
MCL1.LF L.lactating 24657293            1

Adding gene annotation

The Entrez Gene Ids link to gene information in the NCBI database. The org.Mm.eg.db package can be used to complement the gene annotation information. Here, a column of gene symbols is added to y$genes:

> library(org.Mm.eg.db)
> y$genes$Symbol <- mapIds(org.Mm.eg.db, rownames(y),
+                          keytype="ENTREZID", column="SYMBOL")
> head(y$genes)

          Length  Symbol
497097      3634    Xkr4
100503874   3259 Gm19938
100038431   1634 Gm10568
19888       9747     Rp1
20671       3130   Sox17
27395       4203  Mrpl15

Entrez Ids that no longer have official gene symbols are dropped from the analysis. The whole DGEList object, including annotation as well as counts, can be subsetted by rows as if it was a matrix:

> y <- y[!is.na(y$genes$Symbol), ]
> dim(y)

[1] 26143    12

Design matrix

Linear modeling and differential expression analysis in edgeR requires a design matrix to be specified. The design matrix records which treatment conditions were applied to each samples, and it also defines how the experimental effects are parametrized in the linear models. The experimental design for this study can be viewed as a one-way layout and the design matrix can be constructed in a simple and intuitive way by:

> design <- model.matrix(~0+group)
> colnames(design) <- levels(group)
> design

   B.lactating B.pregnant B.virgin L.lactating L.pregnant L.virgin
1            0          0        1           0          0        0
2            0          0        1           0          0        0
3            0          1        0           0          0        0
4            0          1        0           0          0        0
5            1          0        0           0          0        0
6            1          0        0           0          0        0
7            0          0        0           0          0        1
8            0          0        0           0          0        1
9            0          0        0           0          1        0
10           0          0        0           0          1        0
11           0          0        0           1          0        0
12           0          0        0           1          0        0
attr(,"assign")
[1] 1 1 1 1 1 1
attr(,"contrasts")
attr(,"contrasts")$group
[1] "contr.treatment"

This design matrix simply links each group to the samples that belong to it. Each row of the design matrix corresponds to a sample whereas each column represents a coefficient corresponding to one of the six groups.

Filtering to remove low counts

Genes that have very low counts across all the libraries should be removed prior to downstream analysis. This is justified on both biological and statistical grounds. From biological point of view, a gene must be expressed at some minimal level before it is likely to be translated into a protein or to be considered biologically important. From a statistical point of view, genes with consistently low counts are very unlikely be assessed as significantly DE because low counts do not provide enough statistical evidence for a reliable judgement to be made. Such genes can therefore be removed from the analysis without any loss of information.

As a rule of thumb, we require that a gene have a count of at least 10 or so in at least some libraries before it is considered to be expressed in the study. In practice, the filtering is actually based on count-per-million (CPM) values so as to avoid favoring genes that are expressed in larger libraries over those expressed in smaller libraries. In edgeR, the filtering can be accomplished using a function that takes into account the library sizes and the experimental design:

> keep <- filterByExpr(y, design)
> table(keep)

keep
FALSE  TRUE 
10407 15736 

The DGEList object is then subsetted to retain only the non-filtered genes:

> y <- y[keep, , keep.lib.sizes=FALSE]

The option keep.lib.sizes=FALSE causes the library sizes to be recomputed after the filtering. This is generally recommended, although the effect on the downstream analysis is usually small.

The filterByExpr function attempts to keep the maximum number of interesting genes in the analysis, but other sensible filtering criteria are also possible. For example keep <- rowSums(y$counts) > 50 is a very simple criterion that would keep genes with a total read count of more than 50. This would give similar downstream results for this dataset to the filtering actually used.

Another sensible filter rule would be to compute the average-log-CPM for each gene, and to choose a cutoff value heuristically:

> AveLogCPM <- aveLogCPM(y)
> hist(AveLogCPM)

Figure 1: Histogram of average log2 CPM

Again this might give similar downstream results for this data to the filtering actually used.

Whatever the filtering rule, it should be independent of the information in the targets file. It should not make any reference to which RNA libraries belong to which group, because doing so would bias the subsequent differential expression analysis.

Normalization for composition bias

Normalization by trimmed mean of M values (TMM) (Robinson and Oshlack 2010) is performed by using the calcNormFactors function, which returns the DGEList argument with only the norm.factors changed. It calculates a set of normalization factors, one for each sample, to eliminate composition biases between libraries. The product of these factors and the library sizes defines the effective library size, which replaces the original library size in all downstream analyses.

> y <- calcNormFactors(y)
> y$samples

              group lib.size norm.factors
MCL1.DG    B.virgin 23112854        1.237
MCL1.DH    B.virgin 21659854        1.213
MCL1.DI  B.pregnant 23951204        1.126
MCL1.DJ  B.pregnant 22521274        1.070
MCL1.DK B.lactating 21402893        1.037
MCL1.DL B.lactating 19901726        1.088
MCL1.LA    L.virgin 20246050        1.370
MCL1.LB    L.virgin 21541575        1.367
MCL1.LC  L.pregnant 22098630        1.005
MCL1.LD  L.pregnant 21859483        0.923
MCL1.LE L.lactating 24647412        0.528
MCL1.LF L.lactating 24589787        0.534

The normalization factors of all the libraries multiply to unity. A normalization factor below one indicates that a small number of high count genes are monopolizing the sequencing, causing the counts for other genes to be lower than would be usual given the library size. As a result, the effective library size will be scaled down for that sample. Here we see that the luminal-lactating samples have low normalization factors. This is a sign that these samples contain a number of very highly upregulated genes.

Note. In general, we find TMM normalization to be satisfactory for almost all well-designed mRNA gene expression experiments. Single-cell RNA-seq is an exception, for which specialized normalization methods are needed (Lun, Bach, and Marioni 2016). Another, less common, type of study requiring special treatment is that with global differential expression, with more than half of the genome differentially expressed between experimental conditions in the same direction (Wu et al. 2013). Global differential expression should generally be avoided in well designed experiments. When it can’t be avoided, then some normalization reference such as spike-ins needs to be built into the experiment for reliable normalization to be done (Risso et al. 2014).

Exploring differences between libraries

The RNA samples can be clustered in two dimensions using multi-dimensional scaling (MDS) plots. This is both an analysis step and a quality control step to explore the overall differences between the expression profiles of the different samples. Here we decorate the MDS plot to indicate the cell groups:

> pch <- c(0,1,2,15,16,17)
> colors <- rep(c("darkgreen", "red", "blue"), 2)
> plotMDS(y, col=colors[group], pch=pch[group])
> legend("topleft", legend=levels(group), pch=pch, col=colors, ncol=2)

Figure 2: MDS plot showing distances between expression profiles
This provides a type of unsupervised clustering of the samples. In this case, the first dimension separates samples by cell type while the second dimension corresponds to mouse status.

In the MDS plot, the distance between each pair of samples can be interpreted as the leading log-fold change between the samples for the genes that best distinguish that pair of samples. By default, leading fold-change is defined as the root-mean-square of the largest 500 log2-fold changes between that pair of samples. The figure above shows that replicate samples from the same group cluster together while samples from different groups are well separated. In other words, differences between groups are much larger than those within groups, meaning that there are likely to be statistically significant differences between the groups. The distance between basal cells on the left and luminal cells on the right is about six units on the x-axis, corresponding to a leading fold change of about 64-fold between the two cell types. The differences between the virgin, pregnant and lactating expression profiles appear to be magnified in luminal cells compared to basal.

The expression profiles of individual samples can be explored more closely with mean-difference (MD) plots. An MD plot visualizes the library size-adjusted log-fold change between two libraries (the difference) against the average log-expression across those libraries (the mean). The following command produces an MD plot that compares sample 1 to an artificial reference library constructed from the average of all the other samples:

> plotMD(y, column=1)
> abline(h=0, col="red", lty=2, lwd=2)

Figure 3: Mean-difference plot of log2-expression in sample 1 versus the average log2-expression across all other samples
Each point represents a gene, and the red line indicates a log-ratio of zero. The majority of points cluster around the red line.

The bulk of the genes are centered around the line of zero log-fold change. The diagonal lines in the lower left of the plot correspond to genes with counts of 0, 1, 2 and so on in the first sample.

It is good practice to make MD plots for all the samples as a quality check. We now look at one of the luminal-lactating samples that was observed have a low normalization factor:

> plotMD(y, column=11)
> abline(h=0, col="red", lty=2, lwd=2)

Figure 4: Mean-difference plot of log2-expression in sample 11 versus the average log2-expression across all other samples
The plot shows a number of genes that are both highly expressed and highly up-regulated.

For this sample, the log-ratios show noticeable positive skew, with a number of very highly upregulated genes. In particular, there are a number of points in the upper right of the plot, corresponding to genes that are both highly expressed and highly up-regulated in this sample compared to others. These genes explain why the normalization factor for this sample is well below one. By contrast, the log-ratios for sample 1 were somewhat negatively skewed, corresponding to a normalization factor above one.

Dispersion estimation

edgeR uses the negative binomial (NB) distribution to model the read counts for each gene in each sample. The dispersion parameter of the NB distribution accounts for variability between biological replicates (McCarthy, Chen, and Smyth 2012). edgeR estimates an empirical Bayes moderated dispersion for each individual gene. It also estimates a common dispersion, which is a global dispersion estimate averaged over all genes, and a trended dispersion where the dispersion of a gene is predicted from its abundance. Dispersion estimates are most easily obtained from the estimateDisp function:

> y <- estimateDisp(y, design, robust=TRUE)

This returns a DGEList object with additional components (common.dispersion, trended.dispersion and tagwise.dispersion) added to hold the estimated dispersions. Here robust=TRUE has been used to protect the empirical Bayes estimates against the possibility of outlier genes with exceptionally large or small individual dispersions (Phipson et al. 2016).

The dispersion estimates can be visualized with plotBCV:

> plotBCV(y)

Figure 5: Scatterplot of the biological coefficient of variation (BCV) against the average abundance of each gene
The plot shows the square-root estimates of the common, trended and tagwise NB dispersions.

The vertical axis of the plotBCV plot shows square-root dispersion, also known as biological coefficient of variation (BCV) (McCarthy, Chen, and Smyth 2012). For RNA-seq studies, the NB dispersions tend to be higher for genes with very low counts. The dispersion trend tends to decrease smoothly with abundance and to asymptotic to a constant value for genes with larger counts. From our past experience, the asymptotic value for the BCV tends to be in range from 0.05 to 0.2 for genetically identical mice or cell lines, whereas somewhat larger values (\(>0.3\)) are observed for human subjects.

The NB model can be extended with quasi-likelihood (QL) methods to account for gene-specific variability from both biological and technical sources (Lund et al. 2012; Lun, Chen, and Smyth 2016). Under the QL framework, the NB dispersion trend is used to describe the overall biological variability across all genes, and gene-specific variability above and below the overall level is picked up by the QL dispersion. In the QL approach, the individual (tagwise) NB dispersions are not used.

The estimation of QL dispersions is performed using the glmQLFit function:

> fit <- glmQLFit(y, design, robust=TRUE)
> head(fit$coefficients)

       B.lactating B.pregnant B.virgin L.lactating L.pregnant L.virgin
497097      -11.13     -12.01   -11.22       -19.0     -19.03    -19.0
20671       -12.76     -12.51   -12.15       -14.5     -14.30    -14.1
27395       -11.27     -11.29   -11.53       -10.6     -10.86    -10.9
18777       -10.15     -10.21   -10.76       -10.1     -10.38    -10.4
21399        -9.89      -9.73    -9.78       -10.2      -9.97    -10.0
58175       -16.15     -14.85   -15.98       -13.3     -12.29    -12.0

This returns a DGEGLM object with the estimated values of the GLM coefficients for each gene. It also contains a number of empirical Bayes (EB) statistics including the QL dispersion trend, the squeezed QL dispersion estimates and the prior degrees of freedom (df). The QL dispersions can be visualized by plotQLDisp:

> plotQLDisp(fit)

Figure 6: A plot of the quarter-root QL dispersion against the average abundance of each gene
Estimates are shown for the raw (before EB moderation), trended and squeezed (after EB moderation) dispersions. Note that the QL dispersions and trend shown here are relative to the NB dispersion trend show in the previous figure produced using plotBCV().

The QL functions moderate the genewise QL dispersion estimates in the same way that the limma package moderates variances (Smyth 2004). The raw QL dispersion estimates are squeezed towards a global trend, and this moderation reduces the uncertainty of the estimates and improves testing power. The extent of the squeezing is governed by the value of the prior df estimated from the data. Large prior df estimates indicate that the QL dispersions are less variable between genes, meaning that strong EB moderation should be performed. Smaller prior df estimates indicate that the true unknown dispersions are highly variable, so weaker moderation towards the trend is appropriate.

> summary(fit$df.prior)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   2.91    6.84    6.84    6.69    6.84    6.84 

Setting robust=TRUE in glmQLFit is usually recommended (Phipson et al. 2016). This allows gene-specific prior df estimates, with lower values for outlier genes and higher values for the main body of genes. This reduces the chance of getting false positives from genes with extremely high or low raw dispersions, while at the same time increasing statistical power to detect differential expression for the main body of genes.

Testing for differential expression

The next step is to test for differential expression between the experimental groups. One of the most interesting comparisons is that between the basal pregnant and lactating groups. The contrast corresponding to any specified comparison can be constructed conveniently using the makeContrasts function:

> B.LvsP <- makeContrasts(B.lactating-B.pregnant, levels=design)

In subsequent results, a positive \(\log_2\)-fold-change (logFC) will indicate a gene up-regulated in lactating mice relative to pregnant, whereas a negative logFC will indicate a gene more highly expressed in pregnant mice.

We will use QL F-tests instead of the more usual likelihood ratio tests (LRT) as they give stricter error rate control by accounting for the uncertainty in dispersion estimation:

> res <- glmQLFTest(fit, contrast=B.LvsP)

The top DE genes can be viewed with topTags:

> topTags(res)

Coefficient:  1*B.lactating -1*B.pregnant 
       Length  Symbol logFC logCPM   F   PValue      FDR
12992     765 Csn1s2b  6.08  10.19 422 4.30e-11 6.77e-07
211577   2006  Mrgprf  5.14   2.75 343 1.22e-10 7.28e-07
226101   7094    Myof  2.32   6.45 323 1.78e-10 7.28e-07
381290   8292  Atp2b4  2.14   6.15 321 1.85e-10 7.28e-07
140474  11281    Muc4 -7.18   6.06 309 2.39e-10 7.51e-07
231830   3346 Micall2 -2.25   5.19 283 4.01e-10 1.05e-06
24117    2242    Wif1 -1.82   6.77 260 6.65e-10 1.49e-06
12740    1812   Cldn4 -5.32   9.88 298 8.86e-10 1.66e-06
21953     667   Tnni2  5.75   3.86 314 9.47e-10 1.66e-06
231991   2873   Creb5  2.57   4.87 241 1.07e-09 1.68e-06

In order to control the false discovery rate (FDR), multiple testing correction is performed using the Benjamini-Hochberg method. The top DE gene Csn1s2b has a large positive logFC, showing that it is far more highly expressed in the basal cells of lactating than pregnant mice. This gene is indeed known to be a major source of protein in milk.

The total number of DE genes identified at an FDR of 5% can be shown with decideTestsDGE. There are in fact more than 5000 DE genes in this comparison:

> is.de <- decideTestsDGE(res)
> summary(is.de)

       1*B.lactating -1*B.pregnant
Down                          2752
NotSig                       10507
Up                            2477

The magnitude of the differential expression changes can be visualized with a fitted model MD plot:

> plotMD(res, status=is.de, values=c(1,-1), col=c("red","blue"),
+        legend="topright")

Figure 7: MD plot showing the log-fold change and average abundance of each gene
Significantly up and down DE genes are highlighted in red and blue, respectively.

The logFC for each gene is plotted against the average abundance in log2-CPM, i.e., logCPM in the table above. Genes that are significantly DE are highlighted.

Differential expression above a fold-change threshold

glmQLFTest identifies differential expression based on statistical significance regardless of how small the difference might be. For some purposes we might be interested only in genes with reasonably large expression changes. The above analysis found more than 5000 DE genes between the basal pregnant and lactating groups. With such a large number of DE genes, it makes sense to narrow down the list to genes that are more biologically meaningful.

A commonly used approach is to apply FDR and logFC cutoffs simultaneously. However this tends to favor lowly expressed genes, and also fails to control the FDR correctly. A better and more rigorous approach is to modify the statistical test so as to detect expression changes greater than a specified threshold. In edgeR, this can be done using the glmTreat function. This function is analogous to the TREAT method for microarrays (McCarthy and Smyth 2009) but is adapted to the NB framework. Here we test whether the differential expression fold changes are significantly greater than 1.5, that is, whether the logFCs are significantly greater than \(\log_2(1.5)\):

> tr <- glmTreat(fit, contrast=B.LvsP, lfc=log2(1.5))
> topTags(tr)

Coefficient:  1*B.lactating -1*B.pregnant 
       Length  Symbol logFC unshrunk.logFC logCPM   PValue      FDR
12992     765 Csn1s2b  6.08           6.09  10.19 5.65e-11 8.89e-07
211577   2006  Mrgprf  5.14           5.15   2.75 1.76e-10 1.38e-06
140474  11281    Muc4 -7.18          -7.34   6.06 3.87e-10 2.03e-06
226101   7094    Myof  2.32           2.32   6.45 9.05e-10 2.71e-06
12740    1812   Cldn4 -5.32          -5.33   9.88 1.17e-09 2.71e-06
21953     667   Tnni2  5.75           5.76   3.86 1.20e-09 2.71e-06
381290   8292  Atp2b4  2.14           2.14   6.15 1.21e-09 2.71e-06
231830   3346 Micall2 -2.25          -2.25   5.19 2.23e-09 4.38e-06
231991   2873   Creb5  2.57           2.57   4.87 3.99e-09 6.97e-06
16012    1289  Igfbp6  2.87           2.87   3.68 5.12e-09 8.05e-06

Note that the argument is an abbreviation for ``log-fold-change“. About 1100 genes are detected as DE with a FC significantly above 1.5 at an FDR cut-off of 5%.

> is.de <- decideTestsDGE(tr)
> summary(is.de)

       1*B.lactating -1*B.pregnant
Down                           682
NotSig                       14686
Up                             368

The p-values from glmTreat are larger than those from glmQLFTest, and the number of significantly DE genes is fewer, because it is testing an interval null hypothesis and requires stronger evidence for differential expression than does a conventional test. It provides greater specificity for identifying the most important genes with large fold changes.

The test results can be visualized in an MD plot:

> plotMD(tr, status=is.de, values=c(1,-1), col=c("red","blue"),
+        legend="topright")

Figure 8: MD plot showing the log-fold change and average abundance of each gene
Genes with fold-changes significantly greater than 1.5 are highlighted.

The method evaluates variability as well as the magnitude of change of expression values and therefore is not equivalent to a simple fold change cutoff. Nevertheless, all the statistically significant expression changes have logFC greater than 0.8 and almost all (97%) are greater than 0.9. These values compare to the threshold value of \(\log_2(1.5) = 0.58\). In general, an estimated logFC must exceed the TREAT threshold by a number of standard errors for it to be called significant. In other words, the whole confidence interval for the logFC must clear the threshold rather than just the estimated value itself. It is better to interpret the threshold as the FC below which we are definitely not interested in the gene rather than the FC above which we are interested in the gene.

The value of the FC threshold can be varied depending on the dataset. In the presence of a huge number of DE genes, a relatively large FC threshold may be appropriate to narrow down the search to genes of interest. In the absence of DE genes, on the other hand, a small or even no FC threshold shall be used. If the threshold level is set to zero, then glmTreat becomes equivalent to glmQLFTest in the workflow shown here.

In general, using glmTreat to reduce the number of DE genes is better than simply reducing the FDR cutoff, because glmTreat prioritizes genes with larger changes that are likely to be more biologically significant. glmTreat can also be used with edgeR pipelines other than quasi-likelihood, although we don’t demonstrate that here.

Heat map clustering

Heatmaps are a popular way to display differential expression results for publication purposes. To create a heatmap, we first convert the read counts into log2-counts-per-million (logCPM) values. This can be done with the cpm function:

> logCPM <- cpm(y, prior.count=2, log=TRUE)
> rownames(logCPM) <- y$genes$Symbol
> colnames(logCPM) <- paste(y$samples$group, 1:2, sep="-")

The introduction of prior.count is to avoid undefined values and to reduce the variability of the logCPM values for genes with low counts. Larger values for prior.count shrink the logFCs for low count genes towards zero.

We will create a heatmap to visualize the top 30 DE genes according to the TREAT test between B.lactating and B.pregnant. The advantage of a heatmap is that it can display the expression pattern of the genes across all the samples. Visualization of the results is aided by clustering together genes that have correlated expression patterns. First we select the logCPM values for the 30 top genes:

> o <- order(tr$table$PValue)
> logCPM <- logCPM[o[1:30],]

A heat map can then be produced by the coolmap function:

> coolmap(logCPM, margins=c(7,7), lhei=c(1,6), lwid=c(1,3))

Figure 9: Heat map across all the samples using the top 30 most DE genes between the basal lactating group and the basal pregnancy group

By default, coolmap clusters genes by correlation (highly correlated genes are closest) and clusters samples based on Euclidean distance between the expression values. The coolmap has placed the basal samples on the right and the luminal samples on the left. In each case, the virgin and pregnant samples are more like each other than the lactacting samples. As expected, the two replicate samples from each group are clustered together.

There a number of other R functions that can create heatmaps, but coolmap is the simplest because the default clustering metrics are chosen to be appropriate for expression data.

Analysis of deviance

The differential expression analysis comparing two groups can be easily extended to comparisons between three or more groups. This is done by creating a matrix of independent contrasts. In this manner, users can perform a one-way analysis of deviance (ANODEV) for each gene (McCullagh and Nelder 1989).

Suppose we want to compare the three groups in the luminal population, i.e., virgin, pregnant and lactating. An appropriate contrast matrix can be created as shown below, to make pairwise comparisons between all three groups:

> con <- makeContrasts(
+      L.PvsL = L.pregnant - L.lactating,
+      L.VvsL = L.virgin - L.lactating,
+      L.VvsP = L.virgin - L.pregnant, levels=design)

The QL F-test is then applied to identify genes that are DE between the three groups. This combines the three pairwise comparisons into a single F-statistic and p-value. The top set of significant genes can be displayed with topTags:

> res <- glmQLFTest(fit, contrast=con)
> topTags(res)

Coefficient:  LR test on 2 degrees of freedom 
      Length  Symbol logFC.L.PvsL logFC.L.VvsL logFC.L.VvsP logCPM    F
19242   2021     Ptn        -1.54         7.26        8.801   7.97 2382
13645   4757     Egf        -5.36        -7.22       -1.864   3.68 1119
52150   4089   Kcnk6        -2.42        -7.00       -4.579   5.91 1019
12992    765 Csn1s2b        -8.55       -11.36       -2.811  10.19 1053
15439   1345      Hp         1.08         5.42        4.336   4.93  988
14183   5346   Fgfr2        -1.15         3.95        5.096   7.39  954
20856   1793    Stc2        -1.81         3.20        5.006   6.11  917
11941   7050  Atp2b2        -7.37       -10.56       -3.190   6.61 1136
13358   1678 Slc25a1        -4.13        -4.91       -0.784   7.50  890
17068    691    Ly6d         3.42         9.24        5.819   4.69  886
        PValue      FDR
19242 3.16e-17 4.97e-13
13645 3.95e-15 2.75e-11
52150 7.17e-15 2.75e-11
12992 8.55e-15 2.75e-11
15439 8.76e-15 2.75e-11
14183 1.10e-14 2.75e-11
20856 1.41e-14 2.75e-11
11941 1.59e-14 2.75e-11
13358 1.70e-14 2.75e-11
17068 1.75e-14 2.75e-11

Note that the three contrasts of pairwise comparisons are linearly dependent. Constructing the contrast matrix with any two of the contrasts would be sufficient for an ANODEV test. If the contrast matrix contains all three possible pairwise comparisons, then only the log-fold changes of the first two contrasts are shown in the output of topTags.

Complicated contrasts

The flexibility of the GLM framework makes it possible to specify arbitrary contrasts for differential expression tests. Suppose we are interested in testing whether the change in expression between lactating and pregnant mice is the same for basal cells as it is for luminal cells. In statistical terminology, this is the interaction effect between mouse status and cell type. The contrast corresponding to this testing hypothesis can be made as follows.

> con <- makeContrasts(
+      (L.lactating-L.pregnant)-(B.lactating-B.pregnant), 
+      levels=design)

Then the QL F-test is conducted to identify genes that are DE under this contrast. The top set of DE genes are viewed with topTags.

> res <- glmQLFTest(fit, contrast=con)
> topTags(res)

Coefficient:  -1*B.lactating 1*B.pregnant 1*L.lactating -1*L.pregnant 
       Length   Symbol logFC logCPM   F   PValue      FDR
19041    6277      Ppl -4.62   6.97 526 8.43e-12 1.33e-07
231991   2873    Creb5 -5.61   4.87 440 2.58e-11 2.00e-07
20512    4206   Slc1a3  5.03   3.65 413 3.82e-11 2.00e-07
217294   1952 BC006965 -3.88   4.68 371 7.46e-11 2.58e-07
14598    2022     Ggt1  3.18   6.38 358 9.30e-11 2.58e-07
13358    1678  Slc25a1  3.47   7.50 355 9.84e-11 2.58e-07
192166   4558    Sardh  2.92   5.11 340 1.28e-10 2.88e-07
19659    2628     Rbp1 -4.39   6.83 337 1.51e-10 2.97e-07
67547    3707  Slc39a8  6.19   5.07 376 1.72e-10 3.01e-07
14063    2768    F2rl1 -3.92   5.62 303 2.61e-10 3.92e-07

Gene ontology analysis

We now consider the problem of interpreting the differential expression results in terms of higher order biological processes or molecular pathways. One of the most common used resources is gene ontology (GO) databases, which annotate genes according to a dictionary of annotation terms. A simple and often effective way to interpret the list of DE genes is to count the number of DE genes that are annotated with each possible GO term. GO terms that occur frequently in the list of DE genes are said to be over-represented or enriched.

In edgeR, GO analyses can be conveniently conducted using the goana function. Here were apply goana to the output of the TREAT analysis comparing B.lactating to B.pregant. The top most significantly enriched GO terms can be viewed with topGO.

> go <- goana(tr, species="Mm")
> topGO(go, n=15)

                                           Term Ont    N Up Down  P.Up
GO:1903047           mitotic cell cycle process  BP  608  8   84 0.975
GO:0007059               chromosome segregation  BP  277  1   54 0.999
GO:0000070 mitotic sister chromatid segregation  BP  138  0   38 1.000
GO:0000819         sister chromatid segregation  BP  166  0   41 1.000
GO:0022402                   cell cycle process  BP  983 16  108 0.955
GO:0051301                        cell division  BP  524  4   74 0.998
GO:0000278                   mitotic cell cycle  BP  746  9   91 0.992
GO:0000280                     nuclear division  BP  342  6   58 0.815
GO:0098813       nuclear chromosome segregation  BP  219  1   45 0.995
GO:0140014             mitotic nuclear division  BP  239  2   47 0.977
GO:0000776                          kinetochore  CC  126  1   34 0.950
GO:0000775       chromosome, centromeric region  CC  179  1   40 0.986
GO:0007049                           cell cycle  BP 1428 20  132 0.997
GO:0048285                    organelle fission  BP  387  9   58 0.554
GO:0042254                  ribosome biogenesis  BP  266  0   47 1.000
             P.Down
GO:1903047 1.26e-21
GO:0007059 5.21e-21
GO:0000070 1.39e-20
GO:0000819 3.50e-20
GO:0022402 1.01e-19
GO:0051301 1.12e-19
GO:0000278 1.25e-19
GO:0000280 2.08e-19
GO:0098813 1.26e-18
GO:0140014 1.38e-18
GO:0000776 3.02e-18
GO:0000775 4.78e-18
GO:0007049 1.52e-17
GO:0048285 8.20e-17
GO:0042254 1.19e-16

The goana function automatically extracts DE genes from the tr object, and conducts overlap tests for the up- and down-regulated DE genes separately. By default, an FDR cutoff of 5% is used when extracting DE genes, but this can be varied. The row names of the output are the universal identifiers of the GO terms and the Term column gives the human-readable names of the terms. The Ont column shows the ontology domain that each GO term belongs to. The three domains are: biological process (BP), cellular component (CC) and molecular function (MF). The N column represents the total number of genes annotated with each GO term. The Up and Down columns indicate the number of genes within the GO term that are significantly up- and down-regulated in this differential expression comparison, respectively. The P.Up and P.Down columns contain the p-values for over-representation of the GO term in the up- and down-regulated genes, respectively. Note that the p-values are not adjusted for multiple testing—we would usually ignore GO terms with p-values greater than about \(10^{-5}\).

By default the output table from topGO is sorted by the minimum of P.Up and P.Down. Other options are available. For example, topGO(go, sort="up") lists the top GO terms that are over-represented in the up-regulated genes. The domain of the enriched GO terms can also be specified by users. For example, topGO(go, ontology="BP") restricts to the top GO terms belonging to the biological process domain while topGO(go, ontology="MF") restricts to molecular function terms.

The goana function uses the NCBI RefSeq annotation and requires the use of Entrez Gene Identifiers.

KEGG pathway analysis

Another popular annotation database is the Kyoto Encyclopedia of Genes and Genomes (KEGG). Much smaller than GO, this is a curated database of molecular pathways and disease signatures. A KEGG analysis can be done exactly as for GO, but using the kegga function:

> keg <- kegga(tr, species="Mm")
> topKEGG(keg, n=15, truncate=34)

                                         Pathway   N Up Down     P.Up
path:mmu03008 Ribosome biogenesis in eukaryot...  76  0   19 1.00e+00
path:mmu04110                         Cell cycle 119  0   20 1.00e+00
path:mmu05150    Staphylococcus aureus infection  36  1   11 5.74e-01
path:mmu04972               Pancreatic secretion  68  9    4 2.77e-05
path:mmu00100               Steroid biosynthesis  18  5    0 4.54e-05
path:mmu00900    Terpenoid backbone biosynthesis  21  5    0 1.02e-04
path:mmu04970                 Salivary secretion  63  8    7 1.04e-04
path:mmu04610 Complement and coagulation casc...  50  3    9 1.12e-01
path:mmu00240              Pyrimidine metabolism  52  0    9 1.00e+00
path:mmu04925 Aldosterone synthesis and secre...  76  8    6 3.91e-04
path:mmu04911                  Insulin secretion  62  7    5 5.88e-04
path:mmu05144                            Malaria  39  2    7 2.31e-01
path:mmu00983    Drug metabolism - other enzymes  51  2    8 3.36e-01
path:mmu04640         Hematopoietic cell lineage  63  2    9 4.35e-01
path:mmu04510                     Focal adhesion 187 12    8 1.53e-03
                P.Down
path:mmu03008 3.69e-10
path:mmu04110 1.80e-07
path:mmu05150 2.08e-07
path:mmu04972 3.41e-01
path:mmu00100 1.00e+00
path:mmu00900 1.00e+00
path:mmu04970 1.88e-02
path:mmu04610 2.60e-04
path:mmu00240 3.53e-04
path:mmu04925 1.11e-01
path:mmu04911 1.30e-01
path:mmu05144 1.28e-03
path:mmu00983 1.46e-03
path:mmu04640 1.49e-03
path:mmu04510 5.66e-01

The output from topKEGG is the same as from topGO except that row names become KEGG pathway IDs, Term becomes Pathway and there is no Ont column. Both the GO and KEGG analyses show that the cell cycle pathway is strongly down-regulated upon lactation in mammary stem cells.

By default, the kegga function automatically reads the latest KEGG annotation from the Internet each time it is run. The KEGG database uses Entrez Gene Ids, and the kegga function assumes these are available as the row names of tr.

FRY gene set tests

The GO and KEGG analyses shown above are relatively simple analyses that rely on a list of DE genes. The list of DE genes is overlapped with the various GO and KEGG annotation terms. The results will depend on the significance threshold that is used to assess differential expression.

If the aim is to test for particular gene expression signatures or particular pathways, a more nuanced approach is to conduct a roast or fry gene set test (Wu et al. 2010). These functions test whether a set of genes is DE, assessing the whole set of genes as a whole. Gene set tests consider all the genes in the specified set and do not depend on any pre-emptive significance cutoff. The set of genes can be chosen to be representative of any pathway or phenotype of interest.

roast gives p-values using random rotations of the residual space. In the edgeR context, fry is generally recommended over roast. fry gives an accurate analytic approximation to the results that roast would give, with default settings, if an extremely large number of rotations was used.

Here, suppose we are interested in two GO terms related to cytokinesis. Each GO term is used to define a set of genes annotated with that term. The names of these terms are shown below:

> library(GO.db)
> cyt.go <- c("GO:0032465", "GO:0000281")
> term <- select(GO.db, keys=cyt.go, columns="TERM")
> term

        GOID                      TERM
1 GO:0032465 regulation of cytokinesis
2 GO:0000281       mitotic cytokinesis

The first step is to extract the genes associated with each GO term from the GO database. This produces a list of two components, one for each GO term. Each component is a vector of Entrez Gene IDs for that GO term:

> Rkeys(org.Mm.egGO2ALLEGS) <- cyt.go
> cyt.go.genes <- as.list(org.Mm.egGO2ALLEGS)

Suppose the comparison of interest is between the virgin and lactating groups in the basal population. We can use fry to test whether the cytokinesis GO terms are DE for this comparison:

> B.VvsL <- makeContrasts(B.virgin-B.lactating, levels=design)
> fry(y, index=cyt.go.genes, design=design, contrast=B.VvsL)

           NGenes Direction  PValue     FDR PValue.Mixed FDR.Mixed
GO:0032465     70        Up 0.00106 0.00212     6.19e-06  1.24e-05
GO:0000281     68        Up 0.00840 0.00840     1.92e-05  1.92e-05

Each row of the output corresponds to a gene set. The NGenes column provides the number of genes in each set. The Direction column indicates the net direction of change. The PValue column gives the two-sided p-value for testing whether the set is DE as a whole, either up or down. The PValue.Mixed column gives a p-value for testing whether genes in the set tend to be DE, without regard to direction. The PValue column is appropriate when genes in the set are expected to be co-regulated, all or most changing expression in the same direction. The PValue.Mixed column is appropriate when genes in the set are not necessarily co-regulated or may be regulated in different directions for the contrast in question. FDRs are calculated from the corresponding p-values across all sets.

The results of a gene set test can be viewed in a barcode plot produced by the barcodeplot function. Suppose visualization is performed for the gene set defined by the GO term GO:0032465:

> res <- glmQLFTest(fit, contrast=B.VvsL)
> index <- rownames(fit) %in% cyt.go.genes[[1]]
> barcodeplot(res$table$logFC, index=index, labels=c("B.lactating","B.virgin"), 
+             main=cyt.go[1])

Figure 10: Barcode plot showing enrichment of the GO term GO:0032465 in the basal virgin group compared to the basal lactating group
X-axis shows logFC for B.virgin vs B.lactating. Black bars represent genes annotated with the GO term. The worm shows relative enrichment.

In the plot, all genes are ranked from left to right by increasing log-fold change for the contrast and the genes within the gene set are represented by vertical bars, forming the barcode-like pattern. The curve (or worm) above the barcode shows the relative local enrichment of the bars in each part of the plot. The dotted horizontal line indicates neutral enrichment; the worm above the dotted line shows enrichment while the worm below the dotted line shows depletion. In this particular barcode plot the worm shows enrichment on the right for positive logFCs, and depletion on the left for negative logFCs. The conclusion is that genes associated with this GO term tend to be up-regulated in the basal cells of virgin mice compared to lactating mice, confirming the result of the fry test above.

Camera gene set enrichment analysis

Finally we demonstrate a gene set enrichment style analysis using the Molecular Signatures Database (MSigDB) (Subramanian et al. 2005). We will use the C2 collection of the MSigDB, which is a collection of nearly 5000 curated gene sets, each representing the molecular signature of a particular biological process or phenotype. The MSigDB itself is purely human, but the Walter and Eliza Hall Institute (WEHI) maintains a mouse version of the database. We load the mouse version of the C2 collection from the WEHI website:

> load(url("http://bioinf.wehi.edu.au/software/MSigDB/mouse_c2_v5p1.rdata"))

This will load Mm.c2, which is a list of gene sets, each a vector of Entrez Ids. This can be converted to a list of index numbers:

> idx <- ids2indices(Mm.c2,id=rownames(y))

First we compare virgin stem cells to virgin luminal cells:

> BvsL.v <- makeContrasts(B.virgin - L.virgin, levels=design)
> cam <- camera(y, idx, design, contrast=BvsL.v, inter.gene.cor=0.01)
> options(digits=2)
> head(cam,14)

                                                    NGenes Direction  PValue
LIM_MAMMARY_STEM_CELL_UP                               784        Up 1.9e-43
LIM_MAMMARY_LUMINAL_MATURE_DN                          169        Up 3.0e-25
SASAI_RESISTANCE_TO_NEOPLASTIC_TRANSFROMATION           80        Up 3.4e-20
LIM_MAMMARY_STEM_CELL_DN                               666      Down 1.9e-19
FARMER_BREAST_CANCER_CLUSTER_4                          75        Up 3.7e-19
NABA_BASEMENT_MEMBRANES                                 52        Up 1.4e-17
HAEGERSTRAND_RESPONSE_TO_IMATINIB                       35        Up 3.4e-17
ROZANOV_MMP14_TARGETS_SUBSET                            83        Up 4.5e-16
REACTOME_COLLAGEN_FORMATION                             70        Up 1.2e-15
REACTOME_NCAM1_INTERACTIONS                             71        Up 2.0e-15
OXFORD_RALB_TARGETS_UP                                  27        Up 3.9e-15
ANASTASSIOU_CANCER_MESENCHYMAL_TRANSITION_SIGNATURE    149        Up 6.9e-15
PAPASPYRIDONOS_UNSTABLE_ATEROSCLEROTIC_PLAQUE_DN        68        Up 1.1e-14
LIM_MAMMARY_LUMINAL_PROGENITOR_UP                       92      Down 1.6e-14
                                                        FDR
LIM_MAMMARY_STEM_CELL_UP                            9.1e-40
LIM_MAMMARY_LUMINAL_MATURE_DN                       7.1e-22
SASAI_RESISTANCE_TO_NEOPLASTIC_TRANSFROMATION       5.3e-17
LIM_MAMMARY_STEM_CELL_DN                            2.2e-16
FARMER_BREAST_CANCER_CLUSTER_4                      3.5e-16
NABA_BASEMENT_MEMBRANES                             1.1e-14
HAEGERSTRAND_RESPONSE_TO_IMATINIB                   2.3e-14
ROZANOV_MMP14_TARGETS_SUBSET                        2.7e-13
REACTOME_COLLAGEN_FORMATION                         6.1e-13
REACTOME_NCAM1_INTERACTIONS                         9.3e-13
OXFORD_RALB_TARGETS_UP                              1.7e-12
ANASTASSIOU_CANCER_MESENCHYMAL_TRANSITION_SIGNATURE 2.7e-12
PAPASPYRIDONOS_UNSTABLE_ATEROSCLEROTIC_PLAQUE_DN    4.1e-12
LIM_MAMMARY_LUMINAL_PROGENITOR_UP                   5.4e-12

With a large gene set collection, setting inter.gene.cor = 0.01 gives a good compromise between biological interpretability and FDR control. As expected, the mammary stem cell and mammary luminal cell signatures from Lim et al (Lim et al. 2010) are top-ranked, and in the expected directions.

We can visualize the top signature, combining the up and down mammary stem cell signatures to make a bi-directional signature set:

> res <- glmQLFTest(fit, contrast=BvsL.v)
> barcodeplot(res$table$logFC,
+             index=idx[["LIM_MAMMARY_STEM_CELL_UP"]],
+             index2=idx[["LIM_MAMMARY_STEM_CELL_DN"]],
+             labels=c("L.virgin","B.virgin"),
+             main="LIM_MAMMARY_STEM_CELL",
+             alpha=1)

Figure 11: Barcode plot showing strong enrichment of mammary stem cell signature in the stem cell vs luminal cell comparison
Red bars show up signature genes, blue bars show down genes. The worms show relative enrichment.

Download raw sequence files from the SRA

We now revisit the question of recreating the matrix of read counts from the raw sequence reads. Unlike the above workflow, which works for any version of R, read alignment requires Unix or Mac OS and, in practice, a high performance Unix server is recommended. Read alignment and read counting require only one Bioconductor package, Rsubread. However the fastq-dump utility from the SRA Toolkit is also required to convert from SRA to FASTQ format. This can be downloaded from the NCBI website (http://www.ncbi.nlm.nih.gov/Traces/sra/?view=software) and installed on any Unix system.

The first task is to download the raw sequence files, which are stored in SRA format on the SRA repository. The SRA files need to be unpacked into FASTQ format using the fastq-dump utility. The following R code makes a system call to fastq-dump to download each SRA file and convert it to FASTQ format:

for (sra in targets$SRA) system(paste("fastq-dump", sra))

The fastq-dump utility automatically downloads the specified SRA data set from the internet. The above code will produce 12 FASTQ files, in the current working directory, with file names given by the following vector:

all.fastq <- paste0(targets$SRA, ".fastq")

Accuracy of base-calling

Sequencers typically store base-calling quality scores for each read in the FASTQ files. Rsubread’s qualityScores function can be used to extract these scores from any particular file:

QS <- qualityScores("SRR1552444.fastq")

The boxplot function provides a compact way to view the quality scores by position across all reads:

boxplot(QS, ylab="Quality score", xlab="Base position",
        main="SRR1552444.fastq", cex=0.25, col="orange")

Figure 12: Boxplots of quality scores by base position for the first FASTQ file.

The vertical axis shows the Phred quality score, equal to \(-10\log_{10}(p)\) where \(p\) is the probability of an erroneous call. The maximum possible value is 40, and all values above 10 correspond to extremely small error probabilities. The horizontal axis shows position within a read. The file contains 100bp single-end reads, so the scale is from 1 to 100. The plot displays a compact boxplot at each base position. As is very commonly observed, the quality scores are best in the middle of the reads and decrease slightly towards the start and end of the reads. However the quality remains generally good even near the ends of the reads: the scores would need to be very much lower than this before they would cause problems for the alignment. Similar plots can be made for each of the FASTQ files.

Build a genome index

Before the sequence reads can be aligned, we need to build an index for the GRCm38/mm10 (Dec 2011) build of the mouse genome. Most laboratories that use Rsubread regularly will already have an index file prepared, as this is a once-off operation for each genome release. If you are using Rsubread for mouse for the first time, then the latest mouse genome build can be downloaded from the NCBI webpage (https://www.ncbi.nlm.nih.gov/assembly/GCF_000001635.26). The full URL is:

ftp://ftp.ncbi.nlm.nih.gov/genomes/all/GCF/000/001/635/GCF_000001635.26_GRCm38.p6/GCF_000001635.26_GRCm38.p6_genomic.fna.gz

(Note that this link is for patch 6 of the RefSeq mm10 build, which is valid at the time of writing in May 2018. The link will change as new patches are released periodically.) An index can then be built by:

library(Rsubread)
buildindex(basename = "mm10",
           reference = "GCF_000001635.26_GRCm38.p6_genomic.fna.gz")

Aligning reads

The sequence reads can now be aligned to the mouse genome using the align function:

all.bam <- sub(".fastq", ".bam", all.fastq)
align(index="mm10", readfile1=all.fastq, input_format="FASTQ", 
      output_file=all.bam)

This produces a set of BAM files containing the read alignments for each RNA library. The mapping proportions can be summarized by the propmapped function:

> propmapped(all.bam)
          Samples NumTotal NumMapped PropMapped
1  SRR1552450.bam 30109290  26577308      0.883
2  SRR1552451.bam 28322351  24794251      0.875
3  SRR1552452.bam 31688348  27937620      0.882
4  SRR1552453.bam 29614284  26074034      0.880
5  SRR1552454.bam 27225012  24381742      0.896
6  SRR1552455.bam 25433157  22813815      0.897
7  SRR1552444.bam 27919481  23927833      0.857
8  SRR1552445.bam 29731031  25487822      0.857
9  SRR1552446.bam 29879070  25500318      0.853
10 SRR1552447.bam 29245388  25187577      0.861
11 SRR1552448.bam 31425424  27326500      0.870
12 SRR1552449.bam 31276061  27204156      0.870

Ideally, the proportion of mapped reads should be above 80%. By default, only reads with unique mapping locations are reported by Rsubread as being successfully mapped. Restricting to uniquely mapped reads is recommended, as it avoids spurious signal from non-uniquely mapped reads derived from, e.g., repeat regions.

Quantifying read counts for each gene

The read counts for each gene can be quantified using the featureCounts function in Rsubread. Conveniently, the Rsubread package includes inbuilt NCBI RefSeq annotation of the mouse and human genomes. featureCounts generates a matrix of read counts for each gene in each sample:

fc <- featureCounts(all.bam, annot.inbuilt="mm10")

The output is a simple list, containing the matrix of counts (counts), a data frame of gene characteristics (annotation), a vector of file names (targets) and summary mapping statistics (stat):

> names(fc)
[1] "counts"     "annotation" "targets"    "stat"    

The row names of fc$counts are the Entrez gene identifiers for each gene. The column names are the output file names from align, which we simplify here for brevity:

> colnames(fc$counts) <- rownames(targets)

The first six rows of the counts matrix are shown below.

> head(fc$counts)
          MCL1.DG MCL1.DH MCL1.DI MCL1.DJ MCL1.DK MCL1.DL MCL1.LA
497097        438     299      65     237     354     287       0
100503874       1       0       1       1       0       4       0
100038431       0       0       0       0       0       0       0
19888           1       1       0       0       0       0      10
20671         106     181      82     104      43      83      16
27395         309     232     339     290     291     270     558
          MCL1.LB MCL1.LC MCL1.LD MCL1.LE MCL1.LF
497097          0       0       0       0       0
100503874       0       0       0       0       0
100038431       0       0       0       0       0
19888           3      10       2       0       0
20671          25      18       8       3      10
27395         468     488     332     312     344

Finally, a DGEList object can be assembled by:

y <- DGEList(fc$counts, group=group)
y$genes <- fc$annotation[, "Length", drop=FALSE]