Inputs

We assume users are starting with read count data from an RNA-seq experiment, as is typically generated after employing one of many commonly used alignment pipelines (e.g. RSEM, Salmon, etc). The doseR workflow starts with read count data, and not RPKM (or, comparably, FPKM), because RPKM values are calculated during the analysis after selecting the desired library-size normalization factor. RNA-seq data will typically come from distinct treatments (e.g. male, female) and may have one or more replicates per treatment. Users also provide lengths (in basepairs) for each transcript assayed. Finally, annotations indicating the groupings of loci (e.g. chromosome) are also needed.

Normalization

Accounting for differences in library size (i.e. depth of sequencing) between samples is an important step in most statistical analyses involving RNA-seq data. doseR provides a variety of methods for defining the library size for each sample. After defining library sizes, read counts are scaled both by library size and transcript length to give RPKM values that can be meaningfully compared between loci and between samples.

Filtering

One notable concern and potential artifact in dosage compensation analysis is the filtering of “unexpressed” loci. In theory, it is ideal to remove loci prior to analysis since we should be primarily concerned only with actively expressed genes. In practice, however, it is far from clear how best to do this or what criteria should be employed. When “unexpressed” loci are disproportionately represented among chromosomes (or other gene groups), failing to effectively remove them can cause spurious results. At the other extreme, overly aggressive removal of low-abundance transcripts can artificially compress distributions of gene expression, masking true differences in the data. A variety of approaches have been implement in doseR for filtering out loci considered to be “unexpressed”.

Comparing absolute expression

One informative way to assess dosage compensation is to consider the distribution of expression levels within sex between groups of genes, typically for genes on the X or Z versus the autosomes. This is done separately in each sex (or other treatments), providing a direct inference of absolute differences in gene expression among chromosomes (or other gene groupings). However, this approach is limited in that it does not easily support a direct comparison between sexes (or other treatments). doseR includes functions for visualization and statistical tests of differences in absolute gene expression.

Comparing relative expression

Examining the distribution of expression ratios (e.g. Male:Female) between treatments across chromosomes (or other gene groupings) is an alternative approach to assess whether global expression biases exist for particular sets of genes, such as might be expected for uncompensated X or Z chromosomes. While this approach can provide nuanced assessment of dosage effects, it does not indicate what absolute changes in gene expression may be occurring that underlie shifts in expression ratio. doseR provides functions for visualizing and statistically testing variation in expression ratios across chromosomes (or other gene groupings), complementing functions for examining absolute differences in expression among groupings within treatment.

Installation

doseR can be installed from Bioconductor directly using the BiocManager.

if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")
BiocManager::install("doseR")

Once installed, you must load the package.

library(doseR)
library(SummarizedExperiment)
#> Loading required package: MatrixGenerics
#> Loading required package: matrixStats
#> 
#> Attaching package: 'MatrixGenerics'
#> The following objects are masked from 'package:matrixStats':
#> 
#>     colAlls, colAnyNAs, colAnys, colAvgsPerRowSet, colCollapse,
#>     colCounts, colCummaxs, colCummins, colCumprods, colCumsums,
#>     colDiffs, colIQRDiffs, colIQRs, colLogSumExps, colMadDiffs,
#>     colMads, colMaxs, colMeans2, colMedians, colMins, colOrderStats,
#>     colProds, colQuantiles, colRanges, colRanks, colSdDiffs, colSds,
#>     colSums2, colTabulates, colVarDiffs, colVars, colWeightedMads,
#>     colWeightedMeans, colWeightedMedians, colWeightedSds,
#>     colWeightedVars, rowAlls, rowAnyNAs, rowAnys, rowAvgsPerColSet,
#>     rowCollapse, rowCounts, rowCummaxs, rowCummins, rowCumprods,
#>     rowCumsums, rowDiffs, rowIQRDiffs, rowIQRs, rowLogSumExps,
#>     rowMadDiffs, rowMads, rowMaxs, rowMeans2, rowMedians, rowMins,
#>     rowOrderStats, rowProds, rowQuantiles, rowRanges, rowRanks,
#>     rowSdDiffs, rowSds, rowSums2, rowTabulates, rowVarDiffs, rowVars,
#>     rowWeightedMads, rowWeightedMeans, rowWeightedMedians,
#>     rowWeightedSds, rowWeightedVars
#> Loading required package: GenomicRanges
#> Loading required package: stats4
#> Loading required package: BiocGenerics
#> Loading required package: generics
#> 
#> Attaching package: 'generics'
#> The following objects are masked from 'package:base':
#> 
#>     as.difftime, as.factor, as.ordered, intersect, is.element, setdiff,
#>     setequal, union
#> 
#> Attaching package: 'BiocGenerics'
#> The following objects are masked from 'package:stats':
#> 
#>     IQR, mad, sd, var, xtabs
#> The following objects are masked from 'package:base':
#> 
#>     Filter, Find, Map, Position, Reduce, anyDuplicated, aperm, append,
#>     as.data.frame, basename, cbind, colnames, dirname, do.call,
#>     duplicated, eval, evalq, get, grep, grepl, is.unsorted, lapply,
#>     mapply, match, mget, order, paste, pmax, pmax.int, pmin, pmin.int,
#>     rank, rbind, rownames, sapply, saveRDS, table, tapply, unique,
#>     unsplit, which.max, which.min
#> Loading required package: S4Vectors
#> 
#> Attaching package: 'S4Vectors'
#> The following object is masked from 'package:utils':
#> 
#>     findMatches
#> The following objects are masked from 'package:base':
#> 
#>     I, expand.grid, unname
#> Loading required package: IRanges
#> Loading required package: GenomeInfoDb
#> Loading required package: Biobase
#> Welcome to Bioconductor
#> 
#>     Vignettes contain introductory material; view with
#>     'browseVignettes()'. To cite Bioconductor, see
#>     'citation("Biobase")', and for packages 'citation("pkgname")'.
#> 
#> Attaching package: 'Biobase'
#> The following object is masked from 'package:MatrixGenerics':
#> 
#>     rowMedians
#> The following objects are masked from 'package:matrixStats':
#> 
#>     anyMissing, rowMedians

Example data: Heliconius RNA-seq

The primary data used by doseR are read counts from RNA-seq data, in this case generated from legs of H. melpomene, with three biological replicates each for male and female. Read count data should be formatted as a matrix, with replicates in columns and transcripts in rows. We also need a vector of corresponding transcript lengths. Finally, data indicating gene groupings are needed. Here we have a vector giving chromosomal linkage for each transcript (note that these data are limited to only one representative transcript per gene).

data(hmel.data.doser)

These three data elements are used to populate a new SummarizedExperiment, which is the core data structure for the doseR package. This object contains and organizes the read counts, RPKM values, segment lengths, and annotations of gene groupings. However, there are some further data manipulations required before we can create a new object.

First, we need to create a vector indicating to the replicate structure in the data, in this case three male and three female replicates, as organized in the counts matrix.

reps <- c("Male", "Male", "Male", "Female", "Female", "Female")

Second, we must create a dataframe to hold the annotation of gene groupings. In doing this, we will also convert the numeric annotation vector into a factor, which facilitates proper ordering of gene groups in later plotting. Additionally, we will recode the chromosomal linkage information as being Z-linked or autosomal.

annotxn <- data.frame("Chromosome" = factor(hmel.dat$chromosome, 
levels = 1:21))
annotxn$ZA <- factor(ifelse(hmel.dat$chromosome == 21, "Z", "A"), 
levels = c("A", "Z"))

Now we are ready to populate a new SummarizedExperiment object.

counts <- hmel.dat$readcounts
colData <- S4Vectors::DataFrame(Treatment=as.factor(reps), 
row.names=colnames(hmel.dat$readcounts))
rowData <- S4Vectors::DataFrame(annotation = annotxn, 
seglens = hmel.dat$trxLength,
row.names=rownames(hmel.dat$readcounts) )
se2 <- SummarizedExperiment(assays=list(counts=counts), 
colData=colData, rowData=rowData)

Normalization & RPKM

Next we select a method for calculating the library size (sometimes called scaling factors) so that data are normalized for depth of sequencing. Various methods for calculating a library size are provided, but we will use the most straightforward method of summing total read counts.

SummarizedExperiment::colData(se2)$Libsizes <- getLibsizes3(se2, 
estimationType = "total")

With library sizes now stored in the SummExperiment object, we can calculate RPKM values for each locus in each sample and store them in the RPKM slot.

SummarizedExperiment::assays(se2)$rpkm <- make_RPKM(se2)

# se2 now equals se...

data(hmel.se)  # loads hmel.dat list

# MD5 checksum equivalence:
#library(digest)
digest::digest(se) == digest::digest(se2)
#> [1] FALSE

It is always wise when first working with comparisons between genome-wide expression data sets like this to check that there are not clear biases or other artifacts showing up in the data, and that the normalization seems reasonable. Making MA plots is one important visualization to guard agains such problems.

plotMA.se(se, samplesA ="Male", samplesB = "Female", cex = .2 , 
pch = 19, col = rgb(0,0,0, .2), xlab = "Log2(Average RPKM)", 
ylab = "Log2(Male:Female)")

Filtering “unexpressed” loci

It is generally good practice to remove loci considered to be “unexpressed”. In this case we will apply a filter so that included loci must have a mean RPKM value across samples greather than 0.01. Many other approaches to filtering are provided in doseR, and it is generally wise to explore how filtering choices affect assessments of dosage compensation.

f_se <- simpleFilter(se, mean_cutoff = 0.01, counts = FALSE)
#> Filtering removed 4035 (29.63%).

Comparing absolute expression

Having generated filtered RPKM values, we can proceed to comparing distributions of expression among different groupings of genes, as indicated in the annotation slot of the SummExperiment object. Biological replicates are averaged to give a single representative RPKM value per gene. In this case it is clear that the gene expression is reduced on the Z chromosome relative to autosomes in both sexes.

plotExpr(f_se, groupings = "annotation.ZA", clusterby_grouping = FALSE, 
col=c("grey80","red","grey80","red"), notch=TRUE, ylab = "Log2(RPKM)")

Beyond visualizing with boxplots, we will also want statistical summaries and tests applied to these data, which can be done with the generateStats() function. Here we will want to subset the SummarizedExperiment object so that tests are applied using only data from a single treatment. The function returns a list of three items:

1. A distributional summary for each grouping of genes analyzed
2. The results from applying a Kruskal-Wallis test, a non-parametric test of differences among groups
3. The values used for generating 1 & 2, i.e. the average values across replicates for each gene in each group.

Here we demonstrate this only for male samples, but a full analysis would also require the same be done for the female samples.

se.male <- f_se[, colData(f_se)$Treatment == "Male"]
male_ZvA <- generateStats(se.male , groupings = "annotation.ZA", LOG2 = FALSE)
#> View output: outlist$kruskal, outlist$summary
male_ZvA$summary  # distributional summary statistics
#>                    A           Z
#> Min.        0.000000    0.000000
#> 1st Qu.     1.837499    1.093565
#> Median      8.715750    5.795021
#> Mean       54.737996   37.759261
#> 3rd Qu.    23.573567   16.577152
#> Max.    20065.669794 4351.420842
male_ZvA$kruskal  # htest class output from kruskal.test()
#> 
#>  Kruskal-Wallis rank sum test
#> 
#> data:  tmp
#> Kruskal-Wallis chi-squared = 19.006, df = 1, p-value = 1.303e-05
lapply(male_ZvA$data, head) # a record of values used for statistics.
#> $A
#>  HMEL000002  HMEL000003  HMEL000004  HMEL000006  HMEL000007  HMEL000008 
#> 10.71571713  0.09353976 41.72790716 21.12032979  0.00000000  4.87423582 
#> 
#> $Z
#> HMEL002056 HMEL002096 HMEL002142 HMEL002143 HMEL002145 HMEL002156 
#>  4.9311162  0.4912925 27.8965294  6.1170531  1.8668670 99.4424234

It may be of interest to examine other groupings of genes. For instance, how variable are the distributions of expression across chromosomes?
Again, we’ll limit this only to males for the sake of demonstration.

plotExpr(f_se, groupings = "annotation.Chromosome", col=c(rep("grey80", 20), 
"red"), notch=TRUE, ylab = "Log2(RPKM)", las = 2, treatment = "Male",  
clusterby_grouping = TRUE )

Comparing relative expression

Similarly to the plots and statistics given above for absolute expression, doseR provides functions for examing relative expression between pairs of treatments. For instance, we may want to assess whether there is a dosage effect on gene expression for the Z chromosome. This would manifest as a positive shift in the distribution of Male:Female expression levels on the Z relative to autosomes.

We can examine this using boxplots, similar to absolute expression, above.

plotRatioBoxes(f_se, groupings = "annotation.ZA", treatment1 = "Male", 
treatment2 = "Female", outline = FALSE, col = c("grey80", "red"),
ylab = "Log(Male:Female)" )

Alternatively, there is a widely used convention in the dosage compensation literature to visualize these distributions using a density plot, so this functionality is also provided.

plotRatioDensity(f_se, groupings = "annotation.ZA", treatment1 = "Male", 
treatment2 = "Female", type = "l", xlab = "Log(Male:Female)", ylab = "Density")
#> Current order of levels:  A Z

As above, we can apply the same plotting to the chromosomal annotation if desired.

par(mfrow = c(1,2))
plotRatioBoxes(f_se, groupings = "annotation.Chromosome", treatment1 =
"Male", treatment2 = "Female", outline = FALSE, col=c(rep("grey80", 20), 
"red"), ylab = "Log(Male:Female)", xlab = "Chromosome" )

plotRatioDensity(f_se, groupings = "annotation.Chromosome", treatment1 = 
"Male", treatment2 = "Female", type = "l", xlab = "Log(Male:Female)",
ylab = "Density", col=c(rep("grey80", 20), "red"), lty = 1)
#> Current order of levels:  15 18 21 13 7 19 8 3 11 16 9 1 17 6 20 10 5 12 4 14 2

Beyond plotting, we also want to know whether there are statistical differences between the groupings indicated. The test_diffs() function summarizes the distributions of expression ratios among groups and applies a non-parametric Kruskal-Wallis test.

za.ratios.test <- test_diffs(f_se, groupings = "annotation.ZA", 
treatment1 = "Male", treatment2 = "Female", LOG2 = FALSE )
#> View output: outlist$kruskal, outlist$summary
za.ratios.test$summary  # summary statistics for each grouping
#>                   A          Z
#> Min.      0.0000000  0.0000000
#> 1st Qu.   0.6788987  0.7821321
#> Median    0.8677571  1.0212513
#> Mean      0.9956633  1.1136910
#> 3rd Qu.   1.0628770  1.2781894
#> Max.     81.7647412  7.6471211
#> NA's    211.0000000 19.0000000
za.ratios.test$kruskal  # htest class output from kruskal.test()
#> 
#>  Kruskal-Wallis rank sum test
#> 
#> data:  tmp
#> Kruskal-Wallis chi-squared = 65.132, df = 1, p-value = 7.003e-16
lapply(za.ratios.test$data, head) # values used for summaries and tests
#> $A
#> HMEL000002 HMEL000003 HMEL000004 HMEL000006 HMEL000007 HMEL000008 
#>  0.8597425  0.3492448  1.6905856  0.4615780  0.0000000  1.3637461 
#> 
#> $Z
#> HMEL002056 HMEL002096 HMEL002142 HMEL002143 HMEL002145 HMEL002156 
#>  1.0500235  3.9418081  1.2663384  1.0861082  0.6493254  1.6593288

Workflow conclusion

As can be seen from these plots and statistics, these data reveal a distinct reduction in absolute expression for Z linked loci, relative to autosomes, for both sexes. Furthermore, there is a modest but statistically significant dosage effect causing a male-bias in the male:female ratio expression on the Z chromosome. The functions support various comparisons between treatments and among any set of gene groupings, as specified in the annotations.

In some cases, when analyzing more than two gene groupings (e.g. across individual chromosomes), users may want to extend statistical analyses to specific pairwise comparisons. For instance, is the average Z expression specifically different from chromosome 14 in particular? Because the Kruskal-Wallis test is a “global” test for inequality among groups (analogous to an ANOVA), you may want to apply a follow-up non-parametric post-hoc test for specific pairwise comparisons after a significant Kruskal-Wallis test. Several such tests, such as the Nemenyi, are implemented in the [PMCMRplus] (https://cran.r-project.org/web/packages/PMCMRplus/index.html) package.