Single-cell analysis toolkit for expression in R
Revised: November 2, 2019
Package
scater 1.14.6
1 Introduction
This document gives an introduction to and overview of the quality control functionality of the scater package.
scater contains tools to help with the analysis of single-cell transcriptomic data,
focusing on low-level steps such as quality control, normalization and visualization.
It is based on the SingleCellExperiment class (from the SingleCellExperiment package),
and thus is interoperable with many other Bioconductor packages such as scran, batchelor and iSEE.
Note: A more comprehensive description of the use of scater (along with other packages) in a scRNA-seq analysis workflow is available at https://osca.bioconductor.org.
2 Setting up the data
2.1 Generating a SingleCellExperiment object
We assume that you have a matrix containing expression count data summarised at the level of some features (gene, exon, region, etc.).
First, we create a SingleCellExperiment object containing the data, as demonstrated below with a famous brain dataset.
Rows of the object correspond to features, while columns correspond to samples, i.e., cells in the context of single-cell ’omics data.
library(scRNAseq)
example_sce <- ZeiselBrainData()
example_sce## class: SingleCellExperiment
## dim: 20006 3005
## metadata(0):
## assays(1): counts
## rownames(20006): Tspan12 Tshz1 ... mt-Rnr1 mt-Nd4l
## rowData names(1): featureType
## colnames(3005): 1772071015_C02 1772071017_G12 ... 1772066098_A12
## 1772058148_F03
## colData names(10): tissue group # ... level1class level2class
## reducedDimNames(0):
## spikeNames(0):
## altExpNames(2): ERCC repeatWe usually expect (raw) count data to be labelled as "counts" in the assays, which can be easily retrieved with the counts accessor.
Getters and setters are also provided for exprs, tpm, cpm, fpkm and versions of these with the prefix norm_.
str(counts(example_sce))Row and column-level metadata are easily accessed (or modified) as shown below.
There are also dedicated getters and setters for size factor values (sizeFactors()); reduced dimensionality results (reducedDim()); and alternative experimental features (altExp()).
example_sce$whee <- sample(LETTERS, ncol(example_sce), replace=TRUE)
colData(example_sce)## DataFrame with 3005 rows and 11 columns
## tissue group # total mRNA mol well sex
## <character> <numeric> <numeric> <numeric> <numeric>
## 1772071015_C02 sscortex 1 1221 3 3
## 1772071017_G12 sscortex 1 1231 95 1
## 1772071017_A05 sscortex 1 1652 27 1
## 1772071014_B06 sscortex 1 1696 37 3
## 1772067065_H06 sscortex 1 1219 43 3
## ... ... ... ... ... ...
## 1772067059_B04 ca1hippocampus 9 1997 19 1
## 1772066097_D04 ca1hippocampus 9 1415 21 1
## 1772063068_D01 sscortex 9 1876 34 3
## 1772066098_A12 ca1hippocampus 9 1546 88 1
## 1772058148_F03 sscortex 9 1970 15 3
## age diameter cell_id level1class level2class
## <numeric> <numeric> <character> <character> <character>
## 1772071015_C02 2 1 1772071015_C02 interneurons Int10
## 1772071017_G12 1 353 1772071017_G12 interneurons Int10
## 1772071017_A05 1 13 1772071017_A05 interneurons Int6
## 1772071014_B06 2 19 1772071014_B06 interneurons Int10
## 1772067065_H06 6 12 1772067065_H06 interneurons Int9
## ... ... ... ... ... ...
## 1772067059_B04 4 382 1772067059_B04 endothelial-mural Peric
## 1772066097_D04 7 12 1772066097_D04 endothelial-mural Vsmc
## 1772063068_D01 7 268 1772063068_D01 endothelial-mural Vsmc
## 1772066098_A12 7 324 1772066098_A12 endothelial-mural Vsmc
## 1772058148_F03 7 6 1772058148_F03 endothelial-mural Vsmc
## whee
## <character>
## 1772071015_C02 F
## 1772071017_G12 A
## 1772071017_A05 H
## 1772071014_B06 X
## 1772067065_H06 X
## ... ...
## 1772067059_B04 T
## 1772066097_D04 H
## 1772063068_D01 K
## 1772066098_A12 E
## 1772058148_F03 YrowData(example_sce)$stuff <- runif(nrow(example_sce))
rowData(example_sce)## DataFrame with 20006 rows and 2 columns
## featureType stuff
## <character> <numeric>
## Tspan12 endogenous 0.531340830726549
## Tshz1 endogenous 0.245747287524864
## Fnbp1l endogenous 0.841682275990024
## Adamts15 endogenous 0.47632492124103
## Cldn12 endogenous 0.631566006690264
## ... ... ...
## mt-Co2 mito 0.542126515181735
## mt-Co1 mito 0.915390015114099
## mt-Rnr2 mito 0.665483738295734
## mt-Rnr1 mito 0.612728938227519
## mt-Nd4l mito 0.610844046343118Subsetting is very convenient with this class, as both data and metadata are processed in a synchronized manner.
More details about the SingleCellExperiment class can be found in the documentation for SingleCellExperiment package.
2.2 Other methods of data import
Count matrices stored as CSV files or equivalent can be easily read into R session using read.table() from utils or fread() from the data.table package.
It is advisable to coerce the resulting object into a matrix before storing it in a SingleCellExperiment object.
For large data sets, the matrix can be read in chunk-by-chunk with progressive coercion into a sparse matrix from the Matrix package.
This is performed using the readSparseCounts() function and reduces memory usage by not explicitly storing zeroes in memory.
Data from 10X Genomics experiments can be read in using the read10xCounts function from the DropletUtils package.
This will automatically generate a SingleCellExperiment with a sparse matrix, see the documentation for more details.
Transcript abundances from the kallisto and Salmon pseudo-aligners can be imported using methods from the tximeta package.
This produces a SummarizedExperiment object that can be coerced into a SingleCellExperiment simply with as(se, "SingleCellExperiment").
3 Quality control
3.1 Background
scater provides functionality for three levels of quality control (QC):
- QC and filtering of cells
- QC and filtering of features (genes)
- QC of experimental variables
3.2 Cell-level QC
3.2.1 Definition of metrics
Cell-level metrics are computed by the perCellQCMetrics() function and include:
sum: total number of counts for the cell (i.e., the library size).detected: the number of features for the cell that have counts above the detection limit (default of zero).subsets_X_percent: percentage of all counts that come from the feature control set namedX.
library(scater)
per.cell <- perCellQCMetrics(example_sce,
subsets=list(Mito=grep("mt-", rownames(example_sce))))
summary(per.cell$sum)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2574 8130 12913 14954 19284 63505summary(per.cell$detected)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 785 2484 3656 3777 4929 8167summary(per.cell$subsets_Mito_percent)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 3.992 6.653 7.956 10.290 56.955It is often convenient to store this in the colData() of our SingleCellExperiment object for future reference.
(In fact, the addPerCellQC() function will do this automatically.)
colData(example_sce) <- cbind(colData(example_sce), per.cell)3.2.2 Diagnostic plots
Metadata variables can be plotted against each other using the plotColData() function, as shown below.
We expect to see an increasing number of detected genes with increasing total count.
Each point represents a cell that is coloured according to its tissue of origin.
plotColData(example_sce, x = "sum", y="detected", colour_by="tissue") 
Here, we have plotted the total count for each cell against the mitochondrial content. Well-behaved cells should have a large number of expressed features and and a low percentage of expression from feature controls. High percentage expression from feature controls and few expressed features are indicative of blank and failed cells. For some variety, we have faceted by the tissue of origin.
plotColData(example_sce, x = "sum", y="subsets_Mito_percent",
other_fields="tissue") + facet_wrap(~tissue)
3.2.3 Identifying low-quality cells
Column subsetting of the SingeCellExperiment object will only retain the selected cells, thus removing low-quality or otherwise unwanted cells.
We can identify high-quality cells to retain by setting a fixed threshold on particular metrics.
For example, we could retain only cells that have at least 100,000 total counts and at least 500 expressed features:
keep.total <- example_sce$sum > 1e5
keep.n <- example_sce$detected > 500
filtered <- example_sce[,keep.total & keep.n]
dim(filtered)## [1] 20006 0The isOutlier function provides a more data-adaptive way of choosing these thresholds.
This defines the threshold at a certain number of median absolute deviations (MADs) away from the median.
Values beyond this threshold are considered outliers and can be filtered out, assuming that they correspond to low-quality cells.
Here, we define small outliers (using type="lower") for the log-total counts at 3 MADs from the median.
keep.total <- isOutlier(per.cell$sum, type="lower", log=TRUE)
filtered <- example_sce[,keep.total]Detection of outliers can be achieved more conveniently for several common metrics using the quickPerCellQC() function.
This uses the total count, number of detected features and the percentage of counts in gene sets of diagnostic value
(e.g., mitochondrial genes, spike-in transcripts) to identify which cells to discard and for what reason.
qc.stats <- quickPerCellQC(per.cell, percent_subsets="subsets_Mito_percent")
colSums(as.matrix(qc.stats))## low_lib_size low_n_features high_subsets_Mito_percent
## 0 3 128
## discard
## 131filtered <- example_sce[,!qc.stats$discard]The isOutlier approach adjusts to experiment-specific aspects of the data, e.g., sequencing depth, amount of spike-in RNA added, cell type.
In contrast, a fixed threshold would require manual adjustment to account for changes to the experimental protocol or system.
We refer readers to the simpleSingleCell workflow for more details.
3.3 Feature-level QC
3.3.1 Definition of metrics
Feature-level metrics are computed by the perFeatureQCMetrics() function and include:
mean: the mean count of the gene/feature across all cells.detected: the percentage of cells with non-zero counts for each gene.subsets_Y_ratio: ratio of mean counts between the cell control set named Y and all cells.
# Pretending that the first 10 cells are empty wells, for demonstration.
per.feat <- perFeatureQCMetrics(example_sce, subsets=list(Empty=1:10))
summary(per.feat$mean)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0007 0.0097 0.1338 0.7475 0.5763 732.1524summary(per.feat$detected)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.03328 0.76539 9.01830 18.87800 31.24792 99.96672summary(per.feat$subsets_Empty_ratio)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.000 0.000 0.601 1.872 2.016 300.500A more refined calculation of the average is provided by the calculateAverage() function,
which adjusts the counts by the relative library size (or size factor) prior to taking the mean.
ave <- calculateAverage(example_sce)
summary(ave)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0002 0.0109 0.1443 0.7475 0.5674 850.6880We can also compute the number of cells expressing a gene directly.
summary(nexprs(example_sce, byrow=TRUE))## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.0 23.0 271.0 567.3 939.0 3004.03.3.2 Diagnostic plots
We look at a plot that shows the top 50 (by default) most-expressed features.
Each row in the plot below corresponds to a gene, and each bar corresponds to the expression of a gene in a single cell.
The circle indicates the median expression of each gene, with which genes are sorted.
By default, “expression” is defined using the feature counts (if available), but other expression values can be used instead by changing exprs_values.
plotHighestExprs(example_sce, exprs_values = "counts")
We expect to see the “usual suspects”, i.e., mitochondrial genes, actin, ribosomal protein, MALAT1. A few spike-in transcripts may also be present here, though if all of the spike-ins are in the top 50, it suggests that too much spike-in RNA was added. A large number of pseudo-genes or predicted genes may indicate problems with alignment.
3.3.3 Subsetting by row
Genes can be removed by row subsetting of the SingleCellExperiment object.
For example, we can filter out features (genes) that are not expressed in any cells:
keep_feature <- nexprs(example_sce, byrow=TRUE) > 0
example_sce <- example_sce[keep_feature,]
dim(example_sce)## [1] 20006 3005Other filtering can be done using existing annotation. For example, ribosomal protein genes and predicted genes can be identified (and removed) using regular expressions or biotype information. Such genes are often uninteresting when the aim is to characterize population heterogeneity.
3.4 Variable-level QC
Variable-level metrics are computed by the getVarianceExplained() function (after normalization, see below).
This calculates the percentage of variance of each gene’s expression that is explained by each variable in the colData of the SingleCellExperiment object.
example_sce <- logNormCounts(example_sce) # see below.
vars <- getVarianceExplained(example_sce,
variables=c("tissue", "total mRNA mol", "sex", "age"))
head(vars)## tissue total mRNA mol sex age
## Tspan12 0.02207262 0.074086504 0.146344996 0.09472155
## Tshz1 3.36083014 0.003846487 0.001079356 0.31262288
## Fnbp1l 0.43597185 0.421086301 0.003071630 0.64964174
## Adamts15 0.54233888 0.005348505 0.030821621 0.01393787
## Cldn12 0.03506751 0.309128294 0.008341408 0.02363737
## Rxfp1 0.18559637 0.016290703 0.055646799 0.02128006We can then use this to determine which experimental factors are contributing most to the variance in expression. This is useful for diagnosing batch effects or to quickly verify that a treatment has an effect.
plotExplanatoryVariables(vars)
4 Computing expression values
4.1 Normalization for library size differences
The most commonly used function is logNormCounts(), which calculates log2-transformed normalized expression values.
This is done by dividing each count by its size factor, adding a pseudo-count and log-transforming.
The resulting values can be interpreted on the same scale as log-transformed counts, and are stored in "logcounts".
example_sce <- logNormCounts(example_sce)
assayNames(example_sce)## [1] "counts" "logcounts"By default, the size factor is automatically computed from the library size of each cell using the librarySizeFactors() function.
This calculation simply involves scaling the library sizes so that they have a mean of 1 across all cells.
However, if size factors are explicitly provided in the SingleCellExperiment, they will be used by the normalization functions.
summary(librarySizeFactors(example_sce))## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1721 0.5437 0.8635 1.0000 1.2895 4.2466Alternatively, we can calculate counts-per-million using the aptly-named calculateCPM() function.
The output is most appropriately stored as an assay named "cpm" in the assays of the SingleCellExperiment object.
Related functions include calculateTPM() and calculateFPKM(), which do pretty much as advertised.
cpm(example_sce) <- calculateCPM(example_sce)Of course, users can construct any arbitrary matrix of the same dimensions as the count matrix and store it as an assay.
assay(example_sce, "normed") <- normalizeCounts(example_sce,
size_factors=runif(ncol(example_sce)), pseudo_count=1.5)4.2 Visualizing expression values
The plotExpression() function makes it easy to plot expression values for a subset of genes or features.
This can be particularly useful for further examination of features identified from differential expression testing, pseudotime analysis or other analyses.
By default, it uses expression values in the "logcounts" assay, but this can be changed through the exprs_values argument.
plotExpression(example_sce, rownames(example_sce)[1:6], x = "level1class")
Setting x will determine the covariate to be shown on the x-axis.
This can be a field in the column metadata or the name of a feature (to obtain the expression profile across cells).
Categorical covariates will yield grouped violins as shown above, with one panel per feature.
By comparison, continuous covariates will generate a scatter plot in each panel, as shown below.
plotExpression(example_sce, rownames(example_sce)[1:6],
x = rownames(example_sce)[10])
The points can also be coloured, shaped or resized by the column metadata or expression values.
plotExpression(example_sce, rownames(example_sce)[1:6],
x = "level1class", colour_by="tissue")
Directly plotting the gene expression without any x or other visual parameters will generate a set of grouped violin plots, coloured in an aesthetically pleasing manner.
plotExpression(example_sce, rownames(example_sce)[1:6])
5 Dimensionality reduction
5.1 Principal components analysis
Principal components analysis (PCA) is often performed to denoise and compact the data prior to downstream analyses.
The runPCA() function provides a simple wrapper around the base machinery in BiocSingular for computing PCs from log-transformed expression values.
This stores the output in the reducedDims slot of the SingleCellExperiment, which can be easily retrieved (along with the percfentage of variance explained by each PC) as shown below:
example_sce <- runPCA(example_sce)
str(reducedDim(example_sce, "PCA"))## num [1:3005, 1:50] 15.4 15 17.2 16.9 18.4 ...
## - attr(*, "dimnames")=List of 2
## ..$ : chr [1:3005] "1772071015_C02" "1772071017_G12" "1772071017_A05" "1772071014_B06" ...
## ..$ : chr [1:50] "PC1" "PC2" "PC3" "PC4" ...
## - attr(*, "percentVar")= num [1:50] 39.72 9.38 4.25 3.9 2.76 ...By default, runPCA() uses the top 500 genes with the highest variances to compute the first PCs.
This can be tuned by specifying subset_row to pass in an explicit set of genes of interest,
and by using ncomponents to determine the number of components to compute.
The name argument can also be used to change the name of the result in the reducedDims slot.
example_sce <- runPCA(example_sce, name="PCA2",
subset_row=rownames(example_sce)[1:1000],
ncomponents=25)
str(reducedDim(example_sce, "PCA2"))## num [1:3005, 1:25] 20 21 23 23.7 21.5 ...
## - attr(*, "dimnames")=List of 2
## ..$ : chr [1:3005] "1772071015_C02" "1772071017_G12" "1772071017_A05" "1772071014_B06" ...
## ..$ : chr [1:25] "PC1" "PC2" "PC3" "PC4" ...
## - attr(*, "percentVar")= num [1:25] 22.3 5.11 3.42 1.69 1.58 ...5.2 Other dimensionality reduction methods
\(t\)-distributed stochastic neighbour embedding (\(t\)-SNE) is widely used for visualizing complex single-cell data sets.
The same procedure described for PCA plots can be applied to generate \(t\)-SNE plots using plotTSNE, with coordinates obtained using runTSNE via the Rtsne package.
We strongly recommend generating plots with different random seeds and perplexity values, to ensure that any conclusions are robus
t to different visualizations.
# Perplexity of 10 just chosen here arbitrarily.
set.seed(1000)
example_sce <- runTSNE(example_sce, perplexity=10)
head(reducedDim(example_sce, "TSNE"))## [,1] [,2]
## 1772071015_C02 -49.70928 -12.34376
## 1772071017_G12 -52.60643 -10.83418
## 1772071017_A05 -49.34541 -12.32723
## 1772071014_B06 -52.17084 -10.59969
## 1772067065_H06 -51.75725 -10.20202
## 1772071017_E02 -52.71614 -10.29159A more common pattern involves using the pre-existing PCA results as input into the \(t\)-SNE algorithm. This is useful as it improves speed by using a low-rank approximation of the expression matrix; and reduces random noise, by focusing on the major factors of variation. The code below uses the first 10 dimensions of the previously computed PCA result to perform the \(t\)-SNE.
set.seed(1000)
example_sce <- runTSNE(example_sce, perplexity=50,
dimred="PCA", n_dimred=10)
head(reducedDim(example_sce, "TSNE"))## [,1] [,2]
## 1772071015_C02 -37.91782 0.77874503
## 1772071017_G12 -35.71181 0.02937304
## 1772071017_A05 -38.31355 1.25472517
## 1772071014_B06 -38.34157 -0.43358953
## 1772067065_H06 -40.73331 -1.10637835
## 1772071017_E02 -38.59131 2.41607361The same can be done for uniform manifold with approximate projection (UMAP) via the runUMAP() function, itself based on the uwot package.
example_sce <- runUMAP(example_sce)
head(reducedDim(example_sce, "UMAP"))## [,1] [,2]
## 1772071015_C02 -13.13473 -2.747997
## 1772071017_G12 -13.20766 -2.790565
## 1772071017_A05 -13.01717 -2.715320
## 1772071014_B06 -13.17852 -2.794246
## 1772067065_H06 -13.22176 -2.828697
## 1772071017_E02 -13.21017 -2.8100265.3 Visualizing reduced dimensions
Any dimensionality reduction result can be plotted using the plotReducedDim function.
Here, each point represents a cell and is coloured according to its cell type label.
plotReducedDim(example_sce, dimred = "PCA", colour_by = "level1class")
Some result types have dedicated wrappers for convenience, e.g., plotTSNE() for \(t\)-SNE results:
plotTSNE(example_sce, colour_by = "Snap25")
The dedicated plotPCA() function also adds the percentage of variance explained to the axes:
plotPCA(example_sce, colour_by="Mog")
Multiple components can be plotted in a series of pairwise plots. When more than two components are plotted, the diagonal boxes in the scatter plot matrix show the density for each component.
example_sce <- runPCA(example_sce, ncomponents=20)
plotPCA(example_sce, ncomponents = 4, colour_by = "level1class")
We separate the execution of these functions from the plotting to enable the same coordinates to be re-used across multiple plots. This avoids repeatedly recomputing those coordinates just to change an aesthetic across plots.
6 Transitioning from the SCESet class
As of July 2017, scater has switched from the SCESet class previously defined within the package to the more widely applicable SingleCellExperiment class.
From Bioconductor 3.6 (October 2017), the release version of scater will use SingleCellExperiment.
SingleCellExperiment is a more modern and robust class that provides a common data structure used by many single-cell Bioconductor packages.
Advantages include support for sparse data matrices and the capability for on-disk storage of data to minimise memory usage for large single-cell datasets.
It should be straight-forward to convert existing scripts based on SCESet objects to SingleCellExperiment objects, with key changes outlined immediately below.
- The functions
toSingleCellExperimentandupdateSCESet(for backwards compatibility) can be used to convert an oldSCESetobject to aSingleCellExperimentobject; - Create a new
SingleCellExperimentobject with the functionSingleCellExperiment(actually less fiddly than creating a newSCESet); scaterfunctions have been refactored to takeSingleCellExperimentobjects, so once data is in aSingleCellExperimentobject, the user experience is almost identical to that with theSCESetclass.
Users may need to be aware of the following when updating their own scripts:
- Cell names can now be accessed/assigned with the
colnamesfunction (instead ofsampleNamesorcellNamesfor anSCESetobject); - Feature (gene/transcript) names should now be accessed/assigned with the
rownamesfunction (instead offeatureNames); - Cell metadata, stored as
phenoDatain anSCESet, corresponds tocolDatain aSingleCellExperimentobject and is accessed/assigned with thecolDatafunction (this replaces thepDatafunction); - Individual cell-level variables can still be accessed with the
$operator (e.g.sce$sum); - Feature metadata, stored as
featureDatain anSCESet, corresponds torowDatain aSingleCellExperimentobject and is accessed/assigned with therowDatafunction (this replaces thefDatafunction); plotScater, which produces a cumulative expression, overview plot, replaces the genericplotfunction forSCESetobjects.
Session information
sessionInfo()## R version 3.6.1 (2019-07-05)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.3 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.10-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.10-bioc/R/lib/libRlapack.so
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 LC_COLLATE=C
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] parallel stats4 stats graphics grDevices utils datasets
## [8] methods base
##
## other attached packages:
## [1] scater_1.14.6 ggplot2_3.2.1
## [3] scRNAseq_2.0.2 SingleCellExperiment_1.8.0
## [5] SummarizedExperiment_1.16.0 DelayedArray_0.12.0
## [7] BiocParallel_1.20.0 matrixStats_0.55.0
## [9] Biobase_2.46.0 GenomicRanges_1.38.0
## [11] GenomeInfoDb_1.22.0 IRanges_2.20.1
## [13] S4Vectors_0.24.1 BiocGenerics_0.32.0
## [15] BiocStyle_2.14.2
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## loaded via a namespace (and not attached):
## [1] bitops_1.0-6 bit64_0.9-7
## [3] httr_1.4.1 tools_3.6.1
## [5] backports_1.1.5 R6_2.4.1
## [7] irlba_2.3.3 vipor_0.4.5
## [9] uwot_0.1.5 DBI_1.1.0
## [11] lazyeval_0.2.2 colorspace_1.4-1
## [13] withr_2.1.2 tidyselect_0.2.5
## [15] gridExtra_2.3 bit_1.1-14
## [17] curl_4.3 compiler_3.6.1
## [19] BiocNeighbors_1.4.1 labeling_0.3
## [21] bookdown_0.16 scales_1.1.0
## [23] rappdirs_0.3.1 stringr_1.4.0
## [25] digest_0.6.23 rmarkdown_2.0
## [27] XVector_0.26.0 pkgconfig_2.0.3
## [29] htmltools_0.4.0 dbplyr_1.4.2
## [31] fastmap_1.0.1 rlang_0.4.2
## [33] RSQLite_2.1.4 FNN_1.1.3
## [35] shiny_1.4.0 DelayedMatrixStats_1.8.0
## [37] farver_2.0.1 dplyr_0.8.3
## [39] RCurl_1.95-4.12 magrittr_1.5
## [41] BiocSingular_1.2.0 GenomeInfoDbData_1.2.2
## [43] Matrix_1.2-18 Rcpp_1.0.3
## [45] ggbeeswarm_0.6.0 munsell_0.5.0
## [47] viridis_0.5.1 lifecycle_0.1.0
## [49] stringi_1.4.3 yaml_2.2.0
## [51] zlibbioc_1.32.0 plyr_1.8.5
## [53] Rtsne_0.15 BiocFileCache_1.10.2
## [55] AnnotationHub_2.18.0 grid_3.6.1
## [57] blob_1.2.0 promises_1.1.0
## [59] ExperimentHub_1.12.0 crayon_1.3.4
## [61] lattice_0.20-38 cowplot_1.0.0
## [63] zeallot_0.1.0 knitr_1.26
## [65] pillar_1.4.2 reshape2_1.4.3
## [67] glue_1.3.1 BiocVersion_3.10.1
## [69] evaluate_0.14 RcppParallel_4.4.4
## [71] BiocManager_1.30.10 vctrs_0.2.0
## [73] httpuv_1.5.2 gtable_0.3.0
## [75] purrr_0.3.3 assertthat_0.2.1
## [77] xfun_0.11 rsvd_1.0.2
## [79] mime_0.7 xtable_1.8-4
## [81] RSpectra_0.16-0 later_1.0.0
## [83] viridisLite_0.3.0 tibble_2.1.3
## [85] AnnotationDbi_1.48.0 beeswarm_0.2.3
## [87] memoise_1.1.0 interactiveDisplayBase_1.24.0