aggregateBioVar 1.4.0
# For analysis of scRNAseq data
library(aggregateBioVar)
library(SummarizedExperiment, quietly = TRUE)
library(SingleCellExperiment, quietly = TRUE)
library(DESeq2, quietly = TRUE)
# For data transformation and visualization
library(magrittr, quietly = TRUE)
library(dplyr, quietly = TRUE)
library(ggplot2, quietly = TRUE)
library(cowplot, quietly = TRUE)
library(ggtext, quietly = TRUE)
Single cell RNA sequencing (scRNA-seq) studies allow gene expression
quantification at the level of individual cells, and these studies introduce
multiple layers of biological complexity. These include variations in gene
expression between cell states within a sample
(e.g., T cells versus macrophages), between samples within a population
(e.g., biological or technical replicates), and between populations
(e.g., healthy versus diseased individuals).
Because many early scRNA-seq studies involved analysis of only a single sample,
many bioinformatics tools operate on the first layer, comparing gene expression
between cells within a sample.
This software is aimed at organizing scRNA-seq data to permit analysis in the
latter two layers, comparing gene expression between samples and between
populations. An example is given with an implementation of differential
gene expression analysis between populations. From scRNA-seq data stored as a
SingleCellExperiment
(Lun and Risso, 2020) object
with pre-defined cell states, aggregateBioVar()
stratifies data as a list of
SummarizedExperiment
(Morgan et al., 2020) objects,
a standard Bioconductor data structure for
downstream analysis of RNA-seq data.
To illustrate the utility of biological replication for scRNA-seq
sequencing experiments, consider a set of single cell data from
porcine small airway epithelium. In this study, small airway (< 2 mm) tissue
samples were collected from newborn pigs (Sus scrofa) to
investigate gene expression patterns and cellular composition in a cystic
fibrosis phenotype. Single cell sequencing samples were prepared using a 10X
Genomics Chromium controller and sequenced on an Illumina HiSeq4000. Data
obtained from seven individuals include both non-CF
(CFTR+/+; genotype WT
; n=4) and CFTR-knockout subjects expressing a
cystic fibrosis phenotype (CFTR-/-; genotype CFTRKO
; n=3).
Cell types were determined following a standard scRNA-seq pipeline using
Seurat (Stuart et al., 2019), including cell count
normalization, scaling, determination of highly variable genes,
dimension reduction via principal components analysis, and shared
nearest neighbor clustering. Both unsupervised marker detection
(via Seurat::FindMarkers()
) and a list of known marker genes were used to
annotate cell types. The full data set has been uploaded to the
Gene Expression Omnibus
as accession number GSE150211.
small_airway
DatasetA subset of 1339 genes from 2722 cells
assigned as secretory, endothelial, and immune cell types are available in the
small_airway
data set.
The data are formatted as a SingleCellExperiment
class S4 object
(Amezquita et al., 2020), an extension of the
RangedSummarizedExperiment
class from the SummarizedExperiment
package.
small_airway
#> class: SingleCellExperiment
#> dim: 1339 2722
#> metadata(0):
#> assays(1): counts
#> rownames(1339): MPC1 PRKN ... OTOP1 UNC80
#> rowData names(0):
#> colnames(2722): SWT1_AAAGAACAGACATAAC SWT1_AAAGGATTCTCCGAAA ...
#> SCF3_TTTGGAGGTAAGGCTG SCF3_TTTGGTTCAATAGTAG
#> colData names(6): orig.ident nCount_RNA ... Region celltype
#> reducedDimNames(0):
#> mainExpName: NULL
#> altExpNames(0):
The primary data in SingleCellExperiment
objects are stored in the assays
slot. Here, a single assay counts
contains gene counts from the single cell
sequencing data. Each column of the assay count matrix represents a cell and
each row a feature (e.g., gene).
Assay slot data can be obtained by SummarizedExperiment::assay()
, indicating
theSingleCellExperiment
object and name of the assay slot (here, "counts"
).
In the special case of the assay being named "counts"
, the data can be
accessed with SingleCellExperiment::counts()
.
assays(small_airway)
#> List of length 1
#> names(1): counts
# Dimensions of gene-by-cell count matrix
dim(counts(small_airway))
#> [1] 1339 2722
# Access dgCMatrix with gene counts
counts(small_airway)[1:5, 1:30]
#> 5 x 30 sparse Matrix of class "dgCMatrix"
#> [[ suppressing 30 column names 'SWT1_AAAGAACAGACATAAC', 'SWT1_AAAGGATTCTCCGAAA', 'SWT1_AAAGGTATCCACGTAA' ... ]]
#>
#> MPC1 . 1 2 8 15 4 . 1 7 3 . 3 1 4 3 1 7 8 4 2 2 1 3 2 4 . 3 2 3 2
#> PRKN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> SLC22A3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
#> CNKSR3 . . 1 . 1 . . . . . . . . . . . 1 . 1 . . . 2 . . . . . . 3
#> UTRN 2 2 . 4 6 1 . . 1 . 3 6 1 4 1 . 9 2 1 8 1 1 12 5 4 1 2 5 1 14
SingleCellExperiment
objects may also include column metadata with
additional information annotating individual cells.
Here, the metadata variable orig.ident
identifies the biological sample of the
cell while celltype
indicates the assigned cellular identity.
Of the 7 individual
subjects, 3 are CF (SCF1, SCF2, SCF3) and 4 are non-CF (SWT1, SWT2, SWT3, SWT4).
Genotype
indicates the sample genotype, one of WT
or CFTRKO
for non-CF and
CF subjects, respectively.
Column metadata from SingleCellExperiment
objects can be accessed with the $
operator, where the length of a metadata column variable is equal to the number
of columns (i.e., cells) in the feature count matrix from the assays
slot.
# Subject values
table(small_airway$orig.ident)
#>
#> SCF1 SCF2 SCF3 SWT1 SWT2 SWT3 SWT4
#> 450 283 758 324 294 258 355
# Cell type values
table(small_airway$celltype)
#>
#> Endothelial cell Immune cell Secretory cell
#> 915 585 1222
# Subject genotype
table(small_airway$Genotype)
#>
#> CFTRKO WT
#> 1491 1231
The experiment metadata are included as an S4 DataFrame
object.
To access the full column metadata from SingleCellExperiment
objects, use
colData()
from the SummarizedExperiment
package.
Here, metadata include
6 variables for each of
2722 cells.
In addition to the biological sample identifier, cell type, and genotype,
metadata include total unique molecular identifiers (UMIs) and
number of detected features.
colData(small_airway)
#> DataFrame with 2722 rows and 6 columns
#> orig.ident nCount_RNA nFeature_RNA Genotype
#> <character> <numeric> <integer> <character>
#> SWT1_AAAGAACAGACATAAC SWT1 594 169 WT
#> SWT1_AAAGGATTCTCCGAAA SWT1 1133 301 WT
#> SWT1_AAAGGTATCCACGTAA SWT1 1204 281 WT
#> SWT1_AACACACCAATCCTTT SWT1 1998 365 WT
#> SWT1_AACCACAGTTACTCAG SWT1 3268 427 WT
#> ... ... ... ... ...
#> SCF3_TTTGGAGAGCAGTAAT SCF3 1953 301 CFTRKO
#> SCF3_TTTGGAGAGCGTCTGC SCF3 215 95 CFTRKO
#> SCF3_TTTGGAGCATATACCG SCF3 1154 234 CFTRKO
#> SCF3_TTTGGAGGTAAGGCTG SCF3 703 187 CFTRKO
#> SCF3_TTTGGTTCAATAGTAG SCF3 2319 360 CFTRKO
#> Region celltype
#> <character> <factor>
#> SWT1_AAAGAACAGACATAAC Small Immune cell
#> SWT1_AAAGGATTCTCCGAAA Small Secretory cell
#> SWT1_AAAGGTATCCACGTAA Small Secretory cell
#> SWT1_AACACACCAATCCTTT Small Secretory cell
#> SWT1_AACCACAGTTACTCAG Small Secretory cell
#> ... ... ...
#> SCF3_TTTGGAGAGCAGTAAT Small Secretory cell
#> SCF3_TTTGGAGAGCGTCTGC Small Secretory cell
#> SCF3_TTTGGAGCATATACCG Small Secretory cell
#> SCF3_TTTGGAGGTAAGGCTG Small Secretory cell
#> SCF3_TTTGGTTCAATAGTAG Small Secretory cell
The main functionality of this package involves two generalizable operations:
A wrapper function aggregateBioVar()
abstracts away these operations
and applies them on a by-cell type basis. For input, a SingleCellExperiment
object containing gene counts should contain metadata variables for the
subject by which to aggregate cells (e.g., biological sample) and the assigned
cell types.
The first operation involves summing all gene counts by subject. For each gene, counts from all cells within each subject are combined. A gene-by-cell count matrix is converted into a gene-by-subject count matrix.
countsBySubject(scExp = small_airway, subjectVar = "orig.ident")
#> DataFrame with 1339 rows and 7 columns
#> SWT1 SWT2 SWT3 SCF1 SCF2 SWT4 SCF3
#> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric> <numeric>
#> MPC1 977 1039 1053 1100 889 712 2907
#> PRKN 2 0 13 4 3 3 18
#> SLC22A3 13 4 19 10 18 1 13
#> CNKSR3 170 172 400 245 242 249 324
#> UTRN 1322 1060 1355 1617 730 979 1338
#> ... ... ... ... ... ... ... ...
#> CNNM1 0 0 0 0 0 0 0
#> GABRQ 0 0 0 0 0 0 1
#> GIF 0 0 0 0 0 0 0
#> OTOP1 0 0 0 0 0 0 0
#> UNC80 0 0 0 0 0 0 0
The second operation removes metadata variables with intrasubject variation. This effectively retains inter-subject metadata and eliminates variables with intrasubject (i.e., intercellular) variation (e.g., feature or gene counts by cell). This summarized metadata is used for modeling a differential expression design matrix.
subjectMetaData(scExp = small_airway, subjectVar = "orig.ident")
#> DataFrame with 7 rows and 3 columns
#> orig.ident Genotype Region
#> <character> <character> <character>
#> SWT1 SWT1 WT Small
#> SWT2 SWT2 WT Small
#> SWT3 SWT3 WT Small
#> SCF1 SCF1 CFTRKO Small
#> SCF2 SCF2 CFTRKO Small
#> SWT4 SWT4 WT Small
#> SCF3 SCF3 CFTRKO Small
SummarizedExperiment
Both the gene count aggregation and metadata collation steps are combined in
summarizedCounts()
. This function returns a SummarizedExperiment
object with
the gene-by-subject count matrix in the assays
slot, and the summarized
inter-subject metadata as colData
. Notice the column names now correspond
to the subject level, replacing the cellular barcodes in the
SingleCellExperiment
following aggregation of gene counts from
within-subject cells.
summarizedCounts(scExp = small_airway, subjectVar = "orig.ident")
#> class: SummarizedExperiment
#> dim: 1339 7
#> metadata(0):
#> assays(1): counts
#> rownames(1339): MPC1 PRKN ... OTOP1 UNC80
#> rowData names(0):
#> colnames(7): SWT1 SWT2 ... SWT4 SCF3
#> colData names(3): orig.ident Genotype Region
aggregateBioVar()
These operations are applied to each cell type subset with aggregateBioVar()
.
The full SingleCellExperiment
object is subset by cell type (e.g.,
secretory, endothelial, and immune cell), the gene-by-subject aggregate count
matrix and collated metadata are tabulated, and a SummarizedExperiment
object for that cell type is constructed. A list of SummarizedExperiment
objects output by summarizedCounts()
is the returned to the user. The first
element contains the aggregate SummarizedExperiment
across all cells, and
subsequent list elements correspond to the cell type indicated by the metadata
variable cellVar
:
aggregateBioVar(scExp = small_airway,
subjectVar = "orig.ident", cellVar = "celltype")
#> Coercing metadata variable to character: celltype
#> $AllCells
#> class: SummarizedExperiment
#> dim: 1339 7
#> metadata(0):
#> assays(1): counts
#> rownames(1339): MPC1 PRKN ... OTOP1 UNC80
#> rowData names(0):
#> colnames(7): SWT1 SWT2 ... SWT4 SCF3
#> colData names(3): orig.ident Genotype Region
#>
#> $`Immune cell`
#> class: SummarizedExperiment
#> dim: 1339 7
#> metadata(0):
#> assays(1): counts
#> rownames(1339): MPC1 PRKN ... OTOP1 UNC80
#> rowData names(0):
#> colnames(7): SWT1 SWT2 ... SWT4 SCF3
#> colData names(4): orig.ident Genotype Region celltype
#>
#> $`Secretory cell`
#> class: SummarizedExperiment
#> dim: 1339 7
#> metadata(0):
#> assays(1): counts
#> rownames(1339): MPC1 PRKN ... OTOP1 UNC80
#> rowData names(0):
#> colnames(7): SWT1 SWT2 ... SWT4 SCF3
#> colData names(4): orig.ident Genotype Region celltype
#>
#> $`Endothelial cell`
#> class: SummarizedExperiment
#> dim: 1339 7
#> metadata(0):
#> assays(1): counts
#> rownames(1339): MPC1 PRKN ... OTOP1 UNC80
#> rowData names(0):
#> colnames(7): SWT1 SWT2 ... SWT4 SCF3
#> colData names(4): orig.ident Genotype Region celltype
In this case, we want to test for differential
expression between non-CF and CF pigs in the Secretory cell
subset.
To do so, aggregateBioVar()
is run on the SingleCellExperiment
object
by indicated the metadata variables representing the subject-level
(subjectVar
) and assigned cell type (cellVar
).
If multiple assays are included in the input scExp
object,
the first assay slot is used.
# Perform aggregation of counts and metadata by subject and cell type.
aggregate_counts <-
aggregateBioVar(
scExp = small_airway,
subjectVar = "orig.ident", cellVar = "celltype"
)
#> Coercing metadata variable to character: celltype
To visualize the gene-by-subject count aggregation, consider a function to
calculate log2 counts per million cells and display a heatmap
of normalized expression using pheatmap
(Kolde, 2019).
RColorBrewer
(Neuwirth, 2014) and viridis
(Garnier, 2018) are used to
generate discrete and continuous color scales, respectively.
#' Single-cell Counts `pheatmap`
#'
#' @param sumExp `SummarizedExperiment` or `SingleCellExperiment` object
#' with individual cell or aggregate counts by-subject.
#' @param logSample Subset of log2 values to include for clustering.
#' @param ... Forwarding arguments to pheatmap
#' @inheritParams aggregateBioVar
#'
scPHeatmap <- function(sumExp, subjectVar, gtVar, logSample = 1:100, ...) {
orderSumExp <- sumExp[, order(sumExp[[subjectVar]])]
sumExpCounts <- as.matrix(
SummarizedExperiment::assay(orderSumExp, "counts")
)
logcpm <- log2(
1e6*t(t(sumExpCounts) / colSums(sumExpCounts)) + 1
)
annotations <- data.frame(
Genotype = orderSumExp[[gtVar]],
Subject = orderSumExp[[subjectVar]]
)
rownames(annotations) <- colnames(orderSumExp)
singleCellpHeatmap <- pheatmap::pheatmap(
mat = logcpm[logSample, ], annotation_col = annotations,
cluster_cols = FALSE, show_rownames = FALSE, show_colnames = FALSE,
scale = "none", ...
)
return(singleCellpHeatmap)
}
Without aggregation, bulk RNA-seq methods for differential expression analysis would be applied at the cell level (here, secretory cells; Figure 1).
# Subset `SingleCellExperiment` secretory cells.
sumExp <- small_airway[, small_airway$celltype == "Secretory cell"]
# List of annotation color specifications for pheatmap.
ann_colors <- list(
Genotype = c(CFTRKO = "red", WT = "black"),
Subject = c(RColorBrewer::brewer.pal(7, "Accent"))
)
ann_names <- unique(sumExp[["orig.ident"]])
names(ann_colors$Subject) <- ann_names[order(ann_names)]
# Heatmap of log2 expression across all cells.
scPHeatmap(
sumExp = sumExp, logSample = 1:100,
subjectVar = "orig.ident", gtVar = "Genotype",
color = viridis::viridis(75), annotation_colors = ann_colors,
treeheight_row = 0, treeheight_col = 0
)
Summation of gene counts across all cells creates a “pseudo-bulk” data set on which a subject-level test of differential expression is applied (Figure 2).
# List of `SummarizedExperiment` objects with aggregate subject counts.
scExp <-
aggregateBioVar(
scExp = small_airway,
subjectVar = "orig.ident", cellVar = "celltype"
)
#> Coercing metadata variable to character: celltype
# Heatmap of log2 expression from aggregate gene-by-subject count matrix.
scPHeatmap(
sumExp = aggregate_counts$`Secretory cell`, logSample = 1:100,
subjectVar = "orig.ident", gtVar = "Genotype",
color = viridis::viridis(75), annotation_colors = ann_colors,
treeheight_row = 0, treeheight_col = 0
)
To run DESeq2
(Love et al., 2014), a DESeqDataSet
object can be
constructed using DESeqDataSetFromMatrix()
.
Here, the aggregate counts and subject metadata from the secretory cell subset
are modeled by the variable Genotype
.
Differential expression analysis is performed with DESeq
and a results table
is extracted by results()
to obtain log2 fold changes with p-values and
adjusted p-values.
subj_dds_dataset <-
DESeqDataSetFromMatrix(
countData = assay(aggregate_counts$`Secretory cell`, "counts"),
colData = colData(aggregate_counts$`Secretory cell`),
design = ~ Genotype
)
#> converting counts to integer mode
#> Warning in DESeqDataSet(se, design = design, ignoreRank): some variables in
#> design formula are characters, converting to factors
subj_dds <- DESeq(subj_dds_dataset)
#> estimating size factors
#> estimating dispersions
#> gene-wise dispersion estimates
#> mean-dispersion relationship
#> final dispersion estimates
#> fitting model and testing
subj_dds_results <-
results(subj_dds, contrast = c("Genotype", "WT", "CFTRKO"))
For comparison of differential expression with and without aggregation of
gene-by-subject counts, a subset of all secretory cells is used to construct
a DESeqDataSet
and analysis of differential expression is repeated.
cells_secretory <-
small_airway[, which(
as.character(small_airway$celltype) == "Secretory cell")]
cells_secretory$Genotype <- as.factor(cells_secretory$Genotype)
cell_dds_dataset <-
DESeqDataSetFromMatrix(
countData = assay(cells_secretory, "counts"),
colData = colData(cells_secretory),
design = ~ Genotype
)
#> converting counts to integer mode
cell_dds <- DESeq(cell_dds_dataset)
#> estimating size factors
#> estimating dispersions
#> gene-wise dispersion estimates
#> mean-dispersion relationship
#> -- note: fitType='parametric', but the dispersion trend was not well captured by the
#> function: y = a/x + b, and a local regression fit was automatically substituted.
#> specify fitType='local' or 'mean' to avoid this message next time.
#> final dispersion estimates
#> fitting model and testing
#> -- replacing outliers and refitting for 2 genes
#> -- DESeq argument 'minReplicatesForReplace' = 7
#> -- original counts are preserved in counts(dds)
#> estimating dispersions
#> fitting model and testing
cell_dds_results <-
results(cell_dds, contrast = c("Genotype", "WT", "CFTRKO"))
Add a new variable with log10-transformed adjusted P-values.
subj_dds_transf <- as.data.frame(subj_dds_results) %>%
bind_cols(feature = rownames(subj_dds_results)) %>%
mutate(log_padj = - log(.data$padj, base = 10))
cell_dds_transf <- as.data.frame(cell_dds_results) %>%
bind_cols(feature = rownames(cell_dds_results)) %>%
mutate(log_padj = - log(.data$padj, base = 10))
DGE is summarized by volcano plot ggplot
(Wickham and Chang et al., 2020) to show cell-level
(Figure 3A)
and subject-level tests (Figure 3B).
Aggregation of gene counts by subject reduced the number of genes with both
an adjusted p-value < 0.05 and an absolute log2 fold change > 1 from
65 genes to 2 (Figure 3).
# Function to add theme for ggplots of DESeq2 results.
deseq_themes <- function() {
list(
theme_classic(),
lims(x = c(-4, 5), y = c(0, 80)),
labs(
x = "log<sub>2</sub> (fold change)",
y = "-log<sub>10</sub> (p<sub>adj</sub>)"
),
ggplot2::theme(
axis.title.x = ggtext::element_markdown(),
axis.title.y = ggtext::element_markdown())
)
}
# Build ggplots to visualize subject-level differential expression in scRNA-seq
ggplot_full <- ggplot(data = cell_dds_transf) +
geom_point(aes(x = log2FoldChange, y = log_padj), na.rm = TRUE) +
geom_point(
data = filter(
.data = cell_dds_transf,
abs(.data$log2FoldChange) > 1, .data$padj < 0.05
),
aes(x = log2FoldChange, y = log_padj), color = "red"
) +
deseq_themes()
ggplot_subj <- ggplot(data = subj_dds_transf) +
geom_point(aes(x = log2FoldChange, y = log_padj), na.rm = TRUE) +
geom_point(
data = filter(
.data = subj_dds_transf,
abs(.data$log2FoldChange) > 1, .data$padj < 0.05
),
aes(x = log2FoldChange, y = log_padj), color = "red"
) +
geom_label(
data = filter(
.data = subj_dds_transf,
abs(.data$log2FoldChange) > 1, .data$padj < 0.05
),
aes(x = log2FoldChange + 0.5, y = log_padj + 5, label = feature)
) +
deseq_themes()
cowplot::plot_grid(ggplot_full, ggplot_subj, ncol = 2, labels = c("A", "B"))
From the significantly differentially expressed genes CFTR and CD36, the aggregate counts by subject are plotted in Figure 4.
# Extract counts subset by gene to plot normalized counts.
ggplot_counts <- function(dds_obj, gene) {
norm_counts <-
counts(dds_obj, normalized = TRUE)[grepl(gene, rownames(dds_obj)), ]
sc_counts <-
data.frame(
norm_count = norm_counts,
subject = colData(dds_obj)[["orig.ident"]],
genotype = factor(
colData(dds_obj)[["Genotype"]],
levels = c("WT", "CFTRKO")
)
)
count_ggplot <- ggplot(data = sc_counts) +
geom_jitter(
aes(x = genotype, y = norm_count, color = genotype),
height = 0, width = 0.05
) +
scale_color_manual(
"Genotype", values = c("WT" = "blue", "CFTRKO" = "red")
) +
lims(x = c("WT", "CFTRKO"), y = c(0, 350)) +
labs(x = "Genotype", y = "Normalized Counts") +
ggtitle(label = gene) +
theme_classic()
return(count_ggplot)
}
cowplot::plot_grid(
ggplot_counts(dds_obj = subj_dds, gene = "CFTR") +
theme(legend.position = "FALSE"),
ggplot_counts(dds_obj = subj_dds, gene = "CD36") +
theme(legend.position = "FALSE"),
cowplot::get_legend(
plot = ggplot_counts(dds_obj = subj_dds, gene = "CD36")
),
ncol = 3, rel_widths = c(4, 4, 1)
)
Amezquita,R. et al. (2020) Orchestrating single-cell analysis with bioconductor. Nature Methods, 17, 137–145.
Bache,S.M. and Wickham,H. (2014) magrittr: A forward-pipe operator for r.
Garnier,S. (2018) viridis: Default color maps from ’matplotlib’.
Kolde,R. (2019) pheatmap: Pretty heatmaps.
Love,M.I. et al. (2014) Moderated estimation of fold change and dispersion for RNA-seq data with DESeq2. Genome Biology, 15, 550.
Lun,A. and Risso,D. (2020) SingleCellExperiment: S4 classes for single cell data.
Morgan,M. et al. (2020) SummarizedExperiment: SummarizedExperiment container.
Neuwirth,E. (2014) RColorBrewer: ColorBrewer palettes.
Stuart,T. et al. (2019) Comprehensive integration of single-cell data. Cell, 177, 1888–1902.
Wickham,H. et al. (2020) ggplot2: Create elegant data visualisations using the grammar of graphics.
Wickham,H. et al. (2020) dplyr: A grammar of data manipulation.
Wilke,C.O. (2019) cowplot: Streamlined plot theme and plot annotations for ’ggplot2’.
Wilke,C.O. (2020) ggtext: Improved text rendering support for ’ggplot2’.
sessionInfo()
#> R version 4.1.1 (2021-08-10)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 20.04.3 LTS
#>
#> Matrix products: default
#> BLAS: /home/biocbuild/bbs-3.14-bioc/R/lib/libRblas.so
#> LAPACK: /home/biocbuild/bbs-3.14-bioc/R/lib/libRlapack.so
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_GB 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] stats4 stats graphics grDevices utils datasets methods
#> [8] base
#>
#> other attached packages:
#> [1] ggtext_0.1.1 cowplot_1.1.1
#> [3] ggplot2_3.3.5 dplyr_1.0.7
#> [5] magrittr_2.0.1 DESeq2_1.34.0
#> [7] SingleCellExperiment_1.16.0 SummarizedExperiment_1.24.0
#> [9] Biobase_2.54.0 GenomicRanges_1.46.0
#> [11] GenomeInfoDb_1.30.0 IRanges_2.28.0
#> [13] S4Vectors_0.32.0 BiocGenerics_0.40.0
#> [15] MatrixGenerics_1.6.0 matrixStats_0.61.0
#> [17] aggregateBioVar_1.4.0 BiocStyle_2.22.0
#>
#> loaded via a namespace (and not attached):
#> [1] bitops_1.0-7 bit64_4.0.5 RColorBrewer_1.1-2
#> [4] httr_1.4.2 tools_4.1.1 bslib_0.3.1
#> [7] utf8_1.2.2 R6_2.5.1 DBI_1.1.1
#> [10] colorspace_2.0-2 withr_2.4.2 gridExtra_2.3
#> [13] tidyselect_1.1.1 bit_4.0.4 compiler_4.1.1
#> [16] xml2_1.3.2 DelayedArray_0.20.0 labeling_0.4.2
#> [19] bookdown_0.24 sass_0.4.0 scales_1.1.1
#> [22] genefilter_1.76.0 stringr_1.4.0 digest_0.6.28
#> [25] rmarkdown_2.11 XVector_0.34.0 pkgconfig_2.0.3
#> [28] htmltools_0.5.2 highr_0.9 fastmap_1.1.0
#> [31] rlang_0.4.12 RSQLite_2.2.8 farver_2.1.0
#> [34] jquerylib_0.1.4 generics_0.1.1 jsonlite_1.7.2
#> [37] BiocParallel_1.28.0 RCurl_1.98-1.5 GenomeInfoDbData_1.2.7
#> [40] Matrix_1.3-4 Rcpp_1.0.7 munsell_0.5.0
#> [43] fansi_0.5.0 viridis_0.6.2 lifecycle_1.0.1
#> [46] stringi_1.7.5 yaml_2.2.1 zlibbioc_1.40.0
#> [49] grid_4.1.1 blob_1.2.2 parallel_4.1.1
#> [52] crayon_1.4.1 lattice_0.20-45 Biostrings_2.62.0
#> [55] splines_4.1.1 annotate_1.72.0 gridtext_0.1.4
#> [58] KEGGREST_1.34.0 magick_2.7.3 locfit_1.5-9.4
#> [61] knitr_1.36 pillar_1.6.4 markdown_1.1
#> [64] geneplotter_1.72.0 XML_3.99-0.8 glue_1.4.2
#> [67] evaluate_0.14 BiocManager_1.30.16 png_0.1-7
#> [70] vctrs_0.3.8 gtable_0.3.0 purrr_0.3.4
#> [73] assertthat_0.2.1 cachem_1.0.6 xfun_0.27
#> [76] xtable_1.8-4 viridisLite_0.4.0 survival_3.2-13
#> [79] pheatmap_1.0.12 tibble_3.1.5 AnnotationDbi_1.56.0
#> [82] memoise_2.0.0 ellipsis_0.3.2