satuRn - vignette
Jeroen Gilis
14/07/2022
Introduction
satuRn is an R package for performing differential transcript usage analyses in bulk and single-cell transcriptomics datasets. The package has three main functions.
The first function,
fitDTU, is used to model transcript usage profiles by means of a quasi-binomial generalized linear model.Second, the
testDTUfunction tests for differential usage of transcripts between certain groups of interest (e.g. different treatment groups or cell types).Finally, the
plotDTUcan be used to visualize the usage profiles of selected transcripts in different groups of interest.
All details about the satuRn model and statistical tests are described in our preprint (Gilis Jeroen 2021).
In this vignette, we analyze a small subset of the data from (Tasic Bosiljka 2018). More specifically, an expression matrix and the corresponding metadata of the subset data has been provided with the satuRn package. We will adopt this dataset to showcase the different functionalities of satuRn.
Package installation
satuRn (version 1.4.0) can be installed from Bioconductor with:
if(!requireNamespace("BiocManager", quietly = TRUE))
install.packages("BiocManager")
BiocManager::install("satuRn")Alternatively, the development version of satuRn can be downloaded with:
devtools::install_github("statOmics/satuRn")! for this vignette, we use the development version of satuRn. The vignette for the officially released satuRn version 1.4.0 can be viewed from Bioconductor
Load libraries
library(satuRn)
library(AnnotationHub)
library(ensembldb)
library(edgeR)
library(SummarizedExperiment)
library(ggplot2)
library(DEXSeq)
library(stageR)Load data
The following data corresponds to a small subset of the dataset from (Tasic Bosiljka 2018) and is readily available from the satuRn package. To check how the subset was generate, please check ?Tasic_counts_vignette.
data(Tasic_counts_vignette) # transcript expression matrix
data(Tasic_metadata_vignette) # metadataData pre-processing
We start the analysis from scratch, in order to additionally showcase some of the prerequisite steps for performing a DTU analysis.
Import transcript information
First, we need an object that links transcripts to their corresponding genes. We suggest using the BioConductor R packages AnnotationHub and ensembldb for this purpose.
ah <- AnnotationHub() # load the annotation resource.
all <- query(ah, "EnsDb") # query for all available EnsDb databases
ahEdb <- all[["AH75036"]] # for Mus musculus (choose correct release date)
txs <- transcripts(ahEdb)Data wrangling
Next, we perform some data wrangling steps to get the data in a format that is suited for satuRn. First, we create a DataFrame or Matrix linking transcripts to their corresponding genes.
! Important: satuRn is implemented such that the columns with transcript identifiers is names isoform_id, while the column containing gene identifiers should be named gene_id. In addition, following chunk removes transcripts that are the only isoform expressed of a certain gene, as they cannot be used in a DTU analysis.
# Get the transcript information in correct format
txInfo <- as.data.frame(matrix(data = NA, nrow = length(txs), ncol = 2))
colnames(txInfo) <- c("isoform_id", "gene_id")
txInfo$isoform_id <- txs$tx_id
txInfo$gene_id <- txs$gene_id
rownames(txInfo) <- txInfo$isoform_id
# Remove transcripts that are the only isoform expressed of a certain gene
rownames(Tasic_counts_vignette) <- sub("\\..*", "",
rownames(Tasic_counts_vignette))
# remove transcript version identifiers
txInfo <- txInfo[txInfo$isoform_id %in% rownames(Tasic_counts_vignette), ]
txInfo <- subset(txInfo,
duplicated(gene_id) | duplicated(gene_id, fromLast = TRUE))
Tasic_counts_vignette <- Tasic_counts_vignette[which(
rownames(Tasic_counts_vignette) %in% txInfo$isoform_id), ]Filtering
Here we perform some feature-level filtering. For this task, we adopt the filtering criterion that is implemented in the R package edgeR. Alternatively, one could adopt the dmFilter criterion from the DRIMSeq R package, which provides a more stringent filtering when both methods are run in default settings. After filtering, we again remove transcripts that are the only isoform expressed of a certain gene.
filter_edgeR <- filterByExpr(Tasic_counts_vignette,
design = NULL,
group = Tasic_metadata_vignette$brain_region,
lib.size = NULL,
min.count = 10,
min.total.count = 30,
large.n = 20,
min.prop = 0.7
) # more stringent than default to reduce run time of the vignette
table(filter_edgeR)## filter_edgeR
## FALSE TRUE
## 5996 10982Tasic_counts_vignette <- Tasic_counts_vignette[filter_edgeR, ]
# Update txInfo according to the filtering procedure
txInfo <- txInfo[which(
txInfo$isoform_id %in% rownames(Tasic_counts_vignette)), ]
# remove txs that are the only isoform expressed within a gene (after filtering)
txInfo <- subset(txInfo,
duplicated(gene_id) | duplicated(gene_id, fromLast = TRUE))
Tasic_counts_vignette <- Tasic_counts_vignette[which(rownames(
Tasic_counts_vignette) %in% txInfo$isoform_id), ]
# satuRn requires the transcripts in the rowData and
# the transcripts in the count matrix to be in the same order.
txInfo <- txInfo[match(rownames(Tasic_counts_vignette), txInfo$isoform_id), ]Create a design matrix
Here we set up the design matrix of the experiment. The subset of the dataset from (Tasic Bosiljka 2018) contains cells of several different cell types (variable cluster) in two different areas of the mouse neocortex (variable brain_region). As such, we can model the data with a factorial design, i.e. by generating a new variable group that encompasses all different cell type - brain region combinations.
Tasic_metadata_vignette$group <- paste(Tasic_metadata_vignette$brain_region,
Tasic_metadata_vignette$cluster,
sep = ".")Generate SummarizedExperiment
All three main functions of satuRn require a SummarizedExperiment object as an input class. See the SummarizedExperiment vignette (Morgan Martin, n.d.) for more information on this object class.
For the sake of completeness, it is advised to include the design matrix formula in the SummarizedExperiment as indicated below.
sumExp <- SummarizedExperiment::SummarizedExperiment(
assays = list(counts = Tasic_counts_vignette),
colData = Tasic_metadata_vignette,
rowData = txInfo
)
# for sake of completeness: specify design formula from colData
metadata(sumExp)$formula <- ~ 0 + as.factor(colData(sumExp)$group)
sumExp## class: SummarizedExperiment
## dim: 9151 60
## metadata(1): formula
## assays(1): counts
## rownames(9151): ENSMUST00000037739 ENSMUST00000228774 ...
## ENSMUST00000127554 ENSMUST00000132683
## rowData names(2): isoform_id gene_id
## colnames(60): F2S4_160622_013_D01 F2S4_160624_023_C01 ...
## F2S4_160919_010_B01 F2S4_160915_002_D01
## colData names(4): sample_name brain_region cluster groupFit quasi-binomial generalized linear models models
The fitDTU function of satuRn is used to model transcript usage in different groups of samples or cells. Here we adopt the default settings of the function. Without parallelized execution, this code runs for approximately 15 seconds on a 2018 macbook pro laptop.
system.time({
sumExp <- satuRn::fitDTU(
object = sumExp,
formula = ~ 0 + group,
parallel = FALSE,
BPPARAM = BiocParallel::bpparam(),
verbose = TRUE
)
})## user system elapsed
## 16.315 0.340 16.655The resulting model fits are now saved into the rowData of our SummarizedExperiment object under the name fitDTUModels. These models can be accessed as follows:
rowData(sumExp)[["fitDTUModels"]]$"ENSMUST00000037739"## An object of class "StatModel"
## Slot "type":
## [1] "glm"
##
## Slot "params":
## $coefficients
## designgroupALM.L5_IT_ALM_Tmem163_Dmrtb1
## 1.612656
## designgroupALM.L5_IT_ALM_Tnc
## 1.773648
## designgroupVISp.L5_IT_VISp_Hsd11b1_Endou
## 1.232522
##
## $df.residual
## [1] 55
##
## $dispersion
## [1] 28.14375
##
## $vcovUnsc
## designgroupALM.L5_IT_ALM_Tmem163_Dmrtb1
## designgroupALM.L5_IT_ALM_Tmem163_Dmrtb1 0.004760564
## designgroupALM.L5_IT_ALM_Tnc 0.000000000
## designgroupVISp.L5_IT_VISp_Hsd11b1_Endou 0.000000000
## designgroupALM.L5_IT_ALM_Tnc
## designgroupALM.L5_IT_ALM_Tmem163_Dmrtb1 0.000000000
## designgroupALM.L5_IT_ALM_Tnc 0.004363295
## designgroupVISp.L5_IT_VISp_Hsd11b1_Endou 0.000000000
## designgroupVISp.L5_IT_VISp_Hsd11b1_Endou
## designgroupALM.L5_IT_ALM_Tmem163_Dmrtb1 0.000000000
## designgroupALM.L5_IT_ALM_Tnc 0.000000000
## designgroupVISp.L5_IT_VISp_Hsd11b1_Endou 0.004042164
##
##
## Slot "varPosterior":
## [1] 27.73976
##
## Slot "dfPosterior":
## [1] 59.4294The models are instances of the StatModel class as defined in the satuRn package. These contain all relevant information for the downstream analysis. For more details, read the StatModel documentation with ?satuRn::StatModel-class.
Test for DTU
Here we test for differential transcript usage between select groups of interest. In this example, the groups of interest are the three different cell types that are present in the dataset associated with this vignette.
Set up contrast matrix
First, we set up a contrast matrix. This allows us to test for differential transcript usage between groups of interest. The group factor in this toy example contains three levels; (1) ALM.L5_IT_ALM_Tmem163_Dmrtb1, (2) ALM.L5_IT_ALM_Tnc, (3) VISp.L5_IT_VISp_Hsd11b1_Endou. Here we show to assess DTU between cells of the groups 1 and 3 and between cells of groups 2 and 3.
The contrast matrix can be constructed manually;
group <- as.factor(Tasic_metadata_vignette$group)
design <- model.matrix(~ 0 + group) # construct design matrix
colnames(design) <- levels(group)
L <- matrix(0, ncol = 2, nrow = ncol(design)) # initialize contrast matrix
rownames(L) <- colnames(design)
colnames(L) <- c("Contrast1", "Contrast2")
L[c("VISp.L5_IT_VISp_Hsd11b1_Endou","ALM.L5_IT_ALM_Tnc"),1] <-c(1,-1)
L[c("VISp.L5_IT_VISp_Hsd11b1_Endou","ALM.L5_IT_ALM_Tmem163_Dmrtb1"),2] <-c(1,-1)
L # contrast matrix## Contrast1 Contrast2
## ALM.L5_IT_ALM_Tmem163_Dmrtb1 0 -1
## ALM.L5_IT_ALM_Tnc -1 0
## VISp.L5_IT_VISp_Hsd11b1_Endou 1 1This can also be done automatically with the makeContrasts function of the limma R package.
group <- as.factor(Tasic_metadata_vignette$group)
design <- model.matrix(~ 0 + group) # construct design matrix
colnames(design) <- levels(group)
L <- limma::makeContrasts(
Contrast1 = VISp.L5_IT_VISp_Hsd11b1_Endou - ALM.L5_IT_ALM_Tnc,
Contrast2 = VISp.L5_IT_VISp_Hsd11b1_Endou - ALM.L5_IT_ALM_Tmem163_Dmrtb1,
levels = design
)
L # contrast matrix## Contrasts
## Levels Contrast1 Contrast2
## ALM.L5_IT_ALM_Tmem163_Dmrtb1 0 -1
## ALM.L5_IT_ALM_Tnc -1 0
## VISp.L5_IT_VISp_Hsd11b1_Endou 1 1Perform the test
Next we can perform differential usage testing using testDTU. We again adopt default settings. For more information on the parameter settings, please consult the help file of the testDTU function. Note that the arguments diagplot1 and diagplot2 were not yet implemented in satuRn v1.1.1.
sumExp <- satuRn::testDTU(
object = sumExp,
contrasts = L,
diagplot1 = TRUE,
diagplot2 = TRUE,
sort = FALSE
)
When set to TRUE, the diagplot1 and diagplot2 arguments generate a diagnostic plot.
For diagplot1, the histogram of the z-scores (computed from p-values) is displayed using the locfdr function of the locfdr package. The blue dashed curve is fitted to the mid 50% of the z-scores, which are assumed to originate from null transcripts, thus representing the estimated empirical null component densities. The maximum likelihood estimates (MLE) and central matching estimates (CME) of this estimated empirical null distribution are given below the plot. If the MLE estimates for delta and sigma deviate from 0 and 1 respectively, the downstream inference will be influenced by the empirical adjustment implemented in satuRn (see below).
For diagplot2, a plot of the histogram of the “empirically adjusted” test statistics and the standard normal distribution will be displayed. Ideally, the majority (mid portion) of the adjusted test statistics should follow the standard normal. If this is not the case, the inference may be untrustworthy and results should be treated with care. One potential solution is to include (additional) potential covariates in the analysis.
The test results are now saved into the rowData of our SummarizedExperiment object under the name fitDTUResult_ followed by the name of the contrast of interest (i.e. the column names of the contrast matrix). The results can be accessed as follows:
head(rowData(sumExp)[["fitDTUResult_Contrast1"]]) # first contrast## estimates se df t pval
## ENSMUST00000037739 -0.5411265 0.4828721 59.4294 -1.1206416 0.26694865
## ENSMUST00000228774 0.5411265 0.4828721 59.4294 1.1206416 0.26694865
## ENSMUST00000025204 0.1929718 0.1952590 61.4294 0.9882864 0.32688926
## ENSMUST00000237499 -0.1929718 0.1952590 61.4294 -0.9882864 0.32688926
## ENSMUST00000042857 -0.8245461 0.4351069 58.4294 -1.8950427 0.06303775
## ENSMUST00000114415 0.8245461 0.4351069 58.4294 1.8950427 0.06303775
## regular_FDR empirical_pval empirical_FDR
## ENSMUST00000037739 0.6450007 0.3952020 0.9769609
## ENSMUST00000228774 0.6450007 0.4148973 0.9797565
## ENSMUST00000025204 0.6977858 0.4727593 0.9834579
## ENSMUST00000237499 0.6977858 0.4515026 0.9808231
## ENSMUST00000042857 0.3566360 0.1579658 0.9152296
## ENSMUST00000114415 0.3566360 0.1685028 0.9203772head(rowData(sumExp)[["fitDTUResult_Contrast2"]]) # second contrast## estimates se df t pval
## ENSMUST00000037739 -0.3801339 0.4941514 59.4294 -0.769266 0.444782126
## ENSMUST00000228774 0.3801339 0.4941514 59.4294 0.769266 0.444782126
## ENSMUST00000025204 0.2971434 0.1921038 61.4294 1.546786 0.127051689
## ENSMUST00000237499 -0.2971434 0.1921038 61.4294 -1.546786 0.127051689
## ENSMUST00000042857 -1.4866500 0.4997583 58.4294 -2.974738 0.004257964
## ENSMUST00000114415 1.4866500 0.4997583 58.4294 2.974738 0.004257964
## regular_FDR empirical_pval empirical_FDR
## ENSMUST00000037739 0.7772316 0.56104440 0.9893602
## ENSMUST00000228774 0.7772316 0.58504064 0.9893602
## ENSMUST00000025204 0.5021149 0.26790898 0.9893602
## ENSMUST00000237499 0.5021149 0.25297843 0.9893602
## ENSMUST00000042857 0.1491038 0.03349528 0.9893602
## ENSMUST00000114415 0.1491038 0.03654226 0.9893602The results for are, for each contrast, a dataframe with 8 columns:
estimates: The estimated log-odds ratios (log base e). In the most simple case, an estimate of +1 would mean that the odds of picking that transcript from the pool of transcripts within its corresponding gene is exp(1) = 2.72 times larger in condition B than in condition A.se: The standard error on this estimate.df: The posterior degrees of freedom for the test statistic.t: The student’s t-test statistic, computed with a Wald test givenestimatesandse.pval: The “raw” p-value giventanddf.FDR: The false discovery rate, computed using the multiple testing correction of Benjamini and Hochberg onpval.empirical_pval: An “empirical” p-value that is computed by estimating the null distribution of the test statistic empirically. For more details, see our publication.empirical_FDR: The false discovery rate, computed using the multiple testing correction of Benjamini and Hochberg onpval_empirical.
!Note: based on the benchmarks in our publication, we always recommend using the empirical p-values from column 7 over the “raw” p-value from column 5. When the MLE estimates for the mean and standard deviation (delta and sigma) of the empirical null density (blue dashed curve in diagplot1) deviate from 0 and 1 respectively, there will be a discrepancy between the “raw” and “empirically adjusted” p-values. A deviation in the standard deviation only affects the magnitude of the p-values, whereas a deviation in the mean also affects the ranking of transcripts according to their p-value.
Visualize DTU
Finally, we may visualize the usage of select transcripts in select groups of interest.
group1 <- colnames(sumExp)[colData(sumExp)$group ==
"VISp.L5_IT_VISp_Hsd11b1_Endou"]
group2 <- colnames(sumExp)[colData(sumExp)$group ==
"ALM.L5_IT_ALM_Tnc"]
plots <- satuRn::plotDTU(
object = sumExp,
contrast = "Contrast1",
groups = list(group1, group2),
coefficients = list(c(0, 0, 1), c(0, 1, 0)),
summaryStat = "model",
transcripts = c("ENSMUST00000081554",
"ENSMUST00000195963",
"ENSMUST00000132062"),
genes = NULL,
top.n = 6
)
# to have same layout as in our paper
for (i in seq_along(plots)) {
current_plot <- plots[[i]] +
scale_fill_manual(labels = c("VISp", "ALM"), values = c("royalblue4",
"firebrick")) +
scale_x_discrete(labels = c("Hsd11b1_Endou", "Tnc"))
print(current_plot)
}
Optional post-processing of results: Two-stage testing procedure with stageR
satuRn returns transcript-level p-values for each of the specified contrasts. While we have shown that satuRn is able to adequately control the false discovery rate (FDR) at the transcript level (Gilis Jeroen 2021), (Van den Berge Koen 2017) argued that it is often desirable to control the FDR at the gene level. This boosts statistical power and eases downstream biological interpretation and validation, which typically occur at the gene level.
To this end, (Van den Berge Koen 2017) developed a testing procedure that is implemented in the BioConductor R package stageR. The procedure consists of two stages; a screening stage and a confirmation stage.
In the screening stage, gene-level FDR-adjusted p-values are computed, which aggregate the evidence for differential transcript usage over all transcripts within the gene. Only genes with an FDR below the desired nominal level are further considered in the second stage. In the confirmation stage, transcript-level p-values are adjusted for those genes, using a FWER-controlling method on the FDR-adjusted significance level.
In its current implementation, stageR can only perform stage-wise testing if only one contrast is of interest in a DTU setting. An analogous correction for the assessment of multiple contrasts for multiple transcripts per gene has not yet been implemented.
Below, we demonstrate how the transcript-level p-values for the first contrast as returned by satuRn can be post-processed using stageR. We rely on the perGeneQValue function:
# transcript level p-values from satuRn
pvals <- rowData(sumExp)[["fitDTUResult_Contrast1"]]$empirical_pval
# compute gene level q-values
geneID <- factor(rowData(sumExp)$gene_id)
geneSplit <- split(seq(along = geneID), geneID)
pGene <- sapply(geneSplit, function(i) min(pvals[i]))
pGene[is.na(pGene)] <- 1
theta <- unique(sort(pGene))
# gene-level significance testing
q <- DEXSeq:::perGeneQValueExact(pGene, theta, geneSplit)
qScreen <- rep(NA_real_, length(pGene))
qScreen <- q[match(pGene, theta)]
qScreen <- pmin(1, qScreen)
names(qScreen) <- names(geneSplit)
# prepare stageR input
tx2gene <- as.data.frame(rowData(sumExp)[c("isoform_id", "gene_id")])
colnames(tx2gene) <- c("transcript", "gene")
pConfirmation <- matrix(matrix(pvals),
ncol = 1,
dimnames = list(rownames(tx2gene), "transcript")
)
# create a stageRTx object
stageRObj <- stageR::stageRTx(
pScreen = qScreen,
pConfirmation = pConfirmation,
pScreenAdjusted = TRUE,
tx2gene = tx2gene
)
# perform the two-stage testing procedure
stageRObj <- stageR::stageWiseAdjustment(
object = stageRObj,
method = "dtu",
alpha = 0.05,
allowNA = TRUE
)
# retrieves the adjusted p-values from the stageRTx object
padj <- stageR::getAdjustedPValues(stageRObj,
order = TRUE,
onlySignificantGenes = FALSE
)## The returned adjusted p-values are based on a stage-wise testing approach and are only valid for the provided target OFDR level of 5%. If a different target OFDR level is of interest,the entire adjustment should be re-run.head(padj)## geneID txID gene transcript
## 1 ENSMUSG00000058013 ENSMUST00000201421 0.03732585 0.05697406
## 2 ENSMUSG00000058013 ENSMUST00000201700 0.03732585 1.00000000
## 3 ENSMUSG00000058013 ENSMUST00000074733 0.03732585 1.00000000
## 4 ENSMUSG00000058013 ENSMUST00000202217 0.03732585 1.00000000
## 5 ENSMUSG00000058013 ENSMUST00000202196 0.03732585 1.00000000
## 6 ENSMUSG00000058013 ENSMUST00000202308 0.03732585 1.00000000Session
sessionInfo()## R version 4.2.1 (2022-06-23)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.4 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.15-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.15-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] stageR_1.18.0 DEXSeq_1.42.0
## [3] RColorBrewer_1.1-3 DESeq2_1.36.0
## [5] BiocParallel_1.30.3 ggplot2_3.3.6
## [7] SummarizedExperiment_1.26.1 MatrixGenerics_1.8.1
## [9] matrixStats_0.62.0 edgeR_3.38.4
## [11] limma_3.52.2 ensembldb_2.20.2
## [13] AnnotationFilter_1.20.0 GenomicFeatures_1.48.3
## [15] AnnotationDbi_1.58.0 Biobase_2.56.0
## [17] GenomicRanges_1.48.0 GenomeInfoDb_1.32.2
## [19] IRanges_2.30.0 S4Vectors_0.34.0
## [21] AnnotationHub_3.4.0 BiocFileCache_2.4.0
## [23] dbplyr_2.2.1 BiocGenerics_0.42.0
## [25] satuRn_1.4.2 knitr_1.39
##
## loaded via a namespace (and not attached):
## [1] colorspace_2.0-3 hwriter_1.3.2.1
## [3] rjson_0.2.21 ellipsis_0.3.2
## [5] XVector_0.36.0 farver_2.1.1
## [7] bit64_4.0.5 interactiveDisplayBase_1.34.0
## [9] fansi_1.0.3 xml2_1.3.3
## [11] codetools_0.2-18 splines_4.2.1
## [13] cachem_1.0.6 geneplotter_1.74.0
## [15] jsonlite_1.8.0 locfdr_1.1-8
## [17] Rsamtools_2.12.0 annotate_1.74.0
## [19] png_0.1-7 shiny_1.7.2
## [21] BiocManager_1.30.18 compiler_4.2.1
## [23] httr_1.4.3 assertthat_0.2.1
## [25] Matrix_1.4-1 fastmap_1.1.0
## [27] lazyeval_0.2.2 cli_3.3.0
## [29] later_1.3.0 htmltools_0.5.3
## [31] prettyunits_1.1.1 tools_4.2.1
## [33] gtable_0.3.0 glue_1.6.2
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## [45] mime_0.12 lifecycle_1.0.1
## [47] restfulr_0.0.15 statmod_1.4.36
## [49] XML_3.99-0.10 zlibbioc_1.42.0
## [51] scales_1.2.0 hms_1.1.1
## [53] promises_1.2.0.1 ProtGenerics_1.28.0
## [55] parallel_4.2.1 yaml_2.3.5
## [57] curl_4.3.2 memoise_2.0.1
## [59] pbapply_1.5-0 sass_0.4.2
## [61] biomaRt_2.52.0 stringi_1.7.8
## [63] RSQLite_2.2.15 highr_0.9
## [65] genefilter_1.78.0 BiocVersion_3.15.2
## [67] BiocIO_1.6.0 filelock_1.0.2
## [69] boot_1.3-28 rlang_1.0.4
## [71] pkgconfig_2.0.3 bitops_1.0-7
## [73] evaluate_0.15 lattice_0.20-45
## [75] purrr_0.3.4 labeling_0.4.2
## [77] GenomicAlignments_1.32.1 bit_4.0.4
## [79] tidyselect_1.1.2 magrittr_2.0.3
## [81] R6_2.5.1 generics_0.1.3
## [83] DelayedArray_0.22.0 DBI_1.1.3
## [85] withr_2.5.0 pillar_1.8.0
## [87] survival_3.3-1 KEGGREST_1.36.3
## [89] RCurl_1.98-1.8 tibble_3.1.8
## [91] crayon_1.5.1 utf8_1.2.2
## [93] rmarkdown_2.14 progress_1.2.2
## [95] locfit_1.5-9.6 grid_4.2.1
## [97] blob_1.2.3 digest_0.6.29
## [99] xtable_1.8-4 httpuv_1.6.5
## [101] munsell_0.5.0 bslib_0.4.0References
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Tasic Bosiljka, Lucas T. Graybuck, Zizhen Yao. 2018. “Shared and distinct transcriptomic cell types across neocortical areas.” Nature, 72–78. https://doi.org/10.1038/s41586-018-0654-5.
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