Introduction to single-cell RNA-seq analysis
Cluster marker genes
1 Introduction
In order to aid the interpretation of the clustering results that we covered in the previous section, it is helpful to identify genes that contribute to the separation of cells into those clusters.
The main approach to achieve this, is to identify genes that are differently expressed between clusters. These may be, for example, exclusively expressed in a single cluster or perhaps differentiate between a few different clusters. There are different methods to identify expression differences between clusters: using mean expression level, or the ranking of the gene by its expression, or the proportions of cells that express the gene.
Our main objective in this section is to cover some of the methods that can be used to achieve this goal, and obtain a summary table of results. As always, the OSCA chapter on marker detection contains additional detail and advice.
2 Load data
library(scater)
library(scran)
library(tidyverse)
library(patchwork)We will use the data set generated in the clustering session. This contains 7 samples from the Caron data set. For the purposes of these materials, in the interests of time, each sample has been downsampled to only contain 500 cells.
sce <- readRDS("R_objects/Caron_clustered.500.rds")Note that we have also replaced the gene names (rownames) of our
objects to use common gene names instead of Ensembl IDs. This was done
using the uniquifyFeatureNames() function, which makes this
safely by avoiding duplicate gene names.
rownames(sce)[11:20]## [1] "ENSG00000230699" "ENSG00000241180" "SAMD11" "NOC2L"
## [5] "KLHL17" "PLEKHN1" "ENSG00000272512" "HES4"
## [9] "ISG15" "ENSG00000224969"For this demonstration we will investigate the clustering generated
using the Leiden clustering algorithm with k set to 25. The
results of this clustering have been added to a column in the
colData called “label” using the
colLabels() accessor. The advantage of this is that should
we later decide to use a different clustering or labels (such as cell
types), we can simply change the contents of this column and there would
be no need to modify any subsequent code.
Double check that the “label” column contains the clustering that we are interested in:
all(sce$k.25_cluster.fun.leiden == sce$label)## [1] TRUETo remind ourselves, we can visualise the clusters on a UMAP:
plotReducedDim(sce,
dimred = "UMAP_corrected",
colour_by = "label",
text_by = "label")
Our objective is to identify genes that distinguish these clusters from one another - “cluster marker genes”. Intuitively we hope that the clusters relate to specific cell populations, and therefore we are trying to find genes that will allow us to identify the cell types for each cluster.
3 Identifying cluster marker genes
Although we have defined our clusters based on the batch-corrected
expression values, these should not be used for for
gene-based analyses like marker gene detection. Instead, we should
use the uncorrected (normalised) expression values for
differential expression between clusters. This is because data
integration algorithms bring cells together based on their overall gene
expression, but for each gene individually the data transformation may
introduce artificial agreement between batches, which is not ideal for
gene-level differential analysis. Furthermore, the severity of these
biases is dependent on the parameters used for data integration (such as
the number of nearest neighbours in the fastMNN()
method).
Valid assays to use in gene based differential analysis tests are the
normalised counts obtained from the deconvolution method (using
scuttle::computePooledFactors() +
scuttle::logNormCounts()) or from the variance stabilising
transformation method (using sctransform::vst()). In our
SCE object, we have the normalised counts in the “logcounts” assay,
which we can access with assay(sce, "logcounts") (or using
the shortcut logcounts(sce)).
3.1 Pairwise Cluster Comparisons
The basic approach for marker gene identification across clusters is
to perform statistical tests for each gene between every pair of
clusters. The scoreMarkers() function can do this for us,
while accounting for known factors (aka “blocking factors” or “blocks”),
such as sample batch.
The scoreMarkers() function outputs a list of
DataFrame objects, one for each cluster compared to all
others. However, note that the blocking assumes that each pair of
clusters is present in at least one of the blocks. If there are two
clusters which are not both present in at least one block (in our case
Samples), then that pairwise comparison will by necessity be
omitted.
By default the scoreMarkers() function will use the
log-normalised counts as stored in the “logcounts” assay slot of the
single cell object, so there is no need for us to specify it.
markers <- scoreMarkers(sce,
groups = sce$label,
block = sce$SampleName)The returned object is a list of the same length as the number of clusters. We can access the results for a particular cluster thus:
c11_markers <- as.data.frame(markers[["11"]])
head(c11_markers)## self.average other.average self.detected other.detected
## MIR1302-2HG 0.0058065358 4.812855e-05 0.003156631 5.624403e-05
## ENSG00000238009 -0.0002061329 5.748472e-04 0.000847385 1.809860e-03
## ENSG00000239945 0.0000000000 0.000000e+00 0.000000000 6.308085e-19
## ENSG00000241860 -0.0030043795 5.134732e-03 0.000443748 3.279929e-03
## LINC01409 0.0512661529 5.568810e-02 0.021700188 3.344729e-02
## LINC00115 0.0085735810 3.532380e-03 0.010286262 5.154984e-03
## mean.logFC.cohen min.logFC.cohen median.logFC.cohen
## MIR1302-2HG 0.05880487 0.0000000 0.06634459
## ENSG00000238009 -0.02339459 -0.1934260 0.00000000
## ENSG00000239945 0.00000000 0.0000000 0.00000000
## ENSG00000241860 -0.01987293 -0.1415663 0.00000000
## LINC01409 0.01389695 -0.3617223 0.01231636
## LINC00115 0.06025578 -0.1238139 0.06712619
## max.logFC.cohen rank.logFC.cohen mean.AUC min.AUC median.AUC
## MIR1302-2HG 0.1065338 3720 0.5016808 0.5000000 0.5018963
## ENSG00000238009 0.0000000 7217 0.4982228 0.4838812 0.5000000
## ENSG00000239945 0.0000000 7217 0.5000000 0.5000000 0.5000000
## ENSG00000241860 0.0000000 7217 0.4989907 0.4923018 0.5000000
## LINC01409 0.3220065 2887 0.4937806 0.4413265 0.4982456
## LINC00115 0.1494991 2747 0.5013645 0.4875843 0.5025367
## max.AUC rank.AUC mean.logFC.detected min.logFC.detected
## MIR1302-2HG 0.5030451 1500 1.472314e-01 0.000000e+00
## ENSG00000238009 0.5000000 5107 -7.538337e-02 -5.802781e-01
## ENSG00000239945 0.5000000 3397 -2.363895e-18 -1.574028e-16
## ENSG00000241860 0.5000000 3397 -1.319287e-01 -1.015435e+00
## LINC01409 0.5274056 2321 -1.425490e-01 -1.173020e+00
## LINC00115 0.5060901 1920 1.360324e-01 -4.036879e-01
## median.logFC.detected max.logFC.detected rank.logFC.detected
## MIR1302-2HG 0.08453121 4.291304e-01 843
## ENSG00000238009 0.00000000 2.984922e-16 4878
## ENSG00000239945 0.00000000 2.984922e-16 3123
## ENSG00000241860 0.00000000 2.984922e-16 3123
## LINC01409 -0.14347109 6.419939e-01 2850
## LINC00115 0.11201129 6.760815e-01 1288This DataFrame contains the results for cluster 10. The first four columns contain summary statistics:
- self.average - the mean log-expression in the cluster of interest
- other.average - the grand mean across all other clusters
- self.detected - the proportion of cells with detected expression in the cluster of interest
- other.detected - the mean detected proportion across all other clusters.
The remaining columns contain summaries of three scores from the pairwise comparisons. The three scores are:
- logFC.cohen - “Cohen’s d” - this is the log fold change of mean gene expression standardized by the average standard deviation across the groups. This can be interpreted in a similar way to log fold change in that a positive value indicates upregulation in the cluster of interest.
- AUC - “Area Under the Curve” - this quantifies the ability to distinguish between two gene expression distributions. It can be interpreted as the likelihood that any random cell in the cluster of interest will have a higher expression of the gene than any random cell in the other cluster. It ranges from 0 to 1, where 1 can be interpreted as upregulation, 0 downregulation, and 0.5 as no difference.
- logFC.detected - this is the log fold change in the proportion of cells in which the gene is detected in the cluster of interest, versus the proportion of cells in which the gene is detected in the other cluster. Positive values indicate that the gene is detected in more cells in the cluster of interest than the other cluster. Note, this takes no account of the magnitude of the gene expression, instead this metric helps to identify presence/absence differences in gene expression between clusters.
More detail on the differences between these effect size scores can be found in the “Advanced” Marker detection chapter of the OSCA book.
Whilst all the pairwise scores can be retrieved by adding the
argument full.stats=TRUE to scoreMarkers(), by
default this function returns 5 summary statistics for each score:
- mean.X - this is the mean of the score across all pairwise comparisons. It gives the relative expression of the gene versus the average of the other clusters.
- min.X - this is the minimum score obtained across all pairwise comparisons. This is the most stringent summary statistic for detecting upregulated genes, if the score is high, then the gene is upregulated in the cluster of interest relative to all other clusters. Conversely, if the minimum is low, then the gene is downregulated relative to at least one other cluster.
- median.X - this is the median of the score across all pairwise comparisons. It is more robust to outliers than the mean. Whilst this is beneficial in avoiding the situation where the effect size is very large in only a small number of comparisons, it may conversely be detrimental to marker gene selection if there are small number of clusters with very similar effect sizes, as these will be effectively ignored.
- max.X - this is the maximum score obtained across all pairwise comparisons. This is the least stringent summary statistic for detecting upregulated genes as a high score only indicates that the gene is upregulated in the cluster of interest relative to at least one other clusters. Conversely, if the maximum is low, then the gene is downregulated relative to all other clusters.
- rank.X - This is the minimum ranking (“min-rank”) of that gene by that score across all clusters. For each pairwise comparison the genes are ranked according to the score, this summary provides the lowest rank for that gene across all comparisons. Essentially, a gene with a low “min-rank” will be one of the best genes according to that score in at least one comparison.
The choice of the summary used for ranking will effect the stringency of the selection. See the the OSCA books “Basic” chapter on Marker gene detection for further discussion of these different summaries. In general the mean and median make reasonable defaults for most applications. In practice, the minimum and maximum are most helpful for diagnosing discrepancies between the mean and median, rather than being used directly for ranking.
Selecting genes based on a given min-rank, say 5, is useful as it will generate a list of genes that is the union of genes with a rank of 5 or less for any pairwise comparison. This will ensure we get at least 5 genes that distinguish the cluster of interest from all other clusters.
For example using the min-rank for Cohen’s d on cluster 11 yields 20 marker genes:
c11_markers %>%
select(contains("cohen")) %>%
filter(rank.logFC.cohen <= 5) %>%
arrange(rank.logFC.cohen)## mean.logFC.cohen min.logFC.cohen median.logFC.cohen max.logFC.cohen
## AFF3 3.25870277 0.69008443 3.8346605 6.471031
## RPL31 -0.09994739 -1.99649292 -0.6766480 5.326897
## PDE4D 1.99824242 0.71314029 1.5266268 5.594555
## HLA-DRA 2.22816415 -0.17608376 1.6821743 5.317244
## BACH2 3.67263198 1.22912829 3.3564255 8.222750
## MALAT1 0.50524467 -1.70929511 0.6948744 2.084685
## TCL1A 2.82247394 0.81521639 3.2679577 3.580502
## ACSM3 3.04628449 1.94488956 3.1064336 3.928327
## STMN1 0.75305511 -1.81015247 0.9095560 1.650125
## CD74 1.64891950 -0.95454470 1.3520531 5.580450
## CYFIP2 1.21556536 -0.02973559 0.4391526 5.031653
## IGHM 2.84314360 0.08892430 2.6737644 4.967655
## CD79B 3.35174185 1.14853534 4.1286815 5.339618
## RPL10 0.23172959 -1.97234509 -0.1514261 5.090278
## RPS27 -0.21057717 -3.33173460 -0.4042201 4.241107
## CD38 2.08460193 0.65236005 1.8410490 4.907691
## SOX4 1.37967424 0.02979486 1.5566225 2.107456
## CD37 1.37473653 -0.47465698 1.2607056 2.905559
## ZEB2 1.52564919 -0.04630776 1.4328534 3.554641
## PTMA 1.38147498 -1.66770463 1.3342330 4.021871
## SYK 2.47114862 1.16231458 1.7748956 4.076403
## PCDH9 2.54637768 1.38217294 2.5542254 4.736472
## IGLL5 2.19243742 1.13494446 2.3929550 3.150657
## MME 1.34922293 -0.07171903 1.5193523 2.077086
## ATP8A1 1.43524343 0.51940673 0.9753260 4.236140
## RPL34 -0.15027017 -2.44879073 -0.3168768 4.000928
## EBF1 1.93686777 0.14803564 2.6587363 3.220915
## NIBAN3 2.44818551 0.90006097 2.7889517 3.622804
## rank.logFC.cohen
## AFF3 1
## RPL31 1
## PDE4D 1
## HLA-DRA 1
## BACH2 1
## MALAT1 1
## TCL1A 1
## ACSM3 1
## STMN1 2
## CD74 2
## CYFIP2 2
## IGHM 2
## CD79B 2
## RPL10 2
## RPS27 3
## CD38 3
## SOX4 3
## CD37 3
## ZEB2 4
## PTMA 4
## SYK 4
## PCDH9 4
## IGLL5 4
## MME 5
## ATP8A1 5
## RPL34 5
## EBF1 5
## NIBAN3 5As we suspected, cluster 11 is likely to contain monocytes, based on the expression of CST3 and TYROBP, for example.
We can visualise the expression of some of the other top-ranked genes:
p1 <- plotReducedDim(sce,
dimred = "UMAP_corrected",
colour_by = "LYZ",
text_by = "label")
p2 <- plotExpression(sce, features = "LYZ", x = "label")
p1 + p2
Based on the expression of CD3D, which is a known marker for T cells, it seems likely that cells in clusters 6 and 7 are T cells.
plotReducedDim(sce,
dimred = "UMAP_corrected",
colour_by = "CD3D",
text_by = "label")
plotExpression(sce,
features = "CD3D",
x = "label")
We would like to confirm this by identifying other genes that differentiate these two clusters from the rest of the cells.
Start by extracting the marker results for cluster 6 from our list:
c6_markers <- as.data.frame(markers[["6"]])In our case, we chose to then filter our table with two criteria to find genes that:
- are in the top 2 ranking for being mostly detected in this cluster (i.e. a presence/absence criteria)
AND
- have a Cohen’s d in the top 10 (i.e. the average expression difference should be high, relative to the gene’s variance)
c6_top_genes <- c6_markers %>%
filter(rank.logFC.detected <= 2 & rank.logFC.cohen <= 10) %>%
rownames()
c6_top_genes## [1] "DUSP2" "GZMA" "PRKCH" "IL32" "CCL5" "SKAP1" "PITPNC1"
## [8] "NKG7" "CST7"We obtain 9 genes with these criteria. Finally, we visualize the expression of these genes:
plotExpression(sce,
features = c6_top_genes,
x = "label")
We can see that all of these genes behave in a similar way to our known marker CD3D, suggesting they are good markers for these cell types. This makes sense as CD3D and CD3E encode T cell surface proteins. IL32 encodes a cytokine, which is often associated with cancer and BCL11B is a transcription factor that has been linked with T-Cell malignancy. This result could open an avenue for further investigation in this study.
3.2 Heatmap of marker genes
We have already seen how we can use the plotExpression()
function to visualise the distribution of expression in our data between
clusters. We have also seen how to use plotReducedDim() to
visualise a gene’s expression on the projected reduced dimensionality
space.
Another useful type of visualisation is to use heatmaps to show the expression of these genes of interest. We will demonstrate this using the top marker genes for cluster 11.
c11_top_genes <- c11_markers %>%
filter(rank.logFC.cohen <= 5) %>%
rownames()We can make generate a heatmap showing the expression in individual
cells using the function plotHeatmap(). We will arrange the
columns (cells) so that cells from the same cluster and cells from the
same samplegroup are grouped together.
plotHeatmap(sce,
features = c11_top_genes,
order_columns_by = c("label", "SampleGroup"))
Alternatively, we can summarise the expression across sample goups
and generate a heatmap showing the average expression across cells
within each group using the function plotGroupedHeatmap().
We can specify any factors causing batch effects using the
block arguments and the batch effects will be regressed out
of the averages.
plotGroupedHeatmap(sce,
features = c11_top_genes,
group = "label",
block = "SampleGroup")
In both cases, the colour scale of expression is showing the logcounts in their original scale. However, for this kind of visualisation, it may sometimes be useful to scale the data (aka Z-score), which brings all the genes to the same relative scale.
plotHeatmap(sce,
features = c11_top_genes,
order_columns_by = c("label", "SampleGroup"),
scale = TRUE,
center = TRUE,
zlim = c(-3, 3))
plotGroupedHeatmap(sce,
features = c11_top_genes,
group = "label",
block = "SampleGroup",
scale = TRUE,
center = TRUE,
zlim = c(-3, 3))
In this case, the colour scale can be interpreted as the number of standard deviations above/below the mean of that gene across all cells.
Another useful visualisation is to use dot plots of
expression that show both the average gene expression (as a colour
scale) and the number of cells in which the gene is detected (as the
size of the points).
We can generate such a plot using the plotDots()
function:
plotDots(sce,
features = c11_top_genes,
group = "label",
block = "SampleGroup",
scale = TRUE, center = TRUE, zlim = c(-3, 3))
3.3 Adjusting the log-fold change
The AUC and Cohen’s d scores incorporate both the gene expression differences between the clusters and the variance in gene expression scores within each cluster. If a gene has low variance, it is possible that it will be ranked highly even if the magnitude of the difference between the clusters is low. These genes will not necessarily make good marker genes. It may therefore be desirable to favour the detection of genes with larger log-fold changes.
For example, in the results from cluster 11, the gene SNX10 had a min-rank for Cohen’s d of 5:
c11_markers["SNX10", ] %>%
select(min.logFC.cohen, max.logFC.cohen, rank.logFC.cohen)## min.logFC.cohen max.logFC.cohen rank.logFC.cohen
## SNX10 -0.8627907 0.2355124 3702However, we can also see that its LFC goes from 0.3 to 7, which is a large range. Looking at its expression, we can see what might be going on:
plotExpression(sce,
features = "SNX10",
x = "label")
This gene has very low variation in expression in some clusters (because it’s lowly detected), and because Cohen’s d measures average differences scaled by variance, the gene comes up as having a high value for that metric in some comparisons.
To make our analysis more restrictive, we can instead indicate to the
scoreMarkers() function what is the minimum LFC threshold
we want to use to consider a gene for ranking. For example, a LFC >
2:
markers_lfc <- scoreMarkers(sce,
groups = sce$label,
block = sce$SampleName,
lfc = 2)
c11_markers_lfc2 <- as.data.frame(markers_lfc[["11"]])Now, SNX10’s rank dropped substantially:
c11_markers_lfc2["SNX10", c("rank.logFC.cohen")]## [1] 3158In conclusion, using an LFC threshold will change the ranking of the genes, to favour those genes that have highest LFC, even if they have higher variance in expression.
Obtaining p-values from marker gene analysis
You will notice that we did not make use of p-values in this analysis. The rationale for this is explained in the OSCA book:
Given that scoreMarkers() already reports effect sizes, it is tempting to take the next step and obtain p-values for the pairwise comparisons. Unfortunately, the p-values from the relevant tests cannot be reliably used to reject the null hypothesis. This is because DE analysis is performed on the same data used to obtain the clusters, which represents “data dredging” (also known as fishing or data snooping). The hypothesis of interest - are there differences between clusters? - is formulated from the data, so we are more likely to get a positive result when we re-use the data set to test that hypothesis.
The main thing to remember is that, in practice, this is a valid approach to help us annotate groups of cells based on the expression of genes with known cell-specificity and to find new interesting genes for further experiments and validation (e.g. using microscopy or qPCR). In other words, identifying cluster marker genes should be taken as a way to generate new hypothesis from our data, rather than a valid statistical model to test for differential expression between cell types.
4 Session information
sessionInfo()
devtools::session_info()## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.3.3 (2024-02-29)
## os Ubuntu 22.04.4 LTS
## system x86_64, linux-gnu
## ui X11
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz Etc/UTC
## date 2024-04-08
## pandoc 3.1.12.3 @ /opt/miniforge3/envs/R/bin/ (via rmarkdown)
##
## ─ Packages ───────────────────────────────────────────────────────────────────
## package * version date (UTC) lib source
## abind 1.4-5 2016-07-21 [2] CRAN (R 4.3.0)
## beachmat 2.18.0 2023-10-24 [2] Bioconductor
## beeswarm 0.4.0 2021-06-01 [2] CRAN (R 4.3.0)
## Biobase * 2.62.0 2023-10-24 [2] Bioconductor
## BiocGenerics * 0.48.1 2023-11-01 [2] Bioconductor
## BiocNeighbors 1.20.0 2023-10-24 [2] Bioconductor
## BiocParallel 1.36.0 2023-10-24 [2] Bioconductor
## BiocSingular 1.18.0 2023-10-24 [2] Bioconductor
## bitops 1.0-7 2021-04-24 [2] CRAN (R 4.3.0)
## bluster 1.12.0 2023-10-24 [2] Bioconductor
## bslib 0.6.1 2023-11-28 [2] CRAN (R 4.3.2)
## cachem 1.0.8 2023-05-01 [2] CRAN (R 4.3.0)
## cli 3.6.2 2023-12-11 [2] CRAN (R 4.3.2)
## cluster 2.1.6 2023-12-01 [2] CRAN (R 4.3.2)
## codetools 0.2-19 2023-02-01 [2] CRAN (R 4.3.0)
## colorspace 2.1-0 2023-01-23 [2] CRAN (R 4.3.0)
## crayon 1.5.2 2022-09-29 [2] CRAN (R 4.3.0)
## DelayedArray 0.28.0 2023-10-24 [2] Bioconductor
## DelayedMatrixStats 1.24.0 2023-10-24 [2] Bioconductor
## devtools 2.4.5 2022-10-11 [2] CRAN (R 4.3.0)
## digest 0.6.35 2024-03-11 [2] CRAN (R 4.3.3)
## dplyr * 1.1.4 2023-11-17 [2] CRAN (R 4.3.2)
## dqrng 0.3.2 2023-11-29 [2] CRAN (R 4.3.2)
## edgeR 4.0.2 2023-11-19 [2] Bioconductor 3.18 (R 4.3.2)
## ellipsis 0.3.2 2021-04-29 [2] CRAN (R 4.3.0)
## evaluate 0.23 2023-11-01 [2] CRAN (R 4.3.1)
## fansi 1.0.6 2023-12-08 [2] CRAN (R 4.3.2)
## fastmap 1.1.1 2023-02-24 [2] CRAN (R 4.3.0)
## forcats * 1.0.0 2023-01-29 [2] CRAN (R 4.3.0)
## fs 1.6.3 2023-07-20 [2] CRAN (R 4.3.1)
## generics 0.1.3 2022-07-05 [2] CRAN (R 4.3.0)
## GenomeInfoDb * 1.38.1 2023-11-08 [2] Bioconductor
## GenomeInfoDbData 1.2.11 2024-03-19 [2] Bioconductor
## GenomicRanges * 1.54.1 2023-10-29 [2] Bioconductor
## ggbeeswarm 0.7.2 2023-04-29 [2] CRAN (R 4.3.0)
## ggplot2 * 3.5.0 2024-02-23 [2] CRAN (R 4.3.2)
## ggrepel 0.9.5 2024-01-10 [2] CRAN (R 4.3.2)
## glue 1.7.0 2024-01-09 [2] CRAN (R 4.3.2)
## gridExtra 2.3 2017-09-09 [2] CRAN (R 4.3.0)
## gtable 0.3.4 2023-08-21 [2] CRAN (R 4.3.1)
## hms 1.1.3 2023-03-21 [2] CRAN (R 4.3.0)
## htmltools 0.5.7 2023-11-03 [2] CRAN (R 4.3.2)
## htmlwidgets 1.6.4 2023-12-06 [2] CRAN (R 4.3.2)
## httpuv 1.6.14 2024-01-26 [2] CRAN (R 4.3.2)
## igraph 2.0.2 2024-02-17 [2] CRAN (R 4.3.2)
## IRanges * 2.36.0 2023-10-24 [2] Bioconductor
## irlba 2.3.5.1 2022-10-03 [2] CRAN (R 4.3.3)
## jquerylib 0.1.4 2021-04-26 [2] CRAN (R 4.3.0)
## jsonlite 1.8.8 2023-12-04 [2] CRAN (R 4.3.2)
## knitr 1.45 2023-10-30 [2] CRAN (R 4.3.2)
## later 1.3.2 2023-12-06 [2] CRAN (R 4.3.2)
## lattice 0.22-5 2023-10-24 [2] CRAN (R 4.3.1)
## lifecycle 1.0.4 2023-11-07 [2] CRAN (R 4.3.2)
## limma 3.58.1 2023-10-31 [2] Bioconductor
## locfit 1.5-9.9 2024-03-01 [2] CRAN (R 4.3.3)
## lubridate * 1.9.3 2023-09-27 [2] CRAN (R 4.3.1)
## magrittr 2.0.3 2022-03-30 [2] CRAN (R 4.3.0)
## Matrix 1.6-5 2024-01-11 [2] CRAN (R 4.3.2)
## MatrixGenerics * 1.14.0 2023-10-24 [2] Bioconductor
## matrixStats * 1.2.0 2023-12-11 [2] CRAN (R 4.3.2)
## memoise 2.0.1 2021-11-26 [2] CRAN (R 4.3.0)
## metapod 1.10.0 2023-10-24 [2] Bioconductor
## mime 0.12 2021-09-28 [2] CRAN (R 4.3.0)
## miniUI 0.1.1.1 2018-05-18 [2] CRAN (R 4.3.0)
## munsell 0.5.0 2018-06-12 [2] CRAN (R 4.3.0)
## patchwork * 1.2.0 2024-01-08 [2] CRAN (R 4.3.2)
## pillar 1.9.0 2023-03-22 [2] CRAN (R 4.3.0)
## pkgbuild 1.4.4 2024-03-17 [2] CRAN (R 4.3.3)
## pkgconfig 2.0.3 2019-09-22 [2] CRAN (R 4.3.0)
## pkgload 1.3.4 2024-01-16 [2] CRAN (R 4.3.2)
## profvis 0.3.8 2023-05-02 [2] CRAN (R 4.3.1)
## promises 1.2.1 2023-08-10 [2] CRAN (R 4.3.1)
## purrr * 1.0.2 2023-08-10 [2] CRAN (R 4.3.1)
## R6 2.5.1 2021-08-19 [2] CRAN (R 4.3.0)
## Rcpp 1.0.12 2024-01-09 [2] CRAN (R 4.3.2)
## RCurl 1.98-1.14 2024-01-09 [2] CRAN (R 4.3.2)
## readr * 2.1.5 2024-01-10 [2] CRAN (R 4.3.2)
## remotes 2.5.0 2024-03-17 [2] CRAN (R 4.3.3)
## rlang 1.1.3 2024-01-10 [2] CRAN (R 4.3.2)
## rmarkdown 2.26 2024-03-05 [2] CRAN (R 4.3.3)
## rstudioapi 0.15.0 2023-07-07 [2] CRAN (R 4.3.0)
## rsvd 1.0.5 2021-04-16 [2] CRAN (R 4.3.0)
## S4Arrays 1.2.0 2023-10-24 [2] Bioconductor
## S4Vectors * 0.40.2 2023-11-23 [2] Bioconductor 3.18 (R 4.3.2)
## sass 0.4.9 2024-03-15 [2] CRAN (R 4.3.3)
## ScaledMatrix 1.10.0 2023-10-24 [2] Bioconductor
## scales 1.3.0 2023-11-28 [2] CRAN (R 4.3.2)
## scater * 1.30.1 2023-11-16 [2] Bioconductor
## scran * 1.30.0 2023-10-24 [2] Bioconductor
## scuttle * 1.12.0 2023-10-24 [2] Bioconductor
## sessioninfo 1.2.2 2021-12-06 [2] CRAN (R 4.3.0)
## shiny 1.8.0 2023-11-17 [2] CRAN (R 4.3.2)
## SingleCellExperiment * 1.24.0 2023-10-24 [2] Bioconductor
## SparseArray 1.2.2 2023-11-07 [2] Bioconductor
## sparseMatrixStats 1.14.0 2023-10-24 [2] Bioconductor
## statmod 1.5.0 2023-01-06 [2] CRAN (R 4.3.0)
## stringi 1.8.3 2023-12-11 [2] CRAN (R 4.3.2)
## stringr * 1.5.1 2023-11-14 [2] CRAN (R 4.3.2)
## SummarizedExperiment * 1.32.0 2023-10-24 [2] Bioconductor
## tibble * 3.2.1 2023-03-20 [2] CRAN (R 4.3.0)
## tidyr * 1.3.1 2024-01-24 [2] CRAN (R 4.3.2)
## tidyselect 1.2.0 2022-10-10 [2] CRAN (R 4.3.0)
## tidyverse * 2.0.0 2023-02-22 [2] CRAN (R 4.3.0)
## timechange 0.3.0 2024-01-18 [2] CRAN (R 4.3.2)
## tzdb 0.4.0 2023-05-12 [2] CRAN (R 4.3.0)
## urlchecker 1.0.1 2021-11-30 [2] CRAN (R 4.3.0)
## usethis 2.2.3 2024-02-19 [2] CRAN (R 4.3.2)
## utf8 1.2.4 2023-10-22 [2] CRAN (R 4.3.1)
## vctrs 0.6.5 2023-12-01 [2] CRAN (R 4.3.2)
## vipor 0.4.7 2023-12-18 [2] CRAN (R 4.3.2)
## viridis 0.6.5 2024-01-29 [2] CRAN (R 4.3.2)
## viridisLite 0.4.2 2023-05-02 [2] CRAN (R 4.3.0)
## withr 3.0.0 2024-01-16 [2] CRAN (R 4.3.2)
## xfun 0.42 2024-02-08 [2] CRAN (R 4.3.2)
## xtable 1.8-4 2019-04-21 [2] CRAN (R 4.3.0)
## XVector 0.42.0 2023-10-24 [2] Bioconductor
## yaml 2.3.8 2023-12-11 [2] CRAN (R 4.3.2)
## zlibbioc 1.48.0 2023-10-24 [2] Bioconductor
##
## [1] /Users/sawle01/R/x86_64-conda-linux-gnu-library/4.3
## [2] /opt/miniforge3/envs/R/lib/R/library
##
## ──────────────────────────────────────────────────────────────────────────────