Last updated: 2021-03-01

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Rmd 0748309 Peter Carbonetto 2021-02-19 Revised volcano plots in plots_purified_pbmc analysis; working on examine_de_calculations.R.
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Here we perform a differential expression analysis using the topic model fit to the mixture of FACS-purified data, as well as the clusters identified from this topic model.

Load the packages used in the analysis below, as well as additional functions that we will use to generate some of the plots.

library(Matrix)
library(fastTopics)
library(pathways)
library(ggplot2)
library(cowplot)
library(ggrepel)
source("../code/functions_for_plots_purified_pbmc.R")

Load the count data, the \(K = 6\) topic model fit, and the 7 clusters identified in the clustering analysis.

load("../data/pbmc_purified.RData")
fit <- readRDS(file.path("../output/pbmc-purified/rds",
                         "fit-pbmc-purified-scd-ex-k=6.rds"))$fit
fit <- poisson2multinom(fit)
samples <- readRDS("../output/pbmc-purified/clustering-pbmc-purified.rds")

Perform differential expression analysis using the FACS labeling:

celltype <- as.character(samples$celltype)
celltype[celltype == "CD4+/CD45RA+/CD25- Naive T" |
         celltype == "CD4+/CD45RO+ Memory" |
         celltype == "CD8+/CD45RA+ Naive Cytotoxic" |
         celltype == "CD4+ T Helper2" |
         celltype == "CD4+/CD25 T Reg"] <- "T cell"
celltype <- factor(celltype)
table(celltype)
diff_count_facs <- diff_count_clusters(celltype,counts)
# celltype
#   CD14+ Monocyte          CD19+ B            CD34+         CD56+ NK 
#             2612            10085             9232             8385 
# CD8+ Cytotoxic T           T cell 
#            10209            54132 
# Fitting 21952 x 6 = 131712 univariate Poisson models.
# Computing log-fold change statistics.
# Stabilizing log-fold change estimates using adaptive shrinkage.

Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.

These volcano plots summarize the results of the differential expression analysis using the FACS labeling:

p1 <- volcano_plot(diff_count_facs,"CD19+ B",genes$symbol,
                   betamax = 10,label_above_quantile = 0.995,
                   subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("B cells")
p2 <- volcano_plot(diff_count_facs,"CD14+ Monocyte",genes$symbol,
                   betamax = 10,label_above_quantile = 0.995,
                   subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("CD14+ cells")
p3 <- volcano_plot(diff_count_facs,"CD34+",genes$symbol,
                   betamax = 10,label_above_lfc = 2,
                   label_above_quantile = 0.995,
                   subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("CD34+ cells")
p4 <- volcano_plot(diff_count_facs,"CD56+ NK",genes$symbol,
                   betamax = 10,label_above_quantile = 0.995,
                   subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("NK cells")
p5 <- volcano_plot(diff_count_facs,"CD8+ Cytotoxic T",genes$symbol,
                   betamax = 10,label_above_quantile = 0.995,
                   subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("CD8+ T cells")
p6 <- volcano_plot(diff_count_facs,"T cell",genes$symbol,
                   betamax = 10,label_above_quantile = 0.998,
                   subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("T cells")
plot_grid(p1,p2,p3,p4,p5,p6,nrow = 2,ncol = 3)

Version Author Date
93ac093 Peter Carbonetto 2021-03-01
b84788d Peter Carbonetto 2021-03-01
dac053f Peter Carbonetto 2021-02-28
5773c6c Peter Carbonetto 2021-02-25
ced5127 Peter Carbonetto 2021-02-25
d21aab5 Peter Carbonetto 2021-02-24
7be2e95 Peter Carbonetto 2021-02-24
6e2b53a Peter Carbonetto 2021-02-10
9afb462 Peter Carbonetto 2021-02-10
f8e1d99 Peter Carbonetto 2021-02-10
d1d4185 Peter Carbonetto 2021-02-10
f596d8a Peter Carbonetto 2021-02-09
d0775d2 Peter Carbonetto 2021-02-09
ab3eeb8 Peter Carbonetto 2021-01-29
42ebc62 Peter Carbonetto 2021-01-29
a4bc59b Peter Carbonetto 2021-01-06
a0b6c2b Peter Carbonetto 2021-01-06
0411340 Peter Carbonetto 2021-01-06
fad8e3d Peter Carbonetto 2021-01-05

Perform differential expression analysis using the clusters:

table(samples$cluster)
diff_count_clusters <- diff_count_clusters(samples$cluster,counts)
# 
#         B     CD14+     CD34+      CD8+ dendritic        NK         T 
#     10439      2956      8237      3757       308      8380     60578 
# Fitting 21952 x 7 = 153664 univariate Poisson models.
# Computing log-fold change statistics.
# Stabilizing log-fold change estimates using adaptive shrinkage.

Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.

These volcano plots summarize the results of the differential expression analysis using the clusters:

p7 <- volcano_plot(diff_count_clusters,"B",genes$symbol,betamax = 10,
                   label_above_quantile = 0.995,
                   subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("B cells")
p8 <- volcano_plot(diff_count_clusters,"CD14+",genes$symbol,betamax = 10,
                   label_above_quantile = 0.993,
                   subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("CD14+ cells")
p9 <- volcano_plot(diff_count_clusters,"CD34+",genes$symbol,betamax = 10,
                   label_above_lfc = 4,label_above_quantile = 0.99,
                   subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("CD34+ cells")
p10 <- volcano_plot(diff_count_clusters,"dendritic",genes$symbol,betamax = 10,
                    label_above_lfc = 4,label_above_quantile = 0.98,
                    subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("dendritic cells")
p11 <- volcano_plot(diff_count_clusters,"NK",genes$symbol,betamax = 10,
                    label_above_lfc = 2,label_above_quantile = 0.995,
                    subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("NK cells")
p12 <- volcano_plot(diff_count_clusters,"CD8+",genes$symbol,betamax = 10,
                    label_above_lfc = 2,label_above_quantile = 0.98,
                    subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("CD8+ T cells")
p13 <- volcano_plot(diff_count_clusters,"T",genes$symbol,betamax = 10,
                    label_above_lfc = 2,label_above_quantile = 0.995,
                    subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("T cells")
plot_grid(p7,p8,p9,p10,p11,p12,p13,nrow = 3,ncol = 3)

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b84788d Peter Carbonetto 2021-03-01
dac053f Peter Carbonetto 2021-02-28
5773c6c Peter Carbonetto 2021-02-25
ced5127 Peter Carbonetto 2021-02-25
d21aab5 Peter Carbonetto 2021-02-24
7be2e95 Peter Carbonetto 2021-02-24
6e2b53a Peter Carbonetto 2021-02-10
9afb462 Peter Carbonetto 2021-02-10
f8e1d99 Peter Carbonetto 2021-02-10
d1d4185 Peter Carbonetto 2021-02-10
f596d8a Peter Carbonetto 2021-02-09
d0775d2 Peter Carbonetto 2021-02-09
ab3eeb8 Peter Carbonetto 2021-01-29
42ebc62 Peter Carbonetto 2021-01-29
a4bc59b Peter Carbonetto 2021-01-06
a0b6c2b Peter Carbonetto 2021-01-06
0411340 Peter Carbonetto 2021-01-06
fad8e3d Peter Carbonetto 2021-01-05

Perform differential expression analysis using the multinomial topic model, after removing the dendritic cells cluster:

rows <- which(samples$cluster != "dendritic")
fit_no_dendritic <- select_loadings(fit,loadings = rows)
diff_count_topics <- diff_count_analysis(fit_no_dendritic,counts[rows,])
# Fitting 21952 x 6 = 131712 univariate Poisson models.
# Computing log-fold change statistics.
# Stabilizing log-fold change estimates using adaptive shrinkage.

Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.

These volcano plots summarize the results of the differential expression analysis using the topic model:

p14 <- volcano_plot(diff_count_topics,"k3",genes$symbol,
                    label_above_lfc = 4,label_above_quantile = 0.995,
                    subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("topic 3 (B cells)")
p15 <- volcano_plot(diff_count_topics,"k2",genes$symbol,
                    label_above_quantile = 0.994,
                    subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("topic 2 (CD14+ cells)")
p16 <- volcano_plot(diff_count_topics,"k5",genes$symbol,
                    label_above_lfc = 2,label_above_quantile = 0.995,
                    subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("topic 5 (CD34+ cells)")
p17 <- volcano_plot(diff_count_topics,"k4",genes$symbol,
                    label_above_lfc = 4,label_above_quantile = 0.995,
                    subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("topic 4 (NK cells)")
p18 <- volcano_plot(diff_count_topics,"k1",genes$symbol,
                    label_above_quantile = 0.998,
                    subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("topic 1 (T cells)")
p19 <- volcano_plot(diff_count_topics,"k6",genes$symbol,
                    label_above_quantile = 0.998,
                    subsample_below_quantile = 0.5) +
  guides(fill = "none") +
  ggtitle("topic 6 (ribosomal proteins)")
plot_grid(p14,p15,p16,p17,p18,p19,nrow = 2,ncol = 3)

Version Author Date
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b84788d Peter Carbonetto 2021-03-01
dac053f Peter Carbonetto 2021-02-28
5773c6c Peter Carbonetto 2021-02-25
ced5127 Peter Carbonetto 2021-02-25
d21aab5 Peter Carbonetto 2021-02-24
7be2e95 Peter Carbonetto 2021-02-24
6e2b53a Peter Carbonetto 2021-02-10
9afb462 Peter Carbonetto 2021-02-10
f8e1d99 Peter Carbonetto 2021-02-10
d1d4185 Peter Carbonetto 2021-02-10
f596d8a Peter Carbonetto 2021-02-09
d0775d2 Peter Carbonetto 2021-02-09

The results of the differential expression analysis can also be browsed in interactive volcano plots:

volcano_plotly(diff_count_topics,"k3",
               "volcano_plot_purified_pbmc_bcells.html",
               genes$symbol,title = "topic 3 (B cells)",
               subsample_below_quantile = 0.5,
               width = 450,height = 500)
volcano_plotly(diff_count_topics,"k2",
               "volcano_plot_purified_pbmc_cd14.html",
               genes$symbol,title = "topic 2 (CD14+)",
               subsample_below_quantile = 0.5,
               width = 450,height = 500)
volcano_plotly(diff_count_topics,"k5",
               "volcano_plot_purified_pbmc_cd34.html",
               genes$symbol,title = "topic 5 (CD34+)",
               subsample_below_quantile = 0.5,
               width = 450,height = 500)
volcano_plotly(diff_count_topics,"k4",
               "volcano_plot_purified_pbmc_nk.html",
               genes$symbol,title = "topic 4 (NK cells)",
               subsample_below_quantile = 0.5,
               width = 450,height = 500)
volcano_plotly(diff_count_topics,"k1",
               "volcano_plot_purified_pbmc_tcells.html",
               genes$symbol,title = "topic 1 (T cells)",
               subsample_below_quantile = 0.5,
               width = 450,height = 500)
volcano_plotly(diff_count_topics,"k6",
               "volcano_plot_purified_pbmc_ribosomal_proteins.html",
               genes$symbol,title = "topic 6 (ribosomal proteins)",
               subsample_below_quantile = 0.5,
               width = 450,height = 500)
volcano_plotly(diff_count_clusters,"CD8+",
               "volcano_plot_purified_pbmc_cd8.html",
               genes$symbol,title = "CD8+ cluster",
               subsample_below_quantile = 0.5,
               width = 450,height = 500)
volcano_plotly(diff_count_clusters,"dendritic",
               "volcano_plot_purified_pbmc_dendritic.html",
               genes$symbol,title = "dendritic cells cluster",
               subsample_below_quantile = 0.5,
               width = 450,height = 500)

The interactive volcano plots may also be viewed by clicking these links: topic 3 (B cells), topic 4 (NK cells), topic 2 (CD14+), topic 5 (CD34+), topics 1 (T cells), topics 6 (T cells), CD8+ cluster and dendritic cells cluster.

The volcano plot for topic 6 suggests an enrichment of ribosomal protein genes. Indeed, there is a very strong correlation between the topic 6 mixture proportion and the fraction of total expression attributed to ribosomal genes:

rpgenes <- c("RPS2","RPS3","RPS3A","RPS4X","RPS6","RPS7","RPS8","RPS9",
             "RPS10","RPS11","RPS12","RPS13","RPS14","RPS15","RPS15A",
             "RPS16","RPS17","RPS18","RPS19","RPS20","RPS21","RPS23",
             "RPS24","RPS25","RPS26","RPS27","RPS27A","RPS28","RPS29",
             "RPL3","RPL4","RPL5","RPL6","RPL7A","RPL8","RPL9","RPL10",
             "RPL10A","RPL12","RPL13A","RPL14","RPL15","RPL17","RPL18",
             "RPL18A","RPL19","RPL21","RPL22","RPL23","RPL23A","RPL24",
             "RPL26","RPL27A","RPL30","RPL31","RPL32","RPL34","RPL35",
             "RPL36","RPL36A","RPL37","RPL39","RPL41")
rgscatterplot <- function (i, title = NULL) {
  j    <- which(is.element(genes$symbol,rpgenes))
  pdat <- data.frame(x = fit$L[i,6],
                     y = rowSums(counts[i,j])/rowSums(counts[i,]))
  return(ggplot(pdat,aes(x = x,y = y)) +
         geom_point() +
         geom_smooth(method = "lm",se = FALSE,color = "dodgerblue",
                     size = 0.5,linetype = "dashed") +
         ylim(0,0.6) +
         labs(x     = "topic 6 proportion",
              y     = "ribosomal expression",
              title = title) + 
         theme_cowplot(font_size = 10) +
         theme(plot.title = element_text(size = 10,face = "plain")))
}
p20 <- rgscatterplot(which(celltype == "CD19+ B"),"B cells")
p21 <- rgscatterplot(which(celltype == "CD34+"),"CD34+ cells")
p22 <- rgscatterplot(which(!(celltype == "CD19+ B" | celltype == "CD34+")),
                     "all other cells")
plot_grid(p20,p21,p22,nrow = 1,ncol = 3)

Version Author Date
6e2b53a Peter Carbonetto 2021-02-10
9afb462 Peter Carbonetto 2021-02-10

The list of ribosomal protein genes comes from Yoshihama et al (2002).

Four out of the 6topics closely correspond to the FACS cell populations: B cells, T cells, NK cells and CD14+ cells. We would expect then that the differential expression in these 4 topics is similar to differential expression in the corresponding FACS populations. Let’s check this.

celltype <- as.character(celltype)
celltype[celltype == "CD8+ Cytotoxic T"] <- "T cell"
celltype <- factor(celltype)
table(celltype)
diff_count_facs <- diff_count_clusters(celltype,counts)
# celltype
# CD14+ Monocyte        CD19+ B          CD34+       CD56+ NK         T cell 
#           2612          10085           9232           8385          64341 
# Fitting 21952 x 5 = 109760 univariate Poisson models.
# Computing log-fold change statistics.
# Stabilizing log-fold change estimates using adaptive shrinkage.

Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.

These scatterplots compare log-fold change estimated using the FACS labeling and using the topic model. Some of the top genes in each topic are highlighted.

p23 <- lfc_scatterplot(diff_count_facs,diff_count_topics,"CD19+ B","k3",
                       genes$symbol,label_above_lfc = 6,
                       label_above_quantile = 0.99,
                       xlab = "B cells FACS subpopulation",ylab = "topic 3")
p24 <- lfc_scatterplot(diff_count_facs,diff_count_topics,"CD14+ Monocyte",
                       "k2",genes$symbol,label_above_lfc = 6,
                       label_above_quantile = 0.98,
                       xlab = "CD14+ FACS subpopulation",ylab = "topic 2")
p25 <- lfc_scatterplot(diff_count_facs,diff_count_topics,"CD56+ NK","k4",
                       genes$symbol,label_above_lfc = 5,
                       label_above_quantile = 0.99,
                       xlab = "NK cells FACS subpopulation",ylab = "topic 4")
p26 <- lfc_scatterplot(diff_count_facs,diff_count_topics,"T cell","k1",
                       genes$symbol,label_above_lfc = 5,
                       label_above_quantile = 0.99,
                       xlab = "T cells FACS subpopulation",
                       ylab = "topic 1")
plot_grid(p23,p24,p25,p26,nrow = 2,ncol = 2)

Version Author Date
93ac093 Peter Carbonetto 2021-03-01
b84788d Peter Carbonetto 2021-03-01
dac053f Peter Carbonetto 2021-02-28
5773c6c Peter Carbonetto 2021-02-25
ced5127 Peter Carbonetto 2021-02-25

Overall, the LFC estimates are strongly correlated. But the differential expression in the topic is much higher for many of the top genes. In particular, the topic model seems to be more adept at picking out cell-type-specific genes—that is, genes that are uniquely expressed in a cell type.

For each topic, we also perform a gene-set enrichment analysis. Here we only consider gene sets with at least 4 genes and no more than 400 genes.

data(gene_sets_human)
i <- which(with(gene_sets_human,
                colSums(gene_sets) >= 4 &
                colSums(gene_sets) <= 400))
gene_set_info <- gene_sets_human$gene_set_info[i,]
gene_sets     <- gene_sets_human$gene_sets[,i]
gsea_res      <- perform_gsea(gene_sets,diff_count_topics$Z,nproc = 4)
# Using statistics from 17348 genes for gene set enrichment analysis.
# Converting gene set data for fgsea.
# Computing enrichment statistics for 35084 gene sets and
# 6 collections of gene-level statistics:
# k1, k2, k3, k4, k5, k6

Warning: The above code chunk cached its results, but it won’t be re-run if previous chunks it depends on are updated. If you need to use caching, it is highly recommended to also set knitr::opts_chunk$set(autodep = TRUE) at the top of the file (in a chunk that is not cached). Alternatively, you can customize the option dependson for each individual chunk that is cached. Using either autodep or dependson will remove this warning. See the knitr cache options for more details.

The results of the gene set enrichment analysis can be explored in these interactive plots.

gsea_plotly(gsea_res,gene_set_info,"k1",file = "gsea_plot_tcells.html",title = "T cells")
gsea_plotly(gsea_res,gene_set_info,"k2",file = "gsea_plot_cd14.html",title = "CD14+ cells")
gsea_plotly(gsea_res,gene_set_info,"k3",file = "gsea_plot_bcells.html",title = "B cells")
gsea_plotly(gsea_res,gene_set_info,"k4",file = "gsea_plot_nk.html",title = "NK cells")
gsea_plotly(gsea_res,gene_set_info,"k5",file = "gsea_plot_cd34.html",title = "CD34+ cells")
gsea_plotly(gsea_res,gene_set_info,"k6",file = "gsea_plot_rp.html",title = "Ribosomal proteins")

The interactive volcano plots may also be viewed by clicking these links: topic 1 (T cells), topic 2 (CD14+ cells), topic 3 (B cells), topic 4 (NK cells), topic 5 (CD34+ cells) and topic 6 (ribosomal proteins).


sessionInfo()
# R version 3.6.2 (2019-12-12)
# Platform: x86_64-apple-darwin15.6.0 (64-bit)
# Running under: macOS Catalina 10.15.7
# 
# Matrix products: default
# BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
# LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
# 
# locale:
# [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
# 
# attached base packages:
# [1] stats     graphics  grDevices utils     datasets  methods   base     
# 
# other attached packages:
# [1] ggrepel_0.9.0     cowplot_1.0.0     ggplot2_3.3.0     pathways_0.1-20  
# [5] fastTopics_0.5-20 Matrix_1.2-18    
# 
# loaded via a namespace (and not attached):
#  [1] httr_1.4.2           tidyr_1.0.0          splines_3.6.2       
#  [4] jsonlite_1.6         viridisLite_0.3.0    RcppParallel_4.4.2  
#  [7] shiny_1.4.0          assertthat_0.2.1     mixsqp_0.3-44       
# [10] yaml_2.2.0           progress_1.2.2       pillar_1.4.3        
# [13] backports_1.1.5      lattice_0.20-38      quantreg_5.54       
# [16] glue_1.3.1           quadprog_1.5-8       digest_0.6.23       
# [19] promises_1.1.0       colorspace_1.4-1     htmltools_0.4.0     
# [22] httpuv_1.5.2         pkgconfig_2.0.3      invgamma_1.1        
# [25] SparseM_1.78         xtable_1.8-4         purrr_0.3.3         
# [28] scales_1.1.0         whisker_0.4          later_1.0.0         
# [31] Rtsne_0.15           BiocParallel_1.18.1  MatrixModels_0.4-1  
# [34] git2r_0.26.1         tibble_2.1.3         mgcv_1.8-31         
# [37] farver_2.0.1         withr_2.1.2          ashr_2.2-51         
# [40] lazyeval_0.2.2       mime_0.8             magrittr_1.5        
# [43] crayon_1.3.4         mcmc_0.9-6           evaluate_0.14       
# [46] fs_1.3.1             nlme_3.1-142         MASS_7.3-51.4       
# [49] truncnorm_1.0-8      tools_3.6.2          data.table_1.12.8   
# [52] prettyunits_1.1.1    hms_0.5.2            lifecycle_0.1.0     
# [55] stringr_1.4.0        MCMCpack_1.4-5       plotly_4.9.2        
# [58] munsell_0.5.0        irlba_2.3.3          compiler_3.6.2      
# [61] rlang_0.4.5          grid_3.6.2           htmlwidgets_1.5.1   
# [64] crosstalk_1.0.0      labeling_0.3         rmarkdown_2.3       
# [67] gtable_0.3.0         R6_2.4.1             gridExtra_2.3       
# [70] knitr_1.26           dplyr_0.8.3          fastmap_1.0.1       
# [73] zeallot_0.1.0        fastmatch_1.1-0      workflowr_1.6.2.9000
# [76] fgsea_1.15.1         rprojroot_1.3-2      stringi_1.4.3       
# [79] parallel_3.6.2       SQUAREM_2017.10-1    Rcpp_1.0.5          
# [82] vctrs_0.2.1          tidyselect_0.2.5     xfun_0.11           
# [85] coda_0.19-3