Motif and gene analysis using topic modeling results for Buenrostro et al (2018) scATAC-seq result (data processed using chromVAR processed counts with scPeaks)
Kaixuan Luo
Last updated: 2021-01-05
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Knit directory: scATACseq-topics/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | ad94448 | kevinlkx | 2021-01-05 | wflow_publish("analysis/motif_gene_analysis_Buenrostro2018_chomVAR_scPeaks.Rmd") |
| html | 49507aa | kevinlkx | 2021-01-05 | Build site. |
| Rmd | 8f90a29 | kevinlkx | 2021-01-05 | wflow_publish("motif_gene_analysis_Buenrostro2018_chomVAR_scPeaks.Rmd") |
| html | df5f7f4 | kevinlkx | 2021-01-05 | Build site. |
| Rmd | 1d060f3 | kevinlkx | 2021-01-05 | fixed an issue with the gene score results and added motif results using top 2000 regions |
| html | 7aec35f | kevinlkx | 2021-01-05 | Build site. |
| Rmd | 939efd8 | kevinlkx | 2021-01-05 | fixed an issue with the gene score results and added motif results using top 2000 regions |
| html | 9dbeb26 | kevinlkx | 2020-12-23 | Build site. |
| Rmd | be44b91 | kevinlkx | 2020-12-23 | wflow_publish("motif_gene_analysis_Buenrostro2018_chomVAR_scPeaks.Rmd") |
| html | 920a2d0 | kevinlkx | 2020-12-23 | Build site. |
| Rmd | 0f7f879 | kevinlkx | 2020-12-23 | motif and gene analysis for Buenrostro result, data processed using chromVAR processed counts with scPeaks |
Here we perform TF motif and gene analysis for the Buenrostro et al (2018) scATAC-seq result inferred from the multinomial topic model with \(k = 11\).
We use binarized scPeaks based on chromVAR processed counts with peaks accessible in at least 1 sample.
Load packages and some functions used in this analysis
library(Matrix)
library(dplyr)
library(ggplot2)
library(cowplot)
library(fastTopics)
library(dplyr)
library(tidyr)
library(DT)
library(reshape)Load data and topic model results
Load the binarized data and the \(k = 11\) Poisson NMF fit results from Buenrostro et al 2018 dataset using binarized scPeaks based on chromVAR processed counts with peaks accessible in at least 1 sample.
data.dir <- "/project2/mstephens/kevinluo/scATACseq-topics/data/Buenrostro_2018/processed_data_Chen2019pipeline/chromVAR/"
load(file.path(data.dir, "Buenrostro_2018_binarized_scPeaks.RData"))
cat(sprintf("%d x %d counts matrix.\n",nrow(counts),ncol(counts)))# 2034 x 228965 counts matrix.fit.dir <- "/project2/mstephens/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized/"
fit <- readRDS(file.path(fit.dir, "/fit-Buenrostro2018-binarized-scd-ex-k=11.rds"))$fit
fit_multinom <- poisson2multinom(fit)Visualize by Structure plot grouped by cell labels.
set.seed(10)
colors_topics <- c("#a6cee3","#1f78b4","#b2df8a","#33a02c","#fb9a99","#e31a1c",
"#fdbf6f","#ff7f00","#cab2d6","#6a3d9a","#ffff99","#b15928",
"gray")
samples$label <- as.factor(samples$label)
p.structure <- structure_plot(fit_multinom,
grouping = samples[, "label"],n = Inf,gap = 40,
perplexity = 50,topics = 1:11,colors = colors_topics,
num_threads = 4,verbose = FALSE)
print(p.structure)
| Version | Author | Date |
|---|---|---|
| 920a2d0 | kevinlkx | 2020-12-23 |
Differential accessbility analysis of the ATAC-seq regions for the topics
out.dir <- "/project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized/"
diffcount_file <- file.path(out.dir, "diffcount-Buenrostro2018-11topics.rds")
if(file.exists(diffcount_file)){
cat("Load precomputed differential accessbility statistics.\n")
diff_count_topics <- readRDS(diffcount_file)
}else{
cat("Computing differential accessbility statistics from topic model.\n")
timing <- system.time(diff_count_topics <- diff_count_analysis(fit,counts))
cat(sprintf("Computation took %0.2f seconds.\n",timing["elapsed"]))
cat("Saving results.\n")
saveRDS(diff_count_topics, diffcount_file)
}# Load precomputed differential accessbility statistics.Distribution of z-scores
zscore_topics <- melt(diff_count_topics$Z)
colnames(zscore_topics) <- c("region", "topic", "zscore")
levels(zscore_topics$topic) <- colnames(diff_count_topics$Z)
z.quantile.99 <- apply(abs(diff_count_topics$Z), 2, quantile, 0.99)
cat("z-score 99% quantile: \n")
print(z.quantile.99)
p.hist.zscores <- ggplot(zscore_topics, aes(x=zscore)) +
geom_histogram(binwidth=1, color="black", fill="white") +
coord_cartesian(xlim = c(-10, 20)) + theme_cowplot(font_size = 10) +
facet_wrap(~ topic, ncol=4)
print(p.hist.zscores)
| Version | Author | Date |
|---|---|---|
| 920a2d0 | kevinlkx | 2020-12-23 |
# z-score 99% quantile:
# k1 k2 k3 k4 k5 k6 k7 k8
# 5.429064 7.020322 5.828474 6.308036 6.161995 6.931451 4.862751 7.977127
# k9 k10 k11
# 6.756263 6.858868 9.739615Motif enrichment analysis using HOMER
- Details about HOMER motif analysis:
- Motif enrichment result using regions with z-score above 99% quantile.
homer.dir <- paste0(out.dir, "/motifanalysis-Buenrostro2018-k=11-quantile/HOMER/")
cat(sprintf("Directory of motif analysis result: %s \n", homer.dir))
homer_res <- readRDS(file.path(homer.dir, "/homer_knownResults.rds"))
selected_regions <- readRDS(file.path(homer.dir, "/selected_regions.rds"))
cat("Number of regions selected for each topic: \n")
print(mapply(nrow, selected_regions[1:(length(selected_regions)-1)]))
top_motifs <- data.frame(matrix(nrow=10, ncol = ncol(diff_count_topics$Z)))
colnames(top_motifs) <- colnames(diff_count_topics$Z)
for (k in colnames(top_motifs)){
homer_motifs <- homer_res[[k]]
colnames(homer_motifs) <- c("Motif.name", "Consensus", "P-value", "Log.P-value", "q-value (Benjamini)",
"# of Target Sequences with Motif", "% of Target Sequences with Motif",
"# of Background Sequences with Motif", "% of Background Sequences with Motif")
homer_motifs <- homer_motifs %>% separate(Motif.name, c("motif", "experiment", "database"), "/")
top_motifs[,k] <- head(homer_motifs$motif, 10)
}
DT::datatable(data.frame(rank = 1:10, top_motifs), rownames = F,
caption = "Top 10 motifs enriched in each topic.")# Directory of motif analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized//motifanalysis-Buenrostro2018-k=11-quantile/HOMER/
# Number of regions selected for each topic:
# k1 k2 k3 k4 k5 k6 k7 k8 k9 k10 k11
# 2290 2290 2290 2290 2253 2258 2290 2290 2278 2264 2289- Motif enrichment result using regions with top 2000 regions with the highest z-score.
homer.dir <- paste0(out.dir, "/motifanalysis-Buenrostro2018-k=11-topN/HOMER/")
cat(sprintf("Directory of motif analysis result: %s \n", homer.dir))
homer_res <- readRDS(file.path(homer.dir, "/homer_knownResults.rds"))
selected_regions <- readRDS(file.path(homer.dir, "/selected_regions.rds"))
cat("Number of regions selected for each topic: \n")
print(mapply(nrow, selected_regions[1:(length(selected_regions)-1)]))
top_motifs <- data.frame(matrix(nrow=10, ncol = ncol(diff_count_topics$Z)))
colnames(top_motifs) <- colnames(diff_count_topics$Z)
for (k in colnames(top_motifs)){
homer_motifs <- homer_res[[k]]
colnames(homer_motifs) <- c("Motif.name", "Consensus", "P-value", "Log.P-value", "q-value (Benjamini)",
"# of Target Sequences with Motif", "% of Target Sequences with Motif",
"# of Background Sequences with Motif", "% of Background Sequences with Motif")
homer_motifs <- homer_motifs %>% separate(Motif.name, c("motif", "experiment", "database"), "/")
top_motifs[,k] <- head(homer_motifs$motif, 10)
}
DT::datatable(data.frame(rank = 1:10, top_motifs), rownames = F,
caption = "Top 10 motifs enriched in each topic.")# Directory of motif analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized//motifanalysis-Buenrostro2018-k=11-topN/HOMER/
# Number of regions selected for each topic:
# k1 k2 k3 k4 k5 k6 k7 k8 k9 k10 k11
# 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000Top genes
Gene body model
Gene scores were computed using the gene score model (model 42) in the archR paper with some modifications. This model uses bi-directional exponential decays from the gene TSS (extended upstream by 5 kb by default) and the gene transcription termination site (TTS). Note: the current version of the function does not account for neighboring gene boundaries.
- Gene body model, normalized by the l2 norm of weights, as in Stouffer's z-score method.
gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-genebody-l2")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))
top_genes <- data.frame(matrix(nrow=10, ncol = ncol(gene_scores)))
colnames(top_genes) <- colnames(gene_scores)
rownames(gene_scores) <- genes[match(rownames(gene_scores), genes$ENSEMBL), "SYMBOL"]
for (k in colnames(top_genes)){
top_genes[,k] <- rownames(gene_scores)[head(order(abs(gene_scores[,k]), decreasing=TRUE), 10)]
}
DT::datatable(data.frame(rank = 1:10, top_genes), rownames = F,
caption = "Top 10 genes in each topic.")# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized//geneanalysis-Buenrostro2018-k=11-genebody-l2- Gene body model, normalized by the total weights (i.e. weighted averge).
gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-genebody-sum")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))
top_genes <- data.frame(matrix(nrow=10, ncol = ncol(gene_scores)))
colnames(top_genes) <- colnames(gene_scores)
rownames(gene_scores) <- genes[match(rownames(gene_scores), genes$ENSEMBL), "SYMBOL"]
for (k in colnames(top_genes)){
top_genes[,k] <- rownames(gene_scores)[head(order(abs(gene_scores[,k]), decreasing=TRUE), 10)]
}
DT::datatable(data.frame(rank = 1:10, top_genes), rownames = F,
caption = "Top 10 genes in each topic.")# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized//geneanalysis-Buenrostro2018-k=11-genebody-sumTSS model
Gene scores were computed using TSS based method as in Lareau et al. Nature Biotech, 2019 as well as the model 21 in archR paper. This model weights chromatin accessibility around gene promoters by using bi-directional exponential decays from the TSS.
- TSS model, normalized by the l2 norm of weights, as in Stouffer's z-score method.
gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-TSS-l2")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))
top_genes <- data.frame(matrix(nrow=10, ncol = ncol(gene_scores)))
colnames(top_genes) <- colnames(gene_scores)
rownames(gene_scores) <- genes[match(rownames(gene_scores), genes$ENSEMBL), "SYMBOL"]
for (k in colnames(top_genes)){
top_genes[,k] <- rownames(gene_scores)[head(order(abs(gene_scores[,k]), decreasing=TRUE), 10)]
}
DT::datatable(data.frame(rank = 1:10, top_genes), rownames = F,
caption = "Top 10 genes in each topic.")# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized//geneanalysis-Buenrostro2018-k=11-TSS-l2- TSS model, normalized by the total weights (i.e. weighted averge).
gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-TSS-sum")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))
top_genes <- data.frame(matrix(nrow=10, ncol = ncol(gene_scores)))
colnames(top_genes) <- colnames(gene_scores)
rownames(gene_scores) <- genes[match(rownames(gene_scores), genes$ENSEMBL), "SYMBOL"]
for (k in colnames(top_genes)){
top_genes[,k] <- rownames(gene_scores)[head(order(abs(gene_scores[,k]), decreasing=TRUE), 10)]
}
DT::datatable(data.frame(rank = 1:10, top_genes), rownames = F,
caption = "Top 10 genes in each topic.")# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized//geneanalysis-Buenrostro2018-k=11-TSS-sumGene-set enrichment analysis (GSEA)
- Gene body model, normalized by the l2 norm of weights, as in Stouffer's z-score method.
gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-genebody-l2")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))
top_pathways_up <- top_pathways_down <- data.frame(matrix(nrow=10, ncol = ncol(gsea_res$pval)))
colnames(top_pathways_up) <- colnames(top_pathways_down) <- colnames(gsea_res$pval)
for (k in 1:ncol(gsea_res$pval)){
gsea_topic <- data.frame(pathway = rownames(gsea_res$pval),
pval = gsea_res$pval[,k],
log2err = gsea_res$log2err[,k],
ES = gsea_res$ES[,k],
NES = gsea_res$NES[,k])
gsea_up <- gsea_topic[gsea_topic$ES > 0,]
top_IDs_up <- as.character(gsea_up[head(order(gsea_up$pval), 10), "pathway"])
top_pathways_up[,k] <- gene_set_info[match(top_IDs_up, gene_set_info$id),c("name", "id")] %>%
unite("pathway", c("name", "id"), sep = ".", remove = TRUE)
gsea_down <- gsea_topic[gsea_topic$ES < 0,]
top_IDs_down <- as.character(gsea_down[head(order(gsea_down$pval), 10), "pathway"])
top_pathways_down[,k] <- gene_set_info[match(top_IDs_down, gene_set_info$id),c("name", "id")] %>%
unite("pathway", c("name", "id"), sep = ".", remove = TRUE)
}
DT::datatable(data.frame(rank = 1:10, top_pathways_up), rownames = F,
caption = "Top 10 pathways enriched at the top of the gene rank list.")# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized//geneanalysis-Buenrostro2018-k=11-genebody-l2- Gene body model, normalized by the total weights (i.e. weighted averge).
gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-genebody-sum")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))
top_pathways_up <- top_pathways_down <- data.frame(matrix(nrow=10, ncol = ncol(gsea_res$pval)))
colnames(top_pathways_up) <- colnames(top_pathways_down) <- colnames(gsea_res$pval)
for (k in 1:ncol(gsea_res$pval)){
gsea_topic <- data.frame(pathway = rownames(gsea_res$pval),
pval = gsea_res$pval[,k],
log2err = gsea_res$log2err[,k],
ES = gsea_res$ES[,k],
NES = gsea_res$NES[,k])
gsea_up <- gsea_topic[gsea_topic$ES > 0,]
top_IDs_up <- as.character(gsea_up[head(order(gsea_up$pval), 10), "pathway"])
top_pathways_up[,k] <- gene_set_info[match(top_IDs_up, gene_set_info$id),c("name", "id")] %>%
unite("pathway", c("name", "id"), sep = ".", remove = TRUE)
gsea_down <- gsea_topic[gsea_topic$ES < 0,]
top_IDs_down <- as.character(gsea_down[head(order(gsea_down$pval), 10), "pathway"])
top_pathways_down[,k] <- gene_set_info[match(top_IDs_down, gene_set_info$id),c("name", "id")] %>%
unite("pathway", c("name", "id"), sep = ".", remove = TRUE)
}
DT::datatable(data.frame(rank = 1:10, top_pathways_up), rownames = F,
caption = "Top 10 pathways enriched at the top of the gene rank list.")# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized//geneanalysis-Buenrostro2018-k=11-genebody-sum- TSS model, normalized by the l2 norm of weights, as in Stouffer's z-score method.
gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-TSS-l2")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))
top_pathways_up <- top_pathways_down <- data.frame(matrix(nrow=10, ncol = ncol(gsea_res$pval)))
colnames(top_pathways_up) <- colnames(top_pathways_down) <- colnames(gsea_res$pval)
for (k in 1:ncol(gsea_res$pval)){
gsea_topic <- data.frame(pathway = rownames(gsea_res$pval),
pval = gsea_res$pval[,k],
log2err = gsea_res$log2err[,k],
ES = gsea_res$ES[,k],
NES = gsea_res$NES[,k])
gsea_up <- gsea_topic[gsea_topic$ES > 0,]
top_IDs_up <- as.character(gsea_up[head(order(gsea_up$pval), 10), "pathway"])
top_IDs_up <- gene_set_info[match(top_IDs_up, gene_set_info$id),c("name", "id")]
top_pathways_up[,k] <- paste0(top_IDs_up$name, "(", top_IDs_up$id, ")")
gsea_down <- gsea_topic[gsea_topic$ES < 0,]
top_IDs_down <- as.character(gsea_down[head(order(gsea_down$pval), 10), "pathway"])
top_IDs_down <- gene_set_info[match(top_IDs_down, gene_set_info$id),c("name", "id")]
top_pathways_down[,k] <- paste0(top_IDs_down$name, "(", top_IDs_down$id, ")")
}
DT::datatable(data.frame(rank = 1:10, top_pathways_up), rownames = F,
caption = "Top 10 pathways enriched at the top of the gene rank list.")# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized//geneanalysis-Buenrostro2018-k=11-TSS-l2- TSS model, normalized by the total weights (i.e. weighted averge).
gene.dir <- paste0(out.dir, "/geneanalysis-Buenrostro2018-k=11-TSS-sum")
cat(sprintf("Directory of gene analysis result: %s \n", gene.dir))
load(file.path(gene.dir, "genescores_gsea.Rdata"))
top_pathways_up <- top_pathways_down <- data.frame(matrix(nrow=10, ncol = ncol(gsea_res$pval)))
colnames(top_pathways_up) <- colnames(top_pathways_down) <- colnames(gsea_res$pval)
for (k in 1:ncol(gsea_res$pval)){
gsea_topic <- data.frame(pathway = rownames(gsea_res$pval),
pval = gsea_res$pval[,k],
log2err = gsea_res$log2err[,k],
ES = gsea_res$ES[,k],
NES = gsea_res$NES[,k])
gsea_up <- gsea_topic[gsea_topic$ES > 0,]
top_IDs_up <- as.character(gsea_up[head(order(gsea_up$pval), 10), "pathway"])
top_IDs_up <- gene_set_info[match(top_IDs_up, gene_set_info$id),c("name", "id")]
top_pathways_up[,k] <- paste0(top_IDs_up$name, "(", top_IDs_up$id, ")")
gsea_down <- gsea_topic[gsea_topic$ES < 0,]
top_IDs_down <- as.character(gsea_down[head(order(gsea_down$pval), 10), "pathway"])
top_IDs_down <- gene_set_info[match(top_IDs_down, gene_set_info$id),c("name", "id")]
top_pathways_down[,k] <- paste0(top_IDs_down$name, "(", top_IDs_down$id, ")")
}
DT::datatable(data.frame(rank = 1:10, top_pathways_up), rownames = F,
caption = "Top 10 pathways enriched at the top of the gene rank list.")# Directory of gene analysis result: /project2/xinhe/kevinluo/scATACseq-topics/output/Buenrostro_2018_chromVAR_scPeaks/binarized//geneanalysis-Buenrostro2018-k=11-TSS-sum
sessionInfo()# R version 3.6.1 (2019-07-05)
# Platform: x86_64-pc-linux-gnu (64-bit)
# Running under: Scientific Linux 7.4 (Nitrogen)
#
# Matrix products: default
# BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so
#
# locale:
# [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
# [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
# [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] stats graphics grDevices utils datasets methods base
#
# other attached packages:
# [1] reshape_0.8.8 DT_0.16 tidyr_1.1.2 fastTopics_0.4-6
# [5] cowplot_1.1.0 ggplot2_3.3.2 dplyr_1.0.2 Matrix_1.2-18
# [9] workflowr_1.6.2
#
# loaded via a namespace (and not attached):
# [1] ggrepel_0.9.0 Rcpp_1.0.5 lattice_0.20-41 prettyunits_1.1.1
# [5] rprojroot_2.0.2 digest_0.6.27 plyr_1.8.6 R6_2.5.0
# [9] MatrixModels_0.4-1 evaluate_0.14 coda_0.19-4 httr_1.4.2
# [13] pillar_1.4.7 rlang_0.4.9 progress_1.2.2 lazyeval_0.2.2
# [17] data.table_1.13.4 irlba_2.3.3 SparseM_1.78 whisker_0.4
# [21] rmarkdown_2.6 labeling_0.4.2 Rtsne_0.15 stringr_1.4.0
# [25] htmlwidgets_1.5.3 munsell_0.5.0 compiler_3.6.1 httpuv_1.5.4
# [29] xfun_0.19 pkgconfig_2.0.3 mcmc_0.9-7 htmltools_0.5.0
# [33] tidyselect_1.1.0 tibble_3.0.4 quadprog_1.5-8 matrixStats_0.57.0
# [37] viridisLite_0.3.0 crayon_1.3.4 conquer_1.0.2 withr_2.3.0
# [41] later_1.1.0.1 MASS_7.3-53 grid_3.6.1 jsonlite_1.7.2
# [45] gtable_0.3.0 lifecycle_0.2.0 git2r_0.27.1 magrittr_2.0.1
# [49] scales_1.1.1 RcppParallel_5.0.2 stringi_1.5.3 farver_2.0.3
# [53] fs_1.3.1 promises_1.1.1 ellipsis_0.3.1 generics_0.1.0
# [57] vctrs_0.3.6 tools_3.6.1 glue_1.4.2 purrr_0.3.4
# [61] crosstalk_1.1.0.1 hms_0.5.3 yaml_2.2.1 colorspace_2.0-0
# [65] plotly_4.9.2.1 knitr_1.30 quantreg_5.75 MCMCpack_1.4-9