Supporting Material for Trefflich2019
6 November 2019
Contents
1 Context
Fletcher et al. (2013) reconstructed regulons for 809 transcription factors (TFs) using microarray transcriptomic data from breast tissue, either from cancer or normal samples (Curtis et al. 2012). Our goal here is to assess the evolutionary root of the regulons reconstructed by Fletcher et al. (2013) using the geneplast package. This script reproduces the main observations described in Trefflich et al. (2019), which proposed a framework to explore the evolutionary roots of regulons.
2 Package installation and data sets
Please make sure to install all required packages. Installing and then loading the geneplast.data.string.v91 and Fletcher2013b data packages will make available all data required for this case study.
#-- Call packages
library(geneplast)
library(geneplast.data.string.v91)
library(RTN)
library(Fletcher2013b)
library(ggplot2)
library(ggpubr)
library(plyr)3 Inferring evolutionary roots
This analysis will determine the evolutionary root of a gene based on the distribution of its orthologs in a given species tree. We will need two data objects, cogdata and phyloTree, both loaded with the gpdata_string_v91 call. The cogdata is a data.frame object listing orthologous groups (OGs) predicted for 121 eukaryotic species, while the phyloTree is a phylogenetic tree object of class phylo. The groot.preprocess function will check the input data and build an object of class OGR, which will be used in the subsequent steps of the analysis pipeline.
#-- Load orthology data from the 'geneplast.data.string.v91' package
data(gpdata_string_v91)
#-- Create an object of class 'OGR' for a reference 'spid'
ogr <- groot.preprocess(cogdata=cogdata, phyloTree=phyloTree, spid="9606")The groot function addresses the problem of finding the evolutionary root of a feature in an phylogenetic tree. The method infers the probability that such feature was present in the Last Common Ancestor (LCA) of a given lineage. The groot function assesses the presence and absence of the orthologs in the extant species of the phylogenetic tree in order to build a probability distribution, which is used to identify vertical heritage patterns. The spid=9606 parameter sets Homo sapiens as the reference species, which defines the ancestral lineage assessed in the query (i.e. each ortholog of the reference species will be rooted in an ancestor of the reference species).
#-- Run the 'groot' function and infer the evolutionary roots
ogr <- groot(ogr, nPermutations=1000, verbose=TRUE)4 Evolutionary analysis of regulons generated from breast cancer samples
4.1 Mapping root-to-gene annotation
In this section we will map the inferred evolutionary roots (available in the ogr object) to genes annotated in the regulons reconstructed by Fletcher et al. (2013) from breast cancer samples (available in the rtni1st object; for the same analysis using normal samples, please see section 5). For a summary of the regulons in the rtni1st object we recommend using the tni.regulon.summary function, which shows that there are 809 regulatory elements (TFs) and 14131 targets.
#-- Load regulons
data("rtni1st")
tni.regulon.summary(rtni1st)## This regulatory network comprised of 809 regulons.
## -- DPI-filtered network:
## regulatoryElements Targets Edges
## 809 14131 47012
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 10.0 37.0 58.1 80.0 523.0
## -- Reference network:
## regulatoryElements Targets Edges
## 809 14131 617672
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 43 449 764 1245 4148
## ---We will transform the rtni1st into a graph object using the tni.graph function. The resulting graph will be assessed by the ogr2igraph function, which will map the root-to-gene annotation; the results will be available in the roots_df data frame for subsequent analysis.
#-- Put regulons into an 'igraph' object
#-- Note: small regulons (n<15 targets) are romeved in this step.
graph <- tni.graph(rtni1st, gtype = "rmap")
#-- Map the 'ogr' object to the 'igraph' object
graph <- ogr2igraph(ogr, cogdata, graph, idkey = "ENTREZ")
#-- Make a data frame with the gene roots
roots_df <- data.frame(COGID = V(graph)$COGID,
SYMBOL = V(graph)$SYMBOL,
ENTREZ = V(graph)$ENTREZ,
Root = V(graph)$Root,
TRN_element = c("Target","TF")[V(graph)$tfs+1],
stringsAsFactors = FALSE)Please note that some level of missing annotation is expected, as not all gene ids listed in the cogdata might be available in the graph object. Also, small regulons (n < 15 targets) are removed by the tni.graph function. As a final pre-processing step, we will remove genes rooted at the base of the phylogenetic tree, for which the predictions can not discriminate from earlier ancestor roots. Here, 307 TFs and 6308 targets were retained.
#-- Remove NAs from missing annotation
roots_df <- roots_df[complete.cases(roots_df),]
#-- Remove genes rooted at the base of the phylogenetic tree
roots_df <- roots_df[roots_df$Root<max(roots_df$Root),]
rownames(roots_df) <- 1:nrow(roots_df)
#-- Check TF and target counts
table(roots_df$TRN_element)## Target TF
## 6308 3074.2 Comparing regulators and targets
A transcriptional regulatory network (TRN) is formed by regulators (TFs) and target genes. The roots_df data frame lists the evolutionary roots inferred for each TRN element, including whether the TRN element is annotated as TF or target.
head(roots_df)## COGID SYMBOL ENTREZ Root TRN_element
## 1 KOG3119 CEBPG 1054 19 TF
## 2 KOG4217 NR4A2 4929 17 TF
## 3 KOG0493 EN1 2019 17 TF
## 4 NOG80479 TP53 7157 20 TF
## 5 KOG3740 GATAD2A 54815 19 TF
## 6 COG5150 DR1 1810 23 TFtail(roots_df)## COGID SYMBOL ENTREZ Root TRN_element
## 6610 COG5640 F11 2160 19 Target
## 6611 KOG1418 KCNK18 338567 24 Target
## 6612 NOG39443 TMEM220 388335 14 Target
## 6613 NOG43522 C1orf170 84808 7 Target
## 6614 NOG127335 C16orf96 342346 6 Target
## 6615 NOG27843 PANX3 116337 13 TargetFor example, CEBPG gene is placed at root 19 while PANX3 gene is placed at root 13, indicating that the evolutionary root inferred for CEBPG is more ancestral than the evolutionary root inferred for PANX3. Please note that the evolutionary roots are enumerated from the most recent to the most ancestral node of the phylogenetic tree. Also, as the aim of the analysis is to find the root of the orthologs of the reference species, the root enumeration is related to the ancestral lineage of the reference species (for details of the phylogenetic tree, see Figure S4 of the Geneplast’s vignette).
Here we will compare the distribution of the evolutionary roots inferred for TFs and target genes using the Wilcoxon-Mann-Whitney test, and then generate violin plots (please refer to Trefflich et al. (2019) for additional details).
#-- Assess root distribution by TRN_element
wilcox.test(Root ~ TRN_element, data=roots_df)## Wilcoxon rank sum test with continuity correction
## data: Root by TRN_element
## W = 812534, p-value = 1.6e-06
## alternative hypothesis: true location shift is not equal to 0#-- Set roots to display in y-axis
roots <- c(4,8,11,13,19,21,25)
#-- Set a summary function to display dispersion within the violins
data_summary <- function(x) {
y <- mean(x); ymin <- y-sd(x); ymax <- y+sd(x)
return(c(y=y,ymin=ymin,ymax=ymax))
}
#-- (Figure S1) Generate violin plots showing root distribution by TRN_element
p <- ggplot(roots_df, aes(x=TRN_element, y=Root)) +
geom_violin(aes(fill=TRN_element), adjust=2, show.legend=F) +
scale_y_continuous(breaks=roots, labels=paste("root",roots)) +
scale_fill_manual(values=c("#c7eae5","#dfc27d")) +
labs(x="TRN elements", y="Root distribution") +
scale_x_discrete(limits=c("TF","Target"), labels=c("TFs","Targets")) +
theme_classic() +
theme(text=element_text(size=20)) +
stat_summary(fun.data = data_summary)
p + stat_compare_means(method="wilcox.test",
comparisons =list(c("TF","Target")),
label = "p.signif")
Figure S1. Distribution of the inferred evolutionary roots of TFs and target genes using regulons available from the rtni1st data object. ****P-value = 1.6e-06 (Wilcoxon-Mann-Whitney test).
Next we compute the root distance between a TF and its targets, and then generate a pie chart and a boxplot that reproduce the evolutionary scenarios discussed in Trefflich et al. (2019).
#-- Get roots for TFs
idx <- roots_df$TRN_element=="TF"
tfroots <- roots_df$Root[idx]
names(tfroots) <- roots_df$SYMBOL[idx]
#-- Get roots for target genes
regulonlist <- tni.get(rtni1st, what = "regulons", idkey = "ENTREZ")[names(tfroots)]
targetroots <- lapply(regulonlist, function(reg){
roots_df$Root[roots_df$ENTREZ%in%reg]
})
#-- Compute root distances between a TF and its targets
rootdist <- sapply(names(targetroots), function(reg){
targetroots[[reg]]-tfroots[reg]
})
#-- Compute median root distances and sort related objects
rootdist_med <- sort(unlist(lapply(rootdist, median)), decreasing = T)
rootdist <- rootdist[names(rootdist_med)]
tfroots <- tfroots[names(rootdist_med)]
targetroots <- targetroots[names(rootdist_med)]
regulonlist <- regulonlist[names(rootdist_med)]
#-- Set regulon groups based on the median root distances
regulon_grouplist <- -sign(rootdist_med)+2
regulon_groupnames <- c("group_a","group_b","group_c")
regulon_groupcolors = c("#98d1f2","grey","#1c92d5")
names(regulon_groupcolors) <- regulon_groupnames#-- (Figure S2) Generate a pie chart showing regulons grouped based on
#-- the median distance between a TF's root and its targets' roots
n <- as.numeric(table(regulon_grouplist))
pie(n, labels = paste(n,"regulons"), col = regulon_groupcolors,
border="white", cex=1.5, clockwise = TRUE, init.angle=0)
labs <- c("TF-target genes rooted before the TF (group-a)",
"TF-target genes rooted with the TF (group-b)",
"TF-target genes rooted after the TF (group-c)")
legend("bottomleft", fill = regulon_groupcolors, bty = "n", legend = labs)
Figure S2. Regulons grouped based on the median distance between a TF’s root and its targets’ roots.
#-- (Figure S3) Generate a boxplot showing individual regulons
#-- sorted by the median distance to TF root
plot.new()
par(usr=c(c(0,length(rootdist)),range(rootdist)))
boxplot(rootdist, horizontal= F, outline=FALSE, las=2, axes=FALSE, add=T,
pars = list(boxwex = 0.6, boxcol=regulon_groupcolors[regulon_grouplist],
whiskcol=regulon_groupcolors[regulon_grouplist]),
pch="|", lty=1, lwd=0.75,
col = regulon_groupcolors[regulon_grouplist])
abline(h=0, lmitre=5, col="#E69F00", lwd=3, lt=2)
par(mgp=c(2,0.1,0))
axis(side=1, cex.axis=1.2, padj=0.5, hadj=0.5, las=1, lwd=1.5, tcl= -0.2)
par(mgp=c(2.5,1.2,0.5))
axis(side=2, cex.axis=1.2, padj=0.5, hadj=0.5, las=1, lwd=1.5, tcl= -0.2)
legend("topright",legend = labs, fill = regulon_groupcolors, bty = "n")
title(xlab = "Regulons sorted by the median distance to TF root", ylab = "Distance to TF root")
Figure S3. Regulons sorted by the median distance to TF root.
4.3 Comparing transcription factors and transcription co-factors
Transcription co-factors (TcoFs) are critical determinants of TF activities. TcoFs do not bind directly to DNA, but influence the transcriptional regulation by forming protein complexes with TFs. Next we will compare these two classes of regulators using the same approach described by Trefflich et al. (2019), but now assessing the distribution of the evolutionary roots inferred for TFs and TcoFs. In order to run the subsequent snippets we will require the list of human TcoFs avaiable at the TcoF-DB Database (Schmeier et al. 2016) (please, download the ‘TcoF-DB.xlsx’ file as indicated below).
#-- Please, download the 'TcoF-DB.xlsx' file from
#-- https://tools.sschmeier.com/tcof/browse/?type=tcof&species=human&class=all
#-- and then load it with the 'read_excel' function
library(readxl)
TcoF_DB <- read_excel("TcoF-DB.xlsx")
#-- Select high-confidence TcoFs according to TcoF Database
TcoF_DB <- TcoF_DB[TcoF_DB$Type=="TcoF: class HC",]
#-- Map 'TcoF_DB' to 'roots_df'
roots_df_TcoF_DB <- roots_df
roots_df_TcoF_DB$TRN_element <- NA
roots_df_TcoF_DB$TRN_element[roots_df$SYMBOL %in% TcoF_DB$Symbol] <- "TcoF"
roots_df_TcoF_DB$TRN_element[roots_df$TRN_element%in%"TF"] <- "TF"
roots_df_TcoF_DB <- roots_df_TcoF_DB[!is.na(roots_df_TcoF_DB$TRN_element),]
table(roots_df_TcoF_DB$TRN_element)
## TcoF TF
## 146 307#-- Assess root distribution by TRN_element
wilcox.test(Root ~ TRN_element, data=roots_df_TcoF_DB)## Wilcoxon rank sum test with continuity correction
## data: Root by TRN_element
## W = 22226, p-value = 0.884
## alternative hypothesis: true location shift is not equal to 0#-- (Figure S4) Generate violin plots showing root distribution by TRN_element
p <- ggplot(roots_df_TcoF_DB, aes(x=TRN_element, y=Root)) +
geom_violin(aes(fill=TRN_element), adjust=2, show.legend=F) +
scale_y_continuous(breaks=roots, labels=paste("root",roots)) +
scale_fill_manual(values=c("#c7eae5","#dfc27d")) +
labs(x="TRN elements", y="Root distribution") +
scale_x_discrete(limits=c("TF","TcoF"), labels=c("TFs","TcoFs")) +
theme_classic() +
theme(text=element_text(size=20)) +
stat_summary(fun.data = data_summary)
p + stat_compare_means(method="wilcox.test",
comparisons =list(c("TF","TcoF")),
label = "p.signif")
Figure S4. Distribution of the inferred evolutionary roots of TFs and TcoFs (ns = not significant).
4.4 Exploring abundance, diversity and plasticity
In this section we show how to calculate the OG’s abundance, diversity and plasticity, and then map these three metrics to regulons (please, refer to Castro et al. (2008) and Dalmolin et al. (2011) for a detailed description). Briefly, the abundance metric represents the number of orthologs divided by the number of species annotated in a given OG; abundance = 1 indicates an one-to-one relationship between the number of orthologs and species, while abundance > 1 indicates that the number of orthologs exceeds the number of species. A large abundance value suggests a large number of paralogs annotated in the OG. The diversity metric represents the distribution of orthologs and paralogs in a given species tree; high diversity represents an homogeneous distribution (e.g. one ortholog in each species), while low diversity indicates that the orthologous genes are concentrated on few species (e.g. in a single branch of the species tree). The plasticity is the combination of abundance and diversity into a single metric. Low plasticity is observed in OGs of low abundance and high diversity (e.g. few orthologs distributed over many species), while high plasticity is observed in OGs of high abundance and low diversity (e.g. many orthologs concentrated on few species).
#-- Compute OG's abundance, diversity and plasticity
ogp <- gplast.preprocess(cogdata=cogdata, sspids=phyloTree$tip.label)
ogp <- gplast(ogp)
gpres <- gplast.get(ogp, what="results")
head(gpres)## abundance diversity plasticity
## COG0001 1.3871 0.6889 0.4150
## COG0002 1.1346 0.8110 0.2386
## COG0003 1.3243 0.9506 0.1739
## COG0004 4.1753 0.8880 0.5654
## COG0005 2.5455 0.9283 0.4182
## COG0006 4.3167 0.9769 0.5298#-- Map OG's abundance, diversity and plasticity to the 'roots_df' data frame
idx <- match(roots_df$COGID,rownames(gpres))
roots_df$Abundance <- gpres$abundance[idx]
roots_df$Diversity <- gpres$diversity[idx]
roots_df$Plasticity <- gpres$plasticity[idx]
#-- Then map OG's abundance, diversity and plasticity to regulons
stats_df <- lapply(regulonlist, function(reg){
temp <- roots_df[roots_df$ENTREZ%in%reg,]
apply(temp[ , c("Abundance","Diversity","Plasticity")], 2, mean)
})
stats_df <- ldply(stats_df, .id="Regulon", stringsAsFactors=FALSE)
stats_df$regulon_groups <- regulon_grouplist[stats_df$Regulon]
stats_df$regulon_groups <- regulon_groupnames[stats_df$regulon_groups]#-- (Figure S5a) Assess OG's abundance by regulon groups
p <- ggplot(stats_df, aes(x=regulon_groups, y=Abundance, fill=regulon_groups)) +
geom_boxplot(show.legend=F) +
scale_y_continuous(limits = c(0,60)) +
scale_x_discrete(limits=c("group_a","group_c")) +
scale_fill_manual(values=regulon_groupcolors[c("group_a","group_c")]) +
labs(x="Regulon groups", y="OG's abundance") +
theme(panel.grid = element_blank()) +
theme(text=element_text(size=20), axis.line.x=element_blank())
p + stat_compare_means(method="wilcox.test",
comparisons =list(c("group_a","group_c")),
label = "p.signif")#-- (Figure S5b) Assess OG's diversity by regulon groups
p <- ggplot(stats_df, aes(x=regulon_groups, y=Diversity, fill=regulon_groups)) +
geom_boxplot(show.legend=F) +
scale_y_continuous(limits = c(0.5,1)) +
scale_x_discrete(limits=c("group_a","group_c")) +
scale_fill_manual(values=regulon_groupcolors[c("group_a","group_c")]) +
labs(x="Regulon groups", y="OG's diversity") +
theme(panel.grid = element_blank()) +
theme(text=element_text(size=20), axis.line.x=element_blank())
p + stat_compare_means(method="wilcox.test",
comparisons =list(c("group_a","group_c")),
label = "p.signif")#-- (Figure S5c) Assess OG's plasticity by regulon groups
p <- ggplot(stats_df, aes(x=regulon_groups, y=Plasticity, fill=regulon_groups)) +
geom_boxplot(show.legend=F) +
scale_y_continuous(limits = c(0,1)) +
scale_x_discrete(limits=c("group_a","group_c")) +
scale_fill_manual(values=regulon_groupcolors[c("group_a","group_c")]) +
labs(x="Regulon groups", y="OG's plasticity") +
theme(panel.grid = element_blank()) +
theme(text=element_text(size=20), axis.line.x=element_blank())
p + stat_compare_means(method="wilcox.test",
comparisons =list(c("group_a","group_c")),
label = "p.signif")
Figure S5. OG’s abundance (a), diversity (b) and plasticity (c) mapped to regulons grouped based on the distance between the evolutionary roots of TFs and targets. ****P-value = 5.1e-5 (Wilcoxon-Mann-Whitney test); ns = not significant.
The abundance mapped to regulons whose TF-target genes are rooted before the TF (Group-a) is the same from that mapped to regulons whose TF-target genes are rooted after the TF (Group-c) (Figure S5a), suggesting that the number of orthologs per species is similar between the two groups. In contrast, the OG’s diversity mapped to Group-a is higher comparing with Group-c (P-value = 5.1e-5; Wilcoxon-Mann-Whitney test) (Figure S5b). As diversity estimates the dispersion of the orthologous genes in the species tree, this suggests that regulons in Group-a have orthologs more evenly distributed, which is usually observed for OGs rooted at the base of the phylogenetic tree (Castro et al. 2008). We did not detect any difference between Group-a and Group-c using the plasticity scores mapped to regulons (Figure S5c).
5 Evolutionary analysis of regulons generated from normal breast tissue samples
Regulons are constructed based on a gene’s expression varying across a cohort. Large cohorts of tumour samples typically contain multiple molecular subtypes, and typically provide good expression variability for building regulons. In contrast, sample sets that are more homogeneous may be more challenging to explore with regulons, and this may be the case with sets of normal, non-cancerous samples. Despite this challenging, Fletcher et al. (2013) generated regulons using normal breast tissue samples in order to observe regulatory differences between cancer and normal cells. Here we will run the same evolutionary analysis described in section 4, but now using regulons generated from normal breast tissue samples. In the next steps we show how to reproduce the previous results using a diferent TRN.
5.1 Mapping root-to-gene annotation
data("rtniNormals")
graph_normals <- tni.graph(rtniNormals, gtype = "rmap")
graph_normals <- ogr2igraph(ogr, cogdata, graph_normals, idkey = "ENTREZ")
roots_df_normals <- data.frame(COGID = V(graph_normals)$COGID,
SYMBOL = V(graph_normals)$SYMBOL,
ENTREZ = V(graph_normals)$ENTREZ,
Root = V(graph_normals)$Root,
TRN_element = c("Target","TF")[V(graph_normals)$tfs+1])
roots_df_normals <- roots_df_normals[complete.cases(roots_df_normals),]
roots_df_normals <- roots_df_normals[roots_df_normals$Root<max(roots_df_normals$Root),]
rownames(roots_df_normals) <- 1:nrow(roots_df_normals)
table(roots_df_normals$TRN_element)## Target TF
## 2818 1305.2 Comparing regulators and targets
#-- Assess root distribution by TRN_element
wilcox.test(Root ~ TRN_element, data=roots_df_normals)## Wilcoxon rank sum test with continuity correction
## data: Root by TRN_element
## W = 152522, p-value = 0.001148
## alternative hypothesis: true location shift is not equal to 0#-- Set roots to display in y-axis
roots <- c(4,8,11,13,19,21,25)
#-- Set a summary function to display dispersion within the violins
data_summary <- function(x) {
y <- mean(x); ymin <- y-sd(x); ymax <- y+sd(x)
return(c(y=y,ymin=ymin,ymax=ymax))
}
#-- (Figure S6) Generate violin plots showing root distribution by TRN_element
p <- ggplot(roots_df_normals, aes(x=TRN_element, y=Root)) +
geom_violin(aes(fill=TRN_element), adjust=2, show.legend=F) +
scale_y_continuous(breaks=roots, labels=paste("root",roots)) +
scale_fill_manual(values=c("#c7eae5","#dfc27d")) +
labs(x="TRN elements", y="Root distribution") +
scale_x_discrete(limits=c("TF","Target"), labels=c("TFs","Targets")) +
theme_classic() +
theme(text=element_text(size=20)) +
stat_summary(fun.data = data_summary)
p + stat_compare_means(method="wilcox.test",
comparisons =list(c("TF","Target")),
label = "p.signif")
Figure S6. Distribution of the inferred evolutionary roots of TFs and target genes using regulons available from the rtniNormals data object. **P-value = 0.001148 (Wilcoxon-Mann-Whitney test).
6 Session information
## R version 3.6.1 (2019-07-05)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.3 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.10-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.10-bioc/R/lib/libRlapack.so
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_US.UTF-8 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] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] plyr_1.8.4 ggpubr_0.2.3
## [3] magrittr_1.5 ggplot2_3.2.1
## [5] Fletcher2013b_1.22.0 igraph_1.2.4.1
## [7] RedeR_1.34.0 Fletcher2013a_1.22.0
## [9] limma_3.42.0 RTN_2.10.0
## [11] geneplast.data.string.v91_0.99.6 geneplast_1.12.2
## [13] BiocStyle_2.14.0
##
## loaded via a namespace (and not attached):
## [1] Biobase_2.46.0 mixtools_1.1.0
## [3] splines_3.6.1 gtools_3.8.1
## [5] assertthat_0.2.1 minet_3.44.0
## [7] BiocManager_1.30.9 stats4_3.6.1
## [9] GenomeInfoDbData_1.2.2 yaml_2.2.0
## [11] viper_1.20.0 pillar_1.4.2
## [13] lattice_0.20-38 glue_1.3.1
## [15] digest_0.6.22 ggsignif_0.6.0
## [17] GenomicRanges_1.38.0 RColorBrewer_1.1-2
## [19] XVector_0.26.0 colorspace_1.4-1
## [21] htmltools_0.4.0 Matrix_1.2-17
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## [41] nlme_3.1-141 MASS_7.3-51.4
## [43] segmented_1.0-0 gplots_3.0.1.1
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## [59] rlang_0.4.1 futile.logger_1.4.3
## [61] grid_3.6.1 RCurl_1.95-4.12
## [63] bitops_1.0-6 rmarkdown_1.16
## [65] gtable_0.3.0 R6_2.4.0
## [67] dplyr_0.8.3 knitr_1.25
## [69] futile.options_1.0.1 KernSmooth_2.23-16
## [71] ape_5.3 stringi_1.4.3
## [73] parallel_3.6.1 Rcpp_1.0.2
## [75] tidyselect_0.2.5 xfun_0.10References
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