Last updated: 2018-10-22

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    File Version Author Date Message
    Rmd c8dbaf0 Briana Mittleman 2018-10-22 add apa prot rna overlap


I want to use this analysis to look at the genes with a APAQTL and a protein QTL. I am trying to understand how many of these are independent of RNA.

I will first look at genes with significant QTLs in both phenotypes. I can use the pipeline I created in https://brimittleman.github.io/threeprimeseq/swarmPlots_QTLs.html to vizualize these snps.

library(workflowr)
This is workflowr version 1.1.1
Run ?workflowr for help getting started
library(tidyverse)
── Attaching packages ──────────────────────────────────────────────────────────── tidyverse 1.2.1 ──
✔ ggplot2 3.0.0     ✔ purrr   0.2.5
✔ tibble  1.4.2     ✔ dplyr   0.7.6
✔ tidyr   0.8.1     ✔ stringr 1.3.1
✔ readr   1.1.1     ✔ forcats 0.3.0
── Conflicts ─────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
library(data.table)

Attaching package: 'data.table'
The following objects are masked from 'package:dplyr':

    between, first, last
The following object is masked from 'package:purrr':

    transpose
library(cowplot)

Attaching package: 'cowplot'
The following object is masked from 'package:ggplot2':

    ggsave

Gene Names:

geneNames=read.table("../data/ensemble_to_genename.txt", stringsAsFactors = F, header = T, sep="\t")

Significant APA QTLS:

nuclearAPA=read.table("../data/perm_QTL_trans/filtered_APApeaks_merged_allchrom_refseqGenes_pheno_Nuclear_transcript_permResBH.txt", stringsAsFactors = F, header = T) %>% separate(pid, into=c("chr", "start", "end", "id"), sep=":") %>% separate(id, into=c("Gene.name", "strand", "peaknum"), sep="_") %>% dplyr::filter(-log10(bh)>1)
totalAPA=read.table("../data/perm_QTL_trans/filtered_APApeaks_merged_allchrom_refseqGenes_pheno_Total_transcript_permResBH.txt", stringsAsFactors = F, header=T)  %>% separate(pid, into=c("chr", "start", "end", "id"), sep=":") %>% separate(id, into=c("Gene.name", "strand", "peaknum"), sep="_") %>% dplyr::filter(-log10(bh)>1)

Significant Protien QTLs

protQTL=read.table("../data/other_qtls/fastqtl_qqnorm_prot.fixed.perm.out", col.names = c("Gene.stable.ID", "nvar", "shape1", "shape2", "dummy", "sid", "dist", "npval", "slope", "ppval", "bpval"),stringsAsFactors=F) %>% inner_join(geneNames, by="Gene.stable.ID") %>% dplyr::select("Gene.name", "nvar", "shape1", "shape2", "dummy", "sid", "dist", "npval", "slope", "ppval", "bpval")

protQTL$bh=p.adjust(protQTL$bpval, method="fdr")
protQTL_sig= protQTL %>% dplyr::filter(-log10(bh)>1)

Gene Level

Overlap the QTLs by gene name:

genesBothTot=protQTL_sig %>%  inner_join(totalAPA, by=c("Gene.name"))
genesBotNuc=protQTL_sig %>%  inner_join(nuclearAPA, by=c("Gene.name"))

These are the genes that have a significant QTL in both.They are not the same snp. This may be because I am using the permuted snps. I will use the APA snp to make the plot.

plotQTL_func= function(SNP, peak, gene){
  apaN_file=read.table(paste("../data/apaExamp/qtlSNP_PeakAPANuclear.", SNP, peak, ".txt", sep = "" ), header=T)
  apaT_file=read.table(paste("../data/apaExamp/qtlSNP_PeakAPATotal.", SNP, peak, ".txt", sep = "" ), header=T)
  su30_file=read.table(paste("../data/apaExamp/qtlSNP_Peak_4su_30_", SNP, gene, ".txt", sep=""), header = T)
  su60_file=read.table(paste("../data/apaExamp/qtlSNP_Peak_4su_60_", SNP, gene, ".txt", sep=""), header=T)
  RNA_file=read.table(paste("../data/apaExamp/qtlSNP_Peak_RNAseq_", SNP, gene, ".txt", sep=""),header=T)
  RNAg_file=read.table(paste("../data/apaExamp/qtlSNP_Peak_RNAseqGeuvadis_", SNP, gene, ".txt", sep=""), header = T)
  ribo_file=read.table(paste("../data/apaExamp/qtlSNP_Peak_ribo_", SNP, gene, ".txt", sep=""),header=T)
  prot_file=read.table(paste("../data/apaExamp/qtlSNP_Peak_prot.", SNP, gene, ".txt", sep=""), header=T)
  
  ggplot_func= function(file, molPhen,GENE){
    file = file %>% mutate(genotype=Allele1 + Allele2)
    file$genotype= as.factor(as.character(file$genotype))
    plot=ggplot(file, aes(y=Pheno, x=genotype, by=genotype, fill=genotype)) + geom_boxplot(width=.25) + geom_jitter() + labs(y="Phenotpye",title=paste(molPhen, GENE, sep=": ")) + scale_fill_brewer(palette="Paired")
    return(plot)
  }
  
  apaNplot=ggplot_func(apaN_file, "Apa Nuclear", gene)
  apaTplot=ggplot_func(apaT_file, "Apa Total", gene)
  su30plot=ggplot_func(su30_file, "4su30",gene)
  su60plot=ggplot_func(su60_file, "4su60",gene)
  RNAplot=ggplot_func(RNA_file, "RNA Seq",gene)
  RNAgPlot=ggplot_func(RNAg_file, "RNA Seq Geuvadis",gene)
  riboPlot= ggplot_func(ribo_file, "Ribo Seq",gene)
  protplot=ggplot_func(prot_file, "Protein",gene)
  
  full_plot= plot_grid(apaNplot,apaTplot, su30plot, su60plot, RNAplot, RNAgPlot, riboPlot, protplot,nrow=2)
  return (full_plot)
}

Total:

  • MRPL43 peak44585 10:102740271
grep MRPL43 /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000055950


python createQTLsnpAPAPhenTable.py 10 10:102740271  peak44585 Total
python createQTLsnpAPAPhenTable.py 10 10:102740271  peak44585  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "10" "10:102740271" "ENSG00000055950"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*10:102740271* .
plotQTL_func(SNP="10:102740271", peak="peak44585", gene="ENSG00000055950")

Nuclear:

  • SWAP70 peak49384 11:9732917
grep SWAP70 /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000133789


python createQTLsnpAPAPhenTable.py 11 11:9732917  peak49384 Total
python createQTLsnpAPAPhenTable.py 11 11:9732917  peak49384  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "11" "11:9732917" "ENSG00000133789"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*11:9732917* .
plotQTL_func(SNP="11:9732917", peak="peak49384", gene="ENSG00000133789")

  • DHRS7B peak132739 17:21102458
grep DHRS7B /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000109016


python createQTLsnpAPAPhenTable.py 17 17:21102458  peak132739 Total
python createQTLsnpAPAPhenTable.py 17 17:21102458  peak132739  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "17" "17:21102458" "ENSG00000109016"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*17:21102458* .
plotQTL_func(SNP="17:21102458", peak="peak132739", gene="ENSG00000109016")

* UBA6 peak240167 4:68502794

grep UBA6 /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000033178


python createQTLsnpAPAPhenTable.py 4 4:68502794  peak240167 Total
python createQTLsnpAPAPhenTable.py 4 4:68502794  peak240167  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "4" "4:68502794" "ENSG00000033178"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*4:68502794* .
plotQTL_func(SNP="4:68502794", peak="peak240167", gene="ENSG00000033178")

This is not the most effective way to do this because I am overlapping by gene then looking at the effect of the apaQTL snp. I want a method that will look directly at the effect of one snp. I can use the overlap files I created based on the APA qtls in other phenotypes. I can overlap the phenotypes and look for snps that have low pvalues in APA and protien.

SNP level

Total

I want the overlap where I started in APA qtls and found the snp in the mol file. I am starting with the total.

totAPAinsu30=read.table("../data/mol_overlap/APA2molTotal/TotAPAqtlsPval4su30.txt", header = T, stringsAsFactors = F)
totAPAinsu60=read.table("../data/mol_overlap/APA2molTotal/TotAPAqtlsPval4su60.txt", header = T, stringsAsFactors = F)
totAPAinRNA=read.table("../data/mol_overlap/APA2molTotal/TotAPAqtlsPvalRNA.txt", header = T, stringsAsFactors = F)
totAPAinRNAg=read.table("../data/mol_overlap/APA2molTotal/TotAPAqtlsPvalRNAg.txt", header = T, stringsAsFactors = F)
totAPAinRibo=read.table("../data/mol_overlap/APA2molTotal/TotAPAqtlsPvalribo.txt", header = T, stringsAsFactors = F)
totAPAinProt=read.table("../data/mol_overlap/APA2molTotal/TotAPAqtlsPvalProtein.txt", header = T, stringsAsFactors = F)


allOverlap_T=totAPAinsu30 %>%  full_join(totAPAinsu60, by=c("Gene.name", "sid")) %>%  full_join(totAPAinRNA, by=c("Gene.name", "sid")) %>%  full_join(totAPAinRNAg, by=c("Gene.name", "sid"))  %>%  full_join(totAPAinRibo, by=c("Gene.name", "sid"))  %>%  full_join(totAPAinProt, by=c("Gene.name", "sid")) 

colnames(allOverlap_T)=c("Gene.name", "sid", "su30", "su60", "RNA", "RNAg", "ribo", "prot")
plot(sort(allOverlap_T$prot))

plot(allOverlap_T$RNA ~ allOverlap_T$prot)

I want to make a ggplot of these where I color them by RNA pvalue:

allOverlap_T_lowP=allOverlap_T %>% dplyr::filter(prot<.05)
ggplot(allOverlap_T_lowP, aes(x=RNA, y=prot)) + geom_point()+ geom_text(aes(label=Gene.name),hjust=0, vjust=0) + geom_vline(xintercept = .05, col="red")

ggplot(allOverlap_T_lowP, aes(x=RNAg, y=prot)) + geom_point()+ geom_text(aes(label=Gene.name),hjust=0, vjust=0) + geom_vline(xintercept = .05, col="red")

I can use these to look for examples of SNPs that are significant in prot but not in RNA.

Look at some of these:

Total RNA:
* SACM1L
* EBI3
* FBXL18
* PSMF1
* COX17

Total RNAg:
* EBI3
* FBXL18
* APBB1IP * PSMF1

Look at some examples of genes that come up in both.

EBI3 peak152751 19:4236475

Expressed in B lymphocytes in response to EB virus.

grep EBI3 /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000105246


python createQTLsnpAPAPhenTable.py 19 19:4236475  peak152751 Total
python createQTLsnpAPAPhenTable.py 19 19:4236475  peak152751  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "19" "19:4236475" "ENSG00000105246"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*19:4236475* .
plotQTL_func(SNP="19:4236475", peak="peak152751", gene="ENSG00000105246")

FBXL18 peak291746 7:5524129

“The protein encoded by this gene is a member of a family of proteins that contain an approximately 40-amino acid F-box motif. This motif is important for interaction with SKP1 and for targeting some proteins for degradation.” genecards.org

grep FBXL18 /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000155034


python createQTLsnpAPAPhenTable.py 7 7:5524129  peak291746 Total
python createQTLsnpAPAPhenTable.py 7 7:5524129  peak291746  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "7" "7:5524129" "ENSG00000155034"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*7:5524129* .
plotQTL_func(SNP="7:5524129", peak="peak291746", gene="ENSG00000155034")
Warning: Removed 4 rows containing non-finite values (stat_boxplot).
Warning: Removed 4 rows containing missing values (geom_point).

  • PSMF1 peak193648 20:1131308

This gene codes the 26S proteasome.

grep PSMF1 /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000125818


python createQTLsnpAPAPhenTable.py 20 20:1131308   peak193648 Total
python createQTLsnpAPAPhenTable.py 20 20:1131308   peak193648  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "20" "20:1131308" "ENSG00000125818"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*20:1131308* .
plotQTL_func(SNP="20:1131308", peak="peak193648", gene="ENSG00000125818")
Warning: Removed 2 rows containing non-finite values (stat_boxplot).
Warning: Removed 2 rows containing missing values (geom_point).

I want to know the number of these that are <.05 in protien and above .1 in RNA

allOverlap_T_lowP_highRNA=allOverlap_T %>% dplyr::filter(prot<.05) %>% dplyr::filter(RNA>.05)
allOverlap_T_lowP_highRNAg=allOverlap_T %>% dplyr::filter(prot<.05) %>% dplyr::filter(RNAg>.05)

8 snps with < .05 for protein. Of those 6 have RNA pvalues greater than .05

6/8
[1] 0.75

Nuclear

nucAPAinsu30=read.table("../data/mol_overlap/APA2molNuclear/NucAPAqtlsPval4su30.txt", header = T, stringsAsFactors = F)
nucAPAinsu60=read.table("../data/mol_overlap/APA2molNuclear/NucAPAqtlsPval4su60.txt", header = T, stringsAsFactors = F)
nucAPAinRNA=read.table("../data/mol_overlap/APA2molNuclear/NucAPAqtlsPvalRNA.txt", header = T, stringsAsFactors = F)
nucAPAinRNAg=read.table("../data/mol_overlap/APA2molNuclear/NucAPAqtlsPvalRNAg.txt", header = T, stringsAsFactors = F)
nucAPAinRibo=read.table("../data/mol_overlap/APA2molNuclear/NucAPAqtlsPvalribo.txt", header = T, stringsAsFactors = F)
nucAPAinProt=read.table("../data/mol_overlap/APA2molNuclear/NucAPAqtlsPvalProtein.txt", header = T, stringsAsFactors = F)


allOverlap_N=nucAPAinsu30 %>%  full_join(nucAPAinsu60, by=c("Gene.name", "sid")) %>%  full_join(nucAPAinRNA, by=c("Gene.name", "sid")) %>%  full_join(nucAPAinRNAg, by=c("Gene.name", "sid"))  %>%  full_join(nucAPAinRibo, by=c("Gene.name", "sid"))  %>%  full_join(nucAPAinProt, by=c("Gene.name", "sid")) 

colnames(allOverlap_N)=c("Gene.name", "sid", "su30", "su60", "RNA", "RNAg", "ribo", "prot")
#subset by prot < .05  

allOverlap_N_lowP=allOverlap_N %>% dplyr::filter(prot<.05)
ggplot(allOverlap_N_lowP, aes(x=RNA, y=prot)) + geom_point()+ geom_text(aes(label=Gene.name),hjust=0, vjust=0)+ geom_vline(xintercept = .05, col="red")

ggplot(allOverlap_N_lowP, aes(x=RNAg, y=prot)) + geom_point()+ geom_text(aes(label=Gene.name),hjust=0, vjust=0)+ geom_vline(xintercept = .05, col="red")

allOverlap_N_lowP_highRNA=allOverlap_N %>% dplyr::filter(prot<.05) %>% dplyr::filter(RNA>.05)
allOverlap_N_lowP_highRNAg=allOverlap_N %>% dplyr::filter(prot<.05) %>% dplyr::filter(RNAg>.05)

39 snps with < .05 for protein. Of those 28 have RNA pvalues greater than .05

28/39
[1] 0.7179487
inBothN= allOverlap_N_lowP_highRNAg %>%  inner_join(allOverlap_N_lowP_highRNA, by=c("Gene.name", "sid", "su30", "su60", "RNA", "RNAg", "ribo", "prot")) %>% arrange(desc(RNA))
inBothN$Gene.name[1:5]
[1] "MSMO1"  "LYAR"   "CD2BP2" "KDM2A"  "RINT1" 
  • MSMO1 4:166260601 peak249109

contains metal binding motifs, known alternative splice isoforms

grep MSMO1 /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000052802


python createQTLsnpAPAPhenTable.py 4 4:166260601  peak249109 Total
python createQTLsnpAPAPhenTable.py 4 4:166260601  peak249109  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "4" "4:166260601" "ENSG00000052802"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*4:166260601* .
plotQTL_func(SNP="4:166260601", peak="peak249109", gene="ENSG00000052802")
Warning: Removed 3 rows containing non-finite values (stat_boxplot).
Warning: Removed 3 rows containing missing values (geom_point).

* LYAR peak235215 4:4196045

involved in processing pre-rRNA

grep LYAR /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000145220


python createQTLsnpAPAPhenTable.py 4 4:4196045  peak235215 Total
python createQTLsnpAPAPhenTable.py 4 4:4196045  peak235215  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "4" "4:4196045" "ENSG00000145220"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*4:4196045* .
plotQTL_func(SNP="4:4196045", peak="peak235215", gene="ENSG00000145220")

CD2BP2 peak122237 16:29898001

From genecards: “in the cytoplasm, the encoded protein binds the cytoplasmic tail of human surface antigen CD2 via its C-terminal GYF domain, and regulate CD2-triggered T lymphocyte activation. In the nucleus, this protein is a component of the U5 small nuclear ribonucleoprotein complex and is involved in RNA splicing.”

grep CD2BP2 /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000169217


python createQTLsnpAPAPhenTable.py 16 16:29898001 peak122237 Total
python createQTLsnpAPAPhenTable.py 16 16:29898001 peak122237  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "16" "16:29898001" "ENSG00000169217"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*16:29898001* .
plotQTL_func(SNP="16:29898001", peak="peak122237", gene="ENSG00000169217")
Warning: Removed 5 rows containing non-finite values (stat_boxplot).
Warning: Removed 5 rows containing missing values (geom_point).

KDM2A peak55622 11:66851583

grep KDM2A /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000173120


python createQTLsnpAPAPhenTable.py 11 11:66851583 peak55622 Total
python createQTLsnpAPAPhenTable.py 11 11:66851583 peak55622  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "11" "11:66851583" "ENSG00000173120"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*11:66851583* .
plotQTL_func(SNP="11:66851583", peak="peak55622", gene="ENSG00000173120")
Warning: Removed 8 rows containing non-finite values (stat_boxplot).
Warning: Removed 8 rows containing missing values (geom_point).

RINT1 peak303436 7:105155320

Interacts with double strand break repair protiens, regulates cell cycle and telomere length

grep RINT1 /project2/gilad/briana/genome_anotation_data/ensemble_to_genename.txt
#ENSG00000135249


python createQTLsnpAPAPhenTable.py 7 7:105155320 peak303436 Total
python createQTLsnpAPAPhenTable.py 7 7:105155320 peak303436  Nuclear

sbatch run_createQTLsnpMolPhenTable.sh "7" "7:105155320" "ENSG00000135249"

#into apaExamp
scp brimittleman@midway2.rcc.uchicago.edu:/project2/gilad/briana/threeprimeseq/data/ApaQTL_examples/*7:105155320* .
plotQTL_func(SNP="7:105155320", peak="peak303436", gene="ENSG00000135249")
Warning: Removed 2 rows containing non-finite values (stat_boxplot).
Warning: Removed 2 rows containing missing values (geom_point).

Significance

In the next step I need to add significance to the boxplots and think more about the significance cutoffs.

Maybe I can compare 2 other phenotypes for <.05 and >.05 to see if the percentage is less than what I see for RNA and protein.

Session information

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Sierra 10.12.6

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/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] bindrcpp_0.2.2    cowplot_0.9.3     data.table_1.11.8
 [4] forcats_0.3.0     stringr_1.3.1     dplyr_0.7.6      
 [7] purrr_0.2.5       readr_1.1.1       tidyr_0.8.1      
[10] tibble_1.4.2      ggplot2_3.0.0     tidyverse_1.2.1  
[13] workflowr_1.1.1  

loaded via a namespace (and not attached):
 [1] tidyselect_0.2.4   haven_1.1.2        lattice_0.20-35   
 [4] colorspace_1.3-2   htmltools_0.3.6    yaml_2.2.0        
 [7] rlang_0.2.2        R.oo_1.22.0        pillar_1.3.0      
[10] glue_1.3.0         withr_2.1.2        R.utils_2.7.0     
[13] RColorBrewer_1.1-2 modelr_0.1.2       readxl_1.1.0      
[16] bindr_0.1.1        plyr_1.8.4         munsell_0.5.0     
[19] gtable_0.2.0       cellranger_1.1.0   rvest_0.3.2       
[22] R.methodsS3_1.7.1  evaluate_0.11      labeling_0.3      
[25] knitr_1.20         broom_0.5.0        Rcpp_0.12.19      
[28] scales_1.0.0       backports_1.1.2    jsonlite_1.5      
[31] hms_0.4.2          digest_0.6.17      stringi_1.2.4     
[34] grid_3.5.1         rprojroot_1.3-2    cli_1.0.1         
[37] tools_3.5.1        magrittr_1.5       lazyeval_0.2.1    
[40] crayon_1.3.4       whisker_0.3-2      pkgconfig_2.0.2   
[43] xml2_1.2.0         lubridate_1.7.4    assertthat_0.2.0  
[46] rmarkdown_1.10     httr_1.3.1         rstudioapi_0.8    
[49] R6_2.3.0           nlme_3.1-137       git2r_0.23.0      
[52] compiler_3.5.1    



This reproducible R Markdown analysis was created with workflowr 1.1.1