Last updated: 2018-08-13

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    File Version Author Date Message
    Rmd e2ded68 brimittleman 2018-08-13 refseq gene
    html 2e06a70 brimittleman 2018-08-13 Build site.
    Rmd 3901f7e brimittleman 2018-08-13 pre and post clean peaks per gene
    html 38bfbaf brimittleman 2018-08-09 Build site.
    Rmd 03761cb brimittleman 2018-08-09 start peak explore analysis for 54 libraries


I know have 28 individuals sequences on 2 lanes. I have combined these and used the peak coverage pipeline to call and clean peaks. I will use this analysis to explore the library sizes and coverage at these peaks.

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(workflowr)
This is workflowr version 1.1.1
Run ?workflowr for help getting started
library(cowplot)

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

    ggsave
library(reshape2)

Attaching package: 'reshape2'
The following object is masked from 'package:tidyr':

    smiths
library(devtools)

Reads and Mapping Stats:

map_stats=read.csv("../data/comb_map_stats.csv", header=T)
map_stats$line=as.factor(map_stats$line)
map_stats$batch=as.factor(map_stats$batch)

The number of reads for each library and the number of mapped reads.

read_plot=ggplot(map_stats, aes(x=line, y=comb_reads, fill=fraction))+ geom_bar(stat="identity", position="dodge") +labs(y="Reads", title="Reads by line and fraction") 
map_plot=ggplot(map_stats, aes(x=line, y=comb_mapped, fill=fraction))+ geom_bar(stat="identity", position="dodge") +labs(y="Mapped Reads", title="Mapped reads by line and fraction") + geom_hline(yintercept=10000000) + annotate("text",label="10 million mapped reads", y=9000000, x=10)

plot_grid(read_plot, map_plot)

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38bfbaf brimittleman 2018-08-09

The percent of reads that map per line are pretty uniform accross libraries. The mean is 72%.

ggplot(map_stats, aes(x=line, y=comb_prop_mapped, fill=fraction))+ geom_bar(stat="identity", position="dodge") +labs(y="Mapped Percent", title="Percent of reads mapping by line and fraction") 

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38bfbaf brimittleman 2018-08-09

mean(map_stats$comb_prop_mapped)
[1] 0.7230478

Clean peak exploration

peak_quant=read.table(file = "../data/clean_peaks/APAquant.fc.cleanpeaks.fc", header=T)

Fix the names

file_names=colnames(peak_quant)[7:62]
file_names_split=lapply(file_names, function(x)strsplit(x,".", fixed=T))
libraries=c()
for (i in file_names_split){
  unlist_i=unlist(i)
  libraries=c(libraries, paste(unlist_i[10], unlist_i[11], sep="-"))
}
colnames(peak_quant)=c(colnames(peak_quant)[1:6], libraries)  

Explore the peaks before quantifications:

#length of peaks
plot(sort(peak_quant$Length,decreasing = T), main="Peak Lengths", ylab="Peak Length", xlab="Peak index")

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38bfbaf brimittleman 2018-08-09

#mean cov of peaks

peak_cov=peak_quant %>% select(contains("-"))

peak_mean=apply(peak_cov,1,mean)
peak_var=apply(peak_cov, 1, var)

plot(log10(sort(peak_mean,decreasing = T)))

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plot(peak_var)

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plot(log10(peak_var)~log10(peak_mean))

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Plot the coverage vs the length:

plot(peak_mean~peak_quant$Length)

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38bfbaf brimittleman 2018-08-09

Clustering:

CLustering:

pca_peak= prcomp(peak_cov,center = TRUE,scale. = TRUE)
summary(pca_peak)
Importance of components:
                          PC1    PC2     PC3     PC4    PC5    PC6     PC7
Standard deviation     6.5936 2.7291 1.66983 0.71519 0.6392 0.5651 0.52807
Proportion of Variance 0.7763 0.1330 0.04979 0.00913 0.0073 0.0057 0.00498
Cumulative Proportion  0.7763 0.9093 0.95915 0.96828 0.9756 0.9813 0.98626
                           PC8     PC9    PC10    PC11    PC12    PC13
Standard deviation     0.35808 0.29502 0.25231 0.23732 0.22343 0.19515
Proportion of Variance 0.00229 0.00155 0.00114 0.00101 0.00089 0.00068
Cumulative Proportion  0.98855 0.99010 0.99124 0.99224 0.99314 0.99382
                         PC14    PC15    PC16    PC17    PC18    PC19
Standard deviation     0.1832 0.17407 0.16032 0.14346 0.14122 0.13574
Proportion of Variance 0.0006 0.00054 0.00046 0.00037 0.00036 0.00033
Cumulative Proportion  0.9944 0.99496 0.99542 0.99578 0.99614 0.99647
                         PC20    PC21    PC22    PC23    PC24    PC25
Standard deviation     0.1300 0.12760 0.11966 0.11231 0.10982 0.10799
Proportion of Variance 0.0003 0.00029 0.00026 0.00023 0.00022 0.00021
Cumulative Proportion  0.9968 0.99706 0.99732 0.99754 0.99776 0.99796
                          PC26    PC27    PC28    PC29    PC30    PC31
Standard deviation     0.10167 0.09704 0.09243 0.08607 0.08012 0.07887
Proportion of Variance 0.00018 0.00017 0.00015 0.00013 0.00011 0.00011
Cumulative Proportion  0.99815 0.99832 0.99847 0.99860 0.99872 0.99883
                          PC32    PC33    PC34    PC35    PC36    PC37
Standard deviation     0.07689 0.07601 0.07153 0.06993 0.06656 0.06334
Proportion of Variance 0.00011 0.00010 0.00009 0.00009 0.00008 0.00007
Cumulative Proportion  0.99893 0.99904 0.99913 0.99922 0.99929 0.99937
                          PC38    PC39    PC40    PC41    PC42    PC43
Standard deviation     0.06152 0.05822 0.05643 0.05371 0.05236 0.04715
Proportion of Variance 0.00007 0.00006 0.00006 0.00005 0.00005 0.00004
Cumulative Proportion  0.99943 0.99949 0.99955 0.99960 0.99965 0.99969
                          PC44    PC45    PC46    PC47    PC48    PC49
Standard deviation     0.04656 0.04584 0.04252 0.04214 0.03873 0.03696
Proportion of Variance 0.00004 0.00004 0.00003 0.00003 0.00003 0.00002
Cumulative Proportion  0.99973 0.99977 0.99980 0.99983 0.99986 0.99988
                          PC50    PC51    PC52    PC53    PC54    PC55
Standard deviation     0.03557 0.03351 0.03191 0.03020 0.02938 0.02733
Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00001
Cumulative Proportion  0.99991 0.99993 0.99994 0.99996 0.99998 0.99999
                          PC56
Standard deviation     0.02525
Proportion of Variance 0.00001
Cumulative Proportion  1.00000
pc_df=as.data.frame(pca_peak$rotation) %>% rownames_to_column(var="lib") %>% mutate(fraction=ifelse(grepl("T", lib), "total", "nuclear"))

ggplot(pc_df, aes(x=PC1, y=PC2, col=fraction)) + geom_point() + labs(x="PC1: Prop explained 0.7763", y="PC2: Prop explained 0.1330", title="Raw PAS qunatification data")

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2e06a70 brimittleman 2018-08-13
38bfbaf brimittleman 2018-08-09

I now want to explore what the first PC is representing. Some ideas are:

  • batch

  • sequencing depth

  • mapped reads

All of this info is in the map stats.

pc_df=as.data.frame(pca_peak$rotation) %>% rownames_to_column(var="lib") %>% mutate(fraction=ifelse(grepl("T", lib), "total", "nuclear")) %>% mutate(reads=map_stats$comb_reads) %>% mutate(batch=map_stats$batch) %>% mutate(mapped=map_stats$comb_mapped)


batch_gg= ggplot(pc_df, aes(x=PC1, y=PC2, col=batch)) + geom_point() + labs(x="PC1: Prop explained 0.7763", y="PC2: Prop explained 0.1330", title="Batch")

frac_gg= ggplot(pc_df, aes(x=PC1, y=PC2, col=fraction)) + geom_point() + labs(x="PC1: Prop explained 0.7763", y="PC2: Prop explained 0.1330", title="Fraction")

reads_gg= ggplot(pc_df, aes(x=PC1, y=PC2, col=reads)) + geom_point() + labs(x="PC1: Prop explained 0.7763", y="PC2: Prop explained 0.1330", title="Reads")


mapped_gg= ggplot(pc_df, aes(x=PC1, y=PC2, col=mapped)) + geom_point() + labs(x="PC1: Prop explained 0.7763", y="PC2: Prop explained 0.1330", title="Mapped Reads")

plot_grid(frac_gg,batch_gg,reads_gg,mapped_gg)

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2e06a70 brimittleman 2018-08-13

Proportion of reads mapping to peaks. This may be in the feature counts summary.

map_summary=read.table("../data/clean_peaks/APAquant.fc.cleanpeaks.fc.summary", header=T)

colnames(map_summary)=c(colnames(map_summary)[1], libraries) 

map_summary_m=map_summary[,2:57] %>% t 
colnames(map_summary_m)=map_summary$Status

map_summary_m_df= as.data.frame(map_summary_m) %>% mutate(perc_feature=(Assigned/(Assigned+Unassigned_NoFeatures)))
pc_df_mapsum=as.data.frame(pca_peak$rotation) %>% rownames_to_column(var="lib") %>% mutate(fraction=ifelse(grepl("T", lib), "total", "nuclear")) %>% mutate(reads=map_stats$comb_reads) %>% mutate(batch=map_stats$batch) %>% mutate(mapped=map_stats$comb_mapped) %>% mutate(PercFeature=map_summary_m_df$perc_feature)

propfrac_gg= ggplot(pc_df_mapsum, aes(x=PC1, y=PC2, col=PercFeature)) + geom_point() + labs(x="PC1: Prop explained 0.7763", y="PC2: Prop explained 0.1330", title="Percent Reads mapping to a feature")


propfrac_gg

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2e06a70 brimittleman 2018-08-13
38bfbaf brimittleman 2018-08-09

Map peaks to genes

I want to use the bedtools closest command to find the clostest protein coding gene to each peak.

  • -s (require same strandedness)

  • -d add a column with distance to closest (strand spec) report distance wrt the genes

  • A is the peak

  • B is protein coding genes

#!/bin/bash

#SBATCH --job-name=mapgene2peak
#SBATCH --account=pi-yangili1
#SBATCH --time=24:00:00
#SBATCH --output=mapgene2peak.out
#SBATCH --error=mapgene2peak.err
#SBATCH --partition=broadwl
#SBATCH --mem=12G
#SBATCH --mail-type=END

module load Anaconda3
source activate three-prime-env


bedtools closest -s -d -a /project2/gilad/briana/threeprimeseq/data/clean.peaks_comb/APApeaks_combined_clean_fixed.bed -b /project2/gilad/briana/genome_anotation_data/gencode.v19.annotation.proteincodinggene.bed > /project2/gilad/briana/threeprimeseq/data/clean.peaks_comb/APApeaks_comb_clean_dist2gene.txt
clean_peaks=read.table("../data/clean_peaks/APApeaks_combined_clean.bed", header=F)

This scirpt is called fix_cleanpeakbed.py

from misc_helper import *
fout = file("/project2/gilad/briana/threeprimeseq/data/clean.peaks_comb/APApeaks_combined_clean_fixed.bed",'w')
for ln in open("/project2/gilad/briana/threeprimeseq/data/clean.peaks_comb/APApeaks_combined_clean.bed"):
    chrom, start, end, name, cov, strand, score2 = ln.split()
    chrom_nochr= int(chrom[3:])
    start_i = int(start)
    end_i = int(end)
    cov_i=float(cov)
    fout.write("%d\t%d\t%d\t%s\t%f\t%s\n"%(chrom_nochr, start_i, end_i, name, cov_i, strand))
fout.close()

Second option is to use bedtools map. This will tell me directly how many peaks overlap each gene. I will use the -c and -o commands. I want it to tell me the number of peaks rather than the mean of the coverage. I can give it the name column as the -c and -0 count_distinct

#!/bin/bash

#SBATCH --job-name=mapgene2peak2
#SBATCH --account=pi-yangili1
#SBATCH --time=24:00:00
#SBATCH --output=mapgene2peak2.out
#SBATCH --error=mapgene2peak2.err
#SBATCH --partition=broadwl
#SBATCH --mem=12G
#SBATCH --mail-type=END

module load Anaconda3
source activate three-prime-env


bedtools map -c 4 -o count_distinct -a /project2/gilad/briana/genome_anotation_data/gencode.v19.annotation.proteincodinggene.bed -b /project2/gilad/briana/threeprimeseq/data/clean.peaks_comb/APApeaks_combined_clean_fixed.bed > /project2/gilad/briana/threeprimeseq/data/clean.peaks_comb/APApeaks_combined_clean_countdistgenes.txt

First look at the count for peaks in genes. this will not give us information for peaks outside of the annotaiton.

genes_per_peak=read.table("../data/clean_peaks/APApeaks_combined_clean_countdistgenes.txt", header=F, stringsAsFactors = F, col.names = c("chr", "strart", "end", "gene", "score", "strand", "numPeaks"))
nrow(genes_per_peak)
[1] 20345
genes_with_peak= genes_per_peak %>% filter(numPeaks>0) %>% nrow()
genes_with_peak
[1] 12867
genes_with_2peak= genes_per_peak %>% filter(numPeaks>1) %>% nrow()
genes_with_2peak
[1] 10797

There are in total 20,345 genes in the protein coding gene set. There are 12,867 with at least 1 peak and 10,797 with at least 2 peaks.

Look at the distribution:

plot(sort(genes_per_peak$numPeaks, decreasing = T), ylab="Number of Peaks", main="Number of peaks mapping to each protein coding gene")

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2e06a70 brimittleman 2018-08-13

The next dataset has more information aboutthe distance to the gene. If it overlaps, the distance should be 0.

dist_to_peak=read.table("../data/clean_peaks/APApeaks_comb_clean_dist2gene.txt", header=F)

Compare this to RNAseq

rnaseq_18486=read.table("../data/18486.genecov.txt", header=F,col.names = c("chr", "start", "end", "name", "score", "strand", "count"))

expressed_genes=rnaseq_18486 %>% filter(count>0) %>% nrow()
expressed_genes
[1] 16925

Get gene level coverage for 18486T 3’ seq data. I have this in /project2/gilad/briana/threeprimeseq/data/gene_cov.

threeprime_18486T=read.table("../data/YL-SP-18486-T-combined-genecov.txt", header=F, col.names = c("chr", "start", "end", "name", "score", "strand", "count"))
rnaseq_sm=rnaseq_18486 %>% select("name", "count")
threeprime_sm=threeprime_18486T %>% select("name", "count")

gene_cov=rnaseq_sm %>% left_join(threeprime_sm, by= "name") 
names(gene_cov)= c("name", "rnaseq", "threeprime")

ggplot(gene_cov,aes(x=log10(rnaseq), y=log10(threeprime)))+ geom_point(na.rm=TRUE, size=.1) + geom_density2d(na.rm = TRUE, size = 1, colour = 'red') + labs(y='Log(three prime seq gene Count)', x='Log(RNA seq gene Count)', title="Correlation between three prime seq and rna seq read counts") + xlab('Log(RNA seq gene Count)') + geom_smooth(method="lm")
Warning: Removed 6778 rows containing non-finite values (stat_smooth).

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2e06a70 brimittleman 2018-08-13

Subset genes with coverage in RNA seq but not in three prime seq.

genecov_onlyRNA=gene_cov %>% filter(threeprime==0 & rnaseq !=0) %>% arrange(desc(rnaseq))

What I actually want to look at genes with no peaks but RNA reads.

colnames(rnaseq_sm)=c("gene", "RNAseqCount")

cov_rnavthreeprime= rnaseq_sm %>% left_join(genes_per_peak, by="gene") %>% select(gene, RNAseqCount, numPeaks)
Warning: Column `gene` joining factor and character vector, coercing into
character vector
ggplot(cov_rnavthreeprime,aes(x=log10(RNAseqCount), y=log10(numPeaks)))+ geom_point(na.rm=TRUE, size=.1) + geom_density2d(na.rm = TRUE, size = 1, colour = 'red')  + geom_smooth(method="lm")
Warning: Removed 7575 rows containing non-finite values (stat_smooth).

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Version Author Date
2e06a70 brimittleman 2018-08-13

Explore how many genes have coverage in the RNAseq set but not the

NotInThreePrime=cov_rnavthreeprime %>% filter(numPeaks==0 & RNAseqCount !=0) %>% arrange(desc(RNAseqCount))
par(mfrow=c(1,2))

plot(log10(sort(cov_rnavthreeprime$RNAseqCount, decreasing = T)))
plot(log10(NotInThreePrime$RNAseqCount), main="Post-clean up, coverage of RNA seq without a PAS", xlab="gene", ylab="log10 coverage RNA seq 18486")

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Version Author Date
2e06a70 brimittleman 2018-08-13

Top RNA seq without peaks:

  • GAPDH - doesnt male sense. Visually see peak

  • EEF2

  • PFN1

  • PTMA

Try with peaks before cleaning

In looking at IGV the places have coverage and peaks are called in Yang protocol but they are all removed in the cleaning step. I want to look at how many genes have APA when we use the pre-cleaned list of peaks. This file is filtered_APApeaks_merged_allchrom.bed. I need to map these to genes like I did the other peaks.

This scirpt is called fix_dirtypeakbed.py

from misc_helper import *
fout = file("/project2/gilad/briana/threeprimeseq/data/mergedPeaks_comb/filtered_APApeaks_merged_allchrom.named.fixed.bed",'w')
for ln in open("/project2/gilad/briana/threeprimeseq/data/mergedPeaks_comb/filtered_APApeaks_merged_allchrom.named.bed"):
    chrom, start, end, name, cov, strand, score2 = ln.split()
    chrom_nochr= int(chrom[3:])
    start_i = int(start)
    end_i = int(end)
    cov_i=float(cov)
    fout.write("%d\t%d\t%d\t%s\t%f\t%s\n"%(chrom_nochr, start_i, end_i, name, cov_i, strand))
fout.close()

mapgene2peak_dirty.sh

#!/bin/bash

#SBATCH --job-name=mapgene2peak_dirty
#SBATCH --account=pi-yangili1
#SBATCH --time=24:00:00
#SBATCH --output=mapgene2peak_dirty.out
#SBATCH --error=mapgene2peak_dirty.err
#SBATCH --partition=broadwl
#SBATCH --mem=12G
#SBATCH --mail-type=END

module load Anaconda3
source activate three-prime-env


bedtools closest -s -d -a /project2/gilad/briana/threeprimeseq/data/mergedPeaks_comb/filtered_APApeaks_merged_allchrom.named.fixed.bed -b /project2/gilad/briana/genome_anotation_data/gencode.v19.annotation.proteincodinggene.bed > /project2/gilad/briana/threeprimeseq/data/mergedPeaks_comb/filtered_APApeaks_merged_allchrom_dist2gene.txt
#!/bin/bash

#SBATCH --job-name=mapgene2peak2_dirty
#SBATCH --account=pi-yangili1
#SBATCH --time=24:00:00
#SBATCH --output=mapgene2peak2_dirty.out
#SBATCH --error=mapgene2peak2_dirty.err
#SBATCH --partition=broadwl
#SBATCH --mem=12G
#SBATCH --mail-type=END

module load Anaconda3
source activate three-prime-env


bedtools map -c 4 -o count_distinct -a /project2/gilad/briana/genome_anotation_data/gencode.v19.annotation.proteincodinggene.bed -b /project2/gilad/briana/threeprimeseq/data/mergedPeaks_comb/filtered_APApeaks_merged_allchrom.named.fixed.bed > /project2/gilad/briana/threeprimeseq/data/mergedPeaks_comb/filtered_APApeaks_merged_allchrom_countdistgenes.txt
dirty_peak=read.table("../data/clean_peaks/filtered_APApeaks_merged_allchrom_countdistgenes.txt", col.names = c("chr", "start", "end", "gene", "score", "strand", "numPeaks"))


genes_with_peak_dirty= dirty_peak %>% filter(numPeaks>0) %>% nrow()
genes_with_peak_dirty
[1] 14678
genes_with_2peak_dirty=  dirty_peak %>% filter(numPeaks>1) %>% nrow()
genes_with_2peak_dirty
[1] 12761
rnaseq_dirtypeaks=rnaseq_sm %>% left_join(dirty_peak, by="gene") %>% mutate(length=end-start) %>% select(gene, RNAseqCount, numPeaks, length, start, end, chr)


dirty_onlyinRNA= rnaseq_dirtypeaks %>% filter(numPeaks==0 & RNAseqCount !=0) %>% arrange(desc(RNAseqCount))


summary(rnaseq_dirtypeaks$length)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
     59    8547   25654   65309   67508 2304638 
summary(dirty_onlyinRNA$length)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
     59    4500   16166   51003   53592 1117544 
par(mfrow=c(1,2))


plot(log10(dirty_onlyinRNA$RNAseqCount), main="Pre-clean up, \n coverage of RNA seq without a PAS", xlab="gene", ylab="log10 coverage RNA seq 18486")

plot(log10(NotInThreePrime$RNAseqCount), main="Post-clean up, \n coverage of RNA seq without a PAS", xlab="gene", ylab="log10 coverage RNA seq 18486")

Expand here to see past versions of unnamed-chunk-33-1.png:
Version Author Date
2e06a70 brimittleman 2018-08-13

Map to refseq

It looks like mapping to the refseq genes may be more effective here due to the better 3’ UTR annotatations

#!/bin/bash

#SBATCH --job-name=mapgene2peak2_dirty_refseq
#SBATCH --account=pi-yangili1
#SBATCH --time=24:00:00
#SBATCH --output=mapgene2peak2_dirty_rs.out
#SBATCH --error=mapgene2peak2_dirty_rs.err
#SBATCH --partition=broadwl
#SBATCH --mem=12G
#SBATCH --mail-type=END

module load Anaconda3
source activate three-prime-env


bedtools map -c 4 -o count_distinct -a /project2/gilad/briana/genome_anotation_data/ncbiRefSeq_sm_noChr.sort.bed -b /project2/gilad/briana/threeprimeseq/data/mergedPeaks_comb/filtered_APApeaks_merged_allchrom.named.fixed.bed > /project2/gilad/briana/threeprimeseq/data/mergedPeaks_comb/filtered_APApeaks_merged_allchrom_refseq_countdistgenes.txt

Also do coverage for the RNA seq with this.

#!/bin/bash

#SBATCH --job-name=refseq-rnaseqcov18486
#SBATCH --account=pi-yangili1
#SBATCH --time=24:00:00
#SBATCH --output=refseq-rnaseqcov18486.out
#SBATCH --error=refseq-rnaseqcov18486.err
#SBATCH --partition=broadwl
#SBATCH --mem=12G
#SBATCH --mail-type=END


module load Anaconda3  

source activate three-prime-env




bedtools coverage -counts -sorted -a /project2/gilad/briana/genome_anotation_data/ncbiRefSeq_sm.sort.bed-b /project2/gilad/briana/threeprimeseq/data/rnaseq_bed/18486.bed > /project2/gilad/briana/threeprimeseq/data/rnaseq_cov/18486.refseq.gencov.txt

bedfile is currupt. i need to make one from teh original vcf.

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  devtools_1.13.6 reshape2_1.4.3  cowplot_0.9.3  
 [5] workflowr_1.1.1 forcats_0.3.0   stringr_1.3.1   dplyr_0.7.6    
 [9] purrr_0.2.5     readr_1.1.1     tidyr_0.8.1     tibble_1.4.2   
[13] ggplot2_3.0.0   tidyverse_1.2.1

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_2.1.19      
 [7] rlang_0.2.1       R.oo_1.22.0       pillar_1.3.0     
[10] glue_1.3.0        withr_2.1.2       R.utils_2.6.0    
[13] modelr_0.1.2      readxl_1.1.0      bindr_0.1.1      
[16] plyr_1.8.4        munsell_0.5.0     gtable_0.2.0     
[19] cellranger_1.1.0  rvest_0.3.2       R.methodsS3_1.7.1
[22] memoise_1.1.0     evaluate_0.11     labeling_0.3     
[25] knitr_1.20        broom_0.5.0       Rcpp_0.12.18     
[28] backports_1.1.2   scales_0.5.0      jsonlite_1.5     
[31] hms_0.4.2         digest_0.6.15     stringi_1.2.4    
[34] grid_3.5.1        rprojroot_1.3-2   cli_1.0.0        
[37] tools_3.5.1       magrittr_1.5      lazyeval_0.2.1   
[40] crayon_1.3.4      whisker_0.3-2     pkgconfig_2.0.1  
[43] MASS_7.3-50       xml2_1.2.0        lubridate_1.7.4  
[46] assertthat_0.2.0  rmarkdown_1.10    httr_1.3.1       
[49] rstudioapi_0.7    R6_2.2.2          nlme_3.1-137     
[52] git2r_0.23.0      compiler_3.5.1   



This reproducible R Markdown analysis was created with workflowr 1.1.1