---
title: "DEqMS R Markdown vignettes"
author: 
- name: Yafeng Zhu
  affiliation: Karolinska Institute, Stockholm, Sweden
- name: Lukas Orre
  affiliation: Karolinska Institute, Stockholm, Sweden
- name: Yan Tran
  affiliation: Karolinska Institute, Stockholm, Sweden
- name: Georgios Mermelekas
  affiliation: Karolinska Institute, Stockholm, Sweden
- name: Henrik Johansson
  affiliation: Karolinska Institute, Stockholm, Sweden
- name: Alina Malyutina
  affiliation: University of Helsinki, Helsinki, Finland
- name: Simon Anders
  affiliation: Heidelberg University (ZMBH), Heidelberg, Germany
- name: Janne Lehtiö
  affiliation: Karolinska Institute, Stockholm, Sweden
date: "`r Sys.Date()`"
output: 
  BiocStyle::html_document:
    toc_fload: true
  BiocStyle::pdf_document: default   
package: DEqMS
abstract:
  Instructions to perform differential protein expression analysis using DEqMS
vignette: >
    %\VignetteIndexEntry{DEqMS R Markdown vignettes}
    %\VignetteEngine{knitr::rmarkdown}
    %\VignetteEncoding{UTF-8}
---

# Overview of DEqMS

`DEqMS` builds on top of `Limma`, a widely-used R package for microarray data 
analysis (Smyth G. et al 2004), and improves it with proteomics data specific 
properties, accounting for variance dependence on the number of quantified 
peptides or PSMs for statistical testing of differential protein expression.

Limma assumes a common prior variance for all proteinss, the function 
`spectraCounteBayes` in DEqMS package estimate prior variance
for proteins quantified by different number of PSMs.

A documentation of all R functions available in DEqMS is detailed in the PDF 
reference manual on the DEqMS Bioconductor page.

#Load the package
```{r Loadpackage}
library(DEqMS)
```

# Quick start
## Differential protein expression analysis with DEqMS using a protein table
As an example, we analyzed a protemoics dataset (TMT10plex labelled) in which 
A431 cells (human epidermoid carcinoma cell line) were treated with three 
different miRNA mimics (Zhou Y. Et al Oncogene 2017). The raw MS data was 
searched with MS-GF+ (Kim et al Nat Communications 2016) and post processed 
with Percolator (Kall L. et al Nat Method 2007). A tabular text output of 
protein table filtered at 1% protein level FDR is used.

### Download and Read the input protein table
```{r DownloadProteinTable}
url <- "ftp://ftp.pride.ebi.ac.uk/pride/data/archive/2016/06/PXD004163/Yan_miR_Protein_table.flatprottable.txt"
download.file(url, destfile = "./miR_Proteintable.txt",method = "auto")

df.prot = read.table("miR_Proteintable.txt",stringsAsFactors = FALSE,
                     header = TRUE, quote = "", comment.char = "",sep = "\t")
```

### Extract quant data columns for DEqMS
```{r Extractcolumn}
# filter at 1% protein FDR and extract TMT quantifications
TMT_columns = seq(15,33,2)
dat = df.prot[df.prot$miR.FASP_q.value<0.01,TMT_columns]
rownames(dat) = df.prot[df.prot$miR.FASP_q.value<0.01,]$Protein.accession
# The protein dataframe is a typical protein expression matrix structure
# Samples are in columns, proteins are in rows
# use unique protein IDs for rownames
# to view the whole data frame, use the command View(dat)
```

If the protein table is relative abundance (ratios) or intensity values, 
Log2 transform the data. Systematic effects and variance components are 
usually assumed to be additive on log scale (Oberg AL. et al JPR 2008; 
Hill EG. et al JPR 2008).
```{r log2transform1}
dat.log = log2(dat)
#remove rows with NAs
dat.log = na.omit(dat.log)
```

Use boxplot to check if the samples have medians centered.
if not, do median centering.
```{r boxplot1}
boxplot(dat.log,las=2,main="TMT10plex data PXD004163")
# Here the data is already median centered, we skip the following step. 
# dat.log = equalMedianNormalization(dat.log)
```

### Make design table. 
A design table is used to tell how samples are arranged in
different groups/classes. 
```{r,design}
# if there is only one factor, such as treatment. You can define a vector with
# the treatment group in the same order as samples in the protein table.
cond = as.factor(c("ctrl","miR191","miR372","miR519","ctrl",
"miR372","miR519","ctrl","miR191","miR372"))

# The function model.matrix is used to generate the design matrix
design = model.matrix(~0+cond) # 0 means no intercept for the linear model
colnames(design) = gsub("cond","",colnames(design))
```
### Make contrasts
In addition to the design, you need to define the contrast, which tells the 
model to compare the differences between specific groups.
Start with the Limma part.
```{r,limma}
# you can define one or multiple contrasts here
x <- c("miR372-ctrl","miR519-ctrl","miR191-ctrl",
       "miR372-miR519","miR372-miR191","miR519-miR191")
contrast =  makeContrasts(contrasts=x,levels=design)
fit1 <- lmFit(dat.log, design)
fit2 <- contrasts.fit(fit1,contrasts = contrast)
fit3 <- eBayes(fit2)
```

### DEqMS analysis
The above shows Limma part, now we use the function `spectraCounteBayes`
in DEqMS to correct bias of variance estimate based on minimum number of
psms per protein used for quantification.We use the minimum number of PSMs 
used for quantification within and across experiments to model the relation
between variance and PSM count.(See original paper)

```{r, DEqMS1}
# assign a extra variable `count` to fit3 object, telling how many PSMs are 
# quantifed for each protein
library(matrixStats)
count_columns = seq(16,34,2)
psm.count.table = data.frame(count = rowMins(
  as.matrix(df.prot[,count_columns])), row.names =  df.prot$Protein.accession)
fit3$count = psm.count.table[rownames(fit3$coefficients),"count"]
fit4 = spectraCounteBayes(fit3)
```

Outputs of `spectraCounteBayes`:  
object is augmented form of "fit" object from `eBayes` in Limma, with the 
additions being:  
`sca.t` - Spectra Count Adjusted posterior t-value  
`sca.p` - Spectra Count Adjusted posterior p-value  
`sca.dfprior` - DEqMS estimated prior degrees of freedom  
`sca.priorvar`- DEqMS estimated prior variance  
`sca.postvar` - DEqMS estimated posterior variance  
`model` - fitted model

### Visualize the fit curve - variance dependence on quantified PSM 
```{r, plot}
# n=30 limits the boxplot to show only proteins quantified by <= 30 PSMs.
VarianceBoxplot(fit4,n=30,main="TMT10plex dataset PXD004163",xlab="PSM count")
VarianceScatterplot(fit4,main="TMT10plex dataset PXD004163")
```

### Extract the results as a data frame and save it
```{r, result}
DEqMS.results = outputResult(fit4,coef_col = 1)
#if you are not sure which coef_col refers to the specific contrast,type
head(fit4$coefficients)

# a quick look on the DEqMS results table
head(DEqMS.results)
# Save it into a tabular text file
write.table(DEqMS.results,"DEqMS.results.miR372-ctrl.txt",sep = "\t",
            row.names = F,quote=F)
```

Explaination of the columns in `DEqMS.results`:  
`logFC` - log2 fold change between two groups, Here it's log2(miR372/ctrl).   
`AveExpr` - the mean of the log2 ratios/intensities across all samples. Since
input matrix is log2 ratio values, it is the mean log2 ratios of all samples.   
`t` - Limma output t-statistics  
`P.Value`- Limma p-values   
`adj.P.Val` - BH method adjusted Limma p-values  
`B` - Limma B values  
`count` - PSM/peptide count values you assigned  
`sca.t` - DEqMS t-statistics  
`sca.P.Value` - DEqMS p-values  
`sca.adj.pval` - BH method adjusted DEqMS p-values  

### Make volcanoplot
We recommend to plot p-values on y-axis instead of adjusted pvalue or FDR.  
Read about why [here](https://support.bioconductor.org/p/98442/).
```{r volcanoplot1}
library(ggrepel)
# Use ggplot2 allows more flexibility in plotting

DEqMS.results$log.sca.pval = -log10(DEqMS.results$sca.P.Value)
ggplot(DEqMS.results, aes(x = logFC, y =log.sca.pval )) + 
    geom_point(size=0.5 )+
    theme_bw(base_size = 16) + # change theme
    xlab(expression("log2(miR372/ctrl)")) + # x-axis label
    ylab(expression(" -log10(P-value)")) + # y-axis label
    geom_vline(xintercept = c(-1,1), colour = "red") + # Add fold change cutoffs
    geom_hline(yintercept = 3, colour = "red") + # Add significance cutoffs
    geom_vline(xintercept = 0, colour = "black") + # Add 0 lines
    scale_colour_gradient(low = "black", high = "black", guide = FALSE)+
    geom_text_repel(data=subset(DEqMS.results, abs(logFC)>1&log.sca.pval > 3),
                    aes( logFC, log.sca.pval ,label=gene)) # add gene label
```
you can also use `volcanoplot` function from Limma. However, it uses `p.value` 
from Limma. If you want to plot `sca.pvalue` from DEqMS, you need to modify the 
`fit4` object.

```{r volcanoplot2}
fit4$p.value = fit4$sca.p
# volcanoplot highlight top 20 proteins ranked by p-value here
volcanoplot(fit4,coef=1, style = "p-value", highlight = 20,
            names=rownames(fit4$coefficients))
```

## DEqMS analysis using MaxQuant outputs (label-free data)
Here we analyze a published label-free benchmark dataset in which either 
10 or 30 µg of E. coli protein extract was spiked into human protein 
extracts (50 µg) in triplicates (Cox J et al MCP 2014). The data was searched 
by MaxQuant software and the output file "proteinGroups.txt" was used here.

```{r DownloadLabelfreeData}
url2 <- "ftp://ftp.pride.ebi.ac.uk/pride/data/archive/2014/09/PXD000279/proteomebenchmark.zip"
download.file(url2, destfile = "./PXD000279.zip",method = "auto")
unzip("PXD000279.zip")
```
### Read protein table as input and filter it

```{r LFQprotein}
df.prot = read.table("proteinGroups.txt",header=T,sep="\t",stringsAsFactors = F,
                        comment.char = "",quote ="")

# remove decoy matches and matches to contaminant
df.prot = df.prot[!df.prot$Reverse=="+",]
df.prot = df.prot[!df.prot$Contaminant=="+",]

# Extract columns of LFQ intensites
df.LFQ = df.prot[,89:94]
df.LFQ[df.LFQ==0] <- NA

rownames(df.LFQ) = df.prot$Majority.protein.IDs
df.LFQ$na_count_H = apply(df.LFQ,1,function(x) sum(is.na(x[1:3])))
df.LFQ$na_count_L = apply(df.LFQ,1,function(x) sum(is.na(x[4:6])))
# Filter protein table. DEqMS require minimum two values for each group.
df.LFQ.filter = df.LFQ[df.LFQ$na_count_H<2 & df.LFQ$na_count_L<2,1:6]
```

### Make a data frame of unique peptide count per protein
```{r pepCountTable}
library(matrixStats)
# we use minimum peptide count among six samples
# count unique+razor peptides used for quantification
pep.count.table = data.frame(count = rowMins(as.matrix(df.prot[,19:24])),
                             row.names = df.prot$Majority.protein.IDs)
# Minimum peptide count of some proteins can be 0
# add pseudocount 1 to all proteins
pep.count.table$count = pep.count.table$count+1
```

### DEqMS analysis on LFQ data 
```{r labelfreeDEqMS}
protein.matrix = log2(as.matrix(df.LFQ.filter))

class = as.factor(c("H","H","H","L","L","L"))
design = model.matrix(~0+class) # fitting without intercept

fit1 = lmFit(protein.matrix,design = design)
cont <- makeContrasts(classH-classL, levels = design)
fit2 = contrasts.fit(fit1,contrasts = cont)
fit3 <- eBayes(fit2)

fit3$count = pep.count.table[rownames(fit3$coefficients),"count"]

#check the values in the vector fit3$count
#if min(fit3$count) return NA or 0, you should troubleshoot the error first
min(fit3$count)

fit4 = spectraCounteBayes(fit3)
```
### Visualize the fit curve
```{r LFQboxplot}
VarianceBoxplot(fit4, n=20, main = "Label-free dataset PXD000279",
                xlab="peptide count + 1")
```

### Extract outputs from DEqMS
```{r LFQresult}
DEqMS.results = outputResult(fit4,coef_col = 1)
# Add Gene names to the data frame
rownames(df.prot) = df.prot$Majority.protein.IDs
DEqMS.results$Gene.name = df.prot[DEqMS.results$gene,]$Gene.names
head(DEqMS.results)
write.table(DEqMS.results,"H-L.DEqMS.results.txt",sep = "\t",
            row.names = F,quote=F)
```

## DEqMS analysis using a PSM table (isobaric labelled data)
If you want to try different methods to estimate protein abundance,you can 
start with a PSM table and use provided functions in DEqMS to summarize PSM 
quant data into protein quant data. Four different functions are included: `medianSweeping`,`medianSummary`,`medpolishSummary`,`farmsSummary`. 
Check PDF reference manual for detailed description.

### Read PSM table input

```{r retrieveExampleData, message=FALSE}
### retrieve example PSM dataset from ExperimentHub
library(ExperimentHub)
eh = ExperimentHub()
query(eh, "DEqMS")
dat.psm = eh[["EH1663"]]
```

```{r log2transform2}
dat.psm.log = dat.psm
dat.psm.log[,3:12] =  log2(dat.psm[,3:12])
head(dat.psm.log)
```

### Summarization and Normalization
Here, median sweeping is used to summarize PSMs intensities to protein log2 
ratios. In this procedure, we substract the spectrum log2 intensity from the 
median log2 intensities of all samples. The relative abundance estimate for 
each protein is calculated as the median over all PSMs belonging to this 
protein.(Herbrich et al JPR 2012 and D'Angelo et al JPR 2016).  
Assume the log2 intensity of PSM `i` in sample `j` is $y_{i,j}$, its relative 
log2 intensity of PSM `i` in sample `j` is $y'_{i,j}$: 
$$y'_{i,j} = y_{i,j} - median_{j'\in ctrl}\ y_{i,j'} $$
Relative abundance of protein `k` in sample `j` $Y_{k,j}$ is calculated as:
$$Y_{k,j} = median_{i\in protein\ k}\ y'_{i,j} $$

Correction for differences in amounts of material loaded in the channels 
is then done by subtracting the channel median from the relative abundance 
(log2 ratio), centering all channels to have median log2 value of zero.
```{r boxplot2}
dat.gene.nm = medianSweeping(dat.psm.log,group_col = 2)
boxplot(dat.gene.nm,las=2,ylab="log2 ratio",main="TMT10plex dataset PXD004163")
```

### DEqMS analysis
```{r DEqMS2}
gene.matrix = as.matrix(dat.gene.nm)

# make design table
cond = as.factor(c("ctrl","miR191","miR372","miR519","ctrl",
"miR372","miR519","ctrl","miR191","miR372"))
design = model.matrix(~0+cond) 
colnames(design) = gsub("cond","",colnames(design))

#limma part analysis
fit1 <- lmFit(gene.matrix,design)
x <- c("miR372-ctrl","miR519-ctrl","miR191-ctrl")
contrast =  makeContrasts(contrasts=x,levels=design)
fit2 <- eBayes(contrasts.fit(fit1,contrasts = contrast))

#DEqMS part analysis
psm.count.table = as.data.frame(table(dat.psm$gene))
rownames(psm.count.table) = psm.count.table$Var1

fit2$count = psm.count.table[rownames(fit2$coefficients),2]
fit3 = spectraCounteBayes(fit2)
# extract DEqMS results
DEqMS.results = outputResult(fit3,coef_col = 1) 
head(DEqMS.results)
write.table(DEqMS.results,"DEqMS.results.miR372-ctrl.fromPSMtable.txt",
            sep = "\t",row.names = F,quote=F)
```

Generate variance ~ PMS count boxplot, check if the DEqMS correctly find the relation between prior variance and PSM count
```{r PriorVarianceTrend}
VarianceBoxplot(fit3,n=20, xlab="PSM count",main="TMT10plex dataset PXD004163")
```

### PSM/Peptide profile plot
Only possible if you read a PSM or peptide table as input.
`peptideProfilePlot` function will plot log2 intensity of each PSM/peptide of 
the protein in the input table.
```{r PSMintensity}
peptideProfilePlot(dat=dat.psm.log,col=2,gene="TGFBR2")
# col=2 is tell in which column of dat.psm.log to look for the gene
```


# Comparing DEqMS to other methods
The following steps are not required for get the results from DEqMS.
it is used to help users to understand the method better and the differences
to other methods. Here we use the TMT labelled data PXD004163 as an example.

## Compare the variance estimate in DEqMS and Limma 

### Prior variance comparison between DEqMS and Limma
```{r PriorVar}
VarianceScatterplot(fit3, xlab="log2(PSM count)")
limma.prior = fit3$s2.prior
abline(h = log(limma.prior),col="green",lwd=3 )
legend("topright",legend=c("DEqMS prior variance","Limma prior variance"),
        col=c("red","green"),lwd=3)
```

### Residual plot for DEqMS and Limma
```{r Residualplot}
op <- par(mfrow=c(1,2), mar=c(4,4,4,1), oma=c(0.5,0.5,0.5,0))
Residualplot(fit3,  xlab="log2(PSM count)",main="DEqMS")
x = fit3$count
y = log(limma.prior) - log(fit3$sigma^2)
plot(log2(x),y,ylim=c(-6,2),ylab="Variance(estimated-observed)", pch=20, cex=0.5,
     xlab = "log2(PSMcount)",main="Limma")
```
 

### Posterior variance comparison between DEqMS and Limma
The plot here shows posterior variance of proteins "shrink" toward the 
fitted value to different extent depending on PSM number. 
```{r PostVar, echo=TRUE, fig.height=5, fig.width=10}
library(LSD)
op <- par(mfrow=c(1,2), mar=c(4,4,4,1), oma=c(0.5,0.5,0.5,0))
x = fit3$count
y = fit3$s2.post
heatscatter(log2(x),log(y),pch=20, xlab = "log2(PSMcount)", 
     ylab="log(Variance)",
     main="Posterior Variance in Limma")

y = fit3$sca.postvar
heatscatter(log2(x),log(y),pch=20, xlab = "log2(PSMcount)",
     ylab="log(Variance)", 
     main="Posterior Variance in DEqMS")
```

## Compare p-values from DEqMS to ordinary t-test, ANOVA and Limma
We first apply t.test to detect significant protein changes between ctrl 
samples and miR372 treated samples, both have three replicates.

### T-test analysis
```{r t-test}
pval.372 = apply(dat.gene.nm, 1, function(x) 
t.test(as.numeric(x[c(1,5,8)]), as.numeric(x[c(3,6,10)]))$p.value)

logFC.372 = rowMeans(dat.gene.nm[,c(3,6,10)])-rowMeans(dat.gene.nm[,c(1,5,8)])
```

Generate a data.frame of t.test results, add PSM count values and order the 
table by p-value.
```{r,echo=TRUE}
ttest.results = data.frame(gene=rownames(dat.gene.nm),
                    logFC=logFC.372,P.Value = pval.372, 
                    adj.pval = p.adjust(pval.372,method = "BH")) 

ttest.results$PSMcount = psm.count.table[ttest.results$gene,"count"]
ttest.results = ttest.results[with(ttest.results, order(P.Value)), ]
head(ttest.results)
```

### Anova analysis
Anova analysis is equivalent to linear model analysis. The difference to 
Limma analysis is that estimated variance is not moderated using empirical 
bayesian approach as it is done in Limma.

```{r Anova}
ord.t = fit1$coefficients[, 1]/fit1$sigma/fit1$stdev.unscaled[, 1]
ord.p = 2*pt(abs(ord.t), fit1$df.residual, lower.tail = FALSE)
ord.q = p.adjust(ord.p,method = "BH")
anova.results = data.frame(gene=names(fit1$sigma),
                            logFC=fit1$coefficients[,1],
                            t=ord.t, 
                            P.Value=ord.p, 
                            adj.P.Val = ord.q)

anova.results$PSMcount = psm.count.table[anova.results$gene,"count"]
anova.results = anova.results[with(anova.results,order(P.Value)),]

head(anova.results)
```

### Limma
Extract limma results using `topTable` function,  `coef = 1` allows you to 
extract the specific contrast (miR372-ctrl), option `n= Inf` output 
all rows. 
```{r,echo=TRUE}
limma.results = topTable(fit2,coef = 1,n= Inf)
limma.results$gene = rownames(limma.results)
#Add PSM count values in the data frame
limma.results$PSMcount = psm.count.table[limma.results$gene,"count"]

head(limma.results)
```

### Visualize the distribution of p-values by different analysis
plotting all proteins ranked by p-values.

```{r pvalueall}
plot(sort(-log10(limma.results$P.Value),decreasing = TRUE), 
    type="l",lty=2,lwd=2, ylab="-log10(p-value)",ylim = c(0,10),
    xlab="Proteins ranked by p-values",
    col="purple")
lines(sort(-log10(DEqMS.results$sca.P.Value),decreasing = TRUE), 
        lty=1,lwd=2,col="red")
lines(sort(-log10(anova.results$P.Value),decreasing = TRUE), 
        lty=2,lwd=2,col="blue")
lines(sort(-log10(ttest.results$P.Value),decreasing = TRUE), 
        lty=2,lwd=2,col="orange")
legend("topright",legend = c("Limma","DEqMS","Anova","t.test"),
        col = c("purple","red","blue","orange"),lty=c(2,1,2,2),lwd=2)
```

plotting top 500 proteins ranked by p-values.
```{r pvalue500}
plot(sort(-log10(limma.results$P.Value),decreasing = TRUE)[1:500], 
    type="l",lty=2,lwd=2, ylab="-log10(p-value)", ylim = c(2,10),
    xlab="Proteins ranked by p-values",
    col="purple")
lines(sort(-log10(DEqMS.results$sca.P.Value),decreasing = TRUE)[1:500], 
        lty=1,lwd=2,col="red")
lines(sort(-log10(anova.results$P.Value),decreasing = TRUE)[1:500], 
        lty=2,lwd=2,col="blue")
lines(sort(-log10(ttest.results$P.Value),decreasing = TRUE)[1:500], 
        lty=2,lwd=2,col="orange")
legend("topright",legend = c("Limma","DEqMS","Anova","t.test"),
        col = c("purple","red","blue","orange"),lty=c(2,1,2,2),lwd=2)
```
