In samarafk/MLML2R: Maximum Likelihood Estimation of DNA Methylation and Hydroxymethylation Proportions

Introduction

This document presents an example of the usage of the MLML2R package for R.

Install the R package using the following commands on the R console:

install.packages("devtools")
devtools::install_github("samarafk/MLML2R")
library(MLML2R)

Proposed analyses of single-base profiling of either 5-hmC or 5-mC require combining data obtained using bisulfite conversion, oxidative bisulfite conversion or Tet-Assisted bisulfite conversion methods, but doing so naively produces inconsistent estimates of 5-mC or 5-hmC level (Qu et al., 2013).

The function MLML provides maximum likelihood estimates (MLE) for 5-hmC and 5-mC levels using data from any combination of two of the methods: BS-seq, TAB-seq or oxBS-seq. The function also provides MLE when combining these three methods.

The algorithm implemented in the MLML function is based on the Expectation-Maximization (EM) algorithm proposed by Qu et al. (2013). In addition, when only two methods are combined, our implementation is optimized, since we derived the constrained exact MLE in analytical form for 5-mC or 5-hmC levels, and the iterative EM algorithm is not needed. Our improved formulation can, thus, decrease analytic processing time and computational burden, common bottlenecks when processing single-base profiling data from thousands of samples.

Furthermore, our routine is flexible and can be used with both next generation sequencing and Infinium Methylation microarray data in the R-statistical language.

Preparing dataset

We will use the dataset from Johnson et al. (2016), which consists of 30 DNA samples from glioblastoma tumors treated with oxBS-BS and hybridized to the Infinium 450K array.

The steps shown in this section follows the vignette from minfi package.

Getting publicly available data

We start with the steps to get the raw data from the GEO repository. The dataset from Johnson et al. (2016) is available at GEO accession GSE73895.

The sample was divided into four BS and four oxBS replicates.

Platform used: GPL13534 Illumina HumanMethylation450 BeadChip (HumanMethylation450_15017482)

This example has the following dependencies:

library(minfi)
library(GEOquery)

Use the following commands to install these packages in R:

source("http://www.bioconductor.org/biocLite.R")
biocLite(c("minfi", "GEOquery"))

if(! file.exists("GSE73895/GSE73895_RAW.tar"))
{
getGEOSuppFiles("GSE73895")
untar("GSE73895/GSE73895_RAW.tar", exdir = "GSE73895/idat")
head(list.files("GSE73895/idat", pattern = "idat"))
}

getGEOSuppFiles("GSE73895")
untar("GSE73895/GSE73895_RAW.tar", exdir = "GSE73895/idat")
head(list.files("GSE73895/idat", pattern = "idat"))

Decompress the compressed IDAT files:

idatFiles <- list.files("GSE73895/idat", pattern = "idat.gz$", full = TRUE)
sapply(idatFiles, gunzip, overwrite = TRUE)

Now we read the IDAT files in the directory:

rgSet <- read.metharray.exp("GSE73895/idat")
rgSet

pData(rgSet)

sampleNames(rgSet)

The file names consists of a GEO identifier (the GSM part) followed by a standard IDAT naming convention with a 10 digit number which is an array identifier followed by an identifier of the form R01C01. This is because each array actually allows for the hybridization of 12 samples in a 6x2 arrangement. The 3999941120_R03C01 means row 3 and column 1 on chip 3999941120.

We need to identify the samples from different methods: BS-conversion, oxBS-conversion.

if (!file.exists("pD.rds"))
{
geoMat <- getGEO("GSE73895")
pD.all <- pData(geoMat[[1]])
pD <- pD.all[, c("title", "geo_accession", "characteristics_ch1.1", "characteristics_ch1.2","characteristics_ch1.3")]
save(pD,file="pD.rds")
}

geoMat <- getGEO("GSE73895")
pD.all <- pData(geoMat[[1]])
pD <- pD.all[, c("title", "geo_accession", "characteristics_ch1", "characteristics_ch1.2","characteristics_ch1.3")]
pD

load("pD.rds")
pD

names(pD)[c(1,3,4,5)] <- c("method","gender","survival_months","age_years")
pD$gender <- sub("^gender: ", "", pD$gender)
pD$age_years <- as.numeric(sub("^subject age: ", "", pD$age_years))
pD$survival_months <- as.numeric(sapply(pD$survival_months, function(x) strsplit(as.character(x),":")[[1]][2]))
pD$method <- sapply(pD$method, function(x) strsplit(as.character(x),"_")[[1]][3])

We now need to merge this pheno data into the methylation data. The following are commands to make sure we have the same row identifier in both datasets before merging.

sampleNames(rgSet) <- sapply(sampleNames(rgSet),function(x) strsplit(x,"_")[[1]][1])
rownames(pD) <- pD$geo_accession
pD <- pD[sampleNames(rgSet),]
pData(rgSet) <- as(pD,"DataFrame")
rgSet

Preprocessing

We refer the reader to the minfi package tutorials for more preprocessing options.

We need to install the required package bellow:

source("https://bioconductor.org/biocLite.R")
biocLite("IlluminaHumanMethylation450kmanifest")

The rgSet object is a class called RGChannelSet which represents two color data with a green and a red channel. We will use, as input in the MLML funcion, a MethylSet, which contains the methylated and unmethylated signals. The most basic way to construct a MethylSet is to using the function preprocessRaw which uses the array design to match up the different probes and color channels to construct the methylated and unmethylated signals. Here we will use the preprocessNoob function, which does the preprocessing and returns a MethylSet.

Arrays were then normalized using the Noob/ssNoob preprocessing method for Infinium methylation microarrays.

From a MethylSet it is easy to compute Beta values, defined as:

Beta = Meth / (Meth + Unmeth + c)

The c constant is chosen to avoid dividing with small values. Illumina uses a default of c=100. The function getBeta from minfi package can be used to obtain the Beta values.

MSet.noob<- preprocessNoob(rgSet)
densityPlot(MSet.noob, sampGroups= pData(rgSet)$method,
main= sprintf('Beta values', nrow(MSet.noob)))

Using the `MLML2R` package

After all the preprocessing procedures, we now can use the MLML2R package to obtain the maximum likelihood estimates for the 5-hmC and 5-mC levels.

Install the R package using the following commands on the R console:

install.packages("devtools")
devtools::install_github("samarafk/MLML2R")

Prepare de input data:

BS_index <- which(pData(rgSet)$method=="BS")
oxBS_index <- which(pData(rgSet)$method=="oxBS")


MethylatedBS <- getMeth(MSet.noob)[,BS_index]
UnMethylatedBS <- getUnmeth(MSet.noob)[,BS_index]

MethylatedOxBS <- getMeth(MSet.noob)[,oxBS_index]
UnMethylatedOxBS <- getUnmeth(MSet.noob)[,oxBS_index]

Getting the MLE estimates using EM-algorithm:

library(MLML2R)
results_em <- MLML(Tc = MethylatedBS , Uc = UnMethylatedBS, Lc = UnMethylatedOxBS, Mc = MethylatedOxBS,tol=0.0001,iterative = TRUE)

par(mfrow =c(1,3)) 
densityPlot(results_em$hmC,main= "5-hmC using EM-algortihm")
densityPlot(results_em$mC,main= "5-mC using EM-algortihm")
densityPlot(results_em$C,main= "5-C using EM-algortihm")

Getting the constrained exact MLE estimates:

library(MLML2R)
results_exact <- MLML(Tc = MethylatedBS , Uc = UnMethylatedBS, Lc = UnMethylatedOxBS, Mc = MethylatedOxBS)

par(mfrow =c(1,3)) 
densityPlot(results_em$hmC,main= "5-hmC using constrained exact MLE")
densityPlot(results_em$mC,main= "5-mC using constrained exact MLE")
densityPlot(results_em$C,main= "5-C using constrained exact MLE")

Comparing the two methods:

all.equal(results_exact$hmC,results_em$hmC)

Other methods to obtain the estimates

Naive estimates

The naive approach to obtain 5-hmC levels is $\beta_{BS} - \beta_{OxBS}$. This approach results in negative values for the 5-hmC levels.

beta_BS <- getBeta(MSet.noob)[,BS_index]
beta_OxBS <- getBeta(MSet.noob)[,oxBS_index]
hmC_naive <- beta_BS-beta_OxBS
C_naive <- 1-beta_BS
mC_naive <- beta_OxBS

par(mfrow =c(1,3)) 
densityPlot(hmC_naive,main= "5-hmC using naive method")
densityPlot(mC_naive,main= "5-mC using naive method")
densityPlot(C_naive,main= "5-C using naive method")

`OxyBS` estimates

For the specific case where only ox-BS and BS data are available, OxyBS package from Houseman et al. (2016) can be use to obtain estimates.

library(OxyBS)

# Methylated signals from the BS and oxBS arrays
methBS <- MethylatedBS
methOxBS <- MethylatedOxBS
# Unmethylated signals from the BS and oxBS arrays
unmethBS <- UnMethylatedBS
unmethOxBS <- UnMethylatedOxBS

# Calculate Total Signals
signalBS <- methBS+unmethBS
signalOxBS <- methOxBS+unmethOxBS

# Calculate Beta Values
betaBS <- methBS/signalBS
betaOxBS <- methOxBS/signalOxBS

####################################################
# 4. Apply fitOxBS function to preprocessed values
####################################################

# Select the number of CpGs and Subjects to which the method will be applied 
nCpGs <- dim(unmethOxBS)[1]
nSpecimens <- dim(unmethOxBS)[2]

# Create container for the OxyBS results
MethOxy <- array(NA,dim=c(nCpGs,nSpecimens,3))
dimnames(MethOxy) <- list(
  rownames(methBS)[1:nCpGs],
  colnames(methBS)[1:nSpecimens], c("C","5mC","5hmC"))

# Process results (one array at a time, slow)
for(i in 1:nSpecimens){
MethOxy[,i,] <-fitOxBS(betaBS[,i],betaOxBS[,i],signalBS[,i],signalOxBS[,i])
}

save(MethOxy,file="MethOxy.rds")

load("MethOxy.rds")

all.equal(MethOxy[,,3],results_exact$hmC)
all.equal(MethOxy[,,2],results_exact$mC)
all.equal(MethOxy[,,1],results_exact$C)

Plot of the results (we have 4 replicates)

par(mfrow =c(1,3)) 
densityPlot(MethOxy[,,3],main= "5-hmC using OxyBS",xlab="")
densityPlot(MethOxy[,,2],main= "5-mC using OxyBS",xlab="")
densityPlot(MethOxy[,,1],main= "5-C using OxyBS",xlab="")

Comparison of 5-hmC estimates from different methods

library(GGally)
# data for replicate 1 is shown
df <- data.frame(x = as.numeric(results_exact$hmC[,1]),y=as.numeric(results_em$hmC[,1]),
                 z = as.numeric(MethOxy[,1,3]),w=as.numeric(hmC_naive[,1]))
ggpairs(df, title = "5-hmc estimates",  
  axisLabels = "show",columnLabels=c("Exact MLE","EM","OxyBS","Naive"))

library(ggplot2)
ggplot(df,aes(x=x,y=z)) + geom_point(alpha = 0.3) + xlab("Exact MLE") +
  ylab("OxyBS")

ggplot(df,aes(x=y,y=z)) + geom_point(alpha = 0.3) + xlab("EM") +
  ylab("OxyBS")