Introduction

This presentations presents some background on EM-normalization for library size and RNA-composition, as wells as some examples on how this is applied in R using the package edgeR.

Density curves and log-log plots will be used to explore the effects of different normalization methods.

RNA-composition and DE

TPM normalization

Setup simple EM:

sample1 = c(10, 20, 30, 10, 10, 10) # Library size of 100 counts
sample2 = 2 + sample1 * 2 # Double library size
sample3 = 1 + sample1 * 3 # Triple library size
EM = data.frame(sample1, sample2, sample3)

EM

Note the different library sizes:

colSums(EM)

TPM normalization

TPM scaling:

scale(EM, center=FALSE, scale=colSums(EM)) # Lets forget the M-part for now...

Samples can now be compared directly for analysis!

CPM normalization

Introduce DE for some TCs

EM.DE = EM
EM.DE[4:6,2] = EM.DE[4:6,2] * 5
EM.DE[4:6,3] = EM.DE[4:6,3] * 4

EM.DE

The total RNA content of sample2+3 has increased!

CPM normalization

TPM scaling

scale(EM.DE, center=FALSE, scale=colSums(EM.DE))

Non-DE genes are now under-sampled!

CPM normalization

This can affect downstream analysis i.e. distance matrix calculations.

dist(t(scale(EM, center=FALSE, scale=colSums(EM))))
dist(t(scale(EM.DE, center=FALSE, scale=colSums(EM.DE))))

Advanced normalization

Setup

Packages needed for the analysis:

library(ABC2017)
library(edgeR)
library(ggplot2)
theme_set(theme_minimal()) # Make ggplots prettier

We will use the small zebrafish dataset:

data(zebrafish)

The dataset is a list which contains:

The same format is used for the remaining datasets in the ABC2017 package

Setup

EM:

head(zebrafish$Expression)

Annotation:

head(zebrafish$Design)

Plotting distributions

edgeR (via limma) provides the plotDensities function for exploring the effect of normalization

plotDensities(zebrafish$Expression, legend="topright")

Plotting distributions

That did not look to good! Since the data spans multiple orders of magnitude, we can try with a log-scale instead.

This however brings up the problem of 0 counts - for which log is not defined.

The get around this probelm a small pseudo-count can be added to all counts in the EM. This does not necesarily have to be an integer, and is usually chosen to be between 0.1 and 1.0.

Plotting distributions

# Pseoducount and log
plotDensities(log(zebrafish$Expression+1), legend="topright")

Plotting distributions

Notice how the lower quartile is zero - this means that we have a large number of genes with very low counts.

Counts with 1-3 counts are not very interesting, since they are likely to be either noise or expressed at biologically irrelevant levels. It's customary to perform som ad-hoc trimming or filtering to remove these prior to analysis.

Here we only keep genes with at least 2 counts in at least 4 samples:

# Trim
above_one <- rowSums(zebrafish$Expression > 1)

trimmed_em <- subset(zebrafish$Expression, above_one > 3)

# Pseoducount and log
log_trimmed_em <-  log(trimmed_em + 1)

Plotting distributions

plotDensities(log_trimmed_em, legend="topright")

Plotting distributions

Now we have a clearer picture of the distribution of counts within each sample. The large difference in distributions shows the need for normalization, before the samples can be compared.

As with everything in R, we do not have to recode everything from scratch. The edgeR package has a function cpm which has implented a large number of normalization methods and log-transformation.

edgeR does this by implementing the use of normalization factors, which is use to rescale the actual library sizes to take into account differences in RNA-composition.

Using edgeR to normalize

Using edgeR is simple, but first we must save the EM as a DGEList:

# Create DGEList-object from the trimmed em
dge <- DGEList(trimmed_em)

# Use edgeR to calculate normalization factors
dge <- calcNormFactors(object=dge, method="TMM")

# calculate log cpm values
TMM_em <- cpm(x=dge, log=TRUE, prior.count=1.0)

head(TMM_em)

Using edgeR to normalize

The resulting plot shows a nicer alignment of the main peak:

plotDensities(TMM_em)

log-log plots

Another way of visualizing normalization is via a log-log plot. This is simply a scatterplot with paired expression values for two samples.

Although it only allows for pairwise comparison, it is a nice way to see the effect of normalization and the variance of expression at different levels.

log-log plots

First we consider the (trimmed) log(counts+1)

qplot(data=log_trimmed_em, x=Ctl3, y=Trt13, alpha=I(0.1)) + geom_smooth(method="gam") + geom_abline(color="red")

log-log plots

Compare this with edgeR's TMM normalization:

qplot(data=as.data.frame(TMM_em), x=Ctl3, y=Trt13, alpha=I(0.1)) + geom_smooth(method="gam") + geom_abline(color="red")

Exercises

Team up and do the following exercises:

  1. Make a plot of density curves showing the effect of all the different normalization methods implemented by edgeR
  2. Make a plot that compares the estimated normalization factors for the TMM and RLE normalization methods.
  3. Investigate the effect of different pseudocount values using log-log plots.

HINT for 1: Use apply-family and facets to compare multiple datasets. Remember to include method="none".

HINT for 2: Read the calcNormFactors help file to see where the normalization factors are stored

Question 1 code

# Convert to a DGElist
dge <- DGEList(trimmed_em)

# Normalize using each of four methods
edgeR_methods <- c("none", "TMM", "RLE", "upperquartile")
dges <- lapply(edgeR_methods, calcNormFactors, object=dge)

# Calculate CPMs
norms <- lapply(dges, cpm, log=TRUE)

Question 1 plot

par(mfrow=c(2,2))
mapply(plotDensities, norms, edgeR_methods, MoreArgs=list(group=NULL, col=NULL, legend=FALSE))

Question 2 code

# Extract the normalization factors
norm_factors <- sapply(dges, function(x) x$samples$norm.factors)
colnames(norm_factors) <- edgeR_methods

Question 2 plot

plot(as.data.frame(norm_factors))

Question 3 code

# Create DGEList-object from the trimmed em
dge <- DGEList(trimmed_em)
dge <- calcNormFactors(object=dge, method="TMM")

# calculate log cpm values
TMM_v <- cpm(x=dge, log=TRUE, prior.count=0.1)
TMM_w <- cpm(x=dge, log=TRUE, prior.count=1.0)
TMM_x <- cpm(x=dge, log=TRUE, prior.count=5.0)
TMM_y <- cpm(x=dge, log=TRUE, prior.count=10.0)
TMM_z <- cpm(x=dge, log=TRUE, prior.count=20.0)

Question 3 plot v

qplot(data=as.data.frame(TMM_v), x=Ctl3, y=Ctl5, alpha=I(0.1)) + geom_smooth(method="gam") + geom_abline(color="red")

Question 3 plot w

qplot(data=as.data.frame(TMM_w), x=Ctl3, y=Ctl5, alpha=I(0.1)) + geom_smooth(method="gam") + geom_abline(color="red")

Question 3 plot x

qplot(data=as.data.frame(TMM_y), x=Ctl3, y=Ctl5, alpha=I(0.1)) + geom_smooth(method="gam") + geom_abline(color="red")

Question 3 plot y

qplot(data=as.data.frame(TMM_x), x=Ctl3, y=Ctl5, alpha=I(0.1)) + geom_smooth(method="gam") + geom_abline(color="red")

Question 3 plot z

qplot(data=as.data.frame(TMM_z), x=Ctl3, y=Ctl5, alpha=I(0.1)) + geom_smooth(method="gam") + geom_abline(color="red")


MalteThodberg/ABC2017 documentation built on Nov. 18, 2017, 7:51 a.m.