Hello everyone,

I am struggling with the interpretation of a MDS plot. In my study, I am comparing 84 genes of two different groups (control vs SAH). The exploratory MDS plot groups the SAH condition to the left (negative) on the x axis (leading logFC dim 1) and the control group to the right (positive values). How can I interpret this? I double checked my raw data and it rather looks as if the SAH group tends to have higher log fold changes in many gene compared to the control group (and not smaller logFC as in dim 1 of the graph). The plotMDS function details say that

Distances on the plot can be interpreted as leading log2-fold-change, meaning the typical (root-mean-square) log2-fold-change between the samples for the genes that distinguish those samples.

# Unsupervised clustering of samples
library(wesanderson)
lcpm <- cpm(dge, log=TRUE)
par(mfrow=c(1,2))
col.group <- group
col.group <- as.factor(col.group)
levels(col.group) <- wes_palette(nlevels(col.group), name="Darjeeling1")
col.group <- as.character(col.group)
plotMDS(lcpm, top = 500, labels=group, col=col.group)
title(main="Sample groups")

sessionInfo( )
R version 4.2.1 (2022-06-23)

To check this in further detail, I extracted two single differentially expressed genes which are in fact higher expressed in the SAH condition and compared it to the control condition, repeating plotMDS.

sq3=

> par(mfrow=c(1,2))
> col.group <- group
> col.group <- as.factor(col.group)
> levels(col.group) <- wes_palette(nlevels(col.group), name="Darjeeling1")
> col.group <- as.character(col.group)
> plotMDS(sq3, top = 2, labels=group, col=col.group)
> title(main="Sample groups")

Still, logFC dim1 of SAH shows smaller values than the controls.

What am I overlooking (about the code or the calculation behind the plot)?

Thank you so much for your help!

The MDS plot shows the average absolute size of the leading log2-fold-changes, but not the direction of change. Different genes change in different directions, so it would be impossible for the MDS plot to show the direction of change. The +/- sign of the axes in the MDS plot doesn't have any meaning. The plot would have exactly the same interpretation even it was flipped left to right or top to bottom.

The two MDS plots agree with your data. The first plot when you include all genes shows that the typical logFC between SAH and control is about 4-fold (equal to 2 on the log2 scale). The second plot with just two genes shows a typical logFC of about 6 on the log2 scale, which agrees with your data perfectly.

The dimensions are the root-mean-square average of the top differences between samples, which is not the same as the difference between samples for two genes. You are comparing data for two genes (your table) to the average over 500 genes (the plot). It shouldn't be surprising that they are different.

Anyway, the MDS plot isn't really something you need to interpret this way. It's more useful to check for unexpected results (e.g., samples that are grouping unexpectedly which may indicate batch issues, or sample swaps, etc) rather than as a tool to infer fold changes between samples.