Normalize gene expression data between 0 and 1

Question

[m.taheri]

I have a set of RNA-seq gene expression data (normalized by RPM method) from different samples. I need to normalize gene expression values between 0 and 1.

Let:

MIN is minimum gene expression across all genes and all samples

MAX is maximum gene expression across all genes and all samples

MIN_X is minimum expression of gene X across all samples

MAX_X is maximum expression of gene X across all samples

Gene expression values for gene X can be calculated by one of following ways:

1: This results in very small gene expression values:

normalized gene expression X = (gene expression X - MIN ) / (MAX - MIN)

2: This results in loss of information about ratio of gene expression values:

normalized gene expression X = (gene expression X - MIN_X) ./ (MAX_X - MIN_X)

Is there a way to normalize gene expression values in the range [0,1] by avoiding the above issues?

[ATpoint]

Why don't you normalize with Z-score. That will indicate for each gene how much each sample deviates from the mean off all samples (per gene)?

Transform your counts to log2 and then do t(scale(t(log2matrix))).

[m.taheri]

I think by Z-score normalization the expression ratio between genes will be lost. Won't it?

[ATpoint]

Yes, that is exactly the point. Each gene can be visualized on the same scale. If you normalize between zero and one then this will be dominated by highly-expressed genes so it is difficult to see differences between genes that are not highly-expressed.

[m.taheri]

What if I do Z-score normalization by mean and standard deviation of expression of all genes in all samples? Does it have any benefit over using gene-specific mean and standard deviation values? May you please explain about t and scale functions in t(scale(t(log2matrix))) ?

[ATpoint]

You want to divide by gene-specific SD since you have thousands of genes so the mean is not representative for every single gene. The t stands for transpose, and since scale will by default operate column-wise we have to transpose the matrix first to have it row-wise, and then after the job is done transpose it back so genes are again rows and samples are again columns.