Why do we log transform and scale data prior to PCA for scRNA-seq analysis

Question

[Lucy]

Hi,

I have a query as to why it is necessary to both log transform, and center and scale, scRNA-seq data prior to performing PCA. I thought the purpose of both of these steps was similar - to ensure that genes of different expression levels can contribute similarly to the PCA, rather than highly expressed and thus high variance genes dominating.

I thought:

1. Log transformation reduces heteroskedasticity reducing the association between the mean and variance
2. Scaling puts the expression values of all genes on the same scale

Do these not do similar things?

Best wishes,

Lucy