Q:

Scaling by linear regression against the number of reads

I am trying to build the preprocessing pipeline presented in The Tabula Muris Consortium et al. (pp).
It is a pipeline to preprocess single-cell sequencing data. There is one step that is not clear:

Counts were log-normalized (log(1 + counts per N)), then scaled by linear regression against the number of reads (or UMIs), the percent of reads mapping to Rn45s, and the percent of reads to ribosomal genes.

I understand the first part (I assume that log in this context is log2), but I need help on understanding how to scale by linear regression against the number of reads, the percent of reads mapping to Rn45s, and the percent of reads to ribosomal genes.

A:

I don't know if this question has been solved already, but what they try to do is equalize the depth of sequencing for each cell. Therefore, they scale for the total number of reads. If you regress out (via linear or negative binomial regression) the differences in the number of reads per cell, you end up with cells that have been sequenced with the same depth. 
In my opinion they use the ribosomal genes in the same way. They are considered to be a kind of housekeeping genes, which you can use to equalize the sequencing depth.
And yes, the log in this context is log2, used to get fold-change values instead of counts.

