Hello, I am trying to compare relative gene expression between 2 distantly related species, axolotl and mouse. I don't want to do DEG, but to simply compare the level of expression of one very conserved gene relative to a conserved housekeeping gene Rpl4 that is used in qPCR normalization. I have expression levels for different ages of axolotl and mouse, so this is timecourse expression data.

My plan is to divide the sample expression levels of my gene / Rpl4 counts (TPM, length normalized for longest transcript) for age-matched animals, add a scaling factor of 10.000 to make the numbers interpretable and to plot both on a barplot to compare. I am using STAR counts as salmon/kallisto isn't advisable for axolotl's poorly annotated genome, and otherwise working with DESeq2.

I have a number of questions for that, and it would be immensely helpful if someone could advise / provide pointers:

1) Does this approach seem reasonable? I know that TPM isn't ideal as I don't know which isoforms the counts are coming from, but so far I don't see why this wouldn't work, at least as a rough estimate.

2) If this is indeed reasonable, should I divide each sample's expression by respective Rpl4 expression, or by the average of Rpl4 expression across samples? Rpl4 expression is comparatively very stable across age in both animals, but there are some outliers and I am unsure what to do best.

3) Which statistical test could I use per age group to assess significance (my guess would be Mann-Whitney?)

This might be a biostars question, so you might try over there. That said, I have a similar study underway, comparing mouse and acomys, and IMO this paper seems to provide a reasonable way to proceed. The only part that might jam you up is if there are no AXT files for axolotl (probably not), in which case you would need to generate them yourself. There is some information on UCSC about how they generate theirs, and it's barely enough information to get going, but ymmv.