Should PCA be standardized for gene expression? This is a theory/good practice question more than a technical one. If samples are being plotted on a PCA projection of gene expression data, I'm wondering whether it is standard (and if so, why) to center and scale the PCs.

The reason I ask is that in this case the variables (genes) are being measured in the same scale, so I don't know if it would be necessary to center/scale data.
When the gene expression is scaled and centred you reduce the difference between genes. 

Imagine you have one gene A that is highly expressed usually and has a standard deviation of 500 units compared to a gene B that is not much expressed and only have a standard deviation of 5. 

In the scaled and centred genes both contribute the same because A usually is expressed 10000 and B is usually expressed 100 units. So, for both the standard deviation is 5% of their expression. Meaning that a variation in one is as important as in the other. 

If not scaled (and centred) the first gene A will contribute more to the variation than gene B, because the expression variation in absolute numbers is bigger. 

Both are used in publications, but I think the scaled and centred is more used, because the first dimension reflects "better" the differences between samples. Of course you can do both and select the one that is better to show what you want.