Quantify the effects of a gene list between datasets

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I have two datasets of single cell RNA-Seq which contain mostly the same cell types, however differences are apparent between these two datasets (for example a clear separation on tSNE/UMAP before batch correction). I further have a list of several hundred genes of interest (some of which are differentially expressed between our datasets); we would like to quantify the effect/contribution of these genes on the difference between the datasets. I'd be very appreciative for any suggestions.


scRNA-Seq


Comparison


RNA-Seq

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