Assessing evenness of pooled plasmid library

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Hello,

I am wondering what is the best way to assess the evenness of a pooled plasmid library.

I have both the original library consisting of an equimolar pool of individual DNA constructs, and I have a maxi DNA prep of the pooled library that was propagated in E. coli (i.e. E. coli was transformed with the original library).

I have sequenced both samples on the NextSeq. I would like to asses both library evenness and any change that occurred as a result of propagating the library in E. coli.

I know that this kind of analysis is often done for CRISPR GeCKO libraries (gRNA libraries), but my library is different because it is a gene library where the genes have a range of lengths. So I presume that the read counts will need to be normalised to the gene lengths.

I was thinking of using a normalised read count like TPM or similar, since I understand that measure accounts for gene length.

And then, once I have the normalised read count for each construct in the library, I wonder what would be the best algorithm to check for differences between the two samples (i.e. change due to propagation in E. coli).

Any advice would be greatly appreciated.

Thank you.