How to convert enrichment/depletion to frequency for comparing deep sequencing to sequence profile?

I have two datasets, from different sources, that I need to compare.

The first set is deep sequencing results of a directed evolution experiment, where I have the naive library and selected library counts, and have calculated enrichment/depletion (positive and negative values with no upper or lower bound).

The second set is a set of protein sequences for which I calculate amino acid frequencies (positive values from 0-1).

The goal is to calculate a similarity between the two datasets. Typically I have two of the second type of set (protein sequences) and I calculate similarity based on the amino acid frequencies… What’s the best way to convert enrichment/depletion to frequency so I can compare?

Example deep sequencing data, for position 77 of the protein:

$$text{enrichment} = log_2left(frac{F_S}{F_N}right)$$

Where $F_S$ is selected frequency and $F_N$ is naïve frequency.

I came up with a possible solution for frequency equivalent from enrichment ($F_E$) but am open to thoughts if it’s good or not:

$$F_E = frac{displaystylefrac{F_S}{F_N}}{displaystylesum_text{amino acid}frac{F_S}{F_N}}$$