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:
$$\text{enrichment} = \log_2\left(\frac{F_S}{F_N}\right)$$
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:
$$F_E = \frac{\displaystyle\frac{F_S}{F_N}}{\displaystyle\sum_\text{amino acid}\frac{F_S}{F_N}}$$