# 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:

$$\text{enrichment} = \log_2\left(\frac{F_S}{F_N}\right)$$

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:

$$F_E = \frac{\displaystyle\frac{F_S}{F_N}}{\displaystyle\sum_\text{amino acid}\frac{F_S}{F_N}}$$

• Welcome to SE Biology. Your question is unclear to me. It seems like you have RNA or DNA seq quantification and the frequencies that amino acids occur in a set of amino acid sequences. It might help if you clarify what the sets are as well as what you want to achieve by comparing them. Nov 27, 2018 at 8:40
• How did you calculate enrichment? Can you edit your question to add the formula for enrichment? Nov 27, 2018 at 12:20
• @Michael_A, thank you for your response. I edited to add an example of the sequencing data and a possible solution.
– user47696
Nov 27, 2018 at 19:19
• @WYSIWYG, I added an example of my data.
– user47696
Nov 27, 2018 at 19:20
• Since you have the data, why not compute the actual frequencies? Or you convert frequencies of the second set to enrichment. Nov 30, 2018 at 9:44