Question

If you want to do a

saturation library of 4 amino acid positions, how large is your theoretical

diversity for this library? How many samples must you test to achieve this

99% probability?

Answer 1

Biologically, there exist 20 amino acids in the physiological systems. Each of this amino acid is a potential candidate for all the four positions on the saturation library. This is important to note here that all these amino acids can recurrently be placed at single, or all the positions in the library. Thus, the total number of possible combinations for all four positions will be given by 4²⁰ or 1.09 * 10¹².

This suggests that more are the number of amino acid positions, more vast the library would become.

In order to analyse this library to a 99% probability, a total of 99/100 * 1.09 * 10¹² or nearly 1.07*10¹⁰ samples.