Question

You are making a short protein that will be three amino acids long. Assuming that any of the naturally occurring amino acids are available for each position of the small protein, how many unique peptide strands can be made? Your answer must not be in scientific notation. You may use a calculator.

Answer 1

22 Amino acids are naturally incorporated in to polypeptides. They are

Alanine (A), Arginine (R), Asparagine (N), Aspartate (D), Cysteine (C), Glutamate (E), Glutamine (Q), Glycine (G) , Histidine (H), Isoleucine (I), Leucine (L), Lysine (K), Methionine (M), Phenyl alanine (F), Proline (P), Serine(S), Threonine (T), Tryptophan (W), Tyrosine (Y), Valine (V).

In some cases stop codons codes for two amino acids, they are Selenocysteine (UGA) and Pyrrolysine (UAG).

So total 22 amino acids are naturally present.

Each small protein consists 3 amino acids. Here the order of the arrangement is important.

For example , Alanine - Lysine -Serine is one protein and Serine - Lysine - Alanine is another protein.

So here we can apply PERMUTATIONS.

Permutation is an arrangement of all or part of a set of objects with regard to the order of the arrangement.

  nPr = n!/((n-r)! n! = n x (n-1) x (n-3) x ..........x 1

Here n = 22 and r = 3

So P = 22!/(22-3)!

22 x 21 x 20 x 19! 191 = 9,240

Unique peptide strands that can be made from 22 amino acid = 9240