Question

How many possible primary structures exist for a small polypeptide containing four individual amino acids?

Short answer

There are \(160,000\) possible primary structures for a small polypeptide containing four individual amino acids, as calculated using the permutation formula \(20^4\).

Step-by-step solution

Understand the basics of amino acids and polypeptides

Amino acids are the building blocks of proteins, and they can be combined in many different ways to form polypeptides, which ultimately fold into different shapes to become functional proteins. The primary structure of a polypeptide simply refers to the linear sequence of amino acids. In this exercise, the polypeptide contains four individual amino acids.

Calculate the permutations of amino acids

To determine the number of possible primary structures of a polypeptide with four amino acids, we'll use the permutation formula. There are 20 common amino acids found in proteins. Since each of the four positions in the polypeptide can be any of these 20 amino acids and the sequence matters, we can use the formula: Number of permutations = n^r, where n is the number of amino acids and r is the total positions in the polypeptide. In this problem, n = 20 (as there are 20 common amino acids), and r = 4 (polypeptide with four positions).

Calculate the number of possible primary structures

Applying the permutation formula, we get: Number of permutations = 20^4 Number of permutations = 160,000 So, there are 160,000 possible primary structures for a small polypeptide containing four individual amino acids.