Question

Number of cyclic tripeptides formed with 2 amino acids A and B is:

• A. 3
• B. 4
• C. 2
• D. 5

Hint:

For cyclic peptides:
• Count unique sequences considering the cyclic structure to avoid duplicates.
• Use the number of amino acids and their combinations to determine possible arrangements.

Answer 1

The Correct Option is B

To determine the number of cyclic tripeptides that can be formed using two amino acids, A and B, we first need to understand the arrangement of amino acids in a cyclic manner.

A cyclic tripeptide consists of three amino acids connected in a ring structure. For this problem, we have only two types of amino acids, A and B. Therefore, we want to calculate the different sequences of A and B in a cycle.

In a linear sequence of tripeptide, permutations generally matter. However, in a cyclic arrangement, that is not the case because of rotational and reflectional symmetry considerations. Here is how each cyclic combination is distinctively determined:

• AAA: A cyclic sequence with all A's. Only 1 variant.
• BBB: A cyclic sequence with all B's. Only 1 variant.
• AAB: Although AAB, ABA, and BAA may look distinct in a linear arrangement, in a cyclic setting, they all result in the same cyclic peptide due to rotational symmetry. This counts as 1 unique cyclic arrangement.
• ABB: Similar to AAB, the sequences ABB, BBA, and BAB also become identical due to rotation, forming 1 distinct cyclic tripeptide.

Thus, we have the following distinct cyclic tripeptides:

• AAA
• BBB
• AAB
• ABB

Therefore, the number of distinct cyclic tripeptides formed with amino acids A and B is 4.