Q.42 The number of possible unique combination(s) of linear tetrapeptides that can be
made from four different amino acids using each amino acid only once in the chain
is/are _______.
Linear tetrapeptides form through sequential peptide bonds between four distinct amino acids, where order matters due to the directional N-to-C terminus linkage. With each amino acid used exactly once, the problem reduces to permutations of four items. This yields 4!=24 unique sequences.
The number of possible unique linear tetrapeptides from four different amino acids, each used only once, equals 24. This key concept in peptide chemistry and molecular biology appears frequently in CSIR NET Life Sciences exams, testing understanding of biomolecule structure and combinatorial mathematics.
Step-by-Step Solution
A tetrapeptide consists of four amino acids linked by three peptide bonds in a linear chain. Since the four amino acids (e.g., A, B, C, D) differ and each appears exactly once, all positions matter.
Calculate permutations: P(4,4)=4!=4×3×2×1=24.
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First position: 4 choices.
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Second: 3 remaining.
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Third: 2 remaining.
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Fourth: 1 left.
Examples include A-B-C-D, D-C-B-A, B-D-A-C—totaling 24 distinct sequences.
Option Analysis
CSIR NET questions often provide numerical blanks or multiple choices. Common distractors include:
| Option | Value | Why Incorrect/Correct | Explanation |
|---|---|---|---|
| 4 | Combinations C(4,4) | Wrong—ignores sequence | Treats peptides as unordered sets; order defines structure . |
| 6 | 3! | Wrong—underestimates | Fits tripeptides only, not tetrapeptides . |
| 24 | 4! | Correct | Full permutations for distinct linear chains . |
| 64 | 43 or other | Wrong—allows repetition | Applies to cases with reuse, violating “only once” . |
| 256 | 44 | Wrong—full repetition | For any tetrapeptide without restrictions . |
This confirms 24 as the precise answer for non-repeating, linear tetrapeptides.
