Question

The number of possible combinations in a polypeptide containing any 7 amino acids is given by the figure

• A. $7^{4}$
• B. $4^{7}$
• C. $20^{7}$
• D. $7^{20}$

Hint:

Always use the formula \(\mathbf{20^n}\) to find the number of possible sequences for a polypeptide of length \(n\).
This demonstrates how a relatively short peptide can generate a vast range of unique structures.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Polypeptides are linear chains made of amino acid monomers.
In biological organisms, there are 20 standard amino acids used to build proteins.
Any of these 20 amino acids can occupy each position in a growing polypeptide chain.

Step 2: Key Formula or Approach:
For a polypeptide chain of length \(n\) made from \(m\) possible types of amino acids, the number of unique sequences is calculated as:
\[ \text{Total combinations} = m^n \]

Step 3: Detailed Explanation:
Let us apply the values from this problem:
- The number of available amino acid types is \(m = 20\).
- The length of the polypeptide chain is \(n = 7\) amino acids.
At each of the 7 positions along the chain, there are 20 independent choices:
- Position 1: 20 options
- Position 2: 20 options
- ...
- Position 7: 20 options
Multiplying these options together:
\[ 20 \times 20 \times 20 \times 20 \times 20 \times 20 \times 20 = 20^7 \] This exponential relationship demonstrates how a wide variety of proteins can be constructed from only 20 amino acids.

Step 4: Final Answer:
The number of possible combinations for the 7-amino-acid polypeptide is \(20^7\), matching Option (C).