Question

In globular proteins, $\alpha$-helices have an average span of 12 residues, which would correspond to how much length of the helix?

• A. 5.4 \AA
• B. 18 \AA
• C. 3.6 \AA
• D. 36 \AA

Hint:

For standard $\alpha$-helix calculations:
Rise per residue $= 1.5\text{ \AA}$.
To find the total length, multiply the number of residues by $1.5\text{ \AA}$.
For example: $12\text{ residues} \times 1.5\text{ \AA/residue} = 18\text{ \AA}$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The $\alpha$-helix is a common secondary structure element in proteins.
It is a right-handed helical conformation stabilized by hydrogen bonds between the carbonyl oxygen of one amino acid residue and the amide nitrogen of another residue located four positions ahead in the sequence.
Key Formula or Approach:
The dimensions of a standard $\alpha$-helix are defined by two key parameters:
1. Pitch: The vertical rise of the helix per complete turn, which is $5.4\text{ \AA}$ ($0.54\text{ nm}$).
2. Residues per turn: There are $3.6$ amino acid residues per complete turn.
Using these parameters, the vertical translation (rise) per individual amino acid residue along the helical axis is calculated as:
\[ \text{Rise per residue} = \frac{\text{Pitch}}{\text{Residues per turn}} = \frac{5.4\text{ \AA}}{3.6} = 1.5\text{ \AA} \]

Step 2: Detailed Explanation:
The total length of an $\alpha$-helix is calculated by multiplying the number of amino acid residues by the rise per residue.
Given that the average span of an $\alpha$-helix in globular proteins is $12$ residues:
\[ \text{Length} = \text{Number of residues} \times \text{Rise per residue} \]
\[ \text{Length} = 12 \times 1.5\text{ \AA} \]
\[ \text{Length} = 18.0\text{ \AA} \]
This corresponds to $1.8\text{ nm}$ in length.
This structural dimension matches the value of $18\text{ \AA}$ given in the options.

Step 3: Final Answer:
The length of an $\alpha$-helix spanning 12 residues is $18\text{ \AA}$, which corresponds to Option (B).