What is the length of an α-helical section of a polypeptide chain of 20 residues? How do you calculate this?
90 Å
60 Å
30Å
9 Å
3 ÅThe correct answer and explanation is :
The correct answer is 30 Å.
Calculation:
An α-helix is a common secondary structure in proteins. The structural parameters of an α-helix are:
- Each residue advances the helix by 1.5 Å (rise per residue).
- There are 3.6 residues per turn.
- The pitch (height of one complete turn) of the helix is 5.4 Å.
For a polypeptide segment of 20 residues, we calculate the length using the rise per residue:
[
\text{Length} = \text{Number of residues} \times \text{Rise per residue}
]
[
= 20 \times 1.5 \, \text{Å}
]
[
= 30 \, \text{Å}
]
Explanation:
The α-helix is stabilized by hydrogen bonds between the backbone carbonyl oxygen of one residue and the amide hydrogen of another, four residues away. This regular structure makes the α-helix compact and stable.
Each turn of the α-helix contains 3.6 residues, meaning that a 20-residue helix will complete approximately:
[
\frac{20}{3.6} \approx 5.56 \text{ turns}.
]
Since the pitch of an α-helix is 5.4 Å per turn, the total helical length could also be calculated as:
[
5.56 \times 5.4 \approx 30 \, \text{Å}.
]
This confirms our previous calculation.
Conclusion:
For a 20-residue α-helix, the total length of the helix is 30 Å. This information is crucial in understanding protein structure and function, especially in molecular biology and bioinformatics.
Here is the scientific illustration of an α-helix polypeptide chain with labeled dimensions, showing the helical structure, hydrogen bonding, and key measurements.