52. A DNA strand of length 25 nm wraps diametrically around the circumference of a spherical histone–
octamer once. The radius (nm) of the histone–octamer is ___________.
Given data: 𝜋 = 3.14
Final Answer
The radius of the histone octamer is 4 nm.
This result comes from modeling the DNA strand as forming the full circumference of a circle around the spherical core.
Problem Breakdown
A 25 nm DNA strand wraps diametrically once around the histone octamer’s circumference, meaning it traces the full circular path equal to 2πr, where r is the radius in nm.
Given π = 3.14, solve for r using the circumference formula:
C = 2πr
r = C / (2π) = 25 / (2 × 3.14)
Step-by-Step Calculation
- Compute denominator:
2 × 3.14 = 6.28 - Divide DNA length:
25 ÷ 6.28 ≈ 3.9809 - Round appropriately: 3.9809 ≈ 4 nm
This assumes idealized wrapping without DNA thickness or superhelical pitch.
Biological Context
In real nucleosomes, ~147 bp of B-DNA (~50 nm) wrap ~1.7 times around the histone octamer in a left-handed superhelix.
Real histone cores measure close to 4–4.5 nm radius, matching the calculated value.
Common Distractors (Avoid These Errors)
- Mistaking diameter for radius:
25 / 3.14 ≈ 8 nm - Using half-wrap assumptions:
r = 25 / (2 × 3.14 × 0.5) - Forgetting the factor of 2 entirely:
r = 25 / 3.14
Correct formula: r = 25 / (2 × 3.14) = 4 nm
Why This Matters
Understanding histone octamer radius calculations supports concepts in:
- Chromatin structure
- Epigenetics and gene expression
- Nucleosome dynamics
