Q.45 The DNA double helix measures 0.34 𝑛𝑚/𝑏𝑝. The diameter of a nucleosome core
particle is 11 𝑛𝑚. If the ratio of wrapped DNA length to nucleosome diameter is
4.51, the length of DNA around the nucleosome (to the nearest integer)
is _____ 𝑏𝑝.
The length of DNA wrapped around the nucleosome core particle is 146 bp. This numerical answer comes from a direct calculation using the given parameters.
Calculation Steps
The ratio of 4.51 represents wrapped DNA length (in nm) divided by nucleosome diameter (11 nm).
Wrapped DNA length = 4.51 × 11 nm = 49.61 nm.
DNA base pairs = 49.61 nm ÷ 0.34 nm/bp = 145.94 bp, which rounds to 146 bp (nearest integer).
Biological Context
Nucleosome core particles consist of ~147 bp of DNA wrapped ~1.65–1.7 times around a histone octamer in a left-handed superhelix, with a diameter of 11 nm.
The 0.34 nm/bp spacing matches B-form DNA helical rise.
This packaging achieves a ~7:1 length reduction, essential for fitting eukaryotic genomes into nuclei.
Introduction
In molecular biology and CSIR NET Life Sciences preparation, understanding DNA around nucleosome packaging is crucial. The DNA double helix measures 0.34 nm/bp, while the nucleosome core particle diameter is 11 nm. Given a ratio of wrapped DNA length to nucleosome diameter of 4.51, the length of DNA around the nucleosome calculates to 146 bp (nearest integer)—a key concept for chromatin structure questions in competitive exams like GATE Biotechnology and CSIR NET.
Nucleosome Structure Basics
Nucleosomes form the fundamental unit of chromatin, where ~147 bp of DNA wraps around a histone octamer (H2A, H2B, H3, H4 dimers).
The nucleosome core particle diameter of 11 nm accommodates this DNA in ~1.7 superhelical turns, with DNA axis path radius ~4.5 nm (accounting for 2 nm DNA width).
This structure compacts linear DNA, reducing length by 5–7 fold per nucleosome.
Step-by-Step Calculation
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Compute wrapped DNA length: Ratio × nucleosome diameter = 4.51 × 11 nm = 49.61 nm.
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Convert to base pairs: 49.61 nm ÷ 0.34 nm/bp = 145.94 bp.
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Round to nearest integer: 146 bp—matches standard nucleosomal DNA length.
| Parameter | Value | Role in Calculation |
|---|---|---|
| DNA helix rise | 0.34 nm/bp | Converts nm length to bp |
| Nucleosome diameter | 11 nm | Multiplied by ratio 4.51 |
| Wrapped DNA length | 49.61 nm | Intermediate step |
| DNA bp around nucleosome | 146 bp | Final rounded answer [code execution] |
Exam Relevance for CSIR NET/GATE
This problem tests chromatin biophysics, common in Unit 2 (Cell Communication & Signaling) or Unit 6 (Molecular Genetics).
Standard values: 145–147 bp per core, confirming 146 bp validity.
Practice tip: Memorize 0.34 nm/bp for B-DNA and 11 nm nucleosome size for quick solves.
Key Takeaways
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DNA nucleosome wrapping ratio 4.51 directly scales length to diameter.
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Compaction enables 200,000-fold genomic packing in nuclei.
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For CSIR NET aspirants, master these dimensions for numerical problems.
