Mammals contain a diploid genome consisting of at least 10⁹ bp. If this amount of DNA is present as chromatin fibers, where each group of 200 bp of DNA is combined with 9 histones into a nucleosome and each group of 6 nucleosomes is combined into a solenoid, achieving a final packing ratio of 50, determine:
(a) the total number of nucleosomes in all fibers,
(b) the total number of histone molecules combined with DNA in the diploid genome, and
(c) the combined length of all fibers.

Verified step by step guidance

1. Identify the total amount of DNA base pairs (bp) given, which is at least 10⁹ bp for the diploid genome.
2. Calculate the total number of nucleosomes by dividing the total base pairs by the number of base pairs per nucleosome. Since each nucleosome contains 200 bp, use the formula: \(\text{Number of nucleosomes} = \frac{10^{9} \text{ bp}}{200 \text{ bp/nucleosome}}\).
3. Determine the total number of histone molecules by multiplying the number of nucleosomes by the number of histones per nucleosome. Given that each nucleosome has 9 histones, use: \(\text{Total histones} = \text{Number of nucleosomes} \times 9\).
4. Calculate the combined length of all chromatin fibers before packing. First, find the length of DNA per base pair (approximately 0.34 nm per bp), then multiply by the total number of base pairs: \(\text{DNA length} = 10^{9} \text{ bp} \times 0.34 \text{ nm/bp}\).
5. Adjust the length of the fibers to account for the packing ratio of 50, which means the chromatin fiber length is reduced by a factor of 50 compared to the extended DNA length. Use: \(\text{Fiber length} = \frac{\text{DNA length}}{50}\).

Key Concepts

Nucleosome Structure and Composition

A nucleosome is the fundamental unit of chromatin, consisting of approximately 200 base pairs of DNA wrapped around a histone octamer made up of 8 histone proteins. The question states 9 histones per nucleosome, which may include an additional linker histone. Understanding nucleosome composition is essential to calculate the total number of nucleosomes and histones in the genome.

Chromatin Fiber Organization and Solenoid Model

Chromatin fibers are formed by nucleosomes arranged into higher-order structures. Six nucleosomes fold into a solenoid fiber, which compacts DNA further. This hierarchical organization affects the overall length and packing ratio of DNA, crucial for determining the combined length of chromatin fibers.

DNA Packing Ratio and Genome Size

The packing ratio describes how much the DNA length is reduced by chromatin folding. Given a diploid genome size of 10⁹ base pairs and a packing ratio of 50, this ratio helps convert the total DNA length into the length of compacted chromatin fibers, enabling calculations of fiber length and nucleosome numbers.