Question

Mammals contain a diploid genome consisting of at least \(10^{9}\) 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.

Short answer

Answer: The total number of nucleosomes is 5 × 10⁶, the total number of histone molecules is 4.5 × 10⁷, and the combined length of all fibers is 4.17 × 10⁷.

Step-by-step solution

Calculate the total number of nucleosomes

Divide the total DNA base pairs by base pairs in each nucleosome: \(\frac{10^{9} \text{bp}}{200 \text{bp/nucleosome}}\). Total number of nucleosomes = \(\frac{10^{9}}{200} = 5 \times 10^{6}\) nucleosomes.

Calculate the total number of histone molecules

Multiply the total number of nucleosomes with the number of histones in each nucleosome: \((5 \times 10^{6} \text{nucleosomes}) \times (9 \text{histones/nucleosome})\). Total number of histone molecules = \(5 \times 10^{6} \times 9 = 4.5 \times 10^{7}\) histones.

Calculate the combined length of all fibers

First, calculate the length of DNA in each solenoid: \(200 \text{bp/nucleosome} \times 6 \text{nucleosomes/solenoid} = 1200 \text{bp/solenoid}\). Since the packing ratio is \(50\), the length of each fiber is \(\frac{1200 \text{bp}}{50} = 24 \text{bp}\) per solenoid. Now, divide the total DNA base pairs by the length of each fiber: \(\frac{10^{9} \text{bp}}{24 \text{bp/fiber}}\). The combined length of all fibers = \(\frac{10^{9}}{24}= 4.17 \times 10^{7}\) fibers.