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.

Key concepts

nucleosome

In the vast organization of the genome, the nucleosome serves as the fundamental unit of DNA packaging. Imagine the nucleosome as a little spool that DNA wraps around. This is crucial because DNA is incredibly long, and if it were all stretched out, it would be impossible to fit inside the tiny space of a cell nucleus. To address this, the DNA is organized into nucleosomes, which significantly compact the DNA while still keeping it accessible for essential processes like replication and transcription.

Each nucleosome comprises about 200 base pairs (bp) of DNA wound around a core of histone proteins. This setup not only provides structure but also plays a regulatory role in gene expression. When contemplating how many nucleosomes are in something as massive as a diploid mammalian genome—which has over a billion base pairs—the numbers are quite staggering. In this scenario, by dividing the total length of DNA by the amount wrapped around each nucleosome, you find that there are around 5 million nucleosomes needed! This highlights the efficiency of nature in organizing massive amounts of genetic material into manageable units.

histone molecules

Histone molecules act as the architectural backbone of the nucleosome. These proteins are essential in organizing DNA strands into nucleosomes. Each nucleosome contains eight histone molecules, forming a histone octamer, plus a slightly different type called a linker histone that helps compact the structure even further.

Histones carry a positive charge which complements the negatively charged DNA, facilitating a snug fit. This relationship is vital, as it allows the DNA to be packed tightly yet remain bouncy enough to be accessed when needed.

• Histones are divided into five main types: H1, H2A, H2B, H3, and H4.
• Each nucleosome core consists of two molecules each of H2A, H2B, H3, and H4.
• The H1 histone, meanwhile, plays an influential role in linking nucleosomes together.

Given the sheer number of nucleosomes in a genome, the number of histone molecules is proportionally large. For example, in our mammalian genome with 5 million nucleosomes, about 45 million histone molecules are needed—ensuring that the DNA is securely packed and organized.

chromatin fibers

Chromatin fibers represent the next level of DNA organization after nucleosomes. When nucleosomes are further coiled into a compact, helical structure called a solenoid, chromatin fibers are formed.

This process doesn't just save space; it also plays a critical role in managing how DNA is accessed and used by the cell. The solenoid model of chromatin fiber packaging gives a highly compacted form as it arranges nucleosomes into a dense helical coil. This structure is highly dynamic, opening up to allow gene expression when needed and shutting tightly to protect dormant regions.

Imagine each stretch of chromatin as a super highway for cellular machinery that needs to traverse the genome for replication or gene expression. The compact nature means that DNA is not just protected from physical damage, but it can also be systematically accessed and transcribed into RNA when the cell needs proteins.

When put together, the entire process of compacting a billion base pairs of DNA into chromatin fibers reduces its physical length drastically. With a packing ratio of 50, the length of the chromatin is significantly minimized, demonstrating nature's remarkable ability to store complex instructions in a minuscule space.