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 his- tone molecules combined with DNA in the diploid genome, and the combined length of all fibers.

Short answer

Based on the given information and calculations, provide the following values: (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.

Step-by-step solution

Calculate the number of nucleosomes

Using the information that each group of 200 bp forms a nucleosome, we can calculate the number of nucleosomes by dividing the total number of base pairs by the number of base pairs per nucleosome. So, the total number of nucleosomes can be calculated as: Number of nucleosomes = \((10^9\,\text{bp}) / (200\,\text{bp/nucleosome})\)

Calculate the number of histones

Since each nucleosome contains 9 histones, to find the total number of histone molecules combined with DNA in the diploid genome, we multiply the number of nucleosomes by the number of histones per nucleosome: Number of histones = Number of nucleosomes \(\times\) 9 histones/nucleosome

Calculate the DNA length before packing

First, we need to calculate the length of the DNA before it is packed into nucleosomes and solenoids. To do this, we use the given information that there are \(10^9\) base pairs in the diploid genome and that each base pair is 0.34 nm long (a well-established value in biochemistry). Therefore, the total length of DNA before packing is: Length of DNA = \((10^9\,\text{bp})\times (0.34\,\text{nm/bp})\)

Calculate the combined length of all fibers

Now, we need to calculate the length of the fibers after the DNA has been packed into nucleosomes and solenoids. To do this, we will use the packing ratio of 50. This means that the final packed length is 50 times smaller than the original length of the DNA. Therefore, the combined length of all fibers can be calculated as: Length of fibers = Length of DNA / Packing ratio Using the formulas from steps 1-4, we can now find the values for the number of nucleosomes, the number of histones, and the combined length of all fibers. Number of nucleosomes = \((10^9\,\text{bp}) / (200\,\text{bp/nucleosome}) = 5\times 10^6\,\text{nucleosomes}\) Number of histones = \(5\times 10^6\,\text{nucleosomes} \times 9\,\text{histones/nucleosome} = 4.5\times 10^7\,\text{histones}\) Length of DNA = \((10^9\,\text{bp})\times (0.34\,\text{nm/bp}) = 3.4\times 10^8\,\text{nm}\) Length of fibers = \((3.4\times 10^8\,\text{nm}) / 50 = 6.8\times 10^6\,\text{nm}\) So, the total number of nucleosomes in all fibers is \(5\times 10^6\), the total number of histone molecules combined with DNA in the diploid genome is \(4.5\times 10^7\), and the combined length of all fibers is \(6.8\times 10^6\) nm.

Key concepts

Nucleosome

The nucleosome is the fundamental unit of DNA packing in eukaryotic cells, which includes mammalian cells. It consists of a segment of DNA wound around a core of histone proteins. Each nucleosome contains about 147 base pairs (bp) of DNA wrapped around a histone octamer, made up of two each of histones H2A, H2B, H3, and H4, with a histone H1 linking each nucleosome to the next. This structure not only compacts DNA but also plays pivotal roles in gene regulation, as the tightness of the wrapping can influence gene expression.

In the given exercise, the number of nucleosomes was calculated based on 200 bp per nucleosome, slightly more than the typical 147 bp, probably to account for linker DNA and the associated histone H1. This calculation is vital for deeper understanding, as it gives a clear picture of just how much DNA is organized into these units in a mammalian genome.

Histones

Histones are essential proteins around which DNA is tightly wound to form nucleosomes. They play a key role not only in DNA packing but also in regulating access to genetic information. Nine histone molecules are involved in forming a nucleosome, with the core consisting of an octamer containing two molecules each of four histones (H2A, H2B, H3, H4) and the ninth being the linker histone H1.

When the exercise calculates the total number of histone molecules by multiplying the number of nucleosomes by nine, it encompasses the entire protein complex that governs the architecture of chromatin. The exact number of histones provides insight into just how many protein components are required to manage the mammalian genome. Understanding histones also helps to unravel the complexities behind how genes are turned on or off during different cellular processes.

DNA Packing

DNA packing refers to the intricate process by which cells condense their genetic material into the confined space of the nucleus. The first level of this packing is the wrapping of DNA around histone proteins to form nucleosomes. These nucleosomes further coil to create structures known as solenoids, with the help of the histone H1. Multiple levels of folding are involved, with the chromatin fiber eventually being compacted into the highly condensed form seen in chromosomes during cell division.

The packing ratio mentioned in the exercise indicates the degree of compaction of the chromatin fiber. It specifies that the length of DNA in chromatin fibers is 50 times shorter than its length if it were fully stretched out. This illustrates the incredible efficiency of DNA packing, allowing for the fit of vast amounts of genetic information into the microscopic nucleus of a cell.

Mammalian Diploid Genome

A mammalian diploid genome contains two complete sets of chromosomes, one from each parent. This complex set of genetic information dictates the organism's development and functioning. With billions of base pairs to account for, the organization and packaging of this DNA are crucial for proper cellular operations.

In mammals, the diploid genome is efficiently stored within the cell nucleus thanks to the chromatin structure. The exercise underscores the massive scale of mammalian genome organization by calculating the total number of nucleosomes and histones, along with the combined length of all the chromatin fibers. It provides a quantitative glimpse into how the seemingly endless string of DNA is neatly organized, with practical calculations to highlight the immense task cells undertake to maintain and express the genome.