Question

The average molar mass of one base pair of nucleotides in DNA is approximately \(600 \mathrm{~g} / \mathrm{mol}\). The spacing between successive base pairs is about \(0.34 \mathrm{~nm}\), and a complete turn in the helical structure of DNA occurs about every \(3.4 \mathrm{~nm}\). If a DNA molecule has a molar mass of \(4.5 \times 10^{9} \mathrm{~g} / \mathrm{mol}\), approximately how many complete turns exist in the DNA \(\alpha\) -helix structure?

Short answer

The approximate number of complete turns in the DNA helix structure can be calculated as follows: Number of complete turns = \(\frac{(\frac{4.5 \times 10^{9} \mathrm{~g} / \mathrm{mol}}{600 \mathrm{~g} / \mathrm{mol}}) \times (0.34 \ nm)}{3.4 \ nm}\) Number of complete turns ≈ \(2.5 \times 10^6\) complete turns.

Step-by-step solution

Calculate the number of base pairs in the DNA molecule

To do this, we will divide the molar mass of the DNA molecule by the average molar mass of one base pair: Number of base pairs = \(\frac{Molar \ mass \ of \ DNA \ molecule}{Average \ molar \ mass \ of \ one \ base \ pair}\) Number of base pairs = \(\frac{4.5 \times 10^{9} \mathrm{~g} / \mathrm{mol}}{600 \mathrm{~g} / \mathrm{mol}}\)

Calculate the total length of the DNA molecule

Now that we know the number of base pairs, we can calculate the total length of the DNA molecule by multiplying it by the spacing between successive base pairs: Total Length = Number of base pairs × Spacing between successive base pairs Total Length = (Number of base pairs) × (0.34 nm)

Calculate the number of complete turns in the DNA helix structure

To find the number of complete turns in the DNA helix structure, we will divide the total length of the DNA molecule by the length of a complete turn: Number of complete turns = \(\frac{Total \ Length}{Length \ of \ a \ complete \ turn}\) Number of complete turns = \(\frac{Total \ Length}{3.4 \ nm}\) Now, we substitute the values from Steps 1 and 2 into the equation: Number of complete turns = \(\frac{(Number \ of \ base \ pairs) \times (0.34 \ nm)}{3.4 \ nm}\) Number of complete turns = \(\frac{(\frac{4.5 \times 10^{9} \mathrm{~g} / \mathrm{mol}}{600 \mathrm{~g} / \mathrm{mol}}) \times (0.34 \ nm)}{3.4 \ nm}\) Calculate the above expression to obtain the approximate number of complete turns in the DNA helix structure.

Key concepts

Molar Mass of Nucleotides

The molar mass of nucleotides is essential to understanding the structure and weight of DNA. A nucleotide is a building block of DNA, made up of a sugar, a phosphate group, and a nitrogenous base. When nucleotides pair up, they form base pairs, which are the rungs of the DNA ladder. On average, one base pair in DNA weighs about 600 grams per mole.
This average is useful for calculations, such as determining how many base pairs exist in a DNA molecule of a known molar mass.
With this knowledge, students can perform calculations that reveal more about the structure and length of DNA, which is crucial for genetics and molecular biology studies.

Spacing Between Base Pairs

In the DNA structure, base pairs are not tightly packed along the strand; they're separated by a space. This spacing between the base pairs is approximately 0.34 nanometers. This might seem small, but when you consider millions or billions of these base pairs lining up, it adds to a significant length.
This spacing plays a crucial role in the calculations for figuring out the total length of DNA when you know how many base pairs it contains. In real-world terms, this is akin to knowing the distance between spaces on a ruler to measure the total length of an object accurately.

Helical Structure of DNA

The helical structure of DNA is iconic and fundamental to its function. Represented as a twisted ladder, DNA's helical nature arises from the chemical structure and interactions between its components.

• Base pairs are aligned in specific orientations, allowing the double helix to form.
• Every complete twist of this helix occurs over a length of about 3.4 nanometers.

Understanding this helical pattern helps in visualizing how DNA fits within cells, and it impacts how DNA replicates and is transcribed into RNA.

Number of Base Pairs in DNA

Calculating the number of base pairs in a DNA molecule involves dividing the total molar mass of the DNA by the molar mass of a single base pair. For example, if a DNA molecule has a molar mass of 4.5 x 10^9 g/mol, and a single base pair weighs approximately 600 g/mol, this division gives the total count of base pairs.
This count is vital for assessing the amount of genetic information stored within the DNA and often impacts genetic studies, such as sequencing and genome analysis. Counting base pairs gives insights into the complexity and potential mutations within the genetic code.

DNA Helix Complete Turns

Once the number of base pairs is known, you can easily calculate the number of complete turns in a DNA helix. Multiply the number of base pairs by the spacing between them (0.34 nm) to find the total length of DNA. Then divide this total length by the length for a complete turn of the helix (3.4 nm).
This calculation reveals how tightly or loosely the DNA is coiled, which has implications for its stability, accessibility for transcription, and overall cellular functioning. Understanding the number of complete turns is critical for studies involving DNA packing during cell division and replication speed.