Problem 134 - Chemistry An Atoms First Approach

Question

The average molar mass of one base pair of nucleotides in DNA is approximately 600 g/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?

Step-by-Step Solution

Answer

There are approximately 750,000 complete turns in the given DNA α-helix structure.

Step 1: Find the total number of base pairs in the DNA molecule

To find the total number of base pairs in the DNA molecule, we can use the given molar mass of the DNA molecule and the average molar mass of one base pair: Total number of base pairs = (Molar mass of DNA molecule) / (Average molar mass of one base pair) Total number of base pairs = \(\frac{4.5 \times 10^9 \mathrm{g/mol}}{600 \mathrm{g/mol}}\)

Step 2: Calculate the total number of base pairs

Now, let's calculate the total number of base pairs: Total number of base pairs = \(\frac{4.5 \times 10^9}{600}\) Total number of base pairs = \(7.5 \times 10^6\) So, there are 7.5 million base pairs in the given DNA molecule.

Step 3: Calculate the distance for one complete turn

Every complete turn in the helical structure of DNA occurs every 3.4 nm. To find out the number of base pairs in one complete turn, we can divide the distance for one complete turn by the spacing between successive base pairs: Number of base pairs in one complete turn = (Distance for one complete turn) / (Spacing between successive base pairs) Number of base pairs in one complete turn = \(\frac{3.4 \mathrm{nm}}{0.34 \mathrm{nm}}\)

Step 4: Calculate the number of base pairs in one complete turn

Now let's calculate the number of base pairs in one complete turn: Number of base pairs in one complete turn = \(\frac{3.4}{0.34}\) Number of base pairs in one complete turn = 10 So, there are 10 base pairs in one complete turn of the DNA helix structure.

Step 5: Calculate the number of complete turns in the DNA molecule

Finally, to find the number of complete turns in the DNA molecule, we can divide the total number of base pairs by the number of base pairs in one complete turn: Number of complete turns = (Total number of base pairs) / (Number of base pairs in one complete turn) Number of complete turns = \(\frac{7.5 \times 10^6}{10}\)

Step 6: Find the number of complete turns

Now let's find the number of complete turns: Number of complete turns = \(\frac{7.5 \times 10^6}{10}\) Number of complete turns = \(7.5 \times 10^5\) So, there are approximately 750,000 complete turns in the given DNA α-helix structure.

Key Concepts

Helix

The structure of DNA is most famously known for its double helix shape. Imagine it like a twisted ladder. This form isn't just for show, it has a specific function. The helical nature allows DNA to pack tightly into the tiny confines of a cell's nucleus. Each complete twist or turn of the helix is around 3.4 nanometers long. This small size allows for a lot of genetic information to be stored efficiently.

Another important aspect is that the helical structure provides stability to the DNA molecule. Because of the way the helix is twisted, the base pairs are tightly fitted in place, which protects the genetic material from damage. This stability is crucial for the accurate transmission of genetic information. The double helix also plays a role in the process of DNA replication, enabling the molecule to be copied accurately during cell division.

Base pairs

Base pairs are the fundamental units of the DNA double helix. Each base pair consists of two nucleotides bonded together across the two strands of DNA. There are four main types of nucleotides: adenine (A), thymine (T), cytosine (C), and guanine (G).

These nucleotides pair in a specific way: adenine pairs with thymine, and cytosine pairs with guanine. This is known as complementary base pairing, and it's key to the structure of DNA. The sequence of these base pairs constitutes the genetic code, similar to how letters form words and sentences.

Understanding base pairing also helps us comprehend how DNA replicates. Because each base pair lines up with its complement, when the DNA strands separate, new strands can be built along each old strand, using the base-pairing rules to ensure accuracy?

Molecular mass

Molecular mass is a crucial concept when discussing DNA structure. It refers to the mass of a single molecule of a substance, measured in terms of atomic mass units. In DNA, the molar mass is an essential factor because it allows for the calculation of various properties, such as the number of base pairs.

The average molar mass for one base pair in DNA is approximately 600 g/mol. This value helps in determining how many base pairs are present in a DNA strand, given its total molar mass. For instance, if a DNA molecule has a molar mass of 4.5 x 10^9 g/mol, it means that this DNA contains about 7.5 million base pairs.

• Helps in determining DNA's physical properties.
• Essential in genetic engineering and molecular biology.
• Provides insights into the structure and length of DNA.

In essence, knowing the molecular mass allows scientists to estimate the size and complexity of the DNA, providing insights into its genetic capacity.