Question

Supercoiled DNA is slightly unwound compared to relaxed DNA and this enables it to assume a more compact structure with enhanced physical stability. Describe the enzymes that control the number of supercoils present in the \(E\) coli chromosome. How much would you have to reduce the linking number to increase the number of supercoils by five?

Short answer

Answer: The enzymes that control the number of supercoils in the E. coli chromosome are called topoisomerases. To increase the number of supercoils by five, the linking number must be reduced by 2.5 times the action of a type II topoisomerase. However, since enzymes can only change the linking number in increments of 2, it would need to act 3 times for a closest obtainable change of 6 supercoils.

Step-by-step solution

Explain the enzymes that control supercoiling in E. coli

The enzymes that control the number of supercoils in the E. coli chromosome are called topoisomerases. There are two main types: type I topoisomerases and type II topoisomerases. Type I topoisomerases act by creating a single-strand break in the DNA, passing the other strand through the break, and then resealing the break. This changes the linking number by ±1. Type II topoisomerases, such as DNA gyrase, create a double-strand break in the DNA, pass another segment of the double helix through the break, and then reseal the break. This changes the linking number by ±2.

Define the change in linking number for an increase in supercoiling

To determine the reduction in the linking number required for an increase of five supercoils, we can use the relationship between supercoiling and linking number. The formula relating linking number (Lk), twist (Tw), and writhe (Wr) is given by: \[ Lk = Tw + Wr \] Where: - Lk is the linking number, which represents the number of times one DNA strand wraps around the other - Tw is the twist, which represents the number of base pairs in one complete turn of the double helix - Wr is the writhe, which represents the number of times the double helix is coiled or supercoiled

Calculate the change in linking number required to increase supercoils by five

To increase the number of supercoils (Wr) by five, the linking number (Lk) must be reduced by the same amount, keeping the twist (Tw) constant. Assuming that this change in supercoiling is caused by the action of type II topoisomerases, which change the linking number by ±2, we would need to perform the following calculation: \[ ΔLk = -2n \] Where n is the number of actions by the type II topoisomerase and ΔLk is the change in linking number. Since we want to increase the number of supercoils by five (Wr = +5), we can set up the following equation: \[ 5 = -2n \] Solving for n: \[ n = \frac{-5}{-2} = 2.5 \] This means that in theory, the linking number must be reduced by 2.5 times the action of a type II topoisomerase (such as DNA gyrase) to increase the number of supercoils by five. However, since the enzyme can only change the linking number in increments of 2, this means it would need to act 3 times, which would actually result in a reduction of 6 supercoils. It is not possible to achieve an exact increase of 5 supercoils with these enzymes, but 6 is the closest obtainable change.

Key concepts

Topoisomerases

Topoisomerases are crucial enzymes that manage the process of DNA supercoiling, ensuring that the double-helix structure is maintained properly despite the physical manipulations DNA undergoes during cell processes such as replication or transcription.

They achieve this by temporarily cutting one or both strands of the DNA helix, permitting the relaxation of supercoils, and then resealing the strands. This action adjusts the DNA's topology, specifically its 'linking number,' reducing strain and preventing entanglement or breakage.

Types Of Topoisomerases

There are two main types of topoisomerases with distinct mechanisms:

• Type I Topoisomerases: These act on one strand of DNA, enabling the passage of the other strand through the break, which changes the linking number by one unit at a time.
• Type II Topoisomerases: They cut both DNA strands and can change the linking number by two units with each action. DNA gyrase, a type of type II topoisomerase found in E. coli, is known for adding negative supercoils to DNA, which compacts the DNA and is essential for bacterial survival.

Through their actions, topoisomerases keep the DNA in a functional state, ready for various cellular activities, and as a result, they are targeted by certain antibiotics that aim to disrupt bacterial DNA processes.

DNA Gyrase

DNA gyrase is a specific type of bacterial topoisomerase II that introduces negative supercoils into DNA. It is particularly important in bacteria like E. coli as it counteracts the positive supercoiling that tends to occur during DNA unwinding.

Mechanism Of Action

The enzyme works by cutting both strands of the DNA molecule, passing a segment of the double helix through the gap, and then sealing the break. This process uses energy derived from ATP and changes the linking number by increments of two.

Biological Significance

The activity of DNA gyrase is critical for maintaining the densely packed bacterial nucleoid and is also essential for replication and transcription, as these processes require the DNA to be untwisted. Without DNA gyrase, bacteria would struggle to manage DNA supercoiling, leading to possible fatal disruptions in cellular functioning.

Target For Antibiotics

Interestingly, because of its unique action and critical role in bacterial cell processes, DNA gyrase is a prime target for antibiotic drugs, such as quinolones, which inhibit its function and thus can effectively kill bacteria by preventing their ability to manage DNA supercoiling.

Linking Number

The linking number (Lk) is a mathematical expression, describing the total number of times one strand of the DNA double helix wraps around the other. It's an invariant property for a closed loop of DNA, assuming no strand breaks occur during the interaction.

Importance Of Linking Number

Lk is a crucial concept for understanding the topology of DNA. It's intimately related to DNA's secondary structures, like supercoils. A change in the linking number may induce supercoiling, which affects the DNA's ability to function and interact with other cellular components.

Linking Number And Supercoiling

Alterations in the linking number result in supercoiling; when Lk is reduced, DNA becomes negatively supercoiled, and when it is increased, DNA becomes positively supercoiled. The formula for calculating the linking number combines twist (Tw), the number of twists in the DNA helix, with writhe (Wr), the number of times the helix crosses over itself:
\[ Lk = Tw + Wr \]
By manipulating the linking number, enzymes like topoisomerases can either introduce or relieve supercoils, critical for DNA replication, transcription, and compaction. Understanding the linking number is fundamental for comprehending how enzymes exert their influence on DNA topology—a concept essential in molecular biology.