Question

Assume that all plasmid-containing cells have eight plasmids; that an antibiotic is present in the medium, and the plasmid-containing cells are totally resistant; and that a newly born, plasmid-free cell has sufficient enzyme to protect a cell and its progeny for three generations. Estimate the fraction of plasmid-containing cells in the population in a batch reactor starting with only plasmid-containing cells after five generations.

Short answer

After five generations, the fraction of plasmid-containing cells is 100%.

Step-by-step solution

- Understand the problem

We need to estimate the fraction of plasmid-containing cells in a batch reactor after five generations, starting with all plasmid-containing cells. A few key points to understand: plasmid-containing cells are resistant to antibiotics, and plasmid-free cells have enough resistance for three generations.

- Initial Conditions

Start with 100% plasmid-containing cells. Let P0 be the initial number of plasmid-containing cells and N0 be the initial number of plasmid-free cells, where P0 = N0 = 0 for the purpose of calculation simplicity.

- Generation 1 to 3

During the first three generations, plasmid-free cells (though initially nonexistent in our simplified model) will survive because of the inherited enzyme resistance. Plasmid-containing cells will also multiply. After three generations, the fraction of plasmid-containing cells remains unchanged since plasmid-free cells were initially zero.

- Fourth Generation

At the fourth generation, the inherited enzyme resistance ends. All newly born plasmid-free cells will die as they cannot survive the antibiotic environment. Only plasmid-containing cells continue to live and multiply. The fraction of plasmid-containing cells remains 100% since no plasmid-free cells survive.

- Fifth Generation

The environment remains the same with antibiotics present. Plasmid-containing cells will again multiply without competition from plasmid-free cells. Therefore, the fraction of plasmid-containing cells in the population will still be 100%.

Key concepts

Plasmid-Containing Cells

Plasmid-containing cells are bacterial cells that possess extra-chromosomal DNA in the form of plasmids. Plasmids often carry genes that can provide advantages, such as antibiotic resistance, which helps the bacteria survive hostile environments. These cells can replicate their plasmids and pass them on to their progeny, ensuring the survival of these beneficial traits.

In bioprocess engineering, understanding the role of plasmid-containing cells is critical when designing systems for biomanufacturing or antibiotic resistance studies. The plasmids can sometimes carry genes that are essential for bioproduction, making their retention within the cells crucial. In our example exercise, plasmid-containing cells start as the unchallenged population due to their eight plasmids, which confer resistance to antibiotics in the medium.

Batch Reactor

A batch reactor is a type of bioreactor where the reactants are confined within a closed system. This means that no substances are added or removed during the operation. Batch reactors are commonly used in bioprocessing because they can be tightly controlled and are suitable for studying microbial growth and product formation.

In the context of our exercise, the batch reactor allows the population dynamics of plasmid-containing cells versus plasmid-free cells to be observed without external interference. Initially, the system starts with only plasmid-containing cells. Over time and through several generations, the impact of antibiotic resistance provided by the plasmids can be clearly seen.

The closed system ensures the consistency of selective pressure from the antibiotic, making it easier to study the changes in the cell population over the five generations.

Antibiotic Resistance

Antibiotic resistance is the ability of bacteria to survive and multiply even in the presence of an antibiotic that would typically kill them or inhibit their growth. This resistance can be naturally occurring or acquired through horizontal gene transfer, such as through plasmids.

In our specific case, the presence of an antibiotic in the medium ensures that only cells with resistance can thrive. Plasmid-containing cells carry genes that offer this resistance, allowing them to proliferate within the batch reactor. Plasmid-free cells initially survive for up to three generations due to inherited enzyme resistance. However, after these three generations, the plasmid-free cells cannot regenerate their resistance and thus die off in the fourth generation.

By the fifth generation, only plasmid-containing cells survive due to the continuous presence of the antibiotic. This exemplifies the significant role of antibiotic resistance in selective bacterial survival and the maintenance of plasmid-containing cell populations.