Question

A plaque assay is performed beginning with \(1.0 \mathrm{mL}\) of a solution containing bacteriophages. This solution is serially diluted three times by taking \(0.1 \mathrm{mL}\) and adding it to \(9.9 \mathrm{mL}\) of liquid medium. \(0.1 \mathrm{mL}\) of the final dilution is plated and yields 17 plaques. What is the initial density of bacteriophages in the original \(1.0 \mathrm{mL} ?\)

Short answer

Answer: The initial density of bacteriophages in the original 1.0 mL solution is 170,000 plaques/mL.

Step-by-step solution

Find the dilution factor for each step

At each serial dilution, 0.1 mL is taken from the solution and added to 9.9 mL of liquid medium. The dilution factor is calculated as the total volume divided by the sample volume. In this case, the dilution factor for each step is \(\frac{9.9 + 0.1}{0.1} = 10\)

Calculate the total dilution factor

Since there are three serial dilutions, we need to multiply the dilution factor for each step together to find the total dilution factor: \(10 \times 10 \times 10 = 1000\)

Calculate the density of bacteriophages in the last dilution

We know that 0.1 mL of the last dilution yielded 17 plaques. To find the density of bacteriophages in the last dilution, we need to divide the number of plaques by the volume plated: \(\frac{17 \text{ plaques}}{0.1 \text{ mL}} = 170 \text{ plaques/mL}\)

Calculate the initial density of bacteriophages

To find the initial density of bacteriophages in the original 1.0 mL solution, we need to multiply the density of the last dilution by the total dilution factor: \(170 \text{ plaques/mL} \times 1000 = 170000 \text{ plaques/mL}\) So, the initial density of bacteriophages in the original \(1.0 \mathrm{mL}\) solution is \(170,000\) plaques/mL.

Key concepts

Bacteriophage Density Calculation

Bacteriophage density calculation is a crucial step in determining the concentration of bacteriophages—viruses that infect bacteria—in a sample. In the context of a plaque assay, calculating the initial density of bacteriophages helps us understand how many virus particles were present in the original solution. To compute this, we need to know the number of plaques formed and the dilution factor applied to the sample.

• Count the Plaques: Plaques are clear areas on a bacterial lawn, indicating viral infections that have killed their host bacteria. By counting these, we determine the number of bacteriophages.
• Apply the Total Dilution Factor: The number of plaques is adjusted by the total dilution factor to calculate the initial concentration of viruses. This factor accounts for the reduction in concentration due to serial dilutions.

In summary, bacteriophage density is derived by multiplying the plaque count by the reciprocal of the total dilution factor.

Serial Dilution

Serial dilution is a method of diluting a substance in a stepwise manner, typically by consistent factor increments. This technique is particularly useful in microbiology and virology to lower the concentration of a sample. Serial dilutions are performed to ensure the results, such as counting bacteriophage plaques, fall into a countable range.

• Repeating Dilutions: In our example, 0.1 mL of solution is mixed with 9.9 mL of liquid medium. This process is repeated three times, each reducing the concentration of bacteriophages by a factor of 10.
• Progressive Concentration Reduction: After each dilution step, the concentration follows a predictable decrease, which plays a crucial role in calculating the final bacteriophage density.

Serial dilution thus enables manageable concentrations and accurate lab results.

Dilution Factor

The dilution factor is a constant that represents how much a sample has been diluted at each step. It is calculated as the ratio of the final volume to the sample volume. Understanding dilution factors is fundamental not only in calculating bacteriophage densities but also in many laboratory processes.

• Step-by-Step Dilution Factor Calculation: For each step, add the sample volume (0.1 mL) to the diluent volume (9.9 mL) and divide the total volume (10 mL) by the sample volume (0.1 mL), resulting in a factor of 10.
• Combined Total Dilution Factor: Multiply the dilution factor for each step (10) together for each successive dilution, giving a total factor of 1000 after three steps.

This cumulative factor indicates how much the original sample's concentration has decreased.

Plaque Forming Units

Plaque forming units (PFUs) provide a measure of the number of viable virus particles in a sample. These units are determined through plaque assays, and each plaque is assumed to arise from a single phage infecting a bacterial cell. Counting PFUs benefits researchers by offering insights on viral concentration in a given sample.

• Relation to Plaques: PFUs are equivalent to the number of plaques formed on the plate. Each plaque corresponds to one PFU.
• Calculation Example: To determine PFUs/mL, count the plaques on the dish (17 plaques in this scenario) and divide by the sample volume used for plating (0.1 mL), leading to 170 PFUs/mL in the final dilution.

PFUs offer a straightforward way to estimate the virus concentration in various experiments.