Question

A plaque assay is performed beginning with \(1 \mathrm{mL}\) of a solution containing bacteriophages. This solution is serially diluted three times by combining \(0.1 \mathrm{mL}\) of each sequential dilution with \(9.9 \mathrm{mL}\) of liquid medium. Then \(0.1 \mathrm{mL}\) of the final dilution is plated in the plaque assay and yields 17 plaques.What is the initial density of bacteriophages in the original \(1 \mathrm{mL} ?\)

Short answer

Answer: The initial density of bacteriophages in the original 1 mL solution is 170,000,000 plaques/mL.

Step-by-step solution

Identify the dilution factor

We are given that the solution is serially diluted three times by combining 0.1 mL of each sequential dilution with 9.9 mL of liquid medium. So, we need to find the dilution factor for each dilution step. Dilution factor = (Volume of sample)/(Total volume)

Calculate the dilution factors

Let's calculate the dilution factor for each of the three steps: Dilution factor 1: (0.1 mL)/(0.1 mL + 9.9 mL) = 1/100 Dilution factor 2: (0.1 mL)/(0.1 mL + 9.9 mL) = 1/100 Dilution factor 3: (0.1 mL)/(0.1 mL + 9.9 mL) = 1/100

Calculate the combined dilution factor

To find the combined dilution factor, multiply the three individual dilution factors: Combined dilution factor = Dilution factor 1 * Dilution factor 2 * Dilution factor 3 = 1/100 * 1/100 * 1/100 = 1/100^3 = 1/1000000

Determine the concentration of bacteriophages in the final dilution

The final dilution is plated in the plaque assay and yields 17 plaques. We are given that 0.1mL of the final dilution is plated: Concentration_Final = (17 plaques) / (0.1 mL) = 170 plaques/mL

Calculate the initial concentration of bacteriophages

Now, using the combined dilution factor, we can calculate the initial concentration of bacteriophages: Initial concentration = Concentration_Final * Combined dilution factor = 170 plaques/mL * 1000000 = 170000000 plaques/mL Therefore, the initial density of bacteriophages in the original 1 mL solution is 170,000,000 plaques/mL.

Key concepts

Serial Dilution

Understanding the process of serial dilution is essential in a variety of scientific fields, particularly in microbiology, where it's used to reduce the concentration of a substance, such as bacteriophages, viruses that infect bacteria. This technique involves taking a small amount of a concentrated solution and adding it to a new container with a larger volume of solvent to dilute it. This process is then repeated several times to achieve a series of dilutions, each one less concentrated than the previous.

In the exercise provided, the dilution factor for each step is the volume of the sample taken (0.1 mL) divided by the total volume after dilution (10 mL), resulting in a factor of 1/100. By performing the serial dilution three times, we compound this dilution, which is mathematically represented as \(1/100 \times 1/100 \times 1/100 = 1/1,000,000\). The essence of this technique is not just to dilute the solution but to do so in a controlled manner that allows for easy calculation of concentration or density of the original sample, which is why maintaining precise volumes and dilution factors is crucial.

Bacteriophage Density Calculation

Once the serial dilution is performed, it is important to understand how to calculate the density, or concentration, of bacteriophages present in the original sample. The density of bacteriophages is usually expressed in terms of the number of infectious units per milliliter, such as plaque-forming units (pfu/mL).

As outlined in the solution, we start by determining the bacteriophage concentration in the final dilution, which is based on the number of plaques formed when a small volume of the diluted sample is plated. In the provided exercise, the final dilution yields 17 plaques from 0.1 mL, which translates to a concentration of 170 plaques/mL. To calculate the initial density, we simply reverse the dilution process by multiplying this final concentration by the combined dilution factor, here \(170 \times 1,000,000 = 170,000,000\) plaques/mL. Thus, the process of calculating bacteriophage density turns complex experimental data into actionable figures that can inform further research and applications.

Plaque Formation

The plaque assay is a quantitative method used to determine the number of bacteriophages in a sample. It relies on the ability of phages to infect and lyse bacterial cells, forming clear zones called plaques. Each plaque represents an area where bacteria have been destroyed by a single bacteriophage or a cluster of bacteriophages that originated from a single infective event.

During the assay, a mixture of bacteriophages and bacteria is spread over the surface of an agar plate. As the bacteria grow, they form a lawn, except at locations where bacteriophages have infected the cells. Over time, the phages replicate and spread, eventually clearing the bacteria in that spot. These cleared spots, or plaques, are then counted. The number of plaques gives an estimate of the number of viable phages present in the original sample before dilution, which is fundamental for the calculation of bacteriophage density, hence providing critical information for studies involving bacteriophages in both basic and applied sciences.