Question

Assume that one counted 67 plaques on a bacterial plate where \(0.1 \mathrm{ml}\) of a \(10^{-5}\) dilution of phage was added to bacterial culture. What was the initial concentration of the undiluted phage?

Short answer

Answer: The initial concentration of the undiluted phage is \(6.7 * 10^3\) plaques per ml.

Step-by-step solution

Identify the given information

We are given the following information: - Number of plaques: 67 - Volume of diluted phage: \(0.1\,\mathrm{ml}\) - Dilution factor: \(10^{-5}\)

Calculate the initial concentration of undiluted phage

We will use the formula for dilution to find the initial concentration of undiluted phage: Initial concentration of undiluted phage = (Number of plaques * Dilution factor) / Volume of diluted phage Initial concentration of undiluted phage = (67 * \(10^{-5}\)) / \(0.1\,\mathrm{ml}\)

Simplify the expression

Now, we can simplify the expression: Initial concentration of undiluted phage = \((67 * 10^{-5}) / 0.1\) We can now cancel out the 0.1 in the denominator by multiplying the numerator and denominator by 10: Initial concentration of undiluted phage = \((67 * 10^{-4})\)

Calculate the final result

With the expression simplified, we can now find the initial concentration of undiluted phage: Initial concentration of undiluted phage = \(67 * 10^{-4}\) Initial concentration of undiluted phage = \(6.7 * 10^3\) plaques per ml The initial concentration of the undiluted phage is \(6.7 * 10^3\) plaques per ml.

Key concepts

Plaque Assay

Plaque assay is a popular laboratory method used to determine the number of viral particles in a bacterial or eukaryotic cell culture. When bacteriophages, which are viruses that infect bacteria, are mixed with host cells and spread on a solid medium, they can produce clear zones, or "plaques," where the phages have lysed the bacterial cells.
Plaques are visible to the naked eye or under a low magnification microscope. Each plaque corresponds to a single infectious phage that initiated the infection. This method allows scientists to calculate the concentration of phages in the original solution by counting the number of plaques formed.
In the problem provided, 67 plaques were counted on the bacterial plate. This count is essential as it plays a pivotal role in determining the concentration of phages in the original undiluted solution.

Dilution Calculations

Dilution calculations are crucial when working with solutions of phages to achieve measurable results. Dilutions help reduce the concentration of phages in the solution, allowing for a manageable count of plaques.
The dilution factor indicates how many times the original sample has been diluted. For this exercise, the dilution factor is given as \(10^{-5}\). This means the original solution was diluted by a factor of 100,000.
The formula for calculating the concentration with a given dilution factor is:

• Initial Concentration = (Number of Plaques * Dilution Factor) / Volume used for plating

In this scenario, the problem describes \(0.1\, \text{ml}\) of a \(10^{-5}\) dilution being plated. Understanding how to handle dilution factors and appropriately apply them in calculations is fundamental to deducing the initial concentration of phages.

Phage Concentration

Determining the phage concentration involves using both the plaque count and the dilution factor to backtrack to the initial concentration before dilution. The equation used here is:

• Initial concentration of undiluted phage = (Number of plaques * Dilution factor) / Volume of diluted phage

In our example, after counting 67 plaques and knowing the dilution factor and volume, students can calculate the original phage concentration as follows:\[\text{Initial concentration} = (67 * 10^{-5}) / 0.1 = 6.7 * 10^{3} \text{ plaques per ml}\]
This calculated value tells you how densely packed the phages were in the original undiluted solution. Knowing this concentration is critical for applications in research and industrial processes, where exact viral concentrations are necessary for experiments or production. Understanding these connections highlights the importance of quantification in microbiology.