Question

Starting with 10 bacterial cells per milliliter in a sufficient amount of complete culture medium with a 1-hour lag phase and a 30 -minute generation time, how many cells will there be in a liter of medium at the end of 2 hours? At the end of 7 hours?

Short answer

At the end of 2 hours, there will be 40000 cells in a liter of medium, and at the end of 7 hours, there will be approximately 40,960,000,000 cells in a liter of medium.

Step-by-step solution

Calculating Number of Generations

For the first part, at the end of 2 hours, excluding the 1 hour of lag phase, we've just one hour of active growth which corresponds to 2 generations (each one of 30 minutes). For the latter part, at the end of 7 hours, we've 6 hours of active growth which means 12 generations.

Calculate Number of Cells at the End of 2 hours

The number of bacterial cells present at the end of time period can be calculated using the formula: \[N = N_0 \times 2^n\]where:N = Final number of cellsN_0 = Initial number of cellsn = Number of generationsSubstitute N_0 = 10 cells/ml, n = 2 (for 2 hours) into the formula, to get the number of cells per ml. To find the final number of cells per liter, multiply the result by 1000 (since 1 liter = 1000 ml).

Calculate Number of Cells at the End of 7 hours

Using the same formula as in Step 2, substitute N_0 = 10 cells/ml, n = 12 (for 7 hours) to get the number of cells per ml at the end of 7 hours. Multiply the result by 1000 to get the final number of cells per liter.

Key concepts

Understanding Generation Time

When studying bacterial cell division, generation time is a key concept that refers to the time it takes for a population of bacteria to double in number. In essence, it's the duration of one complete cycle of bacterial replication.
In the context of the given exercise, it's mentioned that the generation time is 30 minutes. This means that every half-hour, the number of bacterial cells doubles. Think about it like this:

• If you started with 10 cells, after 30 minutes, you'd have 20 cells.
• After another 30 minutes, those 20 cells would double to 40, and so on.

This concept is crucial for accurately predicting bacterial growth over time, especially in controlled environments like those found in scientific experiments or clinical settings.

Exploring the Lag Phase

The lag phase is the initial period that occurs when bacteria are introduced to a new environment, such as the culture medium in the exercise. During this time, the bacteria are not multiplying. Instead, they are adapting to their surroundings. This can involve acclimating to temperature, pH, nutrient availability, and other conditions.
It’s mentioned in the problem that there is a 1-hour lag phase. This implies that the bacteria won't start doubling until after this period. Think of the lag phase as a preparatory stage where:

• The cells are active internally, though not yet dividing.
• They might be producing enzymes necessary to metabolize the available nutrients.
• The duration of the lag phase can vary based on environmental factors and the physiological state of the bacteria.

Understanding the lag phase helps in accurately modeling the growth pattern of bacterial populations, as it directly affects how quickly the bacteria begin to multiply.

Calculating Microbial Growth

Calculating microbial growth involves determining how many bacteria will be present after a given period. The exercise introduces the formula:\[ N = N_0 \times 2^n \]Here, \(N\) represents the final number of cells, \(N_0\) is the initial number of cells, and \(n\) is the number of generations, which can be found by dividing the active growth time by the generation time.
For example, in the exercise:

• After 2 hours, excluding the 1-hour lag phase, you have 1 hour of growth, resulting in 2 generations (since the generation time is 30 minutes).
• Thus, \(n = 2\) for 2 hours and \(n = 12\) for 7 hours of growth.
• Substitute these values into the formula to find the number of cells per milliliter at each time point, then multiply by 1000 to find the number per liter.

This method allows for calculating the bacterial growth in various laboratory and real-world scenarios, helping scientists and students understand how bacterial populations grow and change over time.