A bacterial strain is growing exponentially. At 10:00 am the titre of the culture is 4 x 106 cells per ml. At 4 pm, the culture is still growing exponentially and the titre has increased to 6 x 108 cells per ml. Assuming that the bacterial strain was in exponential phase growth prior to the measurements at 10:00 am, how many generations would have elapsed between 08:00 am and 4pm? Show all of your calculations. This culture will eventually reach the death phase when the nutrients become limited. What does happen in this phase? What strategies do bacteria develop to cope with nutrient shortages?
Question
A bacterial strain is growing exponentially. At 10:00 am the titre of the culture is 4 x 106 cells per ml. At 4 pm, the culture is still growing exponentially and the titre has increased to 6 x 108 cells per ml. Assuming that the bacterial strain was in exponential phase growth prior to the measurements at 10:00 am, how many generations would have elapsed between 08:00 am and 4pm? Show all of your calculations.
This culture will eventually reach the death phase when the nutrients become limited. What does happen in this phase? What strategies do bacteria develop to cope with nutrient shortages?
Solution
To calculate the number of generations that have elapsed, we first need to determine the growth rate constant (k). The formula for k is:
k = (ln(Nt) - ln(N0)) / t
where: Nt = final population size N0 = initial population size t = time (in hours)
From the problem, we know that Nt = 6 x 10^8 cells/ml, N0 = 4 x 10^6 cells/ml, and t = 6 hours (from 10 am to 4 pm).
Substituting these values into the formula, we get:
k = (ln(6 x 10^8) - ln(4 x 10^6)) / 6
After calculating the above expression, we get the value of k.
Next, we need to calculate the number of generations (g) that have elapsed from 8 am to 4 pm, which is an 8-hour period. The formula for g is:
g = t * k
Substituting the values into the formula, we get the number of generations.
In the death phase, the number of dying cells exceeds the number of new cells being formed, so the overall population decreases. This happens because the nutrients in the medium have become limited, and waste products have accumulated, making the environment unsuitable for growth.
Bacteria have several strategies to cope with nutrient shortages. Some bacteria form endospores, which are resistant to harsh conditions and can remain dormant until conditions improve. Others can adjust their metabolism to use different nutrients. Some bacteria can even become cannibalistic, releasing enzymes to break down other cells and use their components for growth.
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