Bacterial growth is the process of division of one cell to give rise to two daughter cells through binary fission.
Bacterial cells in a batch culture goes through four phases:
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Bacterial growth can be calculated using the simple formula
2^number of generations * initial number of bacteria = total no. of bacteria present after n generations
after each generation cycle one bacteria divides into two, so to calculate no of bacterial cells after n no. of generation just use 2^n no. of generations. Multiplying by the no. of bacterial cells you have inoculated total no of bacterial cells after n no of generations can be calculated.
Example: Bacillus cereus divides every 30 minutes. You have inoculated a culture with exactly 100 bacterial cells. After 3 hours, how many bacteria are present?
In this case you need to calculate no of generations or the divisions bacterial cells takes place in 3 hrs.
3 hours = 3 *60 mins = 180 mins.
TIme for 1 generation is 30 mins,
so in 180 mins bacterial cells divide 6 times (180/30 = 6).
no of generations n =6.
So 2^n ; 2^6 = 64 or 2x2x2x2x2x2
Initial bacterial cells is 100, so
100 x 64 = 6,400 cells
Using the same example, let's say you have determined that your sample contains 6,400
bacterial cells. You know that it incubated 3 hours. How many generations have occurred?
2^n = (log cells at end of incubation ) - (log cells at beginning of incubation)
n= ((log6400) – (log100))/ log2
Therefore, (log 6400) - (log 100) / 0.301 = (3.81 - 2) / 0.301 = 6 generations
To calculate the generation time for a population: 60 min x hours / number of generations
In this example:
60 min x 3 hours / 6 generations = 30 minutes per generation
Practice Problems
1. You perform a serial dilution and determine that the original number of cells in your
sample was 12,000. How many bacteria will be present in 12 hours if the generation time is
15 minutes (assume unlimited food and clean environment)?
Solution:
12*60 = 720mins
1 generation time = 15 mins
so no of generations in 720 mins = 720/15 = 48
Total no of bacterial cells = 2^n * Initial no of cells
2. You determine that a coconut cream pie has 3 million (3 x 10^6 ) Staph. aureus cells in it.
You estimate that the food preparer did not wash his hands and probably inoculated the
cream with 500 Staph. aureus. He also forgot to refrigerate it. If the pie was made 6 hours
ago, how many generations have occurred? How long is each generation?
Solution:
log (3 x 10^6) - log (500) / 0.301 = (6.47 - 2.7) / 0.301 = 12.5 generations
60 minutes x 6 hours / 12.5 generations = 28.8 minutes per generation
3. Using the generation time from problem 2, how many bacteria would be present after 8
hours at room temperature?
Solution:
28.8 minutes per generation, 8 hours x 60 min = 480 minutes
total time to grow
480 / 28.8 = 16.7 generations in 8 hours = n
therefore:
500 x 216.7 = 500 x 1.06 x 10^5
= 5.32 x 10^7 bacterial cells
4. Let's say that flesh eating Strep. pyogenes divides every 10 minutes at body temperature. You fall down and scrape your knee and get infected with 5 Strep. pyogenes cells. After 4 hours, without medical intervention, how many bacteria will be ravaging your body? Let's say that for every 1 million bacteria, a centimeter of flesh is consumed. After 4hours, how much tissue would be lost? Are you still alive and would you want to be? (This problem is not fact based.)
Solution:
6 generations per hour, 24 generations in 4 hours
5 x 224 = 8.4 x 10^7 bacterial cells
8.4 x 10^7 / 1 x 10^6 = 84 million cells
1 cm of flesh per million = 84 cm of flesh (33.5 inches)
You would be alive but you would lose the leg. We are assuming the infection does not become systemic.
Source
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Bacterial cells in a batch culture goes through four phases:
- Log Phase
- Lag / Exponential Phase
- Stationary Phase
- Death Phase
 |
| Bacterial Growth Curve - Log No of Cells Vs Time |
2^number of generations * initial number of bacteria = total no. of bacteria present after n generations
after each generation cycle one bacteria divides into two, so to calculate no of bacterial cells after n no. of generation just use 2^n no. of generations. Multiplying by the no. of bacterial cells you have inoculated total no of bacterial cells after n no of generations can be calculated.
Example: Bacillus cereus divides every 30 minutes. You have inoculated a culture with exactly 100 bacterial cells. After 3 hours, how many bacteria are present?
In this case you need to calculate no of generations or the divisions bacterial cells takes place in 3 hrs.
3 hours = 3 *60 mins = 180 mins.
TIme for 1 generation is 30 mins,
so in 180 mins bacterial cells divide 6 times (180/30 = 6).
no of generations n =6.
So 2^n ; 2^6 = 64 or 2x2x2x2x2x2
Initial bacterial cells is 100, so
100 x 64 = 6,400 cells
Using the same example, let's say you have determined that your sample contains 6,400
bacterial cells. You know that it incubated 3 hours. How many generations have occurred?
2^n = (log cells at end of incubation ) - (log cells at beginning of incubation)
n= ((log6400) – (log100))/ log2
Therefore, (log 6400) - (log 100) / 0.301 = (3.81 - 2) / 0.301 = 6 generations
To calculate the generation time for a population: 60 min x hours / number of generations
In this example:
60 min x 3 hours / 6 generations = 30 minutes per generation
Practice Problems
1. You perform a serial dilution and determine that the original number of cells in your
sample was 12,000. How many bacteria will be present in 12 hours if the generation time is
15 minutes (assume unlimited food and clean environment)?
Solution:
12*60 = 720mins
1 generation time = 15 mins
so no of generations in 720 mins = 720/15 = 48
Total no of bacterial cells = 2^n * Initial no of cells
= 2^48 * 12000
= 3.4*10^18 cells
2. You determine that a coconut cream pie has 3 million (3 x 10^6 ) Staph. aureus cells in it.
You estimate that the food preparer did not wash his hands and probably inoculated the
cream with 500 Staph. aureus. He also forgot to refrigerate it. If the pie was made 6 hours
ago, how many generations have occurred? How long is each generation?
Solution:
log (3 x 10^6) - log (500) / 0.301 = (6.47 - 2.7) / 0.301 = 12.5 generations
60 minutes x 6 hours / 12.5 generations = 28.8 minutes per generation
3. Using the generation time from problem 2, how many bacteria would be present after 8
hours at room temperature?
Solution:
28.8 minutes per generation, 8 hours x 60 min = 480 minutes
total time to grow
480 / 28.8 = 16.7 generations in 8 hours = n
therefore:
500 x 216.7 = 500 x 1.06 x 10^5
= 5.32 x 10^7 bacterial cells
4. Let's say that flesh eating Strep. pyogenes divides every 10 minutes at body temperature. You fall down and scrape your knee and get infected with 5 Strep. pyogenes cells. After 4 hours, without medical intervention, how many bacteria will be ravaging your body? Let's say that for every 1 million bacteria, a centimeter of flesh is consumed. After 4hours, how much tissue would be lost? Are you still alive and would you want to be? (This problem is not fact based.)
Solution:
6 generations per hour, 24 generations in 4 hours
5 x 224 = 8.4 x 10^7 bacterial cells
8.4 x 10^7 / 1 x 10^6 = 84 million cells
1 cm of flesh per million = 84 cm of flesh (33.5 inches)
You would be alive but you would lose the leg. We are assuming the infection does not become systemic.
Source
Internet Sources
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