# If you inoculate fresh Nutrient Broth with 100 cells of Escherichia coli

1. If you inoculate fresh Nutrient Broth with 100 cells of Escherichia coli and keep the culture at the optimal temperature of 37°C, assuming the generation time is 30 minutes, how many generations will take place after 7 hours?

How many bacteria will be present?

Will the number of bacteria continue to double every 30 minutes indefinitely? Why?

2. Starting with four bacterial cells per cm3 in a rich nutrient medium, with a 20-minutes generation time, how many cells will there be in 1 dm3 of this culture after 1 hour?

After 2 hours?

After 2 hours if one of the initial four cells was non viable?

3. After washing your hands, you decide to do a plate count on the soap. You dilute 1 g of the soap to 10-6 and plate it on nutrient agar. After 24 hours of incubation at 37C, there are 168 colonies. How many bacteria were on the soap?

4. You were given a 24-hour liquid culture of T2 coliphage. After aseptically performing the usual 10-fold serial dilution procedure, you plated 0.1 cm3 of the 10-5, 10-6, 10-7 and 10-8 dilutions in three replicates. Plates were incubated at 37ºC for 24 hours, and these are the results you obtained:

Dilution Replicate 1 Replicate 2 Replicate 3

10-5 TNTC TNTC TNTC

10-6 245 234 284

10-7 23 28 29

10-8 2 3 4

TNTC: Too numerous to count

Calculate the average number of plaque forming units per cm3 present in the original culture.

5. Most vaccines licensed for use in the UK are prepared from attenuated (live) viruses. Attenuated viruses are capable of limited replication in the target cell but cannot replicate sufficiently to cause disease. It is important that each dose of the vaccine contains the correct number of virus particles. Too few may not be sufficient to stimulate a protective immune response and too many may cause disease. It is therefore necessary to check all batches of vaccines made for infectivity using a suitable assay.

Three batches of the attenuated Sabin poliovirus vaccine were tested for infectivity using a plaque assay on Vero cells (a cell line derived from monkey kidney cells); 0.1 cm3 aliquots of each batch were tested three times and the following results were obtained.

Batch 1

Dilution Replicate 1 Replicate 2 Replicate 3

10-6 TNTC TNTC TNTC

10-7 200 231 194

10-8 19 26 24

Batch 2

Dilution Replicate 1 Replicate 2 Replicate 3

10-6 TNTC TNTC TNTC

10-7 198 205 220

10-8 25 33 31

Batch 3

Dilution Replicate 1 Replicate 2 Replicate 3

10-6 TNTC TNTC TNTC

10-7 252 199 208

10-8 32 23 27

TNTC = too numerous to count

What is a plaque?

Suggest why only dilutions above 10-5 were tested.

Calculate the average number of PFU (plaque forming units) per cm3 of the original vaccine suspension for each batch.

If each dose of 0.1 cm3 should contain 500 PFU of attenuated virus, by how much should each batch be diluted?

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1. If you inoculate fresh Nutrient Broth with 100 cells of Escherichia coli and keep the culture at the optimal temperature of 37°C, assuming the generation time is 30 minutes, how many generations will take place after 7 hours?

All you need to do is set up a simple unit dimensional analysis.

Like this:

(7 hours)(60 min/hour)(1 gen/30 min) = 14 gen

How many bacteria will be present?

The number of cells will double each generation. Therefore, after the first 30 minutes, there will be 200 cells. After the first hour, those 200 cells will double and become 400 cells, and so on.

Therefore,

(100 cells)(214) = 1,638,400 cells

Notice that the "214" factor is a repeating doubling that occurs 14 times.

Will the number of bacteria continue to double every 30 minutes indefinitely? Why?

No, after a while, the cells will begin to crowd each other and interfere with each other's growth. In addition, they will begin to use up nutrient resources (which will slow down growth of future generations) and they will produce toxins and waste products (that will also slow down and inhibit the growth of other cells).

2. Starting with four bacterial cells per cm3 in a rich nutrient medium, with a 20-minutes generation time, how many cells will there be in 1 dm3 of this culture after 1 hour?

First, let's find out how many cm3 are in 1 dm3. This is a basic conversion you should memorize. 1 cm3 = 1 ml, and 1 dm3 = 1 litre. Therefore, there are 1000 cm3/dm3.

Therefore, we can figure out the number of cells at the start:

(4 cells/ml)(1000 ml) = 4000 cells

The rest of the question is easy. How many doublings are there in 1 hour? Since a doubling time is 20 minutes, there must be 3 doublings in 1 hour.

(4000 cells)(23) = 32,000 cells

After 2 hours?

In 2 hours, there are six rounds ...