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# Genetics of Bacteria Practice Problems

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By McGraw-Hill Professional
Updated on Aug 23, 2011

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## Genetics of Bacteria Practice Problems

#### Practice 1

Under optimal conditions, some bacteria can divide every 20 min. Suppose each cell has a mass of 2 × 10–9 milligrams (mg). The mass of Earth is approximately 5:97 × 1027 grams (g). Determine the time (in hours) required for the progeny of a single cell dividing without restriction at the above rate to equal the weight of Earth.

#### Solution 1

At time zero we have one cell; 20 min later we have two cells; at 40 min there are four cells; at 60 min there are eight cells; etc. Thus, there are three cell divisions per hour. The number of cells at any hour, t, is 23t. The mass of each cell in grams is 2 × 10– 9 mg × 10–3 mg / g = 2 × 1010–12 g. The number of cells equivalent to the weight of Earth is

(5.97 × 1027 g) / 2 × 10–12) = 2:98 × 10–39 = 23t hours(h)

from which 3t log 2 = log 2.98 + log 10–39,

#### Practice 2

The discipline of bacterial genetics began in 1943 when S. E. Luria and M. Delbrüuck published a paper entitled "Mutations of bacteria from virus sensitivity to virus resistance." Before this time, it was not known if the heredity of bacteria changed adaptively in specific ways as a consequence of exposure to specific environments, or whether specific mutants existed in the population prior to an environmental challenge. The former idea was Lamarckian, the latter was neo-Darwinian. Luria and Delbrück found that there was great variation from one trial to another in the number of E. coli that were resistant to lysis by phage T1. In order to determine which of the two hypotheses was correct, they devised the following "fluctuation test." Twenty 0.2-ml "individual cultures" and one 10-ml "bulk culture" of nutrient medium were incubated with about 103 E. coli cells per milliliter. The cultures were incubated until they contained about 108 cells per milliliter. The entire 0.2 ml of each individual culture was spread on a nutrient agar plate heavily seeded with T1 phages. Ten 0.2-ml samples from the bulk culture were also treated in similar fashion. After overnight incubation, the total number of T1-resistant (Tonr) bacterial cells was counted; the results are presented in the following table. What inferences can be drawn from this "fluctuation test"?

#### Solution 2

Variances for each experiment can be calculated from the square of formula (8.2) or (8.3); the individual cultures have a variance of 714.5, whereas the variance of samples from the bulk culture is 16.4.2 In a Poisson distribution, the mean and the variance are essentially identical; hence, the variance/mean ratio should be near unity (1.0). The variance/mean ratio for the bulk culture samples is 16.4/16.7 = 0.98 or nearly 1.0, as expected from a random distribution of rare events. The samples from the bulk culture collectively serve as a control for the individual cultures. The same ratio for the individual cultures, however, is 714.5/11.3 = 63.23, indicating that there are extremely wide fluctuations of the numbers of Tonr cells in each culture around the mean. If resistance to the T1 phages occurs with a given probability only after contact with the phages, then each culture from both the individual and batch experiments should contain approximately the same average number of resistant cells. On the other hand, if Tonr mutants occurred prior to contact with the phages, great variation around the mean is expected from one individual culture to another because some will incur a mutation early and others late (or not at all) during the incubation period. This experiment argues in favor of the mutation hypothesis and against the induced resistance hypothesis.

Certain mutations, such as that to phage resistance, are preadaptive in that their selective advantage only becomes manifest when phages are in the environment as a selective agent; in this case, T1-sensitive bacteria (Tons) are killed by T1 phages, allowing only the few Tonr cells to survive and multiply. Phage resistance depends upon altering the structure of the bacterial receptor sites to which T1 phages normally attach. Immunity to superinfection by a specific phage is based upon production of a repressor of phage replication by a lysogenic cell.

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