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Mutation rates

The basic formula for mutation rate is: mutation rate= # mutation events/(gene x generation). consider a situation when a scientist measures the mutation rate in an organism over several generations. if the scientist observes 10 mutant organisms for a particular gene after 4 generations (assuming 100,000 individuals or 100,000 genes per generation), they might conclude that the mutation rate is 10/(100,000 +100,000 +100,000 +100,000) = 10/(4 x 100,000) =2.5 x 10^-5. however, this analysis neglects a crucial detail: that all the mutants may have originated from a single mutant early in the experiment. for example, all 10 mutants might represent exactly the same mutation, perhaps due to the origination of this mutation in the parental generation. in such a case, we have to consider that only one mutation event has occured; then the true mutation rate would be 1/(4x 100,000) = 2.5 x 10^-6. apply this concept to the following example:

E.coli are grown in minimal medium containing lactose as the only carbon source until their density is 10^4 cells/milliliter; so all cells must have the lac operon to survive and reproduce. one milliliter of these cells is then put into 20 milliliters of rich growth medium containing glucose instead of lactose, but now also containing acridine orange (an intercalculating mutagen). the cells are cultured for 1 hour, the length of time it takes for E.coli to complete two divisions (i.e., double four times) at 37 degrees C; so there have been 2 generations after 1 hour. the cells are then plated on agar plates containing chemicals that can induce the lac operon and turn blue in the prescense of B-galactose.

Fifty-eight white colonies (not turning blue) are observed and picked to identify pure clones of each. of these 58 strains, many of these strains are identicdal. in all, there are only 20 different mutations, so the 58 different strains must have initially started from 20 different cells at some stage of the 2 hour incubation.

a) what is the mutation frequency for the lacZ gene at the end of the experiment>?
b) what is the mutation rate for the lacZ gene?
c) what kind of mutations would you expect to be most frequently caused by the acriding orange?

Solution Preview

[First of all, there's a question. In one place it states a 1 hour incubation, yet later on, it indicates a 2 hour incubation. Whichever it is, you may have to adjust the calculations accordingly. There is another unusual phrase in the question. After stating a 1 hour incubation to complete 2 cell divsions, it says in parenthesis "double four times." I'm not sure what that means. If the cells doubled four times, then there would be four cell divisions, which would make sense if we assumed a 2 hour incubation. One way or the other, you've got to get that sorted out. Was it a 1 hour incubation (population doubling two times), or a 2 hour incubation (population doubling four times)? I will assume a 1 hour incubation that involves two cell divisions, hence a population that doubles two ...

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