245.

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Page 94

		1.5.11— The Distribution of Mutations Is the Same As in the St. Petersburg Game

		If we run many experiments where mutations occur all the time, what is the average number of mutant cells at the end of the experiments?

		Each cell has the same probability of giving birth to a mutant cell. There are few cells at the beginning of the experiment. Thus there is a low probability that a mutation will occur in the first generation of cells. However, if a mutation does occur in the first generation, that cell will produce2N daughter cells in the N generations until the end of the experiment. In the second generation, there are already twice as many cells as the first generation. Thus the probability that a mutation occurs in the second generation is twice as great as that in the first generation. However, that mutant cell will produce only 2N-l daughters in the remaining N-1 generations. Similarly, for all subsequent generations.

		The total number of mutant cells at the end of the experiment is equal to the probability of a mutation occurring in each generation multiplied by the number of daughter cells that it produces until the end of the experiment. This means, on average, that each generation contributes the same number of mutant cells to the final number of mutant cells. This is the same calculation as determining the winnings in the St. Petersburg game described previously. Each generation corresponds to one play of the game, the probability of winning on that play corresponds to the probability that a mutation occurs in that generation, and the money won corresponds to the number of resistant daughter cells at the end of the experiment,

		As is true for the average winnings of the St. Petersburg game, the average number of mutant cells at the end of the experiment is not defined. The average found for a number of experiments will increase as the number of experiments is increased. Because of this large variability, it is not known how to compare the average number of final mutant cells from two sets of experiments to determine if the different conditions of the experiments affected the mutation rate.

 

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