Fluctuation analysis of mutations to nalidixic acid resistance in Escherichia coli

Abstract

Mutations ofEscherichia coli from sensitivity to nalidixic acid resistance were studied by fluctuation analysis.The mutant distributions in replicate cultures were not significantly affected either by the age of the carbon-starved preculture used for inocula or by the inoculum size. The data from 23 fluctuation tests (48 cultures each) were pooled. The mean number of mutations per culture was estimated to be 0.71 from the fraction of cultures without mutants or 0.74 and 0.77 by maximum-likelihood estimation based on the two models under consideration. When the pooled data were compared with the theoretical expectations, the fits were unsatisfactory (P < 0.005). The lack of fit was caused mainly by too high a frequency of cultures with between 17 and 32 mutants and too high a frequency of cultures with more than 128 mutants. Possible reasons for the lack of fit and its implications with respect to estimation of mutation rates from fluctuation tests are discussed.The statistical analysis of bacterial mutations came into prominence with the publication of Luria and Delbruck (16); the system they studied was that of resistance to bacteriophage Ti in Escherichia coli. When a culture of sensitive E. coli is plated in the presence of an excess of the phage, although virtually all the bacteria are killed, a small number survive and give rise to colonies on the plate. The problem analyzed by Luria and Delbruck was whether the survivors were the result of mutations that occurred prior to the plating, i.e., during the growth of the culture, or whether they occurred after plating, i.e., as a direct consequence of the bacteria being exposed to the phage. These two principal conceptions may be labelled the pre-and postadaptive theories, respectively (7). Luria and Delbruck studied the problem using mathematical models. If the mutation occurred postadaptively, the distribution of mutants in a number of replicate (parallel) cultures should be a Poisson distribution, provided that all bacteria have a small, finite probability of mutating to become resistant after the exposure to the phage. The preadaptive mutation theory leads to a quite different prediction. Although the replicate cultures are the same with respect to the total size of population, some may have experienced a mutation at an early generation and thereby yield a large number of mutants, while with others, a mutation may have occurred just prior to the plating so that only one or a few mutants are present in these cultures. The difference in the predictions of the pre-and postadaptive mutation theories could therefore be reduced to a prediction of the variance of the number of mutants in replicate cultures: the postadaptive theory predicted that the variance would equal the mean, whereas the preadaptive mutation theory predicted that the variance would be much larger, owing to a few cultures yielding a large number of mutants.Luria (45)45932809. from each culture. They did not correct for sampling error, nor did they deduce the theoretical distribution expected fr...

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