The parameters for quantitative analysis of mutation rates with cultured mammalian somatic cells

Analysis of the Luria–Delbrück distribution using discrete convolution powers

The Luria–Delbrück distribution arises in birth-and-mutation processes in population genetics that have been systematically studied for the last fifty years. The central result reported in this paper is a new recursion relation for computing this distribution which supersedes all past results in simplicity and computational efficiency: p 0 = e–m ; where m is the expected number of mutations. A new relation for the asymptotic behavior of pn (≈ c/n 2) is also derived. This corresponds to the probability of finding a very large number of mutants. A formula for the z-transform of the distribution is also reported.

Analysis of the Luria–Delbrück distribution using discrete convolution powers

The Luria–Delbrück distribution arises in birth-and-mutation processes in population genetics that have been systematically studied for the last fifty years. The central result reported in this paper is a new recursion relation for computing this distribution which supersedes all past results in simplicity and computational efficiency:p0=e–m;wheremis the expected number of mutations. A new relation for the asymptotic behavior ofpn(≈c/n2) is also derived. This corresponds to the probability of finding a very large number of mutants. A formula for thez-transform of the distribution is also reported.

Experimental design to evaluate directed adaptive mutation in Mammalian cells

BACKGROUND

We describe the experimental design for a methodological approach to determine whether directed adaptive mutation occurs in mammalian cells. Identification of directed adaptive mutation would have profound practical significance for a wide variety of biomedical problems, including disease development and resistance to treatment. In adaptive mutation, the genetic or epigenetic change is not random; instead, the presence and type of selection influences the frequency and character of the mutation event. Adaptive mutation can contribute to the evolution of microbial pathogenesis, cancer, and drug resistance, and may become a focus of novel therapeutic interventions.

OBJECTIVE

Our experimental approach was designed to distinguish between 3 types of mutation: (1) random mutations that are independent of selective pressure, (2) undirected adaptive mutations that arise when selective pressure induces a general increase in the mutation rate, and (3) directed adaptive mutations that arise when selective pressure induces targeted mutations that specifically influence the adaptive response. The purpose of this report is to introduce an experimental design and describe limited pilot experiment data (not to describe a complete set of experiments); hence, it is an early report.

METHODS

An experimental design based on immortalization of mouse embryonic fibroblast cells is presented that links clonal cell growth to reversal of an inactivating polyadenylation site mutation. Thus, cells exhibit growth only in the presence of both the countermutation and an inducing agent (doxycycline). The type and frequency of mutation in the presence or absence of doxycycline will be evaluated. Additional experimental approaches would determine whether the cells exhibit a generalized increase in mutation rate and/or whether the cells show altered expression of error-prone DNA polymerases or of mismatch repair proteins.

RESULTS

We performed the initial stages of characterizing our system and have limited preliminary data from several pilot experiments. Cell growth and DNA sequence data indicate that we have identified a cell clone that exhibits several suitable characteristics, although further study is required to identify a more optimal cell clone.

CONCLUSIONS

The experimental approach is based on a quantum biological model of basis-dependent selection describing a novel mechanism of adaptive mutation. This project is currently inactive due to lack of funding. However, consistent with the objective of early reports, we describe a proposed study that has not produced publishable results, but is worthy of report because of the hypothesis, experimental design, and protocols. We outline the project's rationale and experimental design, with its strengths and weaknesses, to stimulate discussion and analysis, and lay the foundation for future studies in this field.

Unbiased estimation of mutation rates under fluctuating final counts

Estimation methods for mutation rates (or probabilities) in Luria-Delbrück fluctuation analysis usually assume that the final number of cells remains constant from one culture to another. We show that this leads to systematically underestimate the mutation rate. Two levels of information on final numbers are considered: either the coefficient of variation has been independently estimated, or the final number of cells in each culture is known. In both cases, unbiased estimation methods are proposed. Their statistical properties are assessed both theoretically and through Monte-Carlo simulation. As an application, the data from two well known fluctuation analysis studies on Mycobacterium tuberculosis are reexamined.

Fluctuation analysis of mutations to nalidixic acid resistance in Escherichia coli

Mutations of Escherichia 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.

A note on efficient estimation of mutation rates using Luria-Delbrück fluctuation analysis

The maximum likelihood and Luria-Delbrück P0 methods for the estimation of spontaneous mutation rates are compared. The maximum likelihood method is fully efficient, utilizing all available information in a fluctuation experiment, but can be numerically cumbersome. Under certain conditions, there is little loss of efficiency using the P0 method, which is readily implemented numerically. Design considerations should aid investigators in minimizing statistical errors associated with the statistical analysis of fluctuation experiments.

Evaluation of methods for the estimation of mutation rates in cultured mammalian cell populations

A systematic comparison of 5 different statistical methods for the estimation of mutation rate (mu) in cultured Chinese hamster V79 cells is presented. Fluctuation tests were performed with several large batches of parallel cell cultures each allowed to grow for a different length of time in order to reach different population size (Nt). Based on Lea and Coulson's theoretical distribution, a comparison has been made between the experimental data and the expected distribution of the number of ouabain-resistant mutants per culture in these hamster cell populations. The sum of squared deviation between the observed and expected values, or SSD, was used as a means of the adequacy of the estimation method; the method which gives the smallest SSD is regarded as the best one for the estimation of mu. Our results show that when Nt is small, the occurrence of mutation is infrequent, and SSDs from different methods are similar. However, when Nt is large, there is a great discrepancy of the SSD values, suggesting a preference of using the maximum likelihood method, the Po method, the median method, the upper quartile method and the mean method, in that order, for the estimation of mu. The order of preference is correlated with estimation efficiencies. Depending on the size of Nt and the method used, the estimated mu may vary up to more than 3-fold. At a large Nt, the mu obtained from the maximum likelihood method is very precise. This suggests the importance of choosing an appropriate Nt as well as method for the estimation of mu.

Elevated spontaneous mutation rate in SV40-transformed Werner syndrome fibroblast cell lines

Spontaneous mutation rates of the cells from patients with Werner syndrome were examined, and we found that the spontaneous mutation rates at the hypoxanthine-guanine phosphoribosyltransferase locus in SV40-transformed Werner syndrome cell lines were markedly elevated, compared to those in SV40-transformed normal control cell lines. Our results suggest that Werner syndrome is a mutation mutant.

Estimation of mutation rates in cultured mammalian cells

The factors that affect reliable estimations of mutation rates (mu) in cultured mammalian somatic cell populations by fluctuation analysis are studied experimentally and statistically. We analyze the differential effect of the final cell population size in each culture (Nt) and the number of parallel cultures (C) on the variation in the rate estimates (mu) inferred from the P0 method. The analysis can be made after the derivation of the variance of mu, which is a measure of variation of mu for a given combination of Nt and C in a number of repeat experiments. The variance of mu is inversely proportional to C and to the square of Nt . Nt determines the probability of occurrence of mutations in a cell culture. By influencing the size of P0, Nt also determines whether a rate estimate is obtainable from the experiment. Since Po is estimated from the fraction of cultures containing no mutation in a set of C cultures, C becomes a determining factor for the accuracy of mu. The rate estimated from P0 is biased, but the bias is in general 2 orders of magnitude smaller than mu. By the selection of an appropriate combination of Nt and C for the experiment, this bias can be reduced even further. Based on the notion of comparing two proportions, we propose a test statistic and have applied it to experimental results for a test of equality of mutation rates in different cell lines. This development places the comparison of mutation rates on a statistical basis.