Occurrence of copper resistant mutants in the toxic cyanobacteria Microcystis aeruginosa: characterisation and future implications in the use of copper sulphate as algaecide.

The Luria-Delbruck mutation model has been mathematically formulated in a number of ways. This review article examines four most important formulations, focusing on important practical issues closely linked with the distribution of the number of mutants. These issues include the probability generating functions, moments (cumulants), computational methods and asymptotics. This review emphasizes basic principles which not only help to unify existing results but also allow for a few useful extensions. In addition, the review offers a historical perspective and some new explanations of divergent moments.

Progress of a half century in the study of the Luria–Delbrück distribution

Werner syndrome (WRN; MIM #277700) is an uncommon autosomal recessive disease in which features of premature aging are associated with genetic instability and an elevated risk of cancer. The Werner syndrome clinical phenotype mimics premature aging: following puberty, patients rapidly develop premature graying and loss of hair, scleroderma-like skin changes, osteoporosis, atherosclerosis, bilateral cataract formation, diabetes mellitus, and hypogonadism (Epstein et al. 1966; Goto 2000). Spontaneous genetic instability has been identified in multiple cell lineages in WRN patients, and may be an important determinant of the increased risk of cancer (for review, see Goto et al. 1996; Moser et al. 2000a; van Brabant et al. 2000). Most Werner patients die prematurely, of either cancer or cardiovascular disease, with an average age at death of 47 yr (Epstein et al. 1966; Goto 2000).

The chromosome 8p WRN gene encodes a 162 kD member of the human RecQ helicase family that is unique in possessing an N-terminal 3′ → 5′ exonuclease domain in addition to the central, conserved 3′ → 5′ RecQ helicase consensus domain (for review, see Shen and Loeb 2000b). A majority of WRN patients have mutations in the WRN gene that truncate the WRN protein with loss of a C-terminal nuclear localization signal. Cells containing these mutant alleles produce little or no detectable protein (Goto et al. 1999; Moser et al. 1999, 2000b). There is growing evidence that WRN, like most other helicases, functions as part of a multiprotein complex. Other proteins that may associate or act with WRN include replication protein A (RPA), DNA polymerase δ, PCNA, DNA topoisomerase I, p53 and Ku (for review, see Shen and Loeb 2000b). Mutations in genes encoding these or other WRN-interacting proteins may be responsible for the ∼10% of patients who fulfill clinical and diagnostic criteria for WRN, but lack WRN mutations (Goto et al. 1999; J. Oshima, pers. comm.). One example is a well-documented 29-year-old Japanese female who had clinical and cellular phenotypes that were indistinguishable from WRN patients with truncating WRN mutations, but lacked inactivating WRN mutations (Matsumura et al. 1985; Fukuchi et al. 1989; Prince et al. 1999; see below).

RecQ helicases play a role in recombination or genome stability assurance in many organisms (for review, see Chakraverty and Hickson 1999; Shen and Loeb 2000b; van Brabant et al. 2000). Thus we reasoned that WRN might play a comparable role in human somatic cells, and we explored this possibility by using two different chromosomally integrated mitotic recombination reporter plasmids to measure spontaneous mitotic recombination rates, infer potential recombination pathways and determine the outcome of mitotic recombination events in WRN and control fibroblast cell lines.

http://depts.washington.edu/monnatws/pdf/2001_Prince.pdf

Loss of Werner syndrome protein function promotes aberrant mitotic recombination

The Luria–Delbruck 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

In the 47 years since fluctuation analysis was introduced by Luria and Delbruck, it has been widely used to calculate mutation rates. Up to now, in spite of the importance of such calculations, the probability distribution of the number of mutants that will appear in a fluctuation experiment has been known only under the restrictive, and possibly unrealistic, assumptions: (1) that the mutation rate is exactly proportional to the growth rate and (2) that all mutants grow at a rate that is a constant multiple of the growth rate of the original cells. In this paper, we approach the distribution of the number of mutants from a new point of view that will enable researchers to calculate the distribution to be expected using assumptions that they believe to be closer to biological reality. The new idea is to classify mutations according to the number of observable mutants that derive from the mutation when the culture is selectively plated. This approach also simplifies the calculations in situations where two, or many, kinds of mutation may occur in a single culture.

https://www.genetics.org/content/genetics/124/1/175.full.pdf

Fluctuation analysis: the probability distribution of the number of mutants under different conditions

The factors that affect reliable estimations of mutation rates (g) 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 (N t) and the number of parallel cultures (C) on the variation in the rate estimates (tl) inferred from the P0 method. The analysis can be made after the derivation of the variance of/i, which is a measure of variation of tl for a given combination of N t and C in a number of repeat experiments. The variance of ti is inversely proportional to C and to the square of N t. N t 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/2. The rate estimated from/5 o is biased, but the bias is in general 2 orders of magnitude smaller than /i. By the selection of an appropriate combination of N t 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. Since the publication of Luria and Delbriick's paper [19] on the distribution of the number of mutant colonies in a series of parallel cultures, fluctuation analysis has been widely applied as a method for the determination of mutation rates (#) in cell populations. The analysis has since been further developed methodologically by Lea and Coulson [15], Newcombe [22], and Armitage [2,3] and modified theoreti

Estimation of mutation rates in cultured mammalian cells

Summary Unequal growth rates between mutant and wild-type cells in a large population constitute a problem for the estimation of mutation rate. Over a period of cell growth, a selective advantage of one cell type over the other might lead to considerable error in the estimation of mutation rate if equal growth rates are assumed. In this study, we propose a formula and apply it to the estimation of spontaneous mutation rate in a growing population of Chinese hamster V79 cells in which ouabain-resistant mutant cells exhibit a slower growth rate than the wild-type cells. The formula is a generalization of that previously presented by Armitage (1953), and this is the first attempt to apply the deterministic approach for mutation rate estimation to cultured mammalian cells. The value of the estimated rate is compared with that derived from a parallel experiment using the fluctuation test of Luria and Delbri~ck (1943). The limitations and advantages of taking the deterministic approach to mutation rate estimation in mammalian cell systems are discussed.

/pdf/a-deterministic-approach-for-the-estimation-of-mutation-3hd3zvu3tj.pdf

A deterministic approach for the estimation of mutation rates in cultured mammalian cells

Environmental mutagenesis is thought to play an important role in hereditary and somatic diseases in man. Numerous studies have been made in recent years assaying the mutagenic response of cultured mammalian cells, with the hope of better understanding the effects of environmental agents on human populations. Different test systems have been developed to detect either gene or chromosome mutations at the cellular and molecular levels. Although some of the heritable variations could be epigenetic, direct evidence is available demonstrating that true point mutations indeed occur in mammalian cells. It is now possible to identify specific molecular alterations in mammalian cell mutants arising in vitro.

Jiliang Fu

Papers

Estimation of mutation rates in cultured mammalian cells

A deterministic approach for the estimation of mutation rates in cultured mammalian cells

Mutagenesis Studies with Cultured Mammalian Cells: Problems and Prospects