On fluctuation analysis: a new,simple and efficient method for computing the expected number of mutants

Fluctuation analysis, which is often used to demonstrate random mutagenesis in cell lines (and to estimate mutation rates), is based on the properties of a probability distribution known as the Luria-Delbrück distribution (and its generalizations). The two main new results reported in this paper are (i) a simple, completely general, and computationally efficient procedure for calculating probability distributions arising from fluctuation analysis and (ii) the formula for this procedure when cells in a colony have only grown for a finite number of generations after initial seeding. It is also shown that the procedure reduces to one that was developed earlier when an infinite number of generations is assumed. The derivation of the generating function of the distribution is also clarified. The results obtained should also be useful to experimentalists when only a relatively short time elapses between seeding and harvestint cultures for fluctuation analysis.     

Age Distribution of Human Diploid Fibroblasts: A Stochastic Model for In Vitro Aging

Variation in the lifespan of mass cultures and clones of human diploid fibroblasts can be explained on the basis of variation in the length of the mitotic cycle. This variation is of biological significance; the intrinsic standard deviation of culture lifespan is equal to about 10% of the mean. We constructed a two-parameter stochastic model based on the following assumptions: the time between successive divisions of a given cell is of random duration; cells divide or lose the ability to divide independently of one another; the probability that a cell can undergo further division is constant up to some maximum number of divisions and zero thereafter. We determined numerically the proportion of nondividing cells and the distribution of cell generations. Samples taken by Monte Carlo means from a hypothetical in vitro population were compared with clonal survival data obtained experimentally. The fit between experimental and theoretical findings was within the range of sampling variation. If we accept our model as being applicable to human diploid cell culture, we can draw the following conclusions: the proportion of dividing cells is an inadequate index of a population's age; even in populations in which almost all cells are still capable of division, a majority of the cells have less than eight generations remaining to them. At each subcultivation the ultimate fate of a culture is determined by the disposition of a relatively small number of “young” cells.     

The behavior during the initial phase of in vitro aggregation of dissociated imaginal disc cells from Drosophila melanogaster

Aspects of the initial phase of aggregation in vitro of dissociated imaginal disc cells from Drosophila melanogaster are described. Using the methods described certain interdisc differences in the percent decrease in single cell units during the first hour of aggregation can be demonstrated. In addition it is shown that prospective notum cells isolated from the dorsal mesothoracic disc show less of a decrease than do prospective wing cells. This difference shows up in a variety of different wild-type stocks and in several mutant stocks as well. Prospective notum cells from the mutation fu59 show only a limited ability to adhere to one another, while the percentage of single cell units from prospective wing blade cells from r9 larvae grown on pyrimidine-poor medium decrease less compared to cells from the same stock grown on RNA-supplemented medium. There is a significantly greater decrease in the percent single cell units in cultures of prospective eye cells than in cultures of prospective antennal cells. Furthermore, cells from the antennal disc of larvae bearing the homeotic mutation ssa show a significantly lower decrease in single cell units when grown at restrictive temperatures. In contrast, antennal disc cells from the homeotic mutation ophthalmoptera; eyeless Dominant, a mutation which affects the eye disc, are unaffected, while cells from the eye disc are slightly less able to reassociate with one another.     

A stochastic model for estimation of mutation rates in multiple-replication proliferation processes

In this paper we propose a stochastic model based on the branching process for estimation and comparison of the mutation rates in proliferation processes of cells or microbes. We assume in this model that cells or microbes (the elements of a population) are reproduced by generations and thus the model is more suitably applicable to situations in which the new elements in a population are produced by older elements from the previous generation rather than by newly created elements from the same current generation. Cells and bacteria proliferate by binary replication, whereas the RNA viruses proliferate by multiple replication. The model is in terms of multiple replications, which includes the special case of binary replication. We propose statistical procedures for estimation and comparison of the mutation rates from data of multiple cultures with divergent culture sizes. The mutation rate is defined as the probability of mutation per replication per genome and thus can be assumed constant in the entire proliferation process. We derive the number of cultures for planning experiments to achieve desired accuracy for estimation or desired statistical power for comparing the mutation rates of two strains of microbes. We establish the efficiency of the proposed method by demonstrating how the estimation of mutation rates would be affected when the culture sizes were assumed similar but actually diverge.      

Spontaneous mutational effects on reproductive traits of arabidopsis thaliana

A study of spontaneous mutation in Arabidopsis thaliana was initiated from a single inbred Columbia founder; 120 lines were established and advanced 17 generations by single-seed descent. Here, we report an assay of reproductive traits in a random set of 40 lines from generations 8 and 17, grown together at the same time with plants representing generation 0. For three reproductive traits, mean number of seeds per fruit, number of fruits, and dry mass of the infructescence, the means did not differ significantly among generations. Nevertheless, by generation 17, significant divergence among lines was detected for each trait, indicating accumulation of mutations in some lines. Standardized measures of mutational variance accord with those obtained for other organisms. These findings suggest that the distribution of mutational effects for these traits is approximately symmetric, in contrast to the usual assumption that mutations have predominantly negative effects on traits directly related to fitness. Because distinct generations were grown contemporaneously, each line was represented by three sublines, and seeds were equal in age, these estimates are free of potentially substantial sources of bias. The finding of an approximately symmetric distribution of mutational effects invalidates the standard approach for inferring properties of spontaneous mutation and necessitates further development of more general approaches that avoid restrictions on the distribution of mutational effects.     

The Distribution of Spontaneous Mutations on Quantitative Traits and Fitness in Drosophila Melanogaster

Starting from a completely homozygous population of Drosophila melanogaster, two groups of 100 inbred lines each were established and maintained for 46 generations, by a single brother-sister mating and two double first cousin matings, respectively. Sternopleural bristle number, wing length and wing width were simultaneously scored in all lines every 4-5 generations. The means of four lines in each group departed significantly from the overall mean and, in each case, this was attributed to a single mutation of relatively large effect on at least one trait (0.3-1.4 environmental standard deviations in absolute value). Further analyses revealed widespread pleiotropy, similar gene action of a given mutation for all traits affected, and predominant additive action. No apparent association was found between the magnitudes of mutational effects on the traits and fitness. However, all recessive mutations were deleterious. The distribution of mutant effects was asymmetrical (positive for bristles and negative for wing measurements). Moreover, these distributions had a high variance and may be leptokurtic, due to the presence of major genes. Estimates of the ratio of new mutational variance to environmental variance ranged within (0.7-3.4) x 10(-3), those for wing measurements being generally larger. In agreement with theory, the rate of between-line differentiation was independent of population size.     

Persistence of cell cycle times over many generations as determined by heritability of colony sizes of ras oncogene-transformed and non-transformed cells

Abstract. The persistence of cell lifetimes during about 10 successive cell generations was investigated by comparing the number of cells in primary colonies and in secondary colonies derived from primary colonies. Primary colonies were grown from single cells for 3 or 4 days (a time equivalent to an average of five cell generations) and the number of cells in each primary colony determined. Cells in each primary colony were dispersed to initiate secondary colonies, grown for the same time, and the number of cells in secondary colonies determined. Several criteria were used to compare primary and related secondary colonies, the most informative was found to be regression and correlation coefficients between number of cells in primary colonies and mean numbers of cells in related secondary colonies. For two non-transformed mouse fibroblast cell lines, NIH 3T3 and BALB 3T3, the regression and correlation coefficients of cell number in primary and secondary colonies were positive. This suggests inheritance of cell lifetimes over many cell generations. After the addition of an activated ras oncogene (human cellular Harvey ras , or viral Kirsten ras ) some regression and correlation coefficients changed in magnitude but all remained positive. Comparison of experimental data and the results of computer simulations suggest that several models of inheritance of cell lifetimes are not adequate to explain the results, including a model of independence between lifetimes of mother and daughter cells and the common model that describes daughter cells as inheriting the lifetime of their mother with deviation. Simulations do suggest that cell lifetimes are inherited within clones as deviation from the lifetime of the initial cell, and that the ras oncogene does not destroy persistence within clones but does increase heterogeneity of cell lifetimes.     

The rate of mutation of a single gene

The rate of mutation refers to the probability that a unit length of DNA (generally a base pair) mutates with time. Fluctuation analysis or mutant accumulation assays applied to phenotypic changes measure mutation rates of cells. However, only a few phenotypic changes indicative of mutations are known thus limiting the analysis to those rare genes. Direct sequencing overcomes the limitations imposed by phenotypic analysis but is limited by the extensive number of clones or cells that have to be analyzed in fluctuation or mutant accumulation assays. We propose a strategy to determine the rate of mutation of a gene by limited direct sequencing of a few single cells of a defined lineage. To accomplish this, we determined the average number of mutations per position in each DNA length sequenced from the proportion of the non-mutated positions, according to the Poisson process and/or the Taylor series. Measuring the rate of mutation by direct sequencing of genes does not require ascertaining a phenotype and can be applied to any area of the genome in a cell. The approach avoids fluctuation errors.     

Colonial heterogeneity of Thiobacillus versutus.

In acetate-limited chemostat cultures started with single-colony cultures of Thiobacillus versutus, a mutant appeared after approximately 85 volume changes. The inhomogeneity of the culture was detected by the development of two different types of colonies on agar plates. When a pure culture of the mutant was grown in a chemostat, parent colonies appeared after almost the same period of time. Electron micrographs of the mutant grown on butyrate showed the presence of fibrils surrounding the cells. The cells of the parent strain were bald when grown under the same conditions. The growth kinetics of the parent and the mutant were investigated in batch cultures with a variety of substrates and were found to be identical. Major differences between the two strains were observed during growth on mannitol; the mutant attained a lower yield and excreted large amounts of extracellular polysaccharides.     

A Study on a Nearly Neutral Mutation Model in Finite Populations

As a nearly neutral mutation model, the house-of-cards model is studied in finite populations using computer simulations. The distribution of the mutant effect is assumed to be normal. The behavior is mainly determined by the product of the population size, N, and the standard deviation, sigma, of the distribution of the mutant effect. If 4N sigma is large compared to one, a few advantageous mutants are quickly fixed in early generations. Then most mutation becomes deleterious and very slow increase of the average selection coefficient follows. It takes very long for the population to reach the equilibrium state. Substitutions of alleles occur very infrequently in the later stage. If 4N sigma is the order of one or less, the behavior is qualitatively similar to that of the strict neutral case. Gradual increase of the average selection coefficient occurs and in generations of several times the inverse of the mutation rate the population almost reaches the equilibrium state. Both advantageous and neutral (including slightly deleterious) mutations are fixed. Except in the early stage, an increase of the standard deviation of the distribution of the mutant effect decreases the average heterozygosity. The substitution rate is reduced as 4N sigma is increased. Three tests of neutrality, one using the relationship between the average and the variance of heterozygosity, another using the relationship between the average heterozygosity and the average number of substitutions and Watterson's homozygosity test are applied to the consequences of the present model. It is found that deviation from the neutral expectation becomes apparent only when 4N sigma is more than two. Also a simple approximation for the model is developed which works well when the mutation rate is very small.     

Analysis of cell size and DNA content in exponentially growing and stationary-phase batch cultures of Escherichia coli.

Escherichia coli strains were grown in batch cultures in different media, and cell size and DNA content were analyzed by flow cytometry. Steady-state growth required large dilutions and incubation for many generations at low cell concentrations. In rich media, both cell size and DNA content started to decrease at low cell concentrations, long before the cultures left the exponential growth phase. Stationary-phase cultures contained cells with several chromosomes, even after many days, and stationary-phase populations exclusively composed of cells with a single chromosome were never observed, regardless of growth medium. The cells usually contained only one nucleoid, as visualized by phase and fluorescence microscopy. The results have implications for the use of batch cultures to study steady-state and balanced growth and to determine mutation and recombination frequencies in stationary phase.     

Determining mutation rates in bacterial populations

When properly determined, spontaneous mutation rates are a more accurate and biologically meaningful reflection of underlying mutagenic mechanisms than are mutant frequencies. Because bacteria grow exponentially and mutations arise stochastically, methods to estimate mutation rates depend on theoretical models that describe the distribution of mutant numbers among parallel cultures, as in the original Luria-Delbr]uck fluctuation analysis. An accurate determination of mutation rate depends on understanding the strengths and limitations of these methods, and how to design fluctuation assays to optimize a given method. In this paper we describe a number of methods to estimate mutation rates, give brief accounts of their derivations, and discuss how they behave under various experimental conditions.     

Properties of a Novel Pleiotropic Bacteriophage-Resistant Mutant of Staphylococcus aureus H

A phage-resistant mutant of Staphylococcus aureus H (Sm(R)), S. aureus 52A5, was previously shown to lack polymeric teichoic acid. This paper characterizes other phenotypic differences between the strains. In broth cultures the mutant cells grew more slowly, were larger, and formed much larger clumps than the parent strain. The clumps of cells appeared to be covalently linked and could only be separated by mild sonic energy-a process which yielded viable cells. Mutant and parent cells autolyzed at equal rates, whereas isolated cell walls of the mutant strain autolyzed faster than the wild type. Nevertheless, the specific activity of the autolytic enzyme in the wild type soluble fraction was much higher than in the mutant. In contrast to the parent, strain 52A5 failed to accumulate nucleotide-bound murein precursors when treated with penicillin. Mutant strains with these characteristics were repeatedly isolated both spontaneously and by chemical mutagenesis. Strain 52A5 was shown to be fully revertible. Thus, it appears to be a pleiotropic mutation, and the possible nature of the defect which causes these varied effects is discussed.     

Physiological studies of chloramine resistance developed by Klebsiella pneumoniae under low-nutrient growth conditions.

This study investigated the physiological mechanisms of resistance to chloramines developed by Klebsiella pneumoniae grown in a nutrient-limited environment. Growth under these conditions resulted in cells that were smaller than cells grown under high-nutrient conditions and extensively aggregated. Cellular aggregates ranged from 10 to more than 10,000 cells per aggregate, with a mean population aggregate size of 90 cells. This aggregation may have been facilitated by the presence of extracellular polymer material. By using glucose as a reference of capsule content, it was determined that growth under low-nutrient conditions produced cells with 8 x 10(-14) to 41 x 10(-14) g of carbohydrate per cell, with a mean +/- standard deviation of 27 x 10(-14) +/- 16 x 10(-14) g of carbohydrate per cell. In comparison, growth under high-nutrient conditions resulted in 2.7 x 10(-14) to 5.9 x 10(-14) g of carbohydrate per cell, with a mean and standard deviation of 4.3 x 10(-14) +/- 1.2 x 10(-14) g of carbohydrate per cell. Cell wall and cell membrane lipids also varied with growth conditions. The ratio of saturated to unsaturated fatty acids in cells grown under low-nutrient conditions was approximately five times greater than that in cells grown under high-nutrient conditions, suggesting possible differences in membrane permeability. An analysis of sulfhydryl (-SH) groups revealed no quantitative difference with respect to growth conditions. However, upon exposure to chloramines, only 33% of the -SH groups of cells grown under low-nutrient conditions were oxidized, compared with 80% oxidization of -SH groups in cells grown under high-nutrient conditions. The reduced effectiveness of chloramine oxidization of -SH groups in cells grown under low-nutrient conditions may be due to restricted penetration of chloramines into the cells, conformational changes of enzymes, or a combination of both factors. The results of this study suggest that chloramine resistance developed under low-nutrient growth conditions may be a function of multiple physiological factors, including cellular aggregation and protection of sulfhydryl groups within the cell.     

Physiological studies of chloramine resistance developed by Klebsiella pneumoniae under low-nutrient growth conditions.

This study investigated the physiological mechanisms of resistance to chloramines developed by Klebsiella pneumoniae grown in a nutrient-limited environment. Growth under these conditions resulted in cells that were smaller than cells grown under high-nutrient conditions and extensively aggregated. Cellular aggregates ranged from 10 to more than 10,000 cells per aggregate, with a mean population aggregate size of 90 cells. This aggregation may have been facilitated by the presence of extracellular polymer material. By using glucose as a reference of capsule content, it was determined that growth under low-nutrient conditions produced cells with 8 x 10(-14) to 41 x 10(-14) g of carbohydrate per cell, with a mean +/- standard deviation of 27 x 10(-14) +/- 16 x 10(-14) g of carbohydrate per cell. In comparison, growth under high-nutrient conditions resulted in 2.7 x 10(-14) to 5.9 x 10(-14) g of carbohydrate per cell, with a mean and standard deviation of 4.3 x 10(-14) +/- 1.2 x 10(-14) g of carbohydrate per cell. Cell wall and cell membrane lipids also varied with growth conditions. The ratio of saturated to unsaturated fatty acids in cells grown under low-nutrient conditions was approximately five times greater than that in cells grown under high-nutrient conditions, suggesting possible differences in membrane permeability. An analysis of sulfhydryl (-SH) groups revealed no quantitative difference with respect to growth conditions. However, upon exposure to chloramines, only 33% of the -SH groups of cells grown under low-nutrient conditions were oxidized, compared with 80% oxidization of -SH groups in cells grown under high-nutrient conditions. The reduced effectiveness of chloramine oxidization of -SH groups in cells grown under low-nutrient conditions may be due to restricted penetration of chloramines into the cells, conformational changes of enzymes, or a combination of both factors. The results of this study suggest that chloramine resistance developed under low-nutrient growth conditions may be a function of multiple physiological factors, including cellular aggregation and protection of sulfhydryl groups within the cell.     

The application of a linear algebra to the analysis of mutation rates.

Cells and bacteria growing in culture are subject to mutation, and as this mutation is the ultimate substrate for selection and evolution, the factors controlling the mutation rate are of some interest. The mutational event is not observed directly, but is inferred from the phenotype of the original mutant or of its descendants; the rate of mutation is inferred from the number of such mutant phenotypes. Such inference presumes a knowledge of the probability distribution for the size of a clone arising from a single mutation. We develop a mathematical formulation that assists in the design and analysis of experiments which investigate mutation rates and mutant clone size distribution, and we use it to analyse data for which the classical Luria-Delbrück clone-size distribution must be rejected.     

Establishment of Salt Stress Tolerant Rice Plants Through Step Up NaCl Treatment In Vitro

Establishment of salt tolerant rice plants was examined by single step or step up NaCl treatments of shoot bud clumps in vitro, and variation among in vitro salt tolerant plants were examined by rapid amplified polymorphic DNA (RAPD). Shoot bud clumps were necrotic, stubbed or dead when subjected to single step treatment with 1.5 or 2.0 % NaCl. Conversely all the clumps could grow vigorously when subjected to step up salt treatment with 0.5, 1.0, 1.5 and 2.0 % NaCl at 3 week intervals and 2 % NaCl tolerant plants were established. RAPD revealed shoot bud clumps with and without different NaCl treatments, seedlings from field and grown in vitro, and regenerants from callus were genetically close to one another. Conversely, callus cultures were genetically isolated. Growth under different salt stress conditions was not correlated with the genetic variation, suggesting that 2.0 % NaCl tolerant plants might not result from genetic mutation but were due to adaptation of plants by step up NaCl treatment in vitro.     

Survival rates of mutant genes under artificial selection using individual and family information

We have used diffusion and branching process methods to investigate fixation rates, probabilities of survival per generation, and times to fixation of mutant genes under different selection methods incorporating individual and family information. Diffusion approximations fit well to simulated results even for large selection coefficients. Methods that give much weight to family information, such as BLUP evaluation which is widely used in animal breeding, reduce fixation rates of mutant genes because of the reduced effective population sizes. In general, it is observed that even mutants with relatively small heterozygous effects (say 0.1 phenotypic standard deviation) are practically ‘safe’ (i.e. their probability of loss from one generation to the next is smaller than, say, 10%) after just a few generations, typically less than 10. For methods of selection with larger effective size, such as within-family selection, the mutant is ‘safe’ in the population somewhat earlier but eventual fixation takes a longer time. Finally we evaluate the amount by which the use of marker assisted selection reduces the fixation probability of newly arisen mutants.     

SERUM FRACTIONATION AND THE EFFECTS OF BOVINE SERUM FRACTIONS ON HUMAN CELLS GROWN IN A CHEMICALLY DEFINED MEDIUM

Serum has been fractionated by curtain electrophoresis using carboxymethyl cellulose dissolved in sodium bicarbonate electrolyte. Various fractions were produced from bovine serum and added to replicate cultures of Chang's endoepithelial cells and HeLa cells grown in a chemically defined medium. The effects of each of the various fractions on the appearance of the cultures and on cell multiplication were studied. Three different fractions were obtained and two were subjected to further purification. One fraction associated with albumin promoted survival, attachment, and flattening as well as cell multiplication. A second fraction associated with the alpha globulins promoted survival and multiplication of some cells. A third fraction caused cells to aggregate and form free floating clumps. An adequate chemically defined medium for continuous growth of human cells was used throughout the study. The response of cells to alterations in their environment which simulated some of the effects produced by serum fractions is described.     

An in situ protocol for measuring the expression of chemically-induced mutations in mammalian cells

The generation of expression curves and the evaluation of mutagenic responses of mammalian cells using standard mutagenesis assays can be inaccurate because mutant and wild-type cells are usually mixed during the expression phase. If some mutant progenitors or mutants grow more slowly than the wild-type cells during the expression period, there will be a decrease in the mutant to wild-type ratio with time and the mutant fraction will not accurately represent the number of mutational events that occurred. The mutant fraction may also inaccurately assess the number of mutations if these mutations are expressed over a number of generations during the time before selection. We previously showed that recovery of L5178Y mouse cell mutants is not complete when mutations are allowed to express in suspension because slowly growing mutants and/or mutant progenitors are diluted out during this time (Rudd et al., 1990). In order to more accurately quantitate the mutagenic response of the cells, we developed an in situ procedure which segregates and immobilizes cells during expression. Because of this immobilization, slowly growing mutant progenitors and mutants expressed at different times will have an equal probability of being scored as mutants. Thus, one mutation leads to one mutant colony and the measurement of the mutagenic response of the cells to the chemical accurately reflects the mutational events that occurred. We plated L5178Y tk^+/− mouse cells in semisolid medium immediately after treatment. As the cells grew and formed microcolonies, the selective agent TFT was added as an overlay at specified times, permitting only TFT^r cells to survive. In this procedure, each mutation was captured as an individual colony; consequently, the measured mutation fraction accurately reflected the mutational events that occurred at the selected locus. In addition, the induced mutant colonies arising in the agar are the result of independent mutational events. We previously described the in situ protocol for L5178Y cells and showed that the spontaneous mutation rate measured was 50-fold greater than when the cells expressed the phenotype in suspension (Rudd et al., 1990). From this we concluded that the slow growth phenotype was expressed before TFT resistance. In the present paper, we evaluate the effect of chemical treatment on the mutation fraction as a function of the time to TFT addition. Using the in situ protocol, we generated expression curves for three nucleotide analogs, 5-azacytidine, TFT and AraC. The numbers of TFT^r colonies produced at various times after treatment indicated that chemically-treated cultures had higher mutation fractions than the solvent controls. The maximal differential increase in mutation rate occured between 30 and 60 h for 5-azacytidine and between 20 and 40 h for TFT and AraC. Our results document the feasibility of quantitating induced mutation fractions using the in situ protocol, confirm the mutagenicity of AraC and 5azacytidine and demonstrate the mutagenic activity of TFT at the tk locus. In addition to recovering mutants more accurately than the suspension protocol, the in situ protocol has the advantage of being experimentally less labor and time intensive. Therefore, we believe that this method should be considered for evaluation as an assay to measure the potential mutagenic effects of chemicals in mammalian cells in vitro.